Merge pull request #31 from AeneasVerif/son_lean_backend

Improve the Lean backend

160 files changed, 11401 insertions, 10464 deletions

diff --git a/Makefile b/Makefile
index a5d1fd09..1b11592f 100644
--- a/Makefile
+++ b/Makefile
@@ -117,8 +117,8 @@ trans-no_nested_borrows trans-paper: \
 	OPTIONS += -test-units -test-trans-units -no-split-files -no-state
 trans-no_nested_borrows trans-paper: SUBDIR := misc
 tfstar-no_nested_borrows tfstar-paper:
-tlean-no_nested_borrows: SUBDIR := misc-no_nested_borrows
-tlean-paper: SUBDIR := misc-paper
+tlean-no_nested_borrows: SUBDIR :=
+tlean-paper: SUBDIR :=
 thol4-no_nested_borrows: SUBDIR := misc-no_nested_borrows
 thol4-paper: SUBDIR := misc-paper
 
@@ -126,29 +126,29 @@ trans-loops: OPTIONS += -no-state
 trans-loops: SUBDIR := misc
 tfstar-loops: OPTIONS += -decreases-clauses -template-clauses
 tcoq-loops: OPTIONS += -use-fuel -no-split-files
-tlean-loops: SUBDIR := misc-loops
-tlean-loops: OPTIONS += -decreases-clauses -template-clauses
+tlean-loops: SUBDIR :=
 thol4-loops: SUBDIR := misc-loops
 
 trans-hashmap: OPTIONS += -no-state
 trans-hashmap: SUBDIR := hashmap
 tfstar-hashmap: OPTIONS += -decreases-clauses -template-clauses
 tcoq-hashmap: OPTIONS += -use-fuel
-tlean-hashmap: OPTIONS += -decreases-clauses -template-clauses
+tlean-hashmap: SUBDIR :=
+tlean-hashmap: OPTIONS +=
 thol4-hashmap: OPTIONS +=
 
 trans-hashmap_main: OPTIONS +=
 trans-hashmap_main: SUBDIR := hashmap_on_disk
 tfstar-hashmap_main: OPTIONS += -decreases-clauses -template-clauses
 tcoq-hashmap_main: OPTIONS += -use-fuel
-tlean-hashmap_main: OPTIONS += -decreases-clauses -template-clauses
+tlean-hashmap_main: SUBDIR :=
 thol4-hashmap_main: OPTIONS +=
 
 transp-polonius_list: OPTIONS += -test-units -test-trans-units -no-split-files -no-state
 transp-polonius_list: SUBDIR := misc
 tfstarp-polonius_list: OPTIONS +=
 tcoqp-polonius_list: OPTIONS +=
-tleanp-polonius_list: SUBDIR := misc-polonius_list
+tleanp-polonius_list: SUBDIR :=
 tleanp-polonius_list: OPTIONS +=
 thol4p-polonius_list: SUBDIR := misc-polonius_list
 thol4p-polonius_list: OPTIONS +=
@@ -157,7 +157,7 @@ trans-constants: OPTIONS += -test-units -test-trans-units -no-split-files -no-st
 trans-constants: SUBDIR := misc
 tfstar-constants: OPTIONS +=
 tcoq-constants: OPTIONS +=
-tlean-constants: SUBDIR := misc-constants
+tlean-constants: SUBDIR :=
 tlean-constants: OPTIONS +=
 thol4-constants: SUBDIR := misc-constants
 thol4-constants: OPTIONS +=
@@ -166,7 +166,7 @@ trans-external: OPTIONS +=
 trans-external: SUBDIR := misc
 tfstar-external: OPTIONS +=
 tcoq-external: OPTIONS +=
-tlean-external: SUBDIR := misc-external
+tlean-external: SUBDIR :=
 tlean-external: OPTIONS +=
 thol4-external: SUBDIR := misc-external
 thol4-external: OPTIONS +=
@@ -176,7 +176,8 @@ transp-betree_main: OPTIONS += -backward-no-state-update
 transp-betree_main: SUBDIR:=betree
 tfstarp-betree_main: OPTIONS += $(BETREE_FSTAR_OPTIONS)
 tcoqp-betree_main: OPTIONS += -use-fuel
-tleanp-betree_main: OPTIONS += $(BETREE_FSTAR_OPTIONS)
+tleanp-betree_main: SUBDIR :=
+tleanp-betree_main: OPTIONS +=
 thol4-betree_main: OPTIONS +=
 
 # Additional test on the betree: translate it without `-backward-no-state-update`.
@@ -249,8 +250,7 @@ tcoqp-%:
 	$(AENEAS_CMD)
 
 .PHONY: tlean-%
-# TODO: add  -test-trans-units once we remove all the sorry from Primitives.lean
-tlean-%: OPTIONS += -backend lean
+tlean-%: OPTIONS += -backend lean -test-trans-units
 tlean-%: BACKEND_SUBDIR := lean
 tlean-%:
 	$(AENEAS_CMD)
@@ -258,13 +258,7 @@ tlean-%:
 # "p" stands for "Polonius"
 .PHONY: tleanp-%
 
-# TODO: for now we don't extract the betree for Lean because we need to implement
-# proper support for the proofs of termination for the mutually recursive functions.
-tleanp-betree_main:
-	echo "Ignoring Lean betree"
-
-# TODO: add  -test-trans-units once we remove all the sorry from Primitives.lean
-tleanp-%: OPTIONS += -backend lean
+tleanp-%: OPTIONS += -backend lean -test-trans-units
 tleanp-%: BACKEND_SUBDIR := lean
 tleanp-%:
 	$(AENEAS_CMD)
diff --git a/backends/hol4/ilistScript.sml b/backends/hol4/ilistScript.sml
index fb0c7688..2b465af3 100644
--- a/backends/hol4/ilistScript.sml
+++ b/backends/hol4/ilistScript.sml
@@ -23,6 +23,8 @@ val _ = BasicProvers.export_rewrites ["len_def"]
    Remark: we initially added the following case, so that we wouldn't need the
    premise [i < len ls] is [index_eq_EL]:
    “index (i : int) [] = EL (Num i) []”
+
+   TODO: this can be simplified. See the Lean backend.
  *)
 val index_def = Define ‘
   index (i : int) (x :: ls) = if i = 0 then x else (if 0 < i then index (i - 1) ls else ARB)
@@ -44,6 +46,7 @@ Proof
   exfalso >> cooper_tac
 QED
 
+(* TODO: this can be simplified. See the Lean backend. *)
 val update_def = Define ‘
   update ([] : 'a list) (i : int) (y : 'a) : 'a list = [] ∧
 
diff --git a/backends/lean/Base.lean b/backends/lean/Base.lean
new file mode 100644
index 00000000..2077d410
--- /dev/null
+++ b/backends/lean/Base.lean
@@ -0,0 +1,6 @@
+import Base.Utils
+import Base.Primitives
+import Base.Diverge
+import Base.Arith
+import Base.Progress
+import Base.IList
diff --git a/backends/lean/Base/Arith.lean b/backends/lean/Base/Arith.lean
new file mode 100644
index 00000000..c0d09fd2
--- /dev/null
+++ b/backends/lean/Base/Arith.lean
@@ -0,0 +1,2 @@
+import Base.Arith.Int
+import Base.Arith.Scalar
diff --git a/backends/lean/Base/Arith/Arith.lean b/backends/lean/Base/Arith/Arith.lean
new file mode 100644
index 00000000..e69de29b
--- /dev/null
+++ b/backends/lean/Base/Arith/Arith.lean
diff --git a/backends/lean/Base/Arith/Base.lean b/backends/lean/Base/Arith/Base.lean
new file mode 100644
index 00000000..9c11ed45
--- /dev/null
+++ b/backends/lean/Base/Arith/Base.lean
@@ -0,0 +1,60 @@
+import Lean
+import Std.Data.Int.Lemmas
+import Mathlib.Tactic.Linarith
+
+namespace Arith
+
+open Lean Elab Term Meta
+
+-- We can't define and use trace classes in the same file
+initialize registerTraceClass `Arith
+
+-- TODO: move?
+theorem ne_zero_is_lt_or_gt {x : Int} (hne : x ≠ 0) : x < 0 ∨ x > 0 := by
+  cases h: x <;> simp_all
+  . rename_i n;
+    cases n <;> simp_all
+  . apply Int.negSucc_lt_zero
+
+-- TODO: move?
+theorem ne_is_lt_or_gt {x y : Int} (hne : x ≠ y) : x < y ∨ x > y := by
+  have hne : x - y ≠ 0 := by
+    simp
+    intro h
+    have: x = y := by linarith
+    simp_all
+  have h := ne_zero_is_lt_or_gt hne
+  match h with
+  | .inl _ => left; linarith
+  | .inr _ => right; linarith
+
+-- TODO: move?
+theorem add_one_le_iff_le_ne (n m : Nat) (h1 : m ≤ n) (h2 : m ≠ n) : m + 1 ≤ n := by
+  -- Damn, those proofs on natural numbers are hard - I wish Omega was in mathlib4...
+  simp [Nat.add_one_le_iff]
+  simp [Nat.lt_iff_le_and_ne]
+  simp_all
+
+/- Induction over positive integers -/
+-- TODO: move
+theorem int_pos_ind (p : Int → Prop) :
+  (zero:p 0) → (pos:∀ i, 0 ≤ i → p i → p (i + 1)) → ∀ i, 0 ≤ i → p i := by
+  intro h0 hr i hpos
+--  have heq : Int.toNat i = i := by
+--    cases i <;> simp_all
+  have ⟨ n, heq ⟩  : {n:Nat // n = i } := ⟨ Int.toNat i, by cases i <;> simp_all ⟩
+  revert i
+  induction n
+  . intro i hpos heq
+    cases i <;> simp_all
+  . rename_i n hi
+    intro i hpos heq
+    cases i <;> simp_all
+    rename_i m
+    cases m <;> simp_all
+
+-- We sometimes need this to make sure no natural numbers appear in the goals
+-- TODO: there is probably something more general to do
+theorem nat_zero_eq_int_zero : (0 : Nat) = (0 : Int) := by simp
+
+end Arith
diff --git a/backends/lean/Base/Arith/Int.lean b/backends/lean/Base/Arith/Int.lean
new file mode 100644
index 00000000..7a5bbe98
--- /dev/null
+++ b/backends/lean/Base/Arith/Int.lean
@@ -0,0 +1,280 @@
+/- This file contains tactics to solve arithmetic goals -/
+
+import Lean
+import Lean.Meta.Tactic.Simp
+import Init.Data.List.Basic
+import Mathlib.Tactic.RunCmd
+import Mathlib.Tactic.Linarith
+-- TODO: there is no Omega tactic for now - it seems it hasn't been ported yet
+--import Mathlib.Tactic.Omega
+import Base.Utils
+import Base.Arith.Base
+
+namespace Arith
+
+open Utils
+
+-- Remark: I tried a version of the shape `HasScalarProp {a : Type} (x : a)`
+-- but the lookup didn't work
+class HasIntProp (a : Sort u) where
+  prop_ty : a → Prop
+  prop : ∀ x:a, prop_ty x
+
+class PropHasImp (x : Prop) where
+  concl : Prop
+  prop : x → concl
+
+instance (p : Int → Prop) : HasIntProp (Subtype p) where
+  prop_ty := λ x => p x
+  prop := λ x => x.property
+
+-- This also works for `x ≠ y` because this expression reduces to `¬ x = y`
+-- and `Ne` is marked as `reducible`
+instance (x y : Int) : PropHasImp (¬ x = y) where
+  concl := x < y ∨ x > y
+  prop := λ (h:x ≠ y) => ne_is_lt_or_gt h
+
+-- Check if a proposition is a linear integer proposition.
+-- We notably use this to check the goals.
+class IsLinearIntProp (x : Prop) where
+
+instance (x y : Int) : IsLinearIntProp (x < y) where
+instance (x y : Int) : IsLinearIntProp (x > y) where
+instance (x y : Int) : IsLinearIntProp (x ≤ y) where
+instance (x y : Int) : IsLinearIntProp (x ≥ y) where
+instance (x y : Int) : IsLinearIntProp (x ≥ y) where
+instance (x y : Int) : IsLinearIntProp (x = y) where
+/- It seems we don't need to do any special preprocessing when the *goal*
+   has the following shape - I guess `linarith` automatically calls `intro` -/
+instance (x y : Int) : IsLinearIntProp (¬ x = y) where
+
+open Lean Lean.Elab Lean.Meta
+
+-- Explore a term by decomposing the applications (we explore the applied
+-- functions and their arguments, but ignore lambdas, forall, etc. -
+-- should we go inside?).
+partial def foldTermApps (k : α → Expr → MetaM α) (s : α) (e : Expr) : MetaM α := do
+  -- We do it in a very simpler manner: we deconstruct applications,
+  -- and recursively explore the sub-expressions. Note that we do
+  -- not go inside foralls and abstractions (should we?).
+  e.withApp fun f args => do
+    let s ← k s f
+    args.foldlM (foldTermApps k) s
+
+-- Provided a function `k` which lookups type class instances on an expression,
+-- collect all the instances lookuped by applying `k` on the sub-expressions of `e`.
+def collectInstances
+  (k : Expr → MetaM (Option Expr)) (s : HashSet Expr) (e : Expr) : MetaM (HashSet Expr) := do
+  let k s e := do
+    match ← k e with
+    | none => pure s
+    | some i => pure (s.insert i)
+  foldTermApps k s e
+
+-- Similar to `collectInstances`, but explores all the local declarations in the
+-- main context.
+def collectInstancesFromMainCtx (k : Expr → MetaM (Option Expr)) : Tactic.TacticM (HashSet Expr) := do
+  Tactic.withMainContext do
+  -- Get the local context
+  let ctx ← Lean.MonadLCtx.getLCtx
+  -- Just a matter of precaution
+  let ctx ← instantiateLCtxMVars ctx
+  -- Initialize the hashset
+  let hs := HashSet.empty
+  -- Explore the declarations
+  let decls ← ctx.getDecls
+  decls.foldlM (fun hs d => collectInstances k hs d.toExpr) hs
+
+-- Helper
+def lookupProp (fName : String) (className : Name) (e : Expr) : MetaM (Option Expr) := do
+  trace[Arith] fName
+  -- TODO: do we need Lean.observing?
+  -- This actually eliminates the error messages
+  Lean.observing? do
+    trace[Arith] m!"{fName}: observing"
+    let ty ← Lean.Meta.inferType e
+    let hasProp ← mkAppM className #[ty]
+    let hasPropInst ← trySynthInstance hasProp
+    match hasPropInst with
+    | LOption.some i =>
+      trace[Arith] "Found {fName} instance"
+      let i_prop ← mkProjection i (Name.mkSimple "prop")
+      some (← mkAppM' i_prop #[e])
+    | _ => none
+
+-- Return an instance of `HasIntProp` for `e` if it has some
+def lookupHasIntProp (e : Expr) : MetaM (Option Expr) :=
+  lookupProp "lookupHasIntProp" ``HasIntProp e
+
+-- Collect the instances of `HasIntProp` for the subexpressions in the context
+def collectHasIntPropInstancesFromMainCtx : Tactic.TacticM (HashSet Expr) := do
+  collectInstancesFromMainCtx lookupHasIntProp
+
+-- Return an instance of `PropHasImp` for `e` if it has some
+def lookupPropHasImp (e : Expr) : MetaM (Option Expr) := do
+  trace[Arith] "lookupPropHasImp"
+  -- TODO: do we need Lean.observing?
+  -- This actually eliminates the error messages
+  Lean.observing? do
+    trace[Arith] "lookupPropHasImp: observing"
+    let ty ← Lean.Meta.inferType e
+    trace[Arith] "lookupPropHasImp: ty: {ty}"
+    let cl ← mkAppM ``PropHasImp #[ty]
+    let inst ← trySynthInstance cl
+    match inst with
+    | LOption.some i =>
+      trace[Arith] "Found PropHasImp instance"
+      let i_prop ←  mkProjection i (Name.mkSimple "prop")
+      some (← mkAppM' i_prop #[e])
+    | _ => none
+
+-- Collect the instances of `PropHasImp` for the subexpressions in the context
+def collectPropHasImpInstancesFromMainCtx : Tactic.TacticM (HashSet Expr) := do
+  collectInstancesFromMainCtx lookupPropHasImp
+
+elab "display_prop_has_imp_instances" : tactic => do
+  trace[Arith] "Displaying the PropHasImp instances"
+  let hs ← collectPropHasImpInstancesFromMainCtx
+  hs.forM fun e => do
+    trace[Arith] "+ PropHasImp instance: {e}"
+
+example (x y : Int) (_ : x ≠ y) (_ : ¬ x = y) : True := by
+  display_prop_has_imp_instances
+  simp
+
+-- Lookup instances in a context and introduce them with additional declarations.
+def introInstances (declToUnfold : Name) (lookup : Expr → MetaM (Option Expr)) : Tactic.TacticM (Array Expr) := do
+  let hs ← collectInstancesFromMainCtx lookup
+  hs.toArray.mapM fun e => do
+    let type ← inferType e
+    let name ← mkFreshAnonPropUserName
+    -- Add a declaration
+    let nval ← Utils.addDeclTac name e type (asLet := false)
+    -- Simplify to unfold the declaration to unfold (i.e., the projector)
+    Utils.simpAt [declToUnfold] [] [] (Tactic.Location.targets #[mkIdent name] false)
+    -- Return the new value
+    pure nval
+
+def introHasIntPropInstances : Tactic.TacticM (Array Expr) := do
+  trace[Arith] "Introducing the HasIntProp instances"
+  introInstances ``HasIntProp.prop_ty lookupHasIntProp
+
+-- Lookup the instances of `HasIntProp for all the sub-expressions in the context,
+-- and introduce the corresponding assumptions
+elab "intro_has_int_prop_instances" : tactic => do
+  let _ ← introHasIntPropInstances
+
+-- Lookup the instances of `PropHasImp for all the sub-expressions in the context,
+-- and introduce the corresponding assumptions
+elab "intro_prop_has_imp_instances" : tactic => do
+  trace[Arith] "Introducing the PropHasImp instances"
+  let _ ← introInstances ``PropHasImp.concl lookupPropHasImp
+
+example (x y : Int) (h0 : x ≤ y) (h1 : x ≠ y) : x < y := by
+  intro_prop_has_imp_instances
+  rename_i h
+  split_disj h
+  . linarith
+  . linarith
+
+/- Boosting a bit the linarith tac.
+
+   We do the following:
+   - for all the assumptions of the shape `(x : Int) ≠ y` or `¬ (x = y), we
+     introduce two goals with the assumptions `x < y` and `x > y`
+     TODO: we could create a PR for mathlib.
+ -/
+def intTacPreprocess (extraPreprocess :  Tactic.TacticM Unit) : Tactic.TacticM Unit := do
+  Tactic.withMainContext do
+  -- Lookup the instances of PropHasImp (this is how we detect assumptions
+  -- of the proper shape), introduce assumptions in the context and split
+  -- on those
+  -- TODO: get rid of the assumptions that we split
+  let rec splitOnAsms (asms : List Expr) : Tactic.TacticM Unit :=
+    match asms with
+    | [] => pure ()
+    | asm :: asms =>
+      let k := splitOnAsms asms
+      Utils.splitDisjTac asm k k
+  -- Introduce the scalar bounds
+  let _ ← introHasIntPropInstances
+  -- Extra preprocessing, before we split on the disjunctions
+  extraPreprocess
+  -- Split
+  let asms ← introInstances ``PropHasImp.concl lookupPropHasImp
+  splitOnAsms asms.toList
+
+elab "int_tac_preprocess" : tactic =>
+  intTacPreprocess (do pure ())
+
+-- Check if the goal is a linear arithmetic goal
+def goalIsLinearInt : Tactic.TacticM Bool := do
+  Tactic.withMainContext do
+  let gty ← Tactic.getMainTarget
+  match ← trySynthInstance (← mkAppM ``IsLinearIntProp #[gty]) with
+  | .some _ => pure true
+  | _ => pure false
+
+def intTac (splitGoalConjs : Bool) (extraPreprocess :  Tactic.TacticM Unit) : Tactic.TacticM Unit := do
+  Tactic.withMainContext do
+  Tactic.focus do
+  let g ← Tactic.getMainGoal
+  trace[Arith] "Original goal: {g}"
+  -- Introduce all the universally quantified variables (includes the assumptions)
+  let (_, g) ← g.intros
+  Tactic.setGoals [g]
+  -- Preprocess - wondering if we should do this before or after splitting
+  -- the goal. I think before leads to a smaller proof term?
+  Tactic.allGoals (intTacPreprocess extraPreprocess)
+  -- More preprocessing
+  Tactic.allGoals (Utils.simpAt [] [``nat_zero_eq_int_zero] [] .wildcard)
+  -- Split the conjunctions in the goal
+  if splitGoalConjs then Tactic.allGoals (Utils.repeatTac Utils.splitConjTarget)
+  -- Call linarith
+  let linarith := do
+    let cfg : Linarith.LinarithConfig := {
+      -- We do this with our custom preprocessing
+      splitNe := false
+    }
+    Tactic.liftMetaFinishingTactic <| Linarith.linarith false [] cfg
+  Tactic.allGoals do
+    -- We check if the goal is a linear arithmetic goal: if yes, we directly
+    -- call linarith, otherwise we first apply exfalso (we do this because
+    -- linarith is too general and sometimes fails to do this correctly).
+    if ← goalIsLinearInt then do
+      trace[Arith] "linarith goal: {← Tactic.getMainGoal}"
+      linarith
+    else do
+      let g ← Tactic.getMainGoal
+      let gs ← g.apply (Expr.const ``False.elim [.zero])
+      let goals ← Tactic.getGoals
+      Tactic.setGoals (gs ++ goals)
+      Tactic.allGoals do
+        trace[Arith] "linarith goal: {← Tactic.getMainGoal}"
+        linarith
+
+elab "int_tac" args:(" split_goal"?): tactic =>
+  let split := args.raw.getArgs.size > 0
+  intTac split (do pure ())
+
+example (x : Int) (h0: 0 ≤ x) (h1: x ≠ 0) : 0 < x := by
+  int_tac_preprocess
+  linarith
+  linarith
+
+example (x : Int) (h0: 0 ≤ x) (h1: x ≠ 0) : 0 < x := by
+  int_tac
+
+-- Checking that things append correctly when there are several disjunctions
+example (x y : Int) (h0: 0 ≤ x) (h1: x ≠ 0) (h2 : 0 ≤ y) (h3 : y ≠ 0) : 0 < x ∧ 0 < y := by
+  int_tac split_goal
+
+-- Checking that things append correctly when there are several disjunctions
+example (x y : Int) (h0: 0 ≤ x) (h1: x ≠ 0) (h2 : 0 ≤ y) (h3 : y ≠ 0) : 0 < x ∧ 0 < y ∧ x + y ≥ 2 := by
+  int_tac split_goal
+
+-- Checking that we can prove exfalso
+example (a : Prop) (x : Int) (h0: 0 < x) (h1: x < 0) : a := by
+  int_tac
+
+end Arith
diff --git a/backends/lean/Base/Arith/Scalar.lean b/backends/lean/Base/Arith/Scalar.lean
new file mode 100644
index 00000000..b792ff21
--- /dev/null
+++ b/backends/lean/Base/Arith/Scalar.lean
@@ -0,0 +1,49 @@
+import Base.Arith.Int
+import Base.Primitives.Scalar
+
+/- Automation for scalars - TODO: not sure it is worth having two files (Int.lean and Scalar.lean) -/
+namespace Arith
+
+open Lean Lean.Elab Lean.Meta
+open Primitives
+
+def scalarTacExtraPreprocess : Tactic.TacticM Unit := do
+   Tactic.withMainContext do
+   -- Inroduce the bounds for the isize/usize types
+   let add (e : Expr) : Tactic.TacticM Unit := do
+     let ty ← inferType e
+     let _ ← Utils.addDeclTac (← Utils.mkFreshAnonPropUserName) e ty (asLet := false)
+   add (← mkAppM ``Scalar.cMin_bound #[.const ``ScalarTy.Isize []])
+   add (← mkAppM ``Scalar.cMax_bound #[.const ``ScalarTy.Usize []])
+   add (← mkAppM ``Scalar.cMax_bound #[.const ``ScalarTy.Isize []])
+   -- Reveal the concrete bounds
+   Utils.simpAt [``Scalar.min, ``Scalar.max, ``Scalar.cMin, ``Scalar.cMax,
+                 ``I8.min, ``I16.min, ``I32.min, ``I64.min, ``I128.min,
+                 ``I8.max, ``I16.max, ``I32.max, ``I64.max, ``I128.max,
+                 ``U8.min, ``U16.min, ``U32.min, ``U64.min, ``U128.min,
+                 ``U8.max, ``U16.max, ``U32.max, ``U64.max, ``U128.max,
+                 ``Usize.min
+                 ] [] [] .wildcard
+
+elab "scalar_tac_preprocess" : tactic =>
+  intTacPreprocess scalarTacExtraPreprocess
+
+-- A tactic to solve linear arithmetic goals in the presence of scalars
+def scalarTac (splitGoalConjs : Bool) : Tactic.TacticM Unit := do
+  intTac splitGoalConjs scalarTacExtraPreprocess
+
+elab "scalar_tac" : tactic =>
+  scalarTac false
+
+instance (ty : ScalarTy) : HasIntProp (Scalar ty) where
+  -- prop_ty is inferred
+  prop := λ x => And.intro x.hmin x.hmax
+
+example (x y : U32) : x.val ≤ Scalar.max ScalarTy.U32 := by
+  intro_has_int_prop_instances
+  simp [*]
+
+example (x y : U32) : x.val ≤ Scalar.max ScalarTy.U32 := by
+  scalar_tac
+
+end Arith
diff --git a/backends/lean/Base/Diverge.lean b/backends/lean/Base/Diverge.lean
new file mode 100644
index 00000000..c9a2eec2
--- /dev/null
+++ b/backends/lean/Base/Diverge.lean
@@ -0,0 +1,7 @@
+import Lean
+import Lean.Meta.Tactic.Simp
+import Init.Data.List.Basic
+import Mathlib.Tactic.RunCmd
+import Mathlib.Tactic.Linarith
+import Base.Diverge.Base
+import Base.Diverge.Elab
diff --git a/backends/lean/Base/Diverge/Base.lean b/backends/lean/Base/Diverge/Base.lean
new file mode 100644
index 00000000..1d548389
--- /dev/null
+++ b/backends/lean/Base/Diverge/Base.lean
@@ -0,0 +1,1138 @@
+import Lean
+import Lean.Meta.Tactic.Simp
+import Init.Data.List.Basic
+import Mathlib.Tactic.RunCmd
+import Mathlib.Tactic.Linarith
+import Base.Primitives.Base
+import Base.Arith.Base
+
+/- TODO: this is very useful, but is there more? -/
+set_option profiler true
+set_option profiler.threshold 100
+
+namespace Diverge
+
+namespace Fix
+
+  open Primitives
+  open Result
+
+  variable {a : Type u} {b : a → Type v}
+  variable {c d : Type w} -- TODO: why do we have to make them both : Type w?
+
+  /-! # The least fixed point definition and its properties -/
+
+  def least_p (p : Nat → Prop) (n : Nat) : Prop := p n ∧ (∀ m, m < n → ¬ p m)
+  noncomputable def least (p : Nat → Prop) : Nat :=
+    Classical.epsilon (least_p p)
+
+  -- Auxiliary theorem for [least_spec]: if there exists an `n` satisfying `p`,
+  -- there there exists a least `m` satisfying `p`.
+  theorem least_spec_aux (p : Nat → Prop) : ∀ (n : Nat), (hn : p n) → ∃ m, least_p p m := by
+    apply Nat.strongRec'
+    intros n hi hn
+    -- Case disjunction on: is n the smallest n satisfying p?
+    match Classical.em (∀ m, m < n → ¬ p m) with
+    | .inl hlt =>
+      -- Yes: trivial
+      exists n
+    | .inr hlt =>
+      simp at *
+      let ⟨ m, ⟨ hmlt, hm ⟩ ⟩ := hlt
+      have hi := hi m hmlt hm
+      apply hi
+
+  -- The specification of [least]: either `p` is never satisfied, or it is satisfied
+  -- by `least p` and no `n < least p` satisfies `p`.
+  theorem least_spec (p : Nat → Prop) : (∀ n, ¬ p n) ∨ (p (least p) ∧ ∀ n, n < least p → ¬ p n) := by
+    -- Case disjunction on the existence of an `n` which satisfies `p`
+    match Classical.em (∀ n, ¬ p n) with
+    | .inl h =>
+      -- There doesn't exist: trivial
+      apply (Or.inl h)
+    | .inr h =>
+      -- There exists: we simply use `least_spec_aux` in combination with the property
+      -- of the epsilon operator
+      simp at *
+      let ⟨ n, hn ⟩ := h
+      apply Or.inr
+      have hl := least_spec_aux p n hn
+      have he := Classical.epsilon_spec hl
+      apply he
+
+  /-! # The fixed point definitions -/
+
+  def fix_fuel (n : Nat) (f : ((x:a) → Result (b x)) → (x:a) → Result (b x)) (x : a) :
+    Result (b x) :=
+    match n with
+    | 0 => .div
+    | n + 1 =>
+      f (fix_fuel n f) x
+
+  @[simp] def fix_fuel_pred (f : ((x:a) → Result (b x)) → (x:a) → Result (b x))
+    (x : a) (n : Nat) :=
+    not (div? (fix_fuel n f x))
+
+  def fix_fuel_P (f : ((x:a) → Result (b x)) → (x:a) → Result (b x))
+    (x : a) (n : Nat) : Prop :=
+    fix_fuel_pred f x n
+
+  partial
+  def fixImpl (f : ((x:a) → Result (b x)) → (x:a) → Result (b x)) (x : a) : Result (b x) :=
+    f (fixImpl f) x
+
+  -- The fact that `fix` is implemented by `fixImpl` allows us to not mark the
+  -- functions defined with the fixed-point as noncomputable. One big advantage
+  -- is that it allows us to evaluate those functions, for instance with #eval.
+  @[implemented_by fixImpl]
+  def fix (f : ((x:a) → Result (b x)) → (x:a) → Result (b x)) (x : a) : Result (b x) :=
+    fix_fuel (least (fix_fuel_P f x)) f x
+
+  /-! # The validity property -/
+
+  -- Monotonicity relation over results
+  -- TODO: generalize (we should parameterize the definition by a relation over `a`)
+  def result_rel {a : Type u} (x1 x2 : Result a) : Prop :=
+    match x1 with
+    | div => True
+    | fail _ => x2 = x1
+    | ret _ => x2 = x1 -- TODO: generalize
+
+  -- Monotonicity relation over monadic arrows (i.e., Kleisli arrows)
+  def karrow_rel (k1 k2 : (x:a) → Result (b x)) : Prop :=
+    ∀ x, result_rel (k1 x) (k2 x)
+
+  -- Monotonicity property for function bodies
+  def is_mono (f : ((x:a) → Result (b x)) → (x:a) → Result (b x)) : Prop :=
+    ∀ {{k1 k2}}, karrow_rel k1 k2 → karrow_rel (f k1) (f k2)
+
+  -- "Continuity" property.
+  -- We need this, and this looks a lot like continuity. Also see this paper:
+  -- https://inria.hal.science/file/index/docid/216187/filename/tarski.pdf
+  -- We define our "continuity" criteria so that it gives us what we need to
+  -- prove the fixed-point equation, and we can also easily manipulate it.
+  def is_cont (f : ((x:a) → Result (b x)) → (x:a) → Result (b x)) : Prop :=
+    ∀ x, (Hdiv : ∀ n, fix_fuel (.succ n) f x = div) → f (fix f) x = div
+
+  /-! # The proof of the fixed-point equation -/
+  theorem fix_fuel_mono {f : ((x:a) → Result (b x)) → (x:a) → Result (b x)}
+    (Hmono : is_mono f) :
+    ∀ {{n m}}, n ≤ m → karrow_rel (fix_fuel n f) (fix_fuel m f) := by
+    intros n
+    induction n
+    case zero => simp [karrow_rel, fix_fuel, result_rel]
+    case succ n1 Hi =>
+      intros m Hle x
+      simp [result_rel]
+      match m with
+      | 0 =>
+        exfalso
+        zify at *
+        linarith
+      | Nat.succ m1 =>
+        simp_arith at Hle
+        simp [fix_fuel]
+        have Hi := Hi Hle
+        have Hmono := Hmono Hi x
+        simp [result_rel] at Hmono
+        apply Hmono
+
+  @[simp] theorem neg_fix_fuel_P
+    {f : ((x:a) → Result (b x)) → (x:a) → Result (b x)} {x : a} {n : Nat} :
+    ¬ fix_fuel_P f x n ↔ (fix_fuel n f x = div) := by
+    simp [fix_fuel_P, div?]
+    cases fix_fuel n f x <;> simp  
+
+  theorem fix_fuel_fix_mono {f : ((x:a) → Result (b x)) → (x:a) → Result (b x)} (Hmono : is_mono f) :
+    ∀ n, karrow_rel (fix_fuel n f) (fix f) := by
+    intros n x
+    simp [result_rel]
+    have Hl := least_spec (fix_fuel_P f x)
+    simp at Hl
+    match Hl with
+    | .inl Hl => simp [*]
+    | .inr ⟨ Hl, Hn ⟩ =>
+      match Classical.em (fix_fuel n f x = div) with
+      | .inl Hd =>
+        simp [*]
+      | .inr Hd =>
+        have Hineq : least (fix_fuel_P f x) ≤ n := by
+          -- Proof by contradiction
+          cases Classical.em (least (fix_fuel_P f x) ≤ n) <;> simp [*]
+          simp at *
+          rename_i Hineq
+          have Hn := Hn n Hineq
+          contradiction
+        have Hfix : ¬ (fix f x = div) := by
+          simp [fix]
+          -- By property of the least upper bound
+          revert Hd Hl
+          -- TODO: there is no conversion to select the head of a function!
+          conv => lhs; apply congr_fun; apply congr_fun; apply congr_fun; simp [fix_fuel_P, div?]
+          cases fix_fuel (least (fix_fuel_P f x)) f x <;> simp
+        have Hmono := fix_fuel_mono Hmono Hineq x
+        simp [result_rel] at Hmono
+        simp [fix] at *
+        cases Heq: fix_fuel (least (fix_fuel_P f x)) f x <;>
+        cases Heq':fix_fuel n f x <;>
+        simp_all
+
+  theorem fix_fuel_P_least {f : ((x:a) → Result (b x)) → (x:a) → Result (b x)} (Hmono : is_mono f) :
+    ∀ {{x n}}, fix_fuel_P f x n → fix_fuel_P f x (least (fix_fuel_P f x)) := by
+    intros x n Hf
+    have Hfmono := fix_fuel_fix_mono Hmono n x
+    -- TODO: there is no conversion to select the head of a function!
+    conv => apply congr_fun; simp [fix_fuel_P]
+    simp [fix_fuel_P] at Hf
+    revert Hf Hfmono
+    simp [div?, result_rel, fix]
+    cases fix_fuel n f x <;> simp_all
+
+  -- Prove the fixed point equation in the case there exists some fuel for which
+  -- the execution terminates
+  theorem fix_fixed_eq_terminates (f : ((x:a) → Result (b x)) → (x:a) → Result (b x)) (Hmono : is_mono f)
+    (x : a) (n : Nat) (He : fix_fuel_P f x n) :
+    fix f x = f (fix f) x := by
+    have Hl := fix_fuel_P_least Hmono He
+    -- TODO: better control of simplification
+    conv at Hl =>
+      apply congr_fun
+      simp [fix_fuel_P]
+    -- The least upper bound is > 0
+    have ⟨ n, Hsucc ⟩ : ∃ n, least (fix_fuel_P f x) = Nat.succ n := by
+      revert Hl
+      simp [div?]
+      cases least (fix_fuel_P f x) <;> simp [fix_fuel]
+    simp [Hsucc] at Hl
+    revert Hl
+    simp [*, div?, fix, fix_fuel]
+    -- Use the monotonicity
+    have Hfixmono := fix_fuel_fix_mono Hmono n
+    have Hvm := Hmono Hfixmono x
+    -- Use functional extensionality
+    simp [result_rel, fix] at Hvm
+    revert Hvm
+    split <;> simp [*] <;> intros <;> simp [*]
+
+  theorem fix_fixed_eq_forall {{f : ((x:a) → Result (b x)) → (x:a) → Result (b x)}}
+    (Hmono : is_mono f) (Hcont : is_cont f) :
+    ∀ x, fix f x = f (fix f) x := by
+    intros x
+    -- Case disjunction: is there a fuel such that the execution successfully execute?
+    match Classical.em (∃ n, fix_fuel_P f x n) with
+    | .inr He =>
+      -- No fuel: the fixed point evaluates to `div`
+      --simp [fix] at *
+      simp at *
+      conv => lhs; simp [fix]
+      have Hel := He (Nat.succ (least (fix_fuel_P f x))); simp [*, fix_fuel] at *; clear Hel
+      -- Use the "continuity" of `f`
+      have He : ∀ n, fix_fuel (.succ n) f x = div := by intros; simp [*]
+      have Hcont := Hcont x He
+      simp [Hcont]
+    | .inl ⟨ n, He ⟩ => apply fix_fixed_eq_terminates f Hmono x n He
+
+  -- The final fixed point equation
+  theorem fix_fixed_eq {{f : ((x:a) → Result (b x)) → (x:a) → Result (b x)}}
+    (Hmono : is_mono f) (Hcont : is_cont f) :
+    fix f = f (fix f) := by
+    have Heq := fix_fixed_eq_forall Hmono Hcont
+    have Heq1 : fix f = (λ x => fix f x) := by simp
+    rw [Heq1]
+    conv => lhs; ext; simp [Heq]
+
+  /-! # Making the proofs of validity manageable (and automatable) -/
+
+  -- Monotonicity property for expressions
+  def is_mono_p (e : ((x:a) → Result (b x)) → Result c) : Prop :=
+    ∀ {{k1 k2}}, karrow_rel k1 k2 → result_rel (e k1) (e k2)
+
+  theorem is_mono_p_same (x : Result c) :
+    @is_mono_p a b c (λ _ => x) := by
+    simp [is_mono_p, karrow_rel, result_rel]
+    split <;> simp
+
+  theorem is_mono_p_rec (x : a) :
+    @is_mono_p a b (b x) (λ f => f x) := by
+    simp_all [is_mono_p, karrow_rel, result_rel]
+
+  -- The important lemma about `is_mono_p`
+  theorem is_mono_p_bind
+    (g : ((x:a) → Result (b x)) → Result c)
+    (h : c → ((x:a) → Result (b x)) → Result d) :
+    is_mono_p g →
+    (∀ y, is_mono_p (h y)) →
+    @is_mono_p a b d (λ k => @Bind.bind Result _ c d (g k) (fun y => h y k)) := by
+--    @is_mono_p a b d (λ k => do let (y : c) ← g k; h y k) := by
+    intro hg hh
+    simp [is_mono_p]
+    intro fg fh Hrgh
+    simp [karrow_rel, result_rel]
+    have hg := hg Hrgh; simp [result_rel] at hg
+    cases heq0: g fg <;> simp_all
+    rename_i y _
+    have hh := hh y Hrgh; simp [result_rel] at hh
+    simp_all
+
+  -- Continuity property for expressions - note that we take the continuation
+  -- as parameter
+  def is_cont_p (k : ((x:a) → Result (b x)) → (x:a) → Result (b x))
+    (e : ((x:a) → Result (b x)) → Result c) : Prop :=
+    (Hc : ∀ n, e (fix_fuel n k) = .div) →
+    e (fix k) = .div
+
+  theorem is_cont_p_same (k : ((x:a) → Result (b x)) → (x:a) → Result (b x))
+    (x : Result c) :
+    is_cont_p k (λ _ => x) := by
+    simp [is_cont_p]
+
+  theorem is_cont_p_rec (f : ((x:a) → Result (b x)) → (x:a) → Result (b x)) (x : a) :
+    is_cont_p f (λ f => f x) := by
+    simp_all [is_cont_p, fix]
+
+  -- The important lemma about `is_cont_p`
+  theorem is_cont_p_bind
+    (k : ((x:a) → Result (b x)) → (x:a) → Result (b x))
+    (Hkmono : is_mono k)
+    (g : ((x:a) → Result (b x)) → Result c)
+    (h : c → ((x:a) → Result (b x)) → Result d) :
+    is_mono_p g →
+    is_cont_p k g →
+    (∀ y, is_mono_p (h y)) →
+    (∀ y, is_cont_p k (h y)) →
+    is_cont_p k (λ k => do let y ← g k; h y k) := by
+    intro Hgmono Hgcont Hhmono Hhcont
+    simp [is_cont_p]
+    intro Hdiv
+    -- Case on `g (fix... k)`: is there an n s.t. it terminates?
+    cases Classical.em (∀ n, g (fix_fuel n k) = .div) <;> rename_i Hn
+    . -- Case 1: g diverges
+      have Hgcont := Hgcont Hn
+      simp_all
+    . -- Case 2: g doesn't diverge
+      simp at Hn
+      let ⟨ n, Hn ⟩ := Hn
+      have Hdivn := Hdiv n
+      have Hffmono := fix_fuel_fix_mono Hkmono n
+      have Hgeq := Hgmono Hffmono
+      simp [result_rel] at Hgeq
+      cases Heq: g (fix_fuel n k) <;> rename_i y <;> simp_all
+      -- Remains the .ret case
+      -- Use Hdiv to prove that: ∀ n, h y (fix_fuel n f) = div
+      -- We do this in two steps: first we prove it for m ≥ n
+      have Hhdiv: ∀ m, h y (fix_fuel m k) = .div := by
+        have Hhdiv : ∀ m, n ≤ m → h y (fix_fuel m k) = .div := by
+          -- We use the fact that `g (fix_fuel n f) = .div`, combined with Hdiv
+          intro m Hle
+          have Hdivm := Hdiv m
+          -- Monotonicity of g
+          have Hffmono := fix_fuel_mono Hkmono Hle
+          have Hgmono := Hgmono Hffmono
+          -- We need to clear Hdiv because otherwise simp_all rewrites Hdivm with Hdiv
+          clear Hdiv
+          simp_all [result_rel]
+        intro m
+        -- TODO: we shouldn't need the excluded middle here because it is decidable
+        cases Classical.em (n ≤ m) <;> rename_i Hl
+        . apply Hhdiv; assumption
+        . simp at Hl
+          -- Make a case disjunction on `h y (fix_fuel m k)`: if it is not equal
+          -- to div, use the monotonicity of `h y`
+          have Hle : m ≤ n := by linarith
+          have Hffmono := fix_fuel_mono Hkmono Hle
+          have Hmono := Hhmono y Hffmono
+          simp [result_rel] at Hmono
+          cases Heq: h y (fix_fuel m k) <;> simp_all
+      -- We can now use the continuity hypothesis for h
+      apply Hhcont; assumption
+
+  -- The validity property for an expression
+  def is_valid_p (k : ((x:a) → Result (b x)) → (x:a) → Result (b x))
+    (e : ((x:a) → Result (b x)) → Result c) : Prop :=
+    is_mono_p e ∧
+    (is_mono k → is_cont_p k e)
+
+  @[simp] theorem is_valid_p_same
+    (k : ((x:a) → Result (b x)) → (x:a) → Result (b x)) (x : Result c) :
+    is_valid_p k (λ _ => x) := by
+    simp [is_valid_p, is_mono_p_same, is_cont_p_same]
+
+  @[simp] theorem is_valid_p_rec
+    (k : ((x:a) → Result (b x)) → (x:a) → Result (b x)) (x : a) :
+    is_valid_p k (λ k => k x) := by
+    simp_all [is_valid_p, is_mono_p_rec, is_cont_p_rec]
+
+  theorem is_valid_p_ite
+    (k : ((x:a) → Result (b x)) → (x:a) → Result (b x))
+    (cond : Prop) [h : Decidable cond]
+    {e1 e2 : ((x:a) → Result (b x)) → Result c}
+    (he1: is_valid_p k e1) (he2 : is_valid_p k e2) :
+    is_valid_p k (ite cond e1 e2) := by
+    split <;> assumption
+
+  theorem is_valid_p_dite
+    (k : ((x:a) → Result (b x)) → (x:a) → Result (b x))
+    (cond : Prop) [h : Decidable cond]
+    {e1 : cond → ((x:a) → Result (b x)) → Result c}
+    {e2 : Not cond → ((x:a) → Result (b x)) → Result c}
+    (he1: ∀ x, is_valid_p k (e1 x)) (he2 : ∀ x, is_valid_p k (e2 x)) :
+    is_valid_p k (dite cond e1 e2) := by
+    split <;> simp [*]
+
+  -- Lean is good at unification: we can write a very general version
+  -- (in particular, it will manage to figure out `g` and `h` when we
+  -- apply the lemma)
+  theorem is_valid_p_bind
+    {{k : ((x:a) → Result (b x)) → (x:a) → Result (b x)}}
+    {{g : ((x:a) → Result (b x)) → Result c}}
+    {{h : c → ((x:a) → Result (b x)) → Result d}}
+    (Hgvalid : is_valid_p k g)
+    (Hhvalid : ∀ y, is_valid_p k (h y)) :
+    is_valid_p k (λ k => do let y ← g k; h y k) := by
+    let ⟨ Hgmono, Hgcont ⟩ := Hgvalid
+    simp [is_valid_p, forall_and] at Hhvalid
+    have ⟨ Hhmono, Hhcont ⟩ := Hhvalid
+    simp [← imp_forall_iff] at Hhcont
+    simp [is_valid_p]; constructor
+    . -- Monotonicity
+      apply is_mono_p_bind <;> assumption
+    . -- Continuity
+      intro Hkmono
+      have Hgcont := Hgcont Hkmono
+      have Hhcont := Hhcont Hkmono
+      apply is_cont_p_bind <;> assumption
+
+  def is_valid (f : ((x:a) → Result (b x)) → (x:a) → Result (b x)) : Prop :=
+    ∀ k x, is_valid_p k (λ k => f k x)
+
+  theorem is_valid_p_imp_is_valid {{f : ((x:a) → Result (b x)) → (x:a) → Result (b x)}}
+    (Hvalid : is_valid f) :
+    is_mono f ∧ is_cont f := by
+    have Hmono : is_mono f := by
+      intro f h Hr x
+      have Hmono := Hvalid (λ _ _ => .div) x
+      have Hmono := Hmono.left
+      apply Hmono; assumption
+    have Hcont : is_cont f := by
+      intro x Hdiv
+      have Hcont := (Hvalid f x).right Hmono
+      simp [is_cont_p] at Hcont
+      apply Hcont
+      intro n
+      have Hdiv := Hdiv n
+      simp [fix_fuel] at Hdiv
+      simp [*]
+    simp [*]
+
+  theorem is_valid_fix_fixed_eq {{f : ((x:a) → Result (b x)) → (x:a) → Result (b x)}}
+    (Hvalid : is_valid f) :
+    fix f = f (fix f) := by
+    have ⟨ Hmono, Hcont ⟩ := is_valid_p_imp_is_valid Hvalid
+    exact fix_fixed_eq Hmono Hcont
+
+end Fix
+
+namespace FixI
+  /- Indexed fixed-point: definitions with indexed types, convenient to use for mutually
+     recursive definitions. We simply port the definitions and proofs from Fix to a more
+     specific case.
+   -/
+  open Primitives Fix
+
+  -- The index type
+  variable {id : Type u}
+
+  -- The input/output types
+  variable {a : id → Type v} {b : (i:id) → a i → Type w}
+
+  -- Monotonicity relation over monadic arrows (i.e., Kleisli arrows)
+  def karrow_rel (k1 k2 : (i:id) → (x:a i) → Result (b i x)) : Prop :=
+    ∀ i x, result_rel (k1 i x) (k2 i x)
+
+  def kk_to_gen (k : (i:id) → (x:a i) → Result (b i x)) :
+    (x: (i:id) × a i) → Result (b x.fst x.snd) :=
+    λ ⟨ i, x ⟩ => k i x
+
+  def kk_of_gen (k : (x: (i:id) × a i) → Result (b x.fst x.snd)) :
+    (i:id) → (x:a i) → Result (b i x) :=
+    λ i x => k ⟨ i, x ⟩
+
+  def k_to_gen (k : ((i:id) → (x:a i) → Result (b i x)) → (i:id) → (x:a i) → Result (b i x)) :
+    ((x: (i:id) × a i) → Result (b x.fst x.snd)) → (x: (i:id) × a i) → Result (b x.fst x.snd) :=
+    λ kk => kk_to_gen (k (kk_of_gen kk))
+
+  def k_of_gen (k : ((x: (i:id) × a i) → Result (b x.fst x.snd)) → (x: (i:id) × a i) → Result (b x.fst x.snd)) :
+    ((i:id) → (x:a i) → Result (b i x)) → (i:id) → (x:a i) → Result (b i x) :=
+    λ kk => kk_of_gen (k (kk_to_gen kk))
+
+  def e_to_gen (e : ((i:id) → (x:a i) → Result (b i x)) → Result c) :
+    ((x: (i:id) × a i) → Result (b x.fst x.snd)) → Result c :=
+    λ k => e (kk_of_gen k)
+
+  def is_valid_p (k : ((i:id) → (x:a i) → Result (b i x)) → (i:id) → (x:a i) → Result (b i x))
+    (e : ((i:id) → (x:a i) → Result (b i x)) → Result c) : Prop :=
+    Fix.is_valid_p (k_to_gen k) (e_to_gen e)
+
+  def is_valid (f : ((i:id) → (x:a i) → Result (b i x)) → (i:id) → (x:a i) → Result (b i x)) : Prop :=
+    ∀ k i x, is_valid_p k (λ k => f k i x)
+
+  def fix
+    (f : ((i:id) → (x:a i) → Result (b i x)) → (i:id) → (x:a i) → Result (b i x)) :
+    (i:id) → (x:a i) → Result (b i x) :=
+    kk_of_gen (Fix.fix (k_to_gen f))
+
+  theorem is_valid_fix_fixed_eq
+    {{f : ((i:id) → (x:a i) → Result (b i x)) → (i:id) → (x:a i) → Result (b i x)}}
+    (Hvalid : is_valid f) :
+    fix f = f (fix f) := by
+    have Hvalid' : Fix.is_valid (k_to_gen f) := by
+      intro k x
+      simp only [is_valid, is_valid_p] at Hvalid
+      let ⟨ i, x ⟩ := x
+      have Hvalid := Hvalid (k_of_gen k) i x
+      simp only [k_to_gen, k_of_gen, kk_to_gen, kk_of_gen] at Hvalid
+      refine Hvalid
+    have Heq := Fix.is_valid_fix_fixed_eq Hvalid'
+    simp [fix]
+    conv => lhs; rw [Heq]
+
+  /- Some utilities to define the mutually recursive functions -/
+
+  -- TODO: use more
+  abbrev kk_ty (id : Type u) (a : id → Type v) (b : (i:id) → (x:a i) → Type w) :=
+    (i:id) → (x:a i) → Result (b i x)
+  abbrev k_ty (id : Type u) (a : id → Type v) (b : (i:id) → (x:a i) → Type w) :=
+    kk_ty id a b → kk_ty id a b
+
+  abbrev in_out_ty : Type (imax (u + 1) (v + 1)) := (in_ty : Type u) × ((x:in_ty) → Type v)
+  -- TODO: remove?
+  abbrev mk_in_out_ty (in_ty : Type u) (out_ty : in_ty → Type v) :
+    in_out_ty :=
+    Sigma.mk in_ty out_ty
+
+  -- Initially, we had left out the parameters id, a and b.
+  -- However, by parameterizing Funs with those parameters, we can state
+  -- and prove lemmas like Funs.is_valid_p_is_valid_p
+  inductive Funs (id : Type u) (a : id → Type v) (b : (i:id) → (x:a i) → Type w) :
+    List in_out_ty.{v, w} → Type (max (u + 1) (max (v + 1) (w + 1))) :=
+    | Nil : Funs id a b []
+    | Cons {ity : Type v} {oty : ity → Type w} {tys : List in_out_ty}
+           (f : kk_ty id a b → (x:ity) → Result (oty x)) (tl : Funs id a b tys) :
+           Funs id a b (⟨ ity, oty ⟩ :: tys)
+
+  def get_fun {tys : List in_out_ty} (fl : Funs id a b tys) :
+    (i : Fin tys.length) → kk_ty id a b → (x : (tys.get i).fst) →
+         Result ((tys.get i).snd x) :=
+    match fl with
+    | .Nil => λ i => by have h:= i.isLt; simp at h
+    | @Funs.Cons id a b ity oty tys1 f tl =>
+      λ ⟨ i, iLt ⟩ =>
+      match i with
+      | 0 =>
+        Eq.mp (by simp [List.get]) f
+      | .succ j =>
+        have jLt: j < tys1.length := by
+          simp at iLt
+          revert iLt
+          simp_arith
+        let j: Fin tys1.length := ⟨ j, jLt ⟩
+        Eq.mp (by simp) (get_fun tl j)
+
+  def for_all_fin_aux {n : Nat} (f : Fin n → Prop) (m : Nat) (h : m ≤ n) : Prop :=
+    if heq: m = n then True
+    else
+      f ⟨ m, by simp_all [Nat.lt_iff_le_and_ne] ⟩ ∧
+      for_all_fin_aux f (m + 1) (by simp_all [Arith.add_one_le_iff_le_ne])
+  termination_by for_all_fin_aux n _ m h => n - m
+  decreasing_by
+    simp_wf
+    apply Nat.sub_add_lt_sub <;> simp
+    simp_all [Arith.add_one_le_iff_le_ne]
+
+  def for_all_fin {n : Nat} (f : Fin n → Prop) := for_all_fin_aux f 0 (by simp)
+
+  theorem for_all_fin_aux_imp_forall {n : Nat} (f : Fin n → Prop) (m : Nat) :
+    (h : m ≤ n) →
+    for_all_fin_aux f m h → ∀ i, m ≤ i.val → f i
+    := by
+    generalize h: (n - m) = k
+    revert m
+    induction k -- TODO: induction h rather?
+    case zero =>
+      simp_all
+      intro m h1 h2
+      have h: n = m := by
+        linarith
+      unfold for_all_fin_aux; simp_all
+      simp_all
+      -- There is no i s.t. m ≤ i
+      intro i h3; cases i; simp_all
+      linarith
+    case succ k hi =>
+      simp_all
+      intro m hk hmn
+      intro hf i hmi
+      have hne: m ≠ n := by
+        have hineq := Nat.lt_of_sub_eq_succ hk
+        linarith
+      -- m = i?
+      if heq: m = i then
+        -- Yes: simply use the `for_all_fin_aux` hyp
+        unfold for_all_fin_aux at hf
+        simp_all
+        tauto
+      else
+        -- No: use the induction hypothesis
+        have hlt: m < i := by simp_all [Nat.lt_iff_le_and_ne]
+        have hineq: m + 1 ≤ n := by
+          have hineq := Nat.lt_of_sub_eq_succ hk
+          simp [*, Nat.add_one_le_iff]
+        have heq1: n - (m + 1) = k := by
+          -- TODO: very annoying arithmetic proof
+          simp [Nat.sub_eq_iff_eq_add hineq]
+          have hineq1: m ≤ n := by linarith
+          simp [Nat.sub_eq_iff_eq_add hineq1] at hk
+          simp_arith [hk]
+        have hi := hi (m + 1) heq1 hineq
+        apply hi <;> simp_all
+        . unfold for_all_fin_aux at hf
+          simp_all
+        . simp_all [Arith.add_one_le_iff_le_ne]
+
+  -- TODO: this is not necessary anymore
+  theorem for_all_fin_imp_forall (n : Nat) (f : Fin n → Prop) :
+    for_all_fin f → ∀ i, f i
+    := by
+    intro Hf i
+    apply for_all_fin_aux_imp_forall <;> try assumption
+    simp
+
+  /- Automating the proofs -/
+  @[simp] theorem is_valid_p_same
+    (k : ((i:id) → (x:a i) → Result (b i x)) → (i:id) → (x:a i) → Result (b i x)) (x : Result c) :
+    is_valid_p k (λ _ => x) := by
+    simp [is_valid_p, k_to_gen, e_to_gen]
+
+  @[simp] theorem is_valid_p_rec
+     (k : ((i:id) → (x:a i) → Result (b i x)) → (i:id) → (x:a i) → Result (b i x)) (i : id) (x : a i) :
+    is_valid_p k (λ k => k i x) := by
+    simp [is_valid_p, k_to_gen, e_to_gen, kk_to_gen, kk_of_gen]
+
+  theorem is_valid_p_ite
+    (k : ((i:id) → (x:a i) → Result (b i x)) → (i:id) → (x:a i) → Result (b i x))
+    (cond : Prop) [h : Decidable cond]
+    {e1 e2 : ((i:id) → (x:a i) → Result (b i x)) → Result c}
+    (he1: is_valid_p k e1) (he2 : is_valid_p k e2) :
+    is_valid_p k (λ k => ite cond (e1 k) (e2 k)) := by
+    split <;> assumption
+
+  theorem is_valid_p_dite
+    (k : ((i:id) → (x:a i) → Result (b i x)) → (i:id) → (x:a i) → Result (b i x))
+    (cond : Prop) [h : Decidable cond]
+    {e1 : ((i:id) → (x:a i) → Result (b i x)) → cond → Result c}
+    {e2 : ((i:id) → (x:a i) → Result (b i x)) → Not cond → Result c}
+    (he1: ∀ x, is_valid_p k (λ k => e1 k x))
+    (he2 : ∀ x, is_valid_p k (λ k => e2 k x)) :
+    is_valid_p k (λ k => dite cond (e1 k) (e2 k)) := by
+    split <;> simp [*]
+
+  theorem is_valid_p_bind
+    {{k : ((i:id) → (x:a i) → Result (b i x)) → (i:id) → (x:a i) → Result (b i x)}}
+    {{g : ((i:id) → (x:a i) → Result (b i x)) → Result c}}
+    {{h : c → ((i:id) → (x:a i) → Result (b i x)) → Result d}}
+    (Hgvalid : is_valid_p k g)
+    (Hhvalid : ∀ y, is_valid_p k (h y)) :
+    is_valid_p k (λ k => do let y ← g k; h y k) := by
+    apply Fix.is_valid_p_bind
+    . apply Hgvalid
+    . apply Hhvalid
+
+  def Funs.is_valid_p
+    (k : k_ty id a b)
+    (fl : Funs id a b tys) :
+    Prop :=
+    match fl with
+    | .Nil => True
+    | .Cons f fl => (∀ x, FixI.is_valid_p k (λ k => f k x)) ∧ fl.is_valid_p k
+
+  theorem Funs.is_valid_p_Nil (k : k_ty id a b) :
+    Funs.is_valid_p k Funs.Nil := by simp [Funs.is_valid_p]
+
+  def Funs.is_valid_p_is_valid_p_aux
+    {k : k_ty id a b}
+    {tys : List in_out_ty}
+    (fl : Funs id a b tys) (Hvalid : is_valid_p k fl) :
+    ∀ (i : Fin tys.length) (x : (tys.get i).fst), FixI.is_valid_p k (fun k => get_fun fl i k x) := by
+    -- Prepare the induction
+    have ⟨ n, Hn ⟩ : { n : Nat // tys.length = n } := ⟨ tys.length, by rfl ⟩
+    revert tys fl Hvalid
+    induction n
+    --
+    case zero =>
+      intro tys fl Hvalid Hlen;
+      have Heq: tys = [] := by cases tys <;> simp_all
+      intro i x
+      simp_all
+      have Hi := i.isLt
+      simp_all
+    case succ n Hn =>
+      intro tys fl Hvalid Hlen i x;
+      cases fl <;> simp at Hlen i x Hvalid
+      rename_i ity oty tys f fl
+      have ⟨ Hvf, Hvalid ⟩ := Hvalid
+      have Hvf1: is_valid_p k fl := by
+        simp [Hvalid, Funs.is_valid_p]
+      have Hn := @Hn tys fl Hvf1 (by simp [*])
+      -- Case disjunction on i
+      match i with
+      | ⟨ 0, _ ⟩ =>
+        simp at x
+        simp [get_fun]
+        apply (Hvf x)
+      | ⟨ .succ j, HiLt ⟩ =>
+        simp_arith at HiLt
+        simp at x
+        let j : Fin (List.length tys) := ⟨ j, by simp_arith [HiLt] ⟩
+        have Hn := Hn j x
+        apply Hn
+
+  def Funs.is_valid_p_is_valid_p
+    (tys : List in_out_ty)
+    (k : k_ty (Fin (List.length tys)) (λ i => (tys.get i).fst) (fun i x => (List.get tys i).snd x))
+    (fl : Funs (Fin tys.length) (λ i => (tys.get i).fst) (λ i x => (tys.get i).snd x) tys) :
+    fl.is_valid_p k  →
+    ∀ (i : Fin tys.length) (x : (tys.get i).fst),
+      FixI.is_valid_p k (fun k => get_fun fl i k x)
+    := by
+    intro Hvalid
+    apply is_valid_p_is_valid_p_aux; simp [*]
+
+end FixI
+
+namespace Ex1
+  /- An example of use of the fixed-point -/
+  open Primitives Fix
+
+  variable {a : Type} (k : (List a × Int) → Result a)
+
+  def list_nth_body (x : (List a × Int)) : Result a :=
+    let (ls, i) := x
+    match ls with
+    | [] => .fail .panic
+    | hd :: tl =>
+      if i = 0 then .ret hd
+      else k (tl, i - 1)
+
+  theorem list_nth_body_is_valid: ∀ k x, is_valid_p k (λ k => @list_nth_body a k x) := by
+    intro k x
+    simp [list_nth_body]
+    split <;> simp
+    split <;> simp
+
+  def list_nth (ls : List a) (i : Int) : Result a := fix list_nth_body (ls, i)
+
+  -- The unfolding equation - diverges if `i < 0`
+  theorem list_nth_eq (ls : List a) (i : Int) :
+    list_nth ls i =
+      match ls with
+      | [] => .fail .panic
+      | hd :: tl =>
+        if i = 0 then .ret hd
+        else list_nth tl (i - 1)
+    := by
+    have Heq := is_valid_fix_fixed_eq (@list_nth_body_is_valid a)
+    simp [list_nth]
+    conv => lhs; rw [Heq]
+
+end Ex1
+
+namespace Ex2
+  /- Same as Ex1, but we make the body of nth non tail-rec (this is mostly
+     to see what happens when there are let-bindings) -/
+  open Primitives Fix
+
+  variable {a : Type} (k : (List a × Int) → Result a)
+
+  def list_nth_body (x : (List a × Int)) : Result a :=
+    let (ls, i) := x
+    match ls with
+    | [] => .fail .panic
+    | hd :: tl =>
+      if i = 0 then .ret hd
+      else
+        do
+          let y ← k (tl, i - 1)
+          .ret y
+
+  theorem list_nth_body_is_valid: ∀ k x, is_valid_p k (λ k => @list_nth_body a k x) := by
+    intro k x
+    simp [list_nth_body]
+    split <;> simp
+    split <;> simp
+    apply is_valid_p_bind <;> intros <;> simp_all
+
+  def list_nth (ls : List a) (i : Int) : Result a := fix list_nth_body (ls, i)
+
+  -- The unfolding equation - diverges if `i < 0`
+  theorem list_nth_eq (ls : List a) (i : Int) :
+    (list_nth ls i =
+       match ls with
+       | [] => .fail .panic
+       | hd :: tl =>
+         if i = 0 then .ret hd
+         else
+           do
+             let y ← list_nth tl (i - 1)
+             .ret y)
+    := by
+    have Heq := is_valid_fix_fixed_eq (@list_nth_body_is_valid a)
+    simp [list_nth]
+    conv => lhs; rw [Heq]
+
+end Ex2
+
+namespace Ex3
+  /- Mutually recursive functions - first encoding (see Ex4 for a better encoding) -/
+  open Primitives Fix
+
+  /- Because we have mutually recursive functions, we use a sum for the inputs
+     and the output types:
+     - inputs: the sum allows to select the function to call in the recursive
+       calls (and the functions may not have the same input types)
+     - outputs: this case is degenerate because `even` and `odd` have the same
+       return type `Bool`, but generally speaking we need a sum type because
+       the functions in the mutually recursive group may have different
+       return types.
+   -/
+  variable (k : (Int ⊕ Int) → Result (Bool ⊕ Bool))
+
+  def is_even_is_odd_body (x : (Int ⊕ Int)) : Result (Bool ⊕ Bool) :=
+    match x with
+    | .inl i =>
+      -- Body of `is_even`
+      if i = 0
+      then .ret (.inl true) -- We use .inl because this is `is_even`
+      else
+        do
+          let b ←
+            do
+              -- Call `odd`: we need to wrap the input value in `.inr`, then
+              -- extract the output value
+              let r ← k (.inr (i- 1))
+              match r with
+              | .inl _ => .fail .panic -- Invalid output
+              | .inr b => .ret b
+          -- Wrap the return value
+          .ret (.inl b)
+    | .inr i =>
+      -- Body of `is_odd`
+      if i = 0
+      then .ret (.inr false) -- We use .inr because this is `is_odd`
+      else
+        do
+          let b ←
+            do
+              -- Call `is_even`: we need to wrap the input value in .inr, then
+              -- extract the output value
+              let r ← k (.inl (i- 1))
+              match r with
+              | .inl b => .ret b
+              | .inr _ => .fail .panic -- Invalid output
+          -- Wrap the return value
+          .ret (.inr b)
+
+  theorem is_even_is_odd_body_is_valid:
+    ∀ k x, is_valid_p k (λ k => is_even_is_odd_body k x) := by
+    intro k x
+    simp [is_even_is_odd_body]
+    split <;> simp <;> split <;> simp
+    apply is_valid_p_bind; simp
+    intros; split <;> simp
+    apply is_valid_p_bind; simp
+    intros; split <;> simp
+
+  def is_even (i : Int): Result Bool :=
+    do
+      let r ← fix is_even_is_odd_body (.inl i)
+      match r with
+      | .inl b => .ret b
+      | .inr _ => .fail .panic
+
+  def is_odd (i : Int): Result Bool :=
+    do
+      let r ← fix is_even_is_odd_body (.inr i)
+      match r with
+      | .inl _ => .fail .panic
+      | .inr b => .ret b
+
+  -- The unfolding equation for `is_even` - diverges if `i < 0`
+  theorem is_even_eq (i : Int) :
+    is_even i = (if i = 0 then .ret true else is_odd (i - 1))
+    := by
+    have Heq := is_valid_fix_fixed_eq is_even_is_odd_body_is_valid
+    simp [is_even, is_odd]
+    conv => lhs; rw [Heq]; simp; rw [is_even_is_odd_body]; simp
+    -- Very annoying: we need to swap the matches
+    -- Doing this with rewriting lemmas is hard generally speaking
+    -- (especially as we may have to generate lemmas for user-defined
+    -- inductives on the fly).
+    -- The simplest is to repeatedly split then simplify (we identify
+    -- the outer match or monadic let-binding, and split on its scrutinee)
+    split <;> simp
+    cases H0 : fix is_even_is_odd_body (Sum.inr (i - 1)) <;> simp
+    rename_i v
+    split <;> simp
+
+  -- The unfolding equation for `is_odd` - diverges if `i < 0`
+  theorem is_odd_eq (i : Int) :
+    is_odd i = (if i = 0 then .ret false else is_even (i - 1))
+    := by
+    have Heq := is_valid_fix_fixed_eq is_even_is_odd_body_is_valid
+    simp [is_even, is_odd]
+    conv => lhs; rw [Heq]; simp; rw [is_even_is_odd_body]; simp
+    -- Same remark as for `even`
+    split <;> simp
+    cases H0 : fix is_even_is_odd_body (Sum.inl (i - 1)) <;> simp
+    rename_i v
+    split <;> simp
+
+end Ex3
+
+namespace Ex4
+  /- Mutually recursive functions - 2nd encoding -/
+  open Primitives FixI
+
+  /- We make the input type and output types dependent on a parameter -/
+  @[simp] def tys : List in_out_ty := [mk_in_out_ty Int (λ _ => Bool), mk_in_out_ty Int (λ _ => Bool)]
+  @[simp] def input_ty (i : Fin 2) : Type := (tys.get i).fst
+  @[simp] def output_ty (i : Fin 2) (x : input_ty i) : Type :=
+    (tys.get i).snd x
+
+  /- The bodies are more natural -/
+  def is_even_body (k : (i : Fin 2) → (x : input_ty i) → Result (output_ty i x)) (i : Int) : Result Bool :=
+    if i = 0
+      then .ret true
+    else do
+      let b ← k 1 (i - 1)
+      .ret b
+
+  def is_odd_body (k : (i : Fin 2) → (x : input_ty i) → Result (output_ty i x)) (i : Int) : Result Bool :=
+    if i = 0
+      then .ret false
+    else do
+      let b ← k 0 (i - 1)
+      .ret b
+
+  @[simp] def bodies :
+    Funs (Fin 2) input_ty output_ty
+      [mk_in_out_ty Int (λ _ => Bool), mk_in_out_ty Int (λ _ => Bool)] :=
+    Funs.Cons (is_even_body) (Funs.Cons (is_odd_body) Funs.Nil)
+
+  def body (k : (i : Fin 2) → (x : input_ty i) → Result (output_ty i x)) (i: Fin 2) :
+    (x : input_ty i) → Result (output_ty i x) := get_fun bodies i k
+
+  theorem body_is_valid : is_valid body := by
+    -- Split the proof into proofs of validity of the individual bodies
+    rw [is_valid]
+    simp only [body]
+    intro k
+    apply (Funs.is_valid_p_is_valid_p tys)
+    simp [Funs.is_valid_p]
+    (repeat (apply And.intro)) <;> intro x <;> simp at x <;>
+    simp only [is_even_body, is_odd_body]
+    -- Prove the validity of the individual bodies
+    . split <;> simp
+      apply is_valid_p_bind <;> simp
+    . split <;> simp
+      apply is_valid_p_bind <;> simp
+
+  theorem body_fix_eq : fix body = body (fix body) :=
+    is_valid_fix_fixed_eq body_is_valid
+
+  def is_even (i : Int) : Result Bool := fix body 0 i
+  def is_odd (i : Int) : Result Bool := fix body 1 i
+
+  theorem is_even_eq (i : Int) : is_even i =
+    (if i = 0
+       then .ret true
+     else do
+       let b ← is_odd (i - 1)
+       .ret b) := by
+    simp [is_even, is_odd];
+    conv => lhs; rw [body_fix_eq]
+
+  theorem is_odd_eq (i : Int) : is_odd i =
+    (if i = 0
+       then .ret false
+     else do
+       let b ← is_even (i - 1)
+       .ret b) := by
+    simp [is_even, is_odd];
+    conv => lhs; rw [body_fix_eq]
+end Ex4
+
+namespace Ex5
+  /- Higher-order example -/
+  open Primitives Fix
+
+  variable {a b : Type}
+
+  /- An auxiliary function, which doesn't require the fixed-point -/
+  def map (f : a → Result b) (ls : List a) : Result (List b) :=
+    match ls with
+    | [] => .ret []
+    | hd :: tl =>
+      do
+        let hd ← f hd
+        let tl ← map f tl
+        .ret (hd :: tl)
+
+  /- The validity theorem for `map`, generic in `f` -/
+  theorem map_is_valid
+    {{f : (a → Result b) → a → Result c}}
+    (Hfvalid : ∀ k x, is_valid_p k (λ k => f k x))
+    (k : (a → Result b) → a → Result b)
+    (ls : List a) :
+    is_valid_p k (λ k => map (f k) ls) := by
+    induction ls <;> simp [map]
+    apply is_valid_p_bind <;> simp_all
+    intros
+    apply is_valid_p_bind <;> simp_all
+
+  /- An example which uses map -/
+  inductive Tree (a : Type) :=
+  | leaf (x : a)
+  | node (tl : List (Tree a))
+
+  def id_body (k : Tree a → Result (Tree a)) (t : Tree a) : Result (Tree a) :=
+    match t with
+    | .leaf x => .ret (.leaf x)
+    | .node tl =>
+      do
+        let tl ← map k tl
+        .ret (.node tl)
+
+  theorem id_body_is_valid :
+    ∀ k x, is_valid_p k (λ k => @id_body a k x) := by
+    intro k x
+    simp only [id_body]
+    split <;> simp
+    apply is_valid_p_bind <;> simp [*]
+    -- We have to show that `map k tl` is valid
+    apply map_is_valid;
+    -- Remark: if we don't do the intro, then the last step is expensive:
+    -- "typeclass inference of Nonempty took 119ms"
+    intro k x
+    simp only [is_valid_p_same, is_valid_p_rec]
+
+  def id (t : Tree a) := fix id_body t
+
+  -- The unfolding equation
+  theorem id_eq (t : Tree a) :
+    (id t =
+       match t with
+       | .leaf x => .ret (.leaf x)
+       | .node tl =>
+       do
+         let tl ← map id tl
+         .ret (.node tl))
+    := by
+    have Heq := is_valid_fix_fixed_eq (@id_body_is_valid a)
+    simp [id]
+    conv => lhs; rw [Heq]; simp; rw [id_body]
+
+end Ex5
+
+namespace Ex6
+  /- `list_nth` again, but this time we use FixI -/
+  open Primitives FixI
+
+  @[simp] def tys.{u} : List in_out_ty :=
+    [mk_in_out_ty ((a:Type u) × (List a × Int)) (λ ⟨ a, _ ⟩ => a)]
+
+  @[simp] def input_ty (i : Fin 1) := (tys.get i).fst
+  @[simp] def output_ty (i : Fin 1) (x : input_ty i) :=
+    (tys.get i).snd x
+
+  def list_nth_body.{u} (k : (i:Fin 1) → (x:input_ty i) → Result (output_ty i x))
+    (x : (a : Type u) × List a × Int) : Result x.fst :=
+    let ⟨ a, ls, i ⟩ := x
+    match ls with
+    | [] => .fail .panic
+    | hd :: tl =>
+      if i = 0 then .ret hd
+      else k 0 ⟨ a, tl, i - 1 ⟩
+
+  @[simp] def bodies :
+    Funs (Fin 1) input_ty output_ty tys :=
+    Funs.Cons list_nth_body Funs.Nil
+
+  def body (k : (i : Fin 1) → (x : input_ty i) → Result (output_ty i x)) (i: Fin 1) :
+    (x : input_ty i) → Result (output_ty i x) := get_fun bodies i k
+
+  theorem body_is_valid: is_valid body := by
+    -- Split the proof into proofs of validity of the individual bodies
+    rw [is_valid]
+    simp only [body]
+    intro k
+    apply (Funs.is_valid_p_is_valid_p tys)
+    simp [Funs.is_valid_p]
+    (repeat (apply And.intro)); intro x; simp at x
+    simp only [list_nth_body]
+    -- Prove the validity of the individual bodies
+    intro k x
+    simp [list_nth_body]
+    split <;> simp
+    split <;> simp
+
+  -- Writing the proof terms explicitly
+  theorem list_nth_body_is_valid' (k : k_ty (Fin 1) input_ty output_ty)
+    (x : (a : Type u) × List a × Int) : is_valid_p k (fun k => list_nth_body k x) :=
+    let ⟨ a, ls, i ⟩ := x
+    match ls with
+    | [] => is_valid_p_same k (.fail .panic)
+    | hd :: tl =>
+      is_valid_p_ite k (Eq i 0) (is_valid_p_same k (.ret hd)) (is_valid_p_rec k 0 ⟨a, tl, i-1⟩)
+
+  theorem body_is_valid' : is_valid body :=
+    fun k =>
+    Funs.is_valid_p_is_valid_p tys k bodies
+      (And.intro (list_nth_body_is_valid' k) (Funs.is_valid_p_Nil k))
+
+  def list_nth {a: Type u} (ls : List a) (i : Int) : Result a :=
+    fix body 0 ⟨ a, ls , i ⟩
+
+  -- The unfolding equation - diverges if `i < 0`
+  theorem list_nth_eq (ls : List a) (i : Int) :
+    list_nth ls i =
+      match ls with
+      | [] => .fail .panic
+      | hd :: tl =>
+        if i = 0 then .ret hd
+        else list_nth tl (i - 1)
+    := by
+    have Heq := is_valid_fix_fixed_eq body_is_valid
+    simp [list_nth]
+    conv => lhs; rw [Heq]
+
+  -- Write the proof term explicitly: the generation of the proof term (without tactics)
+  -- is automatable, and the proof term is actually a lot simpler and smaller when we
+  -- don't use tactics.
+  theorem list_nth_eq'.{u} {a : Type u} (ls : List a) (i : Int) :
+    list_nth ls i =
+      match ls with
+      | [] => .fail .panic
+      | hd :: tl =>
+        if i = 0 then .ret hd
+        else list_nth tl (i - 1)
+    :=
+    -- Use the fixed-point equation
+    have Heq := is_valid_fix_fixed_eq body_is_valid.{u}
+    -- Add the index
+    have Heqi := congr_fun Heq 0
+    -- Add the input
+    have Heqix := congr_fun Heqi { fst := a, snd := (ls, i) }
+    -- Done
+    Heqix
+
+end Ex6
diff --git a/backends/lean/Base/Diverge/Elab.lean b/backends/lean/Base/Diverge/Elab.lean
new file mode 100644
index 00000000..f109e847
--- /dev/null
+++ b/backends/lean/Base/Diverge/Elab.lean
@@ -0,0 +1,1162 @@
+import Lean
+import Lean.Meta.Tactic.Simp
+import Init.Data.List.Basic
+import Mathlib.Tactic.RunCmd
+import Base.Utils
+import Base.Diverge.Base
+import Base.Diverge.ElabBase
+
+namespace Diverge
+
+/- Automating the generation of the encoding and the proofs so as to use nice
+   syntactic sugar. -/
+
+syntax (name := divergentDef)
+  declModifiers "divergent" "def" declId ppIndent(optDeclSig) declVal : command
+
+open Lean Elab Term Meta Primitives Lean.Meta
+open Utils
+
+/- The following was copied from the `wfRecursion` function. -/
+
+open WF in
+
+def mkProd (x y : Expr) : MetaM Expr :=
+  mkAppM ``Prod.mk #[x, y]
+
+def mkInOutTy (x y : Expr) : MetaM Expr :=
+  mkAppM ``FixI.mk_in_out_ty #[x, y]
+
+-- Return the `a` in `Return a`
+def getResultTy (ty : Expr) : MetaM Expr :=
+  ty.withApp fun f args => do
+  if ¬ f.isConstOf ``Result ∨ args.size ≠ 1 then
+    throwError "Invalid argument to getResultTy: {ty}"
+  else
+    pure (args.get! 0)
+
+/- Deconstruct a sigma type.
+
+   For instance, deconstructs `(a : Type) × List a` into
+   `Type` and `λ a => List a`.
+ -/
+def getSigmaTypes (ty : Expr) : MetaM (Expr × Expr) := do
+  ty.withApp fun f args => do
+  if ¬ f.isConstOf ``Sigma ∨ args.size ≠ 2 then
+    throwError "Invalid argument to getSigmaTypes: {ty}"
+  else
+    pure (args.get! 0, args.get! 1)
+
+/- Generate a Sigma type from a list of *variables* (all the expressions
+   must be variables).
+
+   Example:
+   - xl = [(a:Type), (ls:List a), (i:Int)]
+
+   Generates:
+   `(a:Type) × (ls:List a) × (i:Int)`
+
+ -/
+def mkSigmasType (xl : List Expr) : MetaM Expr :=
+  match xl with
+  | [] => do
+    trace[Diverge.def.sigmas] "mkSigmasOfTypes: []"
+    pure (Expr.const ``PUnit.unit [])
+  | [x] => do
+    trace[Diverge.def.sigmas] "mkSigmasOfTypes: [{x}]"
+    let ty ← Lean.Meta.inferType x
+    pure ty
+  | x :: xl => do
+    trace[Diverge.def.sigmas] "mkSigmasOfTypes: [{x}::{xl}]"
+    let alpha ← Lean.Meta.inferType x
+    let sty ← mkSigmasType xl
+    trace[Diverge.def.sigmas] "mkSigmasOfTypes: [{x}::{xl}]: alpha={alpha}, sty={sty}"
+    let beta ← mkLambdaFVars #[x] sty
+    trace[Diverge.def.sigmas] "mkSigmasOfTypes: ({alpha}) ({beta})"
+    mkAppOptM ``Sigma #[some alpha, some beta]
+
+/- Apply a lambda expression to some arguments, simplifying the lambdas -/
+def applyLambdaToArgs (e : Expr) (xs : Array Expr) : MetaM Expr := do
+  lambdaTelescopeN e xs.size fun vars body =>
+  -- Create the substitution
+  let s : HashMap FVarId Expr := HashMap.ofList (List.zip (vars.toList.map Expr.fvarId!) xs.toList)
+  -- Substitute in the body
+  pure (body.replace fun e =>
+    match e with
+    | Expr.fvar fvarId => match s.find? fvarId with
+      | none   => e
+      | some v => v
+    | _ => none)
+
+/- Group a list of expressions into a dependent tuple.
+
+   Example:
+   xl = [`a : Type`, `ls : List a`]
+   returns:
+   `⟨ (a:Type), (ls: List a) ⟩`
+
+   We need the type argument because as the elements in the tuple are
+   "concrete", we can't in all generality figure out the type of the tuple.
+
+   Example:
+   `⟨ True, 3 ⟩ : (x : Bool) × (if x then Int else Unit)`
+ -/
+def mkSigmasVal (ty : Expr) (xl : List Expr) : MetaM Expr :=
+  match xl with
+  | [] => do
+    trace[Diverge.def.sigmas] "mkSigmasVal: []"
+    pure (Expr.const ``PUnit.unit [])
+  | [x] => do
+    trace[Diverge.def.sigmas] "mkSigmasVal: [{x}]"
+    pure x
+  | fst :: xl => do
+    trace[Diverge.def.sigmas] "mkSigmasVal: [{fst}::{xl}]"
+    -- Deconstruct the type
+    let (alpha, beta) ← getSigmaTypes ty
+    -- Compute the "second" field
+    -- Specialize beta for fst
+    let nty ← applyLambdaToArgs beta #[fst]
+    -- Recursive call
+    let snd ← mkSigmasVal nty xl
+    -- Put everything together
+    trace[Diverge.def.sigmas] "mkSigmasVal:\n{alpha}\n{beta}\n{fst}\n{snd}"
+    mkAppOptM ``Sigma.mk #[some alpha, some beta, some fst, some snd]
+
+def mkAnonymous (s : String) (i : Nat) : Name :=
+  .num (.str .anonymous s) i
+
+/- Given a list of values `[x0:ty0, ..., xn:ty1]`, where every `xi` might use the previous
+   `xj` (j < i) and a value `out` which uses `x0`, ..., `xn`, generate the following
+   expression:
+   ```
+   fun x:((x0:ty0) × ... × (xn:tyn) => -- **Dependent** tuple
+   match x with
+   | (x0, ..., xn) => out
+   ```
+
+   The `index` parameter is used for naming purposes: we use it to numerotate the
+   bound variables that we introduce.
+
+   We use this function to currify functions (the function bodies given to the
+   fixed-point operator must be unary functions).
+
+   Example:
+   ========
+   - xl = `[a:Type, ls:List a, i:Int]`
+   - out = `a`
+   - index = 0
+
+   generates (getting rid of most of the syntactic sugar):
+   ```
+   λ scrut0 => match scrut0 with
+   | Sigma.mk x scrut1 =>
+     match scrut1 with
+     | Sigma.mk ls i =>
+       a
+   ```
+-/
+partial def mkSigmasMatch (xl : List Expr) (out : Expr) (index : Nat := 0) : MetaM Expr :=
+  match xl with
+  | [] => do
+    -- This would be unexpected
+    throwError "mkSigmasMatch: empyt list of input parameters"
+  | [x] => do
+    -- In the example given for the explanations: this is the inner match case
+    trace[Diverge.def.sigmas] "mkSigmasMatch: [{x}]"
+    mkLambdaFVars #[x] out
+  | fst :: xl => do
+    -- In the example given for the explanations: this is the outer match case
+    -- Remark: for the naming purposes, we use the same convention as for the
+    -- fields and parameters in `Sigma.casesOn` and `Sigma.mk` (looking at
+    -- those definitions might help)
+    --
+    -- We want to build the match expression:
+    -- ```
+    -- λ scrut =>
+    -- match scrut with
+    -- | Sigma.mk x ...  -- the hole is given by a recursive call on the tail
+    -- ```
+    trace[Diverge.def.sigmas] "mkSigmasMatch: [{fst}::{xl}]"
+    let alpha ← Lean.Meta.inferType fst
+    let snd_ty ← mkSigmasType xl
+    let beta ← mkLambdaFVars #[fst] snd_ty
+    let snd ← mkSigmasMatch xl out (index + 1)
+    let mk ← mkLambdaFVars #[fst] snd
+    -- Introduce the "scrut" variable
+    let scrut_ty ← mkSigmasType (fst :: xl)
+    withLocalDeclD (mkAnonymous "scrut" index) scrut_ty fun scrut => do
+    trace[Diverge.def.sigmas] "mkSigmasMatch: scrut: ({scrut}) : ({← inferType scrut})"
+    -- TODO: make the computation of the motive more efficient
+    let motive ← do
+      let out_ty ← inferType out
+      match out_ty  with
+      | .sort _ | .lit _ | .const .. =>
+        -- The type of the motive doesn't depend on the scrutinee
+        mkLambdaFVars #[scrut] out_ty
+      | _ =>
+        -- The type of the motive *may* depend on the scrutinee
+        -- TODO: make this more efficient (we could change the output type of
+        -- mkSigmasMatch
+        mkSigmasMatch (fst :: xl) out_ty
+    -- The final expression: putting everything together
+    trace[Diverge.def.sigmas] "mkSigmasMatch:\n  ({alpha})\n  ({beta})\n  ({motive})\n  ({scrut})\n  ({mk})"
+    let sm ← mkAppOptM ``Sigma.casesOn #[some alpha, some beta, some motive, some scrut, some mk]
+    -- Abstracting the "scrut" variable
+    let sm ← mkLambdaFVars #[scrut] sm
+    trace[Diverge.def.sigmas] "mkSigmasMatch: sm: {sm}"
+    pure sm
+
+/- Small tests for list_nth: give a model of what `mkSigmasMatch` should generate -/
+private def list_nth_out_ty_inner (a :Type) (scrut1: @Sigma (List a) (fun (_ls : List a) => Int)) :=
+  @Sigma.casesOn (List a)
+                 (fun (_ls : List a) => Int)
+                 (fun (_scrut1:@Sigma (List a) (fun (_ls : List a) => Int)) => Type)
+                 scrut1
+                 (fun (_ls : List a) (_i : Int) => Primitives.Result a)
+
+private def list_nth_out_ty_outer (scrut0 : @Sigma (Type) (fun (a:Type) =>
+                      @Sigma (List a) (fun (_ls : List a) => Int))) :=
+  @Sigma.casesOn (Type)
+                 (fun (a:Type) => @Sigma (List a) (fun (_ls : List a) => Int))
+                 (fun (_scrut0:@Sigma (Type) (fun (a:Type) => @Sigma (List a) (fun (_ls : List a) => Int))) => Type)
+                 scrut0
+                 (fun (a : Type) (scrut1: @Sigma (List a) (fun (_ls : List a) => Int)) =>
+                  list_nth_out_ty_inner a scrut1)
+/- -/
+
+-- Return the expression: `Fin n`
+-- TODO: use more
+def mkFin (n : Nat) : Expr :=
+  mkAppN (.const ``Fin []) #[.lit (.natVal n)]
+
+-- Return the expression: `i : Fin n`
+def mkFinVal (n i : Nat) : MetaM Expr := do
+  let n_lit : Expr := .lit (.natVal (n - 1))
+  let i_lit : Expr := .lit (.natVal i)
+  -- We could use `trySynthInstance`, but as we know the instance that we are
+  -- going to use, we can save the lookup
+  let ofNat ← mkAppOptM ``Fin.instOfNatFinHAddNatInstHAddInstAddNatOfNat #[n_lit, i_lit]
+  mkAppOptM ``OfNat.ofNat #[none, none, ofNat]
+
+/- Generate and declare as individual definitions the bodies for the individual funcions:
+   - replace the recursive calls with calls to the continutation `k`
+   - make those bodies take one single dependent tuple as input
+
+   We name the declarations: "[original_name].body".
+   We return the new declarations.
+ -/
+def mkDeclareUnaryBodies (grLvlParams : List Name) (kk_var : Expr)
+  (inOutTys : Array (Expr × Expr)) (preDefs : Array PreDefinition) :
+  MetaM (Array Expr) := do
+  let grSize := preDefs.size
+
+  -- Compute the map from name to (index × input type).
+  -- Remark: the continuation has an indexed type; we use the index (a finite number of
+  -- type `Fin`) to control which function we call at the recursive call site.
+  let nameToInfo : HashMap Name (Nat × Expr) :=
+    let bl := preDefs.mapIdx fun i d => (d.declName, (i.val, (inOutTys.get! i.val).fst))
+    HashMap.ofList bl.toList
+
+  trace[Diverge.def.genBody] "nameToId: {nameToInfo.toList}"
+
+  -- Auxiliary function to explore the function bodies and replace the
+  -- recursive calls
+  let visit_e (i : Nat) (e : Expr) : MetaM Expr := do
+    trace[Diverge.def.genBody] "visiting expression (dept: {i}): {e}"
+    let ne ← do
+      match e with
+      | .app .. => do
+        e.withApp fun f args => do
+          trace[Diverge.def.genBody] "this is an app: {f} {args}"
+          -- Check if this is a recursive call
+          if f.isConst then
+            let name := f.constName!
+            match nameToInfo.find? name with
+            | none => pure e
+            | some (id, in_ty) =>
+              trace[Diverge.def.genBody] "this is a recursive call"
+              -- This is a recursive call: replace it
+              -- Compute the index
+              let i ← mkFinVal grSize id
+              -- Put the arguments in one big dependent tuple
+              let args ← mkSigmasVal in_ty args.toList
+              mkAppM' kk_var #[i, args]
+          else
+            -- Not a recursive call: do nothing
+            pure e
+       | .const name _ =>
+         -- Sanity check: we eliminated all the recursive calls
+         if (nameToInfo.find? name).isSome then
+           throwError "mkUnaryBodies: a recursive call was not eliminated"
+         else pure e
+       | _ => pure e
+    trace[Diverge.def.genBody] "done with expression (depth: {i}): {e}"
+    pure ne
+
+  -- Explore the bodies
+  preDefs.mapM fun preDef => do
+    -- Replace the recursive calls
+    trace[Diverge.def.genBody] "About to replace recursive calls in {preDef.declName}"
+    let body ← mapVisit visit_e preDef.value
+    trace[Diverge.def.genBody] "Body after replacement of the recursive calls: {body}"
+
+    -- Currify the function by grouping the arguments into a dependent tuple
+    -- (over which we match to retrieve the individual arguments).
+    lambdaTelescope body fun args body => do
+    let body ← mkSigmasMatch args.toList body 0
+
+    -- Add the declaration
+    let value ← mkLambdaFVars #[kk_var] body
+    let name := preDef.declName.append "body"
+    let levelParams := grLvlParams
+    let decl := Declaration.defnDecl {
+      name := name
+      levelParams := levelParams
+      type := ← inferType value -- TODO: change the type
+      value := value
+      hints := ReducibilityHints.regular (getMaxHeight (← getEnv) value + 1)
+      safety := .safe
+      all := [name]
+    }
+    addDecl decl
+    trace[Diverge.def] "individual body of {preDef.declName}: {body}"
+    -- Return the constant
+    let body := Lean.mkConst name (levelParams.map .param)
+    -- let body ← mkAppM' body #[kk_var]
+    trace[Diverge.def] "individual body (after decl): {body}"
+    pure body
+
+-- Generate a unique function body from the bodies of the mutually recursive group,
+-- and add it as a declaration in the context.
+-- We return the list of bodies (of type `FixI.Funs ...`) and the mutually recursive body.
+def mkDeclareMutRecBody (grName : Name) (grLvlParams : List Name)
+  (kk_var i_var : Expr)
+  (in_ty out_ty : Expr) (inOutTys : List (Expr × Expr))
+  (bodies : Array Expr) : MetaM (Expr × Expr) := do
+  -- Generate the body
+  let grSize := bodies.size
+  let finTypeExpr := mkFin grSize
+  -- TODO: not very clean
+  let inOutTyType ← do
+    let (x, y) := inOutTys.get! 0
+    inferType (← mkInOutTy x y)
+  let rec mkFuns (inOutTys : List (Expr × Expr)) (bl : List Expr) : MetaM Expr :=
+    match inOutTys, bl with
+    | [], [] =>
+      mkAppOptM ``FixI.Funs.Nil #[finTypeExpr, in_ty, out_ty]
+    | (ity, oty) :: inOutTys, b :: bl => do
+      -- Retrieving ity and oty - this is not very clean
+      let inOutTysExpr ← mkListLit inOutTyType (← inOutTys.mapM (λ (x, y) => mkInOutTy x y))
+      let fl ← mkFuns inOutTys bl
+      mkAppOptM ``FixI.Funs.Cons #[finTypeExpr, in_ty, out_ty, ity, oty, inOutTysExpr, b, fl]
+    | _, _ => throwError "mkDeclareMutRecBody: `tys` and `bodies` don't have the same length"
+  let bodyFuns ← mkFuns inOutTys bodies.toList
+  -- Wrap in `get_fun`
+  let body ← mkAppM ``FixI.get_fun #[bodyFuns, i_var, kk_var]
+  -- Add the index `i` and the continuation `k` as a variables
+  let body ← mkLambdaFVars #[kk_var, i_var] body
+  trace[Diverge.def] "mkDeclareMutRecBody: body: {body}"
+  -- Add the declaration
+  let name := grName.append "mut_rec_body"
+  let levelParams := grLvlParams
+  let decl := Declaration.defnDecl {
+    name := name
+    levelParams := levelParams
+    type := ← inferType body
+    value := body
+    hints := ReducibilityHints.regular (getMaxHeight (← getEnv) body + 1)
+    safety := .safe
+    all := [name]
+  }
+  addDecl decl
+  -- Return the bodies and the constant
+  pure (bodyFuns, Lean.mkConst name (levelParams.map .param))
+
+def isCasesExpr (e : Expr) : MetaM Bool := do
+  let e := e.getAppFn
+  if e.isConst then
+    return isCasesOnRecursor (← getEnv) e.constName
+  else return false
+
+structure MatchInfo where
+  matcherName       : Name
+  matcherLevels     : Array Level
+  params            : Array Expr
+  motive            : Expr
+  scruts            : Array Expr
+  branchesNumParams : Array Nat
+  branches          : Array Expr
+
+instance : ToMessageData MatchInfo where
+  -- This is not a very clean formatting, but we don't need more
+  toMessageData := fun me => m!"\n- matcherName: {me.matcherName}\n- params: {me.params}\n- motive: {me.motive}\n- scruts: {me.scruts}\n- branchesNumParams: {me.branchesNumParams}\n- branches: {me.branches}"
+
+-- Small helper: prove that an expression which doesn't use the continuation `kk`
+-- is valid, and return the proof.
+def proveNoKExprIsValid (k_var : Expr) (e : Expr) : MetaM Expr := do
+  trace[Diverge.def.valid] "proveNoKExprIsValid: {e}"
+  let eIsValid ← mkAppM ``FixI.is_valid_p_same #[k_var, e]
+  trace[Diverge.def.valid] "proveNoKExprIsValid: result:\n{eIsValid}:\n{← inferType eIsValid}"
+  pure eIsValid
+
+mutual
+
+/- Prove that an expression is valid, and return the proof.
+
+   More precisely, if `e` is an expression which potentially uses the continution
+   `kk`, return an expression of type:
+   ```
+   is_valid_p k (λ kk => e)
+   ```
+ -/
+partial def proveExprIsValid (k_var kk_var : Expr) (e : Expr) : MetaM Expr := do
+  trace[Diverge.def.valid] "proveValid: {e}"
+  match e with
+  | .const _ _ => throwError "Unimplemented" -- Shouldn't get there?
+  | .bvar _
+  | .fvar _
+  | .lit _
+  | .mvar _
+  | .sort _ => throwError "Unreachable"
+  | .lam .. => throwError "Unimplemented"
+  | .forallE .. => throwError "Unreachable" -- Shouldn't get there
+  | .letE .. => do
+    -- Telescope all the let-bindings (remark: this also telescopes the lambdas)
+    lambdaLetTelescope e fun xs body => do
+    -- Note that we don't visit the bound values: there shouldn't be
+    -- recursive calls, lambda expressions, etc. inside
+    -- Prove that the body is valid
+    let isValid ← proveExprIsValid k_var kk_var body
+    -- Add the let-bindings around.
+    -- Rem.: the let-binding should be *inside* the `is_valid_p`, not outside,
+    -- but because it reduces in the end it doesn't matter. More precisely:
+    -- `P (let x := v in y)` and `let x := v in P y` reduce to the same expression.
+    mkLambdaFVars xs isValid (usedLetOnly := false)
+  | .mdata _ b => proveExprIsValid k_var kk_var b
+  | .proj _ _ _ =>
+    -- The projection shouldn't use the continuation
+    proveNoKExprIsValid k_var e
+  | .app .. =>
+    e.withApp fun f args => do
+      -- There are several cases: first, check if this is a match/if
+      -- Check if the expression is a (dependent) if then else.
+      -- We treat the if then else expressions differently from the other matches,
+      -- and have dedicated theorems for them.
+      let isIte := e.isIte
+      if isIte || e.isDIte then do
+        e.withApp fun f args => do
+        trace[Diverge.def.valid] "ite/dite: {f}:\n{args}"
+        if args.size ≠ 5 then
+           throwError "Wrong number of parameters for {f}: {args}"
+        let cond := args.get! 1
+        let dec := args.get! 2
+        -- Prove that the branches are valid
+        let br0 := args.get! 3
+        let br1 := args.get! 4
+        let proveBranchValid (br : Expr) : MetaM Expr :=
+          if isIte then proveExprIsValid k_var kk_var br
+          else do
+            -- There is a lambda
+            lambdaOne br fun x br => do
+            let brValid ← proveExprIsValid k_var kk_var br
+            mkLambdaFVars #[x] brValid
+        let br0Valid ← proveBranchValid br0
+        let br1Valid ← proveBranchValid br1
+        let const := if isIte then ``FixI.is_valid_p_ite else ``FixI.is_valid_p_dite
+        let eIsValid ← mkAppOptM const #[none, none, none, none, some k_var, some cond, some dec, none, none, some br0Valid, some br1Valid]
+        trace[Diverge.def.valid] "ite/dite: result:\n{eIsValid}:\n{← inferType eIsValid}"
+        pure eIsValid
+      -- Check if the expression is a match (this case is for when the elaborator
+      -- introduces auxiliary definitions to hide the match behind syntactic
+      -- sugar):
+      else if let some me := ← matchMatcherApp? e then do
+        trace[Diverge.def.valid]
+          "matcherApp:
+           - params: {me.params}
+           - motive: {me.motive}
+           - discrs: {me.discrs}
+           - altNumParams: {me.altNumParams}
+           - alts: {me.alts}
+           - remaining: {me.remaining}"
+        -- matchMatcherApp does all the work for us: we simply need to gather
+        -- the information and call the auxiliary helper `proveMatchIsValid`
+        if me.remaining.size ≠ 0 then
+          throwError "MatcherApp: non empty remaining array: {me.remaining}"
+        let me : MatchInfo := {
+          matcherName := me.matcherName
+          matcherLevels := me.matcherLevels
+          params := me.params
+          motive := me.motive
+          scruts := me.discrs
+          branchesNumParams := me.altNumParams
+          branches := me.alts
+        }
+        proveMatchIsValid k_var kk_var me
+      -- Check if the expression is a raw match (this case is for when the expression
+      -- is a direct call to the primitive `casesOn` function, without syntactic sugar).
+      -- We have to check this case because functions like `mkSigmasMatch`, which we
+      -- use to currify function bodies, introduce such raw matches.
+      else if ← isCasesExpr f then do
+        trace[Diverge.def.valid] "rawMatch: {e}"
+        -- Deconstruct the match, and call the auxiliary helper `proveMatchIsValid`.
+        --
+        -- The casesOn definition is always of the following shape:
+        -- - input parameters (implicit parameters)
+        -- - motive (implicit), -- the motive gives the return type of the match
+        -- - scrutinee (explicit)
+        -- - branches (explicit).
+        -- In particular, we notice that the scrutinee is the first *explicit*
+        -- parameter - this is how we spot it.
+        let matcherName := f.constName!
+        let matcherLevels := f.constLevels!.toArray
+        -- Find the first explicit parameter: this is the scrutinee
+        forallTelescope (← inferType f) fun xs _ => do
+        let rec findFirstExplicit (i : Nat) : MetaM Nat := do
+          if i ≥ xs.size then throwError "Unexpected: could not find an explicit parameter"
+          else
+            let x := xs.get! i
+            let xFVarId := x.fvarId!
+            let localDecl ← xFVarId.getDecl
+            match localDecl.binderInfo with
+            | .default => pure i
+            | _ => findFirstExplicit (i + 1)
+        let scrutIdx ← findFirstExplicit 0
+        -- Split the arguments
+        let params := args.extract 0 (scrutIdx - 1)
+        let motive := args.get! (scrutIdx - 1)
+        let scrut := args.get! scrutIdx
+        let branches := args.extract (scrutIdx + 1) args.size
+        -- Compute the number of parameters for the branches: for this we use
+        -- the type of the uninstantiated casesOn constant (we can't just
+        -- destruct the lambdas in the branch expressions because the result
+        -- of a match might be a lambda expression).
+        let branchesNumParams : Array Nat ← do
+          let env ← getEnv
+          let decl := env.constants.find! matcherName
+          let ty := decl.type
+          forallTelescope ty fun xs _ => do
+          let xs := xs.extract (scrutIdx + 1) xs.size
+          xs.mapM fun x => do
+          let xty ← inferType x
+          forallTelescope xty fun ys _ => do
+          pure ys.size
+        let me : MatchInfo := {
+          matcherName,
+          matcherLevels,
+          params,
+          motive,
+          scruts := #[scrut],
+          branchesNumParams,
+          branches,
+        }
+        proveMatchIsValid k_var kk_var me
+      -- Check if this is a monadic let-binding
+      else if f.isConstOf ``Bind.bind then do
+        trace[Diverge.def.valid] "bind:\n{args}"
+        -- We simply need to prove that the subexpressions are valid, and call
+        -- the appropriate lemma.
+        let x := args.get! 4
+        let y := args.get! 5
+        -- Prove that the subexpressions are valid
+        let xValid ← proveExprIsValid k_var kk_var x
+        trace[Diverge.def.valid] "bind: xValid:\n{xValid}:\n{← inferType xValid}"
+        let yValid ← do
+          -- This is a lambda expression
+          lambdaOne y fun x y => do
+          trace[Diverge.def.valid] "bind: y: {y}"
+          let yValid ← proveExprIsValid k_var kk_var y
+          trace[Diverge.def.valid] "bind: yValid (no forall): {yValid}"
+          trace[Diverge.def.valid] "bind: yValid: x: {x}"
+          let yValid ← mkLambdaFVars #[x] yValid
+          trace[Diverge.def.valid] "bind: yValid (forall): {yValid}: {← inferType yValid}"
+          pure yValid
+        -- Put everything together
+        trace[Diverge.def.valid] "bind:\n- xValid: {xValid}: {← inferType xValid}\n- yValid: {yValid}: {← inferType yValid}"
+        mkAppM ``FixI.is_valid_p_bind #[xValid, yValid]
+      -- Check if this is a recursive call, i.e., a call to the continuation `kk`
+      else if f.isFVarOf kk_var.fvarId! then do
+        trace[Diverge.def.valid] "rec: args: \n{args}"
+        if args.size ≠ 2 then throwError "Recursive call with invalid number of parameters: {args}"
+        let i_arg := args.get! 0
+        let x_arg := args.get! 1
+        let eIsValid ← mkAppM ``FixI.is_valid_p_rec #[k_var, i_arg, x_arg]
+        trace[Diverge.def.valid] "rec: result: \n{eIsValid}"
+        pure eIsValid
+      else do
+        -- Remaining case: normal application.
+        -- It shouldn't use the continuation.
+        proveNoKExprIsValid k_var e
+
+-- Prove that a match expression is valid.
+partial def proveMatchIsValid (k_var kk_var : Expr) (me : MatchInfo) : MetaM Expr := do
+  trace[Diverge.def.valid] "proveMatchIsValid: {me}"
+  -- Prove the validity of the branch expressions
+  let branchesValid:Array Expr ← me.branches.mapIdxM fun idx br => do
+    -- Go inside the lambdas - note that we have to be careful: some of the
+    -- binders might come from the match, and some of the binders might come
+    -- from the fact that the expression in the match is a lambda expression:
+    -- we use the branchesNumParams field for this reason
+    let numParams := me.branchesNumParams.get! idx
+    lambdaTelescopeN br numParams fun xs br => do
+    -- Prove that the branch expression is valid
+    let brValid ← proveExprIsValid k_var kk_var br
+    -- Reconstruct the lambda expression
+    mkLambdaFVars xs brValid
+  trace[Diverge.def.valid] "branchesValid:\n{branchesValid}"
+  -- Compute the motive, which has the following shape:
+  -- ```
+  -- λ scrut => is_valid_p k (λ k => match scrut with ...)
+  --                                 ^^^^^^^^^^^^^^^^^^^^
+  --                         this is the original match expression, with the
+  --                        the difference that the scrutinee(s) is a variable
+  -- ```
+  let validMotive : Expr ← do
+    -- The motive is a function of the scrutinees (i.e., a lambda expression):
+    -- introduce binders for the scrutinees
+    let declInfos := me.scruts.mapIdx fun idx scrut =>
+      let name : Name := mkAnonymous "scrut" idx
+      let ty := λ (_ : Array Expr) => inferType scrut
+      (name, ty)
+    withLocalDeclsD declInfos fun scrutVars => do
+    -- Create a match expression but where the scrutinees have been replaced
+    -- by variables
+    let params : Array (Option Expr) := me.params.map some
+    let motive : Option Expr := some me.motive
+    let scruts : Array (Option Expr) := scrutVars.map some
+    let branches : Array (Option Expr) := me.branches.map some
+    let args := params ++ [motive] ++ scruts ++ branches
+    let matchE ← mkAppOptM me.matcherName args
+    -- Wrap in the `is_valid_p` predicate
+    let matchE ← mkLambdaFVars #[kk_var] matchE
+    let validMotive ← mkAppM ``FixI.is_valid_p #[k_var, matchE]
+    -- Abstract away the scrutinee variables
+    mkLambdaFVars scrutVars validMotive
+  trace[Diverge.def.valid] "valid motive: {validMotive}"
+  -- Put together
+  let valid ← do
+    -- We let Lean infer the parameters
+    let params : Array (Option Expr) := me.params.map (λ _ => none)
+    let motive := some validMotive
+    let scruts := me.scruts.map some
+    let branches := branchesValid.map some
+    let args := params ++ [motive] ++ scruts ++ branches
+    mkAppOptM me.matcherName args
+  trace[Diverge.def.valid] "proveMatchIsValid:\n{valid}:\n{← inferType valid}"
+  pure valid
+
+end
+
+-- Prove that a single body (in the mutually recursive group) is valid.
+--
+-- For instance, if we define the mutually recursive group [`is_even`, `is_odd`],
+-- we prove that `is_even.body` and `is_odd.body` are valid.
+partial def proveSingleBodyIsValid
+  (k_var : Expr) (preDef : PreDefinition) (bodyConst : Expr) :
+  MetaM Expr := do
+  trace[Diverge.def.valid] "proveSingleBodyIsValid: bodyConst: {bodyConst}"
+  -- Lookup the definition (`bodyConst` is a const, we want to retrieve its
+  -- definition to dive inside)
+  let name := bodyConst.constName!
+  let env ← getEnv
+  let body := (env.constants.find! name).value!
+  trace[Diverge.def.valid] "body: {body}"
+  lambdaTelescope body fun xs body => do
+  assert! xs.size = 2
+  let kk_var := xs.get! 0
+  let x_var := xs.get! 1
+  -- State the type of the theorem to prove
+  let thmTy ← mkAppM ``FixI.is_valid_p
+    #[k_var, ← mkLambdaFVars #[kk_var] (← mkAppM' bodyConst #[kk_var, x_var])]
+  trace[Diverge.def.valid] "thmTy: {thmTy}"
+  -- Prove that the body is valid
+  let proof ← proveExprIsValid k_var kk_var body
+  let proof ← mkLambdaFVars #[k_var, x_var] proof
+  trace[Diverge.def.valid] "proveSingleBodyIsValid: proof:\n{proof}:\n{← inferType proof}"
+  -- The target type (we don't have to do this: this is simply a sanity check,
+  -- and this allows a nicer debugging output)
+  let thmTy ← do
+    let body ← mkAppM' bodyConst #[kk_var, x_var]
+    let body ← mkLambdaFVars #[kk_var] body
+    let ty ← mkAppM ``FixI.is_valid_p #[k_var, body]
+    mkForallFVars #[k_var, x_var] ty
+  trace[Diverge.def.valid] "proveSingleBodyIsValid: thmTy\n{thmTy}:\n{← inferType thmTy}"
+  -- Save the theorem
+  let name := preDef.declName ++ "body_is_valid"
+  let decl := Declaration.thmDecl {
+    name
+    levelParams := preDef.levelParams
+    type := thmTy
+    value := proof
+    all := [name]
+  }
+  addDecl decl
+  trace[Diverge.def.valid] "proveSingleBodyIsValid: added thm: {name}"
+  -- Return the theorem
+  pure (Expr.const name (preDef.levelParams.map .param))
+
+-- Prove that the list of bodies are valid.
+--
+-- For instance, if we define the mutually recursive group [`is_even`, `is_odd`],
+-- we prove that `Funs.Cons is_even.body (Funs.Cons is_odd.body Funs.Nil)` is
+-- valid.
+partial def proveFunsBodyIsValid (inOutTys: Expr) (bodyFuns : Expr)
+  (k_var : Expr) (bodiesValid : Array Expr) : MetaM Expr := do
+  -- Create the big "and" expression, which groups the validity proof of the individual bodies
+  let rec mkValidConj (i : Nat) : MetaM Expr := do
+    if i = bodiesValid.size then
+      -- We reached the end
+      mkAppM ``FixI.Funs.is_valid_p_Nil #[k_var]
+    else do
+      -- We haven't reached the end: introduce a conjunction
+      let valid := bodiesValid.get! i
+      let valid ← mkAppM' valid #[k_var]
+      mkAppM ``And.intro #[valid, ← mkValidConj (i + 1)]
+  let andExpr ← mkValidConj 0
+  -- Wrap in the `is_valid_p_is_valid_p` theorem, and abstract the continuation
+  let isValid ← mkAppM ``FixI.Funs.is_valid_p_is_valid_p #[inOutTys, k_var, bodyFuns, andExpr]
+  mkLambdaFVars #[k_var] isValid
+
+-- Prove that the mut rec body (i.e., the unary body which groups the bodies
+-- of all the functions in the mutually recursive group and on which we will
+-- apply the fixed-point operator) is valid.
+--
+-- We save the proof in the theorem "[GROUP_NAME]."mut_rec_body_is_valid",
+-- which we return.
+--
+-- TODO: maybe this function should introduce k_var itself
+def proveMutRecIsValid
+  (grName : Name) (grLvlParams : List Name)
+  (inOutTys : Expr) (bodyFuns mutRecBodyConst : Expr)
+  (k_var : Expr) (preDefs : Array PreDefinition)
+  (bodies : Array Expr) : MetaM Expr := do
+  -- First prove that the individual bodies are valid
+  let bodiesValid ←
+    bodies.mapIdxM fun idx body => do
+      let preDef := preDefs.get! idx
+      trace[Diverge.def.valid] "## Proving that the body {body} is valid"
+      proveSingleBodyIsValid k_var preDef body
+  -- Then prove that the mut rec body is valid
+  trace[Diverge.def.valid] "## Proving that the 'Funs' body is valid"
+  let isValid ← proveFunsBodyIsValid inOutTys bodyFuns k_var bodiesValid
+  -- Save the theorem
+  let thmTy ← mkAppM ``FixI.is_valid #[mutRecBodyConst]
+  let name := grName ++ "mut_rec_body_is_valid"
+  let decl := Declaration.thmDecl {
+    name
+    levelParams := grLvlParams
+    type := thmTy
+    value := isValid
+    all := [name]
+  }
+  addDecl decl
+  trace[Diverge.def.valid] "proveFunsBodyIsValid: added thm: {name}:\n{thmTy}"
+  -- Return the theorem
+  pure (Expr.const name (grLvlParams.map .param))
+
+-- Generate the final definions by using the mutual body and the fixed point operator.
+--
+-- For instance:
+-- ```
+-- def is_even (i : Int) : Result Bool := mut_rec_body 0 i
+-- def is_odd (i : Int) : Result Bool := mut_rec_body 1 i
+-- ```
+def mkDeclareFixDefs (mutRecBody : Expr) (inOutTys : Array (Expr × Expr)) (preDefs : Array PreDefinition) :
+  TermElabM (Array Name) := do
+  let grSize := preDefs.size
+  let defs ← preDefs.mapIdxM fun idx preDef => do
+    lambdaTelescope preDef.value fun xs _ => do
+    -- Retrieve the input type
+    let in_ty := (inOutTys.get! idx.val).fst
+    -- Create the index
+    let idx ← mkFinVal grSize idx.val
+    -- Group the inputs into a dependent tuple
+    let input ← mkSigmasVal in_ty xs.toList
+    -- Apply the fixed point
+    let fixedBody ← mkAppM ``FixI.fix #[mutRecBody, idx, input]
+    let fixedBody ← mkLambdaFVars xs fixedBody
+    -- Create the declaration
+    let name := preDef.declName
+    let decl := Declaration.defnDecl {
+      name := name
+      levelParams := preDef.levelParams
+      type := preDef.type
+      value := fixedBody
+      hints := ReducibilityHints.regular (getMaxHeight (← getEnv) fixedBody + 1)
+      safety := .safe
+      all := [name]
+    }
+    addDecl decl
+    pure name
+  pure defs
+
+-- Prove the equations that we will use as unfolding theorems
+partial def proveUnfoldingThms (isValidThm : Expr) (inOutTys : Array (Expr × Expr))
+  (preDefs : Array PreDefinition) (decls : Array Name) : MetaM Unit := do
+  let grSize := preDefs.size
+  let proveIdx (i : Nat) : MetaM Unit := do
+    let preDef := preDefs.get! i
+    let defName := decls.get! i
+    -- Retrieve the arguments
+    lambdaTelescope preDef.value fun xs body => do
+    trace[Diverge.def.unfold] "proveUnfoldingThms: xs: {xs}"
+    trace[Diverge.def.unfold] "proveUnfoldingThms: body: {body}"
+    -- The theorem statement
+    let thmTy ← do
+      -- The equation: the declaration gives the lhs, the pre-def gives the rhs
+      let lhs ← mkAppOptM defName (xs.map some)
+      let rhs := body
+      let eq ← mkAppM ``Eq #[lhs, rhs]
+      mkForallFVars xs eq
+    trace[Diverge.def.unfold] "proveUnfoldingThms: thm statement: {thmTy}"
+    -- The proof
+    -- Use the fixed-point equation
+    let proof ← mkAppM ``FixI.is_valid_fix_fixed_eq #[isValidThm]
+    -- Add the index
+    let idx ← mkFinVal grSize i
+    let proof ← mkAppM ``congr_fun #[proof, idx]
+    -- Add the input argument
+    let arg ← mkSigmasVal (inOutTys.get! i).fst xs.toList
+    let proof ← mkAppM ``congr_fun #[proof, arg]
+    -- Abstract the arguments away
+    let proof ← mkLambdaFVars xs proof
+    trace[Diverge.def.unfold] "proveUnfoldingThms: proof: {proof}:\n{← inferType proof}"
+    -- Declare the theorem
+    let name := preDef.declName ++ "unfold"
+    let decl := Declaration.thmDecl {
+      name
+      levelParams := preDef.levelParams
+      type := thmTy
+      value := proof
+      all := [name]
+    }
+    addDecl decl
+    -- Add the unfolding theorem to the equation compiler
+    eqnsAttribute.add preDef.declName #[name]
+    trace[Diverge.def.unfold] "proveUnfoldingThms: added thm: {name}:\n{thmTy}"
+  let rec prove (i : Nat) : MetaM Unit := do
+    if i = preDefs.size then pure ()
+    else do
+      proveIdx i
+      prove (i + 1)
+  --
+  prove 0
+
+def divRecursion (preDefs : Array PreDefinition) : TermElabM Unit := do
+  let msg := toMessageData <| preDefs.map fun pd => (pd.declName, pd.levelParams, pd.type, pd.value)
+  trace[Diverge.def] ("divRecursion: defs:\n" ++ msg)
+
+  -- TODO: what is this?
+  for preDef in preDefs do
+    applyAttributesOf #[preDef] AttributeApplicationTime.afterCompilation
+
+  -- Retrieve the name of the first definition, that we will use as the namespace
+  -- for the definitions common to the group
+  let def0 := preDefs[0]!
+  let grName := def0.declName
+  trace[Diverge.def] "group name: {grName}"
+
+  /- # Compute the input/output types of the continuation `k`. -/
+  let grLvlParams := def0.levelParams
+  trace[Diverge.def] "def0 universe levels: {def0.levelParams}"
+
+  -- We first compute the list of pairs: (input type × output type)
+  let inOutTys : Array (Expr × Expr) ←
+      preDefs.mapM (fun preDef => do
+        withRef preDef.ref do -- is the withRef useful?
+        -- Check the universe parameters - TODO: I'm not sure what the best thing
+        -- to do is. In practice, all the type parameters should be in Type 0, so
+        -- we shouldn't have universe issues.
+        if preDef.levelParams ≠ grLvlParams then
+          throwError "Non-uniform polymorphism in the universes"
+        forallTelescope preDef.type (fun in_tys out_ty => do
+          let in_ty ← liftM (mkSigmasType in_tys.toList)
+          -- Retrieve the type in the "Result"
+          let out_ty ← getResultTy out_ty
+          let out_ty ← liftM (mkSigmasMatch in_tys.toList out_ty)
+          pure (in_ty, out_ty)
+        )
+      )
+  trace[Diverge.def] "inOutTys: {inOutTys}"
+  -- Turn the list of input/output type pairs into an expresion
+  let inOutTysExpr ← inOutTys.mapM (λ (x, y) => mkInOutTy x y)
+  let inOutTysExpr ← mkListLit (← inferType (inOutTysExpr.get! 0)) inOutTysExpr.toList
+
+  -- From the list of pairs of input/output types, actually compute the
+  -- type of the continuation `k`.
+  -- We first introduce the index `i : Fin n` where `n` is the number of
+  -- functions in the group.
+  let i_var_ty := mkFin preDefs.size
+  withLocalDeclD (mkAnonymous "i" 0) i_var_ty fun i_var => do
+  let in_out_ty ← mkAppM ``List.get #[inOutTysExpr, i_var]
+  trace[Diverge.def] "in_out_ty := {in_out_ty} : {← inferType in_out_ty}"
+  -- Add an auxiliary definition for `in_out_ty`
+  let in_out_ty ← do
+    let value ← mkLambdaFVars #[i_var] in_out_ty
+    let name := grName.append "in_out_ty"
+    let levelParams := grLvlParams
+    let decl := Declaration.defnDecl {
+      name := name
+      levelParams := levelParams
+      type := ← inferType value
+      value := value
+      hints := .abbrev
+      safety := .safe
+      all := [name]
+    }
+    addDecl decl
+    -- Return the constant
+    let in_out_ty := Lean.mkConst name (levelParams.map .param)
+    mkAppM' in_out_ty #[i_var]
+  trace[Diverge.def] "in_out_ty (after decl) := {in_out_ty} : {← inferType in_out_ty}"
+  let in_ty ← mkAppM ``Sigma.fst #[in_out_ty]
+  trace[Diverge.def] "in_ty: {in_ty}"
+  withLocalDeclD (mkAnonymous "x" 1) in_ty fun input => do
+  let out_ty ← mkAppM' (← mkAppM ``Sigma.snd #[in_out_ty]) #[input]
+  trace[Diverge.def] "out_ty: {out_ty}"
+
+  -- Introduce the continuation `k`
+  let in_ty ← mkLambdaFVars #[i_var] in_ty
+  let out_ty ← mkLambdaFVars #[i_var, input] out_ty
+  let kk_var_ty ← mkAppM ``FixI.kk_ty #[i_var_ty, in_ty, out_ty]
+  trace[Diverge.def] "kk_var_ty: {kk_var_ty}"
+  withLocalDeclD (mkAnonymous "kk" 2) kk_var_ty fun kk_var => do
+  trace[Diverge.def] "kk_var: {kk_var}"
+
+  -- Replace the recursive calls in all the function bodies by calls to the
+  -- continuation `k` and and generate for those bodies declarations
+  trace[Diverge.def] "# Generating the unary bodies"
+  let bodies ← mkDeclareUnaryBodies grLvlParams kk_var inOutTys preDefs
+  trace[Diverge.def] "Unary bodies (after decl): {bodies}"
+  -- Generate the mutually recursive body
+  trace[Diverge.def] "# Generating  the mut rec body"
+  let (bodyFuns, mutRecBody) ← mkDeclareMutRecBody grName grLvlParams kk_var i_var in_ty out_ty inOutTys.toList bodies
+  trace[Diverge.def] "mut rec body (after decl): {mutRecBody}"
+
+  -- Prove that the mut rec body satisfies the validity criteria required by
+  -- our fixed-point
+  let k_var_ty ← mkAppM ``FixI.k_ty #[i_var_ty, in_ty, out_ty]
+  withLocalDeclD (mkAnonymous "k" 3) k_var_ty fun k_var => do
+  trace[Diverge.def] "# Proving that the mut rec body is valid"
+  let isValidThm ← proveMutRecIsValid grName grLvlParams inOutTysExpr bodyFuns mutRecBody k_var preDefs bodies
+
+  -- Generate the final definitions
+  trace[Diverge.def] "# Generating the final definitions"
+  let decls ← mkDeclareFixDefs mutRecBody inOutTys preDefs
+
+  -- Prove the unfolding theorems
+  trace[Diverge.def] "# Proving the unfolding theorems"
+  proveUnfoldingThms isValidThm inOutTys preDefs decls
+
+  -- Generating code -- TODO
+  addAndCompilePartialRec preDefs
+
+-- The following function is copy&pasted from Lean.Elab.PreDefinition.Main
+-- This is the only part where we make actual changes and hook into the equation compiler.
+-- (I've removed all the well-founded stuff to make it easier to read though.)
+
+open private ensureNoUnassignedMVarsAtPreDef betaReduceLetRecApps partitionPreDefs
+  addAndCompilePartial addAsAxioms from Lean.Elab.PreDefinition.Main
+
+def addPreDefinitions (preDefs : Array PreDefinition) : TermElabM Unit := withLCtx {} {} do
+  for preDef in preDefs do
+    trace[Diverge.elab] "{preDef.declName} : {preDef.type} :=\n{preDef.value}"
+  let preDefs ← preDefs.mapM ensureNoUnassignedMVarsAtPreDef
+  let preDefs ← betaReduceLetRecApps preDefs
+  let cliques := partitionPreDefs preDefs
+  let mut hasErrors := false
+  for preDefs in cliques do
+    trace[Diverge.elab] "{preDefs.map (·.declName)}"
+    try
+      withRef (preDefs[0]!.ref) do
+        divRecursion preDefs
+    catch ex =>
+      -- If it failed, we add the functions as partial functions
+      hasErrors := true
+      logException ex
+      let s ← saveState
+      try
+        if preDefs.all fun preDef => preDef.kind == DefKind.def ||
+           preDefs.all fun preDef => preDef.kind == DefKind.abbrev then
+          -- try to add as partial definition
+          try
+            addAndCompilePartial preDefs (useSorry := true)
+          catch _ =>
+            -- Compilation failed try again just as axiom
+            s.restore
+            addAsAxioms preDefs
+        else return ()
+      catch _ => s.restore
+
+-- The following two functions are copy-pasted from Lean.Elab.MutualDef
+
+open private elabHeaders levelMVarToParamHeaders getAllUserLevelNames withFunLocalDecls elabFunValues
+  instantiateMVarsAtHeader instantiateMVarsAtLetRecToLift checkLetRecsToLiftTypes withUsed from Lean.Elab.MutualDef
+
+def Term.elabMutualDef (vars : Array Expr) (views : Array DefView) : TermElabM Unit := do
+    let scopeLevelNames ← getLevelNames
+    let headers ← elabHeaders views
+    let headers ← levelMVarToParamHeaders views headers
+    let allUserLevelNames := getAllUserLevelNames headers
+    withFunLocalDecls headers fun funFVars => do
+      for view in views, funFVar in funFVars do
+        addLocalVarInfo view.declId funFVar
+        -- Add fake use site to prevent "unused variable" warning (if the
+        -- function is actually not recursive, Lean would print this warning).
+        -- Remark: we could detect this case and encode the function without
+        -- using the fixed-point. In practice it shouldn't happen however:
+        -- we define non-recursive functions with the `divergent` keyword
+        -- only for testing purposes.
+        addTermInfo' view.declId funFVar
+      let values ←
+        try
+          let values ← elabFunValues headers
+          Term.synthesizeSyntheticMVarsNoPostponing
+          values.mapM (instantiateMVars ·)
+        catch ex =>
+          logException ex
+          headers.mapM fun header => mkSorry header.type (synthetic := true)
+      let headers ← headers.mapM instantiateMVarsAtHeader
+      let letRecsToLift ← getLetRecsToLift
+      let letRecsToLift ← letRecsToLift.mapM instantiateMVarsAtLetRecToLift
+      checkLetRecsToLiftTypes funFVars letRecsToLift
+      withUsed vars headers values letRecsToLift fun vars => do
+        let preDefs ← MutualClosure.main vars headers funFVars values letRecsToLift
+        for preDef in preDefs do
+          trace[Diverge.elab] "{preDef.declName} : {preDef.type} :=\n{preDef.value}"
+        let preDefs ← withLevelNames allUserLevelNames <| levelMVarToParamPreDecls preDefs
+        let preDefs ← instantiateMVarsAtPreDecls preDefs
+        let preDefs ← fixLevelParams preDefs scopeLevelNames allUserLevelNames
+        for preDef in preDefs do
+          trace[Diverge.elab] "after eraseAuxDiscr, {preDef.declName} : {preDef.type} :=\n{preDef.value}"
+        checkForHiddenUnivLevels allUserLevelNames preDefs
+        addPreDefinitions preDefs
+
+open Command in
+def Command.elabMutualDef (ds : Array Syntax) : CommandElabM Unit := do
+  let views ← ds.mapM fun d => do
+    let `($mods:declModifiers divergent def $id:declId $sig:optDeclSig $val:declVal) := d
+      | throwUnsupportedSyntax
+    let modifiers ← elabModifiers mods
+    let (binders, type) := expandOptDeclSig sig
+    let deriving? := none
+    pure { ref := d, kind := DefKind.def, modifiers,
+           declId := id, binders, type? := type, value := val, deriving? }
+  runTermElabM fun vars => Term.elabMutualDef vars views
+
+-- Special command so that we don't fall back to the built-in mutual when we produce an error.
+local syntax "_divergent" Parser.Command.mutual : command
+elab_rules : command | `(_divergent mutual $decls* end) => Command.elabMutualDef decls
+
+macro_rules
+  | `(mutual $decls* end) => do
+    unless !decls.isEmpty && decls.all (·.1.getKind == ``divergentDef) do
+      Macro.throwUnsupported
+    `(command| _divergent mutual $decls* end)
+
+open private setDeclIdName from Lean.Elab.Declaration
+elab_rules : command
+  | `($mods:declModifiers divergent%$tk def $id:declId $sig:optDeclSig $val:declVal) => do
+    let (name, _) := expandDeclIdCore id
+    if (`_root_).isPrefixOf name then throwUnsupportedSyntax
+    let view := extractMacroScopes name
+    let .str ns shortName := view.name | throwUnsupportedSyntax
+    let shortName' := { view with name := shortName }.review
+    let cmd ← `(mutual $mods:declModifiers divergent%$tk def $(⟨setDeclIdName id shortName'⟩):declId $sig:optDeclSig $val:declVal end)
+    if ns matches .anonymous then
+      Command.elabCommand cmd
+    else
+      Command.elabCommand <| ← `(namespace $(mkIdentFrom id ns) $cmd end $(mkIdentFrom id ns))
+
+namespace Tests
+  /- Some examples of partial functions -/
+
+  divergent def list_nth {a: Type} (ls : List a) (i : Int) : Result a :=
+    match ls with
+    | [] => .fail .panic
+    | x :: ls =>
+      if i = 0 then return x
+      else return (← list_nth ls (i - 1))
+
+  #check list_nth.unfold
+
+  example {a: Type} (ls : List a) :
+    ∀ (i : Int),
+    0 ≤ i → i < ls.length →
+    ∃ x, list_nth ls i = .ret x := by
+    induction ls
+    . intro i hpos h; simp at h; linarith
+    . rename_i hd tl ih
+      intro i hpos h
+      -- We can directly use `rw [list_nth]`!
+      rw [list_nth]; simp
+      split <;> simp [*]
+      . tauto
+      . -- TODO: we shouldn't have to do that
+        have hneq : 0 < i := by cases i <;> rename_i a _ <;> simp_all; cases a <;> simp_all
+        simp at h
+        have ⟨ x, ih ⟩ := ih (i - 1) (by linarith) (by linarith)
+        simp [ih]
+        tauto
+
+  mutual
+    divergent def is_even (i : Int) : Result Bool :=
+      if i = 0 then return true else return (← is_odd (i - 1))
+
+    divergent def is_odd (i : Int) : Result Bool :=
+      if i = 0 then return false else return (← is_even (i - 1))
+  end
+
+  #check is_even.unfold
+  #check is_odd.unfold
+
+  mutual
+    divergent def foo (i : Int) : Result Nat :=
+      if i > 10 then return (← foo (i / 10)) + (← bar i) else bar 10
+
+    divergent def bar (i : Int) : Result Nat :=
+      if i > 20 then foo (i / 20) else .ret 42
+  end
+
+  #check foo.unfold
+  #check bar.unfold
+
+  -- Testing dependent branching and let-bindings
+  -- TODO: why the linter warning?
+  divergent def isNonZero (i : Int) : Result Bool :=
+    if _h:i = 0 then return false
+    else
+      let b := true
+      return b
+
+  #check isNonZero.unfold
+
+  -- Testing let-bindings
+  divergent def iInBounds {a : Type} (ls : List a) (i : Int) : Result Bool :=
+    let i0 := ls.length
+    if i < i0
+    then Result.ret True
+    else Result.ret False
+
+  #check iInBounds.unfold
+
+  divergent def isCons
+    {a : Type} (ls : List a) : Result Bool :=
+    let ls1 := ls
+    match ls1 with
+    | [] => Result.ret False
+    | _ :: _ => Result.ret True
+
+  #check isCons.unfold
+
+  -- Testing what happens when we use concrete arguments in dependent tuples
+  divergent def test1
+    (_ : Option Bool) (_ : Unit) :
+    Result Unit
+    :=
+    test1 Option.none ()
+
+  #check test1.unfold
+
+end Tests
+
+end Diverge
diff --git a/backends/lean/Base/Diverge/ElabBase.lean b/backends/lean/Base/Diverge/ElabBase.lean
new file mode 100644
index 00000000..fedb1c74
--- /dev/null
+++ b/backends/lean/Base/Diverge/ElabBase.lean
@@ -0,0 +1,15 @@
+import Lean
+
+namespace Diverge
+
+open Lean Elab Term Meta
+
+-- We can't define and use trace classes in the same file
+initialize registerTraceClass `Diverge.elab
+initialize registerTraceClass `Diverge.def
+initialize registerTraceClass `Diverge.def.sigmas
+initialize registerTraceClass `Diverge.def.genBody
+initialize registerTraceClass `Diverge.def.valid
+initialize registerTraceClass `Diverge.def.unfold
+
+end Diverge
diff --git a/backends/lean/Base/IList.lean b/backends/lean/Base/IList.lean
new file mode 100644
index 00000000..31b66ffa
--- /dev/null
+++ b/backends/lean/Base/IList.lean
@@ -0,0 +1 @@
+import Base.IList.IList
diff --git a/backends/lean/Base/IList/IList.lean b/backends/lean/Base/IList/IList.lean
new file mode 100644
index 00000000..93047a1b
--- /dev/null
+++ b/backends/lean/Base/IList/IList.lean
@@ -0,0 +1,284 @@
+/- Complementary list functions and lemmas which operate on integers rather
+   than natural numbers. -/
+
+import Std.Data.Int.Lemmas
+import Base.Arith
+
+namespace List
+
+def len (ls : List α) : Int :=
+  match ls with
+  | [] => 0
+  | _ :: tl => 1 + len tl
+
+@[simp] theorem len_nil : len ([] : List α) = 0 := by simp [len]
+@[simp] theorem len_cons : len ((x :: tl) : List α) = 1 + len tl := by simp [len]
+
+theorem len_pos : 0 ≤ (ls : List α).len := by
+  induction ls <;> simp [*]
+  linarith
+
+instance (a : Type u) : Arith.HasIntProp (List a) where
+  prop_ty := λ ls => 0 ≤ ls.len
+  prop := λ ls => ls.len_pos
+
+-- Remark: if i < 0, then the result is none
+def indexOpt (ls : List α) (i : Int) : Option α :=
+  match ls with
+  | [] => none
+  | hd :: tl => if i = 0 then some hd else indexOpt tl (i - 1)
+
+@[simp] theorem indexOpt_nil : indexOpt ([] : List α) i = none := by simp [indexOpt]
+@[simp] theorem indexOpt_zero_cons : indexOpt ((x :: tl) : List α) 0 = some x := by simp [indexOpt]
+@[simp] theorem indexOpt_nzero_cons (hne : i ≠ 0) : indexOpt ((x :: tl) : List α) i = indexOpt tl (i - 1) := by simp [*, indexOpt]
+
+-- Remark: if i < 0, then the result is the defaul element
+def index [Inhabited α] (ls : List α) (i : Int) : α :=
+  match ls with
+  | [] => Inhabited.default
+  | x :: tl =>
+    if i = 0 then x else index tl (i - 1)
+
+@[simp] theorem index_zero_cons [Inhabited α] : index ((x :: tl) : List α) 0 = x := by simp [index]
+@[simp] theorem index_nzero_cons [Inhabited α] (hne : i ≠ 0) : index ((x :: tl) : List α) i = index tl (i - 1) := by simp [*, index]
+
+theorem indexOpt_bounds (ls : List α) (i : Int) :
+  ls.indexOpt i = none ↔ i < 0 ∨ ls.len ≤ i :=
+  match ls with
+  | [] =>
+    have : ¬ (i < 0) → 0 ≤ i := by int_tac
+    by simp; tauto
+  | _ :: tl =>
+    have := indexOpt_bounds tl (i - 1)
+    if h: i = 0 then
+      by
+        simp [*];
+        int_tac
+    else by
+      simp [*]
+      constructor <;> intros <;>
+      casesm* _ ∨ _ <;> -- splits all the disjunctions
+      first | left; int_tac | right; int_tac
+
+theorem indexOpt_eq_index [Inhabited α] (ls : List α) (i : Int) :
+  0 ≤ i →
+  i < ls.len →
+  ls.indexOpt i = some (ls.index i) :=
+  match ls with
+  | [] => by simp; intros; linarith
+  | hd :: tl =>
+    if h: i = 0 then
+      by simp [*]
+    else
+      have hi := indexOpt_eq_index tl (i - 1)
+      by simp [*]; intros;  apply hi <;> int_tac
+
+-- Remark: the list is unchanged if the index is not in bounds (in particular
+-- if it is < 0)
+def update (ls : List α) (i : Int) (y : α) : List α :=
+  match ls with
+  | [] => []
+  | x :: tl => if i = 0 then y :: tl else x :: update tl (i - 1) y
+
+-- Remark: the whole list is dropped if the index is not in bounds (in particular
+-- if it is < 0)
+def idrop (i : Int) (ls : List α) : List α :=
+  match ls with
+  | [] => []
+  | x :: tl => if i = 0 then x :: tl else idrop (i - 1) tl
+
+section Lemmas
+
+variable {α : Type u} 
+
+@[simp] theorem update_nil : update ([] : List α) i y = [] := by simp [update]
+@[simp] theorem update_zero_cons : update ((x :: tl) : List α) 0 y = y :: tl := by simp [update]
+@[simp] theorem update_nzero_cons (hne : i ≠ 0) : update ((x :: tl) : List α) i y = x :: update tl (i - 1) y := by simp [*, update]
+
+@[simp] theorem idrop_nil : idrop i ([] : List α) = [] := by simp [idrop]
+@[simp] theorem idrop_zero : idrop 0 (ls : List α) = ls := by cases ls <;> simp [idrop]
+@[simp] theorem idrop_nzero_cons (hne : i ≠ 0) : idrop i ((x :: tl) : List α) = idrop (i - 1) tl := by simp [*, idrop]
+
+theorem len_eq_length (ls : List α) : ls.len = ls.length := by
+  induction ls
+  . rfl
+  . simp [*, Int.ofNat_succ, Int.add_comm]
+
+@[simp] theorem len_append (l1 l2 : List α) : (l1 ++ l2).len = l1.len + l2.len := by
+  -- Remark: simp loops here because of the following rewritings:
+  -- @Nat.cast_add: ↑(List.length l1 + List.length l2) ==> ↑(List.length l1) + ↑(List.length l2)
+  -- Int.ofNat_add_ofNat: ↑(List.length l1) + ↑(List.length l2) ==> ↑(List.length l1 + List.length l2)
+  -- TODO: post an issue?
+  simp only [len_eq_length]
+  simp only [length_append]
+  simp only [Int.ofNat_add]
+
+@[simp]
+theorem length_update (ls : List α) (i : Int) (x : α) : (ls.update i x).length = ls.length := by
+  revert i
+  induction ls <;> simp_all [length, update]
+  intro; split <;> simp [*]
+
+@[simp]
+theorem len_update (ls : List α) (i : Int) (x : α) : (ls.update i x).len = ls.len := by
+  simp [len_eq_length]
+
+@[simp]
+theorem len_map (ls : List α) (f : α → β) : (ls.map f).len = ls.len := by
+  simp [len_eq_length]
+
+theorem left_length_eq_append_eq (l1 l2 l1' l2' : List α) (heq : l1.length = l1'.length) :
+  l1 ++ l2 = l1' ++ l2' ↔ l1 = l1' ∧ l2 = l2' := by
+  revert l1'
+  induction l1
+  . intro l1'; cases l1' <;> simp [*]
+  . intro l1'; cases l1' <;> simp_all; tauto
+
+theorem right_length_eq_append_eq (l1 l2 l1' l2' : List α) (heq : l2.length = l2'.length) :
+  l1 ++ l2 = l1' ++ l2' ↔ l1 = l1' ∧ l2 = l2' := by
+  have := left_length_eq_append_eq l1 l2 l1' l2'
+  constructor <;> intro heq2 <;>
+  have : l1.length + l2.length = l1'.length + l2'.length := by
+    have : (l1 ++ l2).length = (l1' ++ l2').length := by simp [*]
+    simp only [length_append] at this
+    apply this
+  . simp [heq] at this
+    tauto
+  . tauto
+
+theorem left_len_eq_append_eq (l1 l2 l1' l2' : List α) (heq : l1.len = l1'.len) :
+  l1 ++ l2 = l1' ++ l2' ↔ l1 = l1' ∧ l2 = l2' := by
+  simp [len_eq_length] at heq
+  apply left_length_eq_append_eq
+  assumption
+
+theorem right_len_eq_append_eq (l1 l2 l1' l2' : List α) (heq : l2.len = l2'.len) :
+  l1 ++ l2 = l1' ++ l2' ↔ l1 = l1' ∧ l2 = l2' := by
+  simp [len_eq_length] at heq
+  apply right_length_eq_append_eq
+  assumption
+
+open Arith in
+theorem idrop_eq_nil_of_le (hineq : ls.len ≤ i) : idrop i ls = [] := by
+  revert i
+  induction ls <;> simp [*]
+  rename_i hd tl hi
+  intro i hineq
+  if heq: i = 0 then
+    simp [*] at *
+    have := tl.len_pos
+    linarith
+  else
+    simp at hineq
+    have : 0 < i := by int_tac
+    simp [*]
+    apply hi
+    linarith
+
+@[simp]
+theorem index_ne
+  {α : Type u} [Inhabited α] (l: List α) (i: ℤ) (j: ℤ) (x: α) :
+   0 ≤ i → i < l.len → 0 ≤ j → j < l.len → j ≠ i →
+    (l.update i x).index j = l.index j
+  :=
+  λ _ _ _ _ _ => match l with
+  | [] => by simp at *
+  | hd :: tl =>
+    if h: i = 0 then
+      have : j ≠ 0 := by scalar_tac
+      by simp [*]
+    else if h : j = 0 then
+      have : i ≠ 0 := by scalar_tac
+      by simp [*]
+    else
+      by
+        simp [*]
+        simp at *
+        apply index_ne <;> scalar_tac
+
+@[simp]
+theorem index_eq
+  {α : Type u} [Inhabited α] (l: List α) (i: ℤ) (x: α) :
+   0 ≤ i → i < l.len →
+    (l.update i x).index i = x
+  :=
+  fun _ _ => match l with
+  | [] => by simp at *; scalar_tac
+  | hd :: tl =>
+    if h: i = 0 then
+      by
+        simp [*]
+    else
+      by
+        simp [*]
+        simp at *
+        apply index_eq <;> scalar_tac
+
+theorem update_map_eq {α : Type u} {β : Type v} (ls : List α) (i : Int) (x : α) (f : α → β) :
+  (ls.update i x).map f = (ls.map f).update i (f x) :=
+  match ls with
+  | [] => by simp
+  | hd :: tl =>
+    if h : i = 0 then by simp [*]
+    else
+      have hi := update_map_eq tl (i - 1) x f
+      by simp [*]
+
+theorem len_flatten_update_eq {α : Type u} (ls : List (List α)) (i : Int) (x : List α)
+  (h0 : 0 ≤ i) (h1 : i < ls.len) :
+  (ls.update i x).flatten.len = ls.flatten.len + x.len - (ls.index i).len :=
+  match ls with
+  | [] => by simp at h1; int_tac
+  | hd :: tl => by
+    simp at h1
+    if h : i = 0 then simp [*]; int_tac
+    else
+      have hi := len_flatten_update_eq tl (i - 1) x (by int_tac) (by int_tac)
+      simp [*]
+      int_tac
+
+@[simp]
+theorem index_map_eq {α : Type u} {β : Type v} [Inhabited α] [Inhabited β] (ls : List α) (i : Int) (f : α → β)
+  (h0 : 0 ≤ i) (h1 : i < ls.len) :
+  (ls.map f).index i = f (ls.index i) :=
+  match ls with
+  | [] => by simp at h1; int_tac
+  | hd :: tl =>
+    if h : i = 0 then by
+      simp [*]
+    else
+      have hi := index_map_eq tl (i - 1) f (by int_tac) (by simp at h1; int_tac)
+      by
+        simp [*]
+
+def allP {α : Type u} (l : List α) (p: α → Prop) : Prop :=
+  foldr (fun a r => p a ∧ r) True l
+
+@[simp]
+theorem allP_nil {α : Type u} (p: α → Prop) : allP [] p :=
+  by simp [allP, foldr]
+
+@[simp]
+theorem allP_cons {α : Type u} (hd: α) (tl : List α) (p: α → Prop) :
+  allP (hd :: tl) p ↔ p hd ∧ allP tl p
+  := by simp [allP, foldr]
+
+def pairwise_rel
+  {α : Type u} (rel : α → α → Prop) (l: List α) : Prop
+  := match l with
+  | [] => True
+  | hd :: tl => allP tl (rel hd) ∧ pairwise_rel rel tl
+
+@[simp]
+theorem pairwise_rel_nil {α : Type u} (rel : α → α → Prop) :
+  pairwise_rel rel []
+  := by simp [pairwise_rel]
+
+@[simp]
+theorem pairwise_rel_cons {α : Type u} (rel : α → α → Prop) (hd: α) (tl: List α) :
+  pairwise_rel rel (hd :: tl) ↔ allP tl (rel hd) ∧ pairwise_rel rel tl
+  := by simp [pairwise_rel]
+
+end Lemmas
+
+end List
diff --git a/backends/lean/Base/Primitives.lean b/backends/lean/Base/Primitives.lean
new file mode 100644
index 00000000..91823cb6
--- /dev/null
+++ b/backends/lean/Base/Primitives.lean
@@ -0,0 +1,3 @@
+import Base.Primitives.Base
+import Base.Primitives.Scalar
+import Base.Primitives.Vec
diff --git a/backends/lean/Base/Primitives/Base.lean b/backends/lean/Base/Primitives/Base.lean
new file mode 100644
index 00000000..7c0fa3bb
--- /dev/null
+++ b/backends/lean/Base/Primitives/Base.lean
@@ -0,0 +1,130 @@
+import Lean
+
+namespace Primitives
+
+--------------------
+-- ASSERT COMMAND --Std.
+--------------------
+
+open Lean Elab Command Term Meta
+
+syntax (name := assert) "#assert" term: command
+
+@[command_elab assert]
+unsafe
+def assertImpl : CommandElab := fun (_stx: Syntax) => do
+  runTermElabM (fun _ => do
+    let r ← evalTerm Bool (mkConst ``Bool) _stx[1]
+    if not r then
+      logInfo ("Assertion failed for:\n" ++ _stx[1])
+      throwError ("Expression reduced to false:\n"  ++ _stx[1])
+    pure ())
+
+#eval 2 == 2
+#assert (2 == 2)
+
+-------------
+-- PRELUDE --
+-------------
+
+-- Results & monadic combinators
+
+inductive Error where
+   | assertionFailure: Error
+   | integerOverflow: Error
+   | divisionByZero: Error
+   | arrayOutOfBounds: Error
+   | maximumSizeExceeded: Error
+   | panic: Error
+deriving Repr, BEq
+
+open Error
+
+inductive Result (α : Type u) where
+  | ret (v: α): Result α
+  | fail (e: Error): Result α
+  | div
+deriving Repr, BEq
+
+open Result
+
+instance Result_Inhabited (α : Type u) : Inhabited (Result α) :=
+  Inhabited.mk (fail panic)
+
+instance Result_Nonempty (α : Type u) : Nonempty (Result α) :=
+  Nonempty.intro div
+
+/- HELPERS -/
+
+def ret? {α: Type u} (r: Result α): Bool :=
+  match r with
+  | ret _ => true
+  | fail _ | div => false
+
+def div? {α: Type u} (r: Result α): Bool :=
+  match r with
+  | div => true
+  | ret _ | fail _ => false
+
+def massert (b:Bool) : Result Unit :=
+  if b then ret () else fail assertionFailure
+
+def eval_global {α: Type u} (x: Result α) (_: ret? x): α :=
+  match x with
+  | fail _ | div => by contradiction
+  | ret x => x
+
+/- DO-DSL SUPPORT -/
+
+def bind {α : Type u} {β : Type v} (x: Result α) (f: α → Result β) : Result β :=
+  match x with
+  | ret v  => f v 
+  | fail v => fail v
+  | div => div
+
+-- Allows using Result in do-blocks
+instance : Bind Result where
+  bind := bind
+
+-- Allows using return x in do-blocks
+instance : Pure Result where
+  pure := fun x => ret x
+
+@[simp] theorem bind_ret (x : α) (f : α → Result β) : bind (.ret x) f = f x := by simp [bind]
+@[simp] theorem bind_fail (x : Error) (f : α → Result β) : bind (.fail x) f = .fail x := by simp [bind]
+@[simp] theorem bind_div (f : α → Result β) : bind .div f = .div := by simp [bind]
+
+/- CUSTOM-DSL SUPPORT -/
+
+-- Let-binding the Result of a monadic operation is oftentimes not sufficient,
+-- because we may need a hypothesis for equational reasoning in the scope. We
+-- rely on subtype, and a custom let-binding operator, in effect recreating our
+-- own variant of the do-dsl
+
+def Result.attach {α: Type} (o : Result α): Result { x : α // o = ret x } :=
+  match o with
+  | ret x => ret ⟨x, rfl⟩
+  | fail e => fail e
+  | div => div
+
+@[simp] theorem bind_tc_ret (x : α) (f : α → Result β) :
+  (do let y ← .ret x; f y) = f x := by simp [Bind.bind, bind]
+
+@[simp] theorem bind_tc_fail (x : Error) (f : α → Result β) :
+  (do let y ← fail x; f y) = fail x := by simp [Bind.bind, bind]
+
+@[simp] theorem bind_tc_div (f : α → Result β) :
+  (do let y ← div; f y) = div := by simp [Bind.bind, bind]
+
+----------
+-- MISC --
+----------
+
+@[simp] def mem.replace (a : Type) (x : a) (_ : a) : a := x
+@[simp] def mem.replace_back (a : Type) (_ : a) (y : a) : a := y
+
+/-- Aeneas-translated function -- useful to reduce non-recursive definitions.
+ Use with `simp [ aeneas ]` -/
+register_simp_attr aeneas
+
+end Primitives
diff --git a/backends/lean/Base/Primitives/Scalar.lean b/backends/lean/Base/Primitives/Scalar.lean
new file mode 100644
index 00000000..2e5be8bf
--- /dev/null
+++ b/backends/lean/Base/Primitives/Scalar.lean
@@ -0,0 +1,831 @@
+import Lean
+import Lean.Meta.Tactic.Simp
+import Mathlib.Tactic.Linarith
+import Base.Primitives.Base
+import Base.Diverge.Base
+import Base.Progress.Base
+import Base.Arith.Int
+
+namespace Primitives
+
+----------------------
+-- MACHINE INTEGERS --
+----------------------
+
+-- We redefine our machine integers types.
+
+-- For Isize/Usize, we reuse `getNumBits` from `USize`. You cannot reduce `getNumBits`
+-- using the simplifier, meaning that proofs do not depend on the compile-time value of
+-- USize.size. (Lean assumes 32 or 64-bit platforms, and Rust doesn't really support, at
+-- least officially, 16-bit microcontrollers, so this seems like a fine design decision
+-- for now.)
+
+-- Note from Chris Bailey: "If there's more than one salient property of your
+-- definition then the subtyping strategy might get messy, and the property part
+-- of a subtype is less discoverable by the simplifier or tactics like
+-- library_search." So, we will not add refinements on the return values of the
+-- operations defined on Primitives, but will rather rely on custom lemmas to
+-- invert on possible return values of the primitive operations.
+
+-- Machine integer constants, done via `ofNatCore`, which requires a proof that
+-- the `Nat` fits within the desired integer type. We provide a custom tactic.
+
+open Result Error
+open System.Platform.getNumBits
+
+-- TODO: is there a way of only importing System.Platform.getNumBits?
+--
+@[simp] def size_num_bits : Nat := (System.Platform.getNumBits ()).val
+
+-- Remark: Lean seems to use < for the comparisons with the upper bounds by convention.
+
+-- The "structured" bounds
+def Isize.smin : Int := - (HPow.hPow 2 (size_num_bits - 1))
+def Isize.smax : Int := (HPow.hPow 2 (size_num_bits - 1)) - 1
+def I8.smin    : Int := - (HPow.hPow 2 7)
+def I8.smax    : Int := HPow.hPow 2 7 - 1
+def I16.smin   : Int := - (HPow.hPow 2 15)
+def I16.smax   : Int := HPow.hPow 2 15 - 1
+def I32.smin   : Int := -(HPow.hPow 2 31)
+def I32.smax   : Int := HPow.hPow 2 31 - 1
+def I64.smin   : Int := -(HPow.hPow 2 63)
+def I64.smax   : Int := HPow.hPow 2 63 - 1
+def I128.smin  : Int := -(HPow.hPow 2 127)
+def I128.smax  : Int := HPow.hPow 2 127 - 1
+def Usize.smin : Int := 0
+def Usize.smax : Int := HPow.hPow 2 size_num_bits - 1
+def U8.smin    : Int := 0
+def U8.smax    : Int := HPow.hPow 2 8 - 1
+def U16.smin   : Int := 0
+def U16.smax   : Int := HPow.hPow 2 16 - 1
+def U32.smin   : Int := 0
+def U32.smax   : Int := HPow.hPow 2 32 - 1
+def U64.smin   : Int := 0
+def U64.smax   : Int := HPow.hPow 2 64 - 1
+def U128.smin  : Int := 0
+def U128.smax  : Int := HPow.hPow 2 128 - 1
+
+-- The "normalized" bounds, that we use in practice
+def I8.min    : Int   := -128
+def I8.max    : Int   := 127
+def I16.min   : Int  := -32768
+def I16.max   : Int  := 32767
+def I32.min   : Int  := -2147483648
+def I32.max   : Int  := 2147483647
+def I64.min   : Int  := -9223372036854775808
+def I64.max   : Int  := 9223372036854775807
+def I128.min  : Int := -170141183460469231731687303715884105728
+def I128.max  : Int := 170141183460469231731687303715884105727
+@[simp]
+def U8.min    : Int   := 0
+def U8.max    : Int   := 255
+@[simp]
+def U16.min   : Int  := 0
+def U16.max   : Int  := 65535
+@[simp]
+def U32.min   : Int  := 0
+def U32.max   : Int  := 4294967295
+@[simp]
+def U64.min   : Int  := 0
+def U64.max   : Int  := 18446744073709551615
+@[simp]
+def U128.min  : Int := 0
+def U128.max  : Int := 340282366920938463463374607431768211455
+@[simp]
+def Usize.min : Int := 0
+
+def Isize.refined_min : { n:Int // n = I32.min ∨ n = I64.min } :=
+  ⟨ Isize.smin, by
+    simp [Isize.smin]
+    cases System.Platform.numBits_eq <;>
+    unfold System.Platform.numBits at * <;> simp [*] ⟩
+
+def Isize.refined_max : { n:Int // n = I32.max ∨ n = I64.max } :=
+  ⟨ Isize.smax, by
+    simp [Isize.smax]
+    cases System.Platform.numBits_eq <;>
+    unfold System.Platform.numBits at * <;> simp [*] ⟩
+
+def Usize.refined_max : { n:Int // n = U32.max ∨ n = U64.max } :=
+  ⟨ Usize.smax, by
+    simp [Usize.smax]
+    cases System.Platform.numBits_eq <;>
+    unfold System.Platform.numBits at * <;> simp [*] ⟩
+
+def Isize.min := Isize.refined_min.val
+def Isize.max := Isize.refined_max.val
+def Usize.max := Usize.refined_max.val
+
+inductive ScalarTy :=
+| Isize
+| I8
+| I16
+| I32
+| I64
+| I128
+| Usize
+| U8
+| U16
+| U32
+| U64
+| U128
+
+def ScalarTy.isSigned (ty : ScalarTy) : Bool :=
+  match ty with
+  | Isize
+  | I8
+  | I16
+  | I32
+  | I64
+  | I128 => true
+  | Usize
+  | U8
+  | U16
+  | U32
+  | U64
+  | U128 => false
+
+
+def Scalar.smin (ty : ScalarTy) : Int :=
+  match ty with
+  | .Isize => Isize.smin
+  | .I8    => I8.smin
+  | .I16   => I16.smin
+  | .I32   => I32.smin
+  | .I64   => I64.smin
+  | .I128  => I128.smin
+  | .Usize => Usize.smin
+  | .U8    => U8.smin
+  | .U16   => U16.smin
+  | .U32   => U32.smin
+  | .U64   => U64.smin
+  | .U128  => U128.smin
+
+def Scalar.smax (ty : ScalarTy) : Int :=
+  match ty with
+  | .Isize => Isize.smax
+  | .I8    => I8.smax
+  | .I16   => I16.smax
+  | .I32   => I32.smax
+  | .I64   => I64.smax
+  | .I128  => I128.smax
+  | .Usize => Usize.smax
+  | .U8    => U8.smax
+  | .U16   => U16.smax
+  | .U32   => U32.smax
+  | .U64   => U64.smax
+  | .U128  => U128.smax
+
+def Scalar.min (ty : ScalarTy) : Int :=
+  match ty with
+  | .Isize => Isize.min
+  | .I8    => I8.min
+  | .I16   => I16.min
+  | .I32   => I32.min
+  | .I64   => I64.min
+  | .I128  => I128.min
+  | .Usize => Usize.min
+  | .U8    => U8.min
+  | .U16   => U16.min
+  | .U32   => U32.min
+  | .U64   => U64.min
+  | .U128  => U128.min
+
+def Scalar.max (ty : ScalarTy) : Int :=
+  match ty with
+  | .Isize => Isize.max
+  | .I8    => I8.max
+  | .I16   => I16.max
+  | .I32   => I32.max
+  | .I64   => I64.max
+  | .I128  => I128.max
+  | .Usize => Usize.max
+  | .U8    => U8.max
+  | .U16   => U16.max
+  | .U32   => U32.max
+  | .U64   => U64.max
+  | .U128  => U128.max
+
+def Scalar.smin_eq (ty : ScalarTy) : Scalar.min ty = Scalar.smin ty := by
+  cases ty <;> rfl
+
+def Scalar.smax_eq (ty : ScalarTy) : Scalar.max ty = Scalar.smax ty := by
+  cases ty <;> rfl
+
+-- "Conservative" bounds
+-- We use those because we can't compare to the isize bounds (which can't
+-- reduce at compile-time). Whenever we perform an arithmetic operation like
+-- addition we need to check that the result is in bounds: we first compare
+-- to the conservative bounds, which reduce, then compare to the real bounds.
+-- This is useful for the various #asserts that we want to reduce at
+-- type-checking time.
+def Scalar.cMin (ty : ScalarTy) : Int :=
+  match ty with
+  | .Isize => Scalar.min .I32
+  | _ => Scalar.min ty
+
+def Scalar.cMax (ty : ScalarTy) : Int :=
+  match ty with
+  | .Isize => Scalar.max .I32
+  | .Usize => Scalar.max .U32
+  | _ => Scalar.max ty
+
+theorem Scalar.cMin_bound ty : Scalar.min ty ≤ Scalar.cMin ty := by
+  cases ty <;> simp [Scalar.min, Scalar.max, Scalar.cMin, Scalar.cMax] at *
+  have h := Isize.refined_min.property
+  cases h <;> simp [*, Isize.min]
+
+theorem Scalar.cMax_bound ty : Scalar.cMax ty ≤ Scalar.max ty := by
+  cases ty <;> simp [Scalar.min, Scalar.max, Scalar.cMin, Scalar.cMax] at *
+  . have h := Isize.refined_max.property
+    cases h <;> simp [*, Isize.max]
+  . have h := Usize.refined_max.property
+    cases h <;> simp [*, Usize.max]
+
+theorem Scalar.cMin_suffices ty (h : Scalar.cMin ty ≤ x) : Scalar.min ty ≤ x := by
+  have := Scalar.cMin_bound ty
+  linarith
+
+theorem Scalar.cMax_suffices ty (h : x ≤ Scalar.cMax ty) : x ≤ Scalar.max ty := by
+  have := Scalar.cMax_bound ty
+  linarith
+
+structure Scalar (ty : ScalarTy) where
+  val : Int
+  hmin : Scalar.min ty ≤ val
+  hmax : val ≤ Scalar.max ty
+deriving Repr
+
+theorem Scalar.bound_suffices (ty : ScalarTy) (x : Int) :
+  Scalar.cMin ty ≤ x ∧ x ≤ Scalar.cMax ty ->
+  Scalar.min ty ≤ x ∧ x ≤ Scalar.max ty
+  :=
+  λ h => by
+  apply And.intro <;> have hmin := Scalar.cMin_bound ty <;> have hmax := Scalar.cMax_bound ty <;> linarith
+
+def Scalar.ofIntCore {ty : ScalarTy} (x : Int)
+  (hmin : Scalar.min ty ≤ x) (hmax : x ≤ Scalar.max ty) : Scalar ty :=
+  { val := x, hmin := hmin, hmax := hmax }
+
+-- Tactic to prove that integers are in bounds
+-- TODO: use this: https://leanprover.zulipchat.com/#narrow/stream/270676-lean4/topic/instance.20with.20tactic.20autoparam
+syntax "intlit" : tactic
+macro_rules
+  | `(tactic| intlit) => `(tactic| apply Scalar.bound_suffices; decide)
+
+def Scalar.ofInt {ty : ScalarTy} (x : Int)
+  (h : Scalar.min ty ≤ x ∧ x ≤ Scalar.max ty := by intlit) : Scalar ty :=
+  -- Remark: we initially wrote:
+  --  let ⟨ hmin, hmax ⟩ := h
+  --  Scalar.ofIntCore x hmin hmax
+  -- We updated to the line below because a similar pattern in `Scalar.tryMk`
+  -- made reduction block. Both versions seem to work for `Scalar.ofInt`, though.
+  -- TODO: investigate
+  Scalar.ofIntCore x h.left h.right
+
+@[simp] def Scalar.check_bounds (ty : ScalarTy) (x : Int) : Bool :=
+  (Scalar.cMin ty ≤ x || Scalar.min ty ≤ x) ∧ (x ≤ Scalar.cMax ty || x ≤ Scalar.max ty)
+
+theorem Scalar.check_bounds_prop {ty : ScalarTy} {x : Int} (h: Scalar.check_bounds ty x) :
+  Scalar.min ty ≤ x ∧ x ≤ Scalar.max ty := by
+  simp at *
+  have ⟨ hmin, hmax ⟩ := h
+  have hbmin := Scalar.cMin_bound ty
+  have hbmax := Scalar.cMax_bound ty
+  cases hmin <;> cases hmax <;> apply And.intro <;> linarith
+
+-- Further thoughts: look at what has been done here:
+-- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/Fin/Basic.lean
+-- and
+-- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/UInt.lean
+-- which both contain a fair amount of reasoning already!
+def Scalar.tryMk (ty : ScalarTy) (x : Int) : Result (Scalar ty) :=
+  if h:Scalar.check_bounds ty x then
+    -- If we do:
+    -- ```
+    -- let ⟨ hmin, hmax ⟩ := (Scalar.check_bounds_prop h)
+    -- Scalar.ofIntCore x hmin hmax
+    -- ```
+    -- then normalization blocks (for instance, some proofs which use reflexivity fail).
+    -- However, the version below doesn't block reduction (TODO: investigate):
+    return Scalar.ofInt x (Scalar.check_bounds_prop h)
+  else fail integerOverflow
+
+def Scalar.neg {ty : ScalarTy} (x : Scalar ty) : Result (Scalar ty) := Scalar.tryMk ty (- x.val)
+
+-- Our custom remainder operation, which satisfies the semantics of Rust
+-- TODO: is there a better way?
+def scalar_rem (x y : Int) : Int :=
+  if 0 ≤ x then x % y
+  else - (|x| % |y|)
+
+@[simp]
+def scalar_rem_nonneg {x y : Int} (hx : 0 ≤ x) : scalar_rem x y = x % y := by
+  intros
+  simp [*, scalar_rem]
+
+-- Our custom division operation, which satisfies the semantics of Rust
+-- TODO: is there a better way?
+def scalar_div (x y : Int) : Int :=
+  if 0 ≤ x && 0 ≤ y then x / y
+  else if 0 ≤ x && y < 0 then - (|x| / |y|)
+  else if x < 0 && 0 ≤ y then - (|x| / |y|)
+  else |x| / |y|
+
+@[simp]
+def scalar_div_nonneg {x y : Int} (hx : 0 ≤ x) (hy : 0 ≤ y) : scalar_div x y = x / y := by
+  intros
+  simp [*, scalar_div]
+
+-- Checking that the remainder operation is correct
+#assert scalar_rem 1 2 = 1
+#assert scalar_rem (-1) 2 = -1
+#assert scalar_rem 1 (-2) = 1
+#assert scalar_rem (-1) (-2) = -1
+#assert scalar_rem 7 3 = (1:Int)
+#assert scalar_rem (-7) 3 = -1
+#assert scalar_rem 7 (-3) = 1
+#assert scalar_rem (-7) (-3) = -1
+
+-- Checking that the division operation is correct
+#assert scalar_div 3 2 = 1
+#assert scalar_div (-3) 2 = -1
+#assert scalar_div 3 (-2) = -1
+#assert scalar_div (-3) (-2) = 1
+#assert scalar_div 7 3 = 2
+#assert scalar_div (-7) 3 = -2
+#assert scalar_div 7 (-3) = -2
+#assert scalar_div (-7) (-3) = 2
+
+def Scalar.div {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
+  if y.val != 0 then Scalar.tryMk ty (scalar_div x.val y.val) else fail divisionByZero
+
+def Scalar.rem {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
+  if y.val != 0 then Scalar.tryMk ty (scalar_rem x.val y.val) else fail divisionByZero
+
+def Scalar.add {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
+  Scalar.tryMk ty (x.val + y.val)
+
+def Scalar.sub {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
+  Scalar.tryMk ty (x.val - y.val)
+
+def Scalar.mul {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
+  Scalar.tryMk ty (x.val * y.val)
+
+-- TODO: instances of +, -, * etc. for scalars
+
+-- Cast an integer from a [src_ty] to a [tgt_ty]
+-- TODO: check the semantics of casts in Rust
+def Scalar.cast {src_ty : ScalarTy} (tgt_ty : ScalarTy) (x : Scalar src_ty) : Result (Scalar tgt_ty) :=
+  Scalar.tryMk tgt_ty x.val
+
+-- The scalar types
+-- We declare the definitions as reducible so that Lean can unfold them (useful
+-- for type class resolution for instance).
+@[reducible] def Isize := Scalar .Isize
+@[reducible] def I8    := Scalar .I8
+@[reducible] def I16   := Scalar .I16
+@[reducible] def I32   := Scalar .I32
+@[reducible] def I64   := Scalar .I64
+@[reducible] def I128  := Scalar .I128
+@[reducible] def Usize := Scalar .Usize
+@[reducible] def U8    := Scalar .U8
+@[reducible] def U16   := Scalar .U16
+@[reducible] def U32   := Scalar .U32
+@[reducible] def U64   := Scalar .U64
+@[reducible] def U128  := Scalar .U128
+
+-- TODO: below: not sure this is the best way.
+-- Should we rather overload operations like +, -, etc.?
+-- Also, it is possible to automate the generation of those definitions
+-- with macros (but would it be a good idea? It would be less easy to
+-- read the file, which is not supposed to change a lot)
+
+-- Negation
+
+/--
+Remark: there is no heterogeneous negation in the Lean prelude: we thus introduce
+one here.
+
+The notation typeclass for heterogeneous addition.
+This enables the notation `- a : β` where `a : α`.
+-/
+class HNeg (α : Type u) (β : outParam (Type v)) where
+  /-- `- a` computes the negation of `a`.
+  The meaning of this notation is type-dependent. -/
+  hNeg : α → β
+
+prefix:75  "-"   => HNeg.hNeg
+
+instance : HNeg Isize (Result Isize) where hNeg x := Scalar.neg x
+instance : HNeg I8 (Result I8) where hNeg x := Scalar.neg x
+instance : HNeg I16 (Result I16) where hNeg x := Scalar.neg x
+instance : HNeg I32 (Result I32) where hNeg x := Scalar.neg x
+instance : HNeg I64 (Result I64) where hNeg x := Scalar.neg x
+instance : HNeg I128 (Result I128) where hNeg x := Scalar.neg x
+
+-- Addition
+instance {ty} : HAdd (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
+  hAdd x y := Scalar.add x y
+
+-- Substraction
+instance {ty} : HSub (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
+  hSub x y := Scalar.sub x y
+
+-- Multiplication
+instance {ty} : HMul (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
+  hMul x y := Scalar.mul x y
+
+-- Division
+instance {ty} : HDiv (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
+  hDiv x y := Scalar.div x y
+
+-- Remainder
+instance {ty} : HMod (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
+  hMod x y := Scalar.rem x y
+
+-- Generic theorem - shouldn't be used much
+@[cpspec]
+theorem Scalar.add_spec {ty} {x y : Scalar ty}
+  (hmin : Scalar.min ty ≤ x.val + y.val)
+  (hmax : x.val + y.val ≤ Scalar.max ty) :
+  ∃ z, x + y = ret z ∧ z.val = x.val + y.val := by
+  simp [HAdd.hAdd, add, Add.add]
+  simp [tryMk]
+  split
+  . simp [pure]
+    rfl
+  . tauto
+
+theorem Scalar.add_unsigned_spec {ty} (s: ¬ ty.isSigned) {x y : Scalar ty}
+  (hmax : x.val + y.val ≤ Scalar.max ty) :
+  ∃ z, x + y = ret z ∧ z.val = x.val + y.val := by
+  have hmin : Scalar.min ty ≤ x.val + y.val := by
+    have hx := x.hmin
+    have hy := y.hmin
+    cases ty <;> simp [min] at * <;> linarith
+  apply add_spec <;> assumption
+
+/- Fine-grained theorems -/
+@[cepspec] theorem Usize.add_spec {x y : Usize} (hmax : x.val + y.val ≤ Usize.max) :
+  ∃ z, x + y = ret z ∧ z.val = x.val + y.val := by
+  apply Scalar.add_unsigned_spec <;> simp only [Scalar.max, *]
+
+@[cepspec] theorem U8.add_spec {x y : U8} (hmax : x.val + y.val ≤ U8.max) :
+  ∃ z, x + y = ret z ∧ z.val = x.val + y.val := by
+  apply Scalar.add_unsigned_spec <;> simp only [Scalar.max, *]
+
+@[cepspec] theorem U16.add_spec {x y : U16} (hmax : x.val + y.val ≤ U16.max) :
+  ∃ z, x + y = ret z ∧ z.val = x.val + y.val := by
+  apply Scalar.add_unsigned_spec <;> simp only [Scalar.max, *]
+
+@[cepspec] theorem U32.add_spec {x y : U32} (hmax : x.val + y.val ≤ U32.max) :
+  ∃ z, x + y = ret z ∧ z.val = x.val + y.val := by
+  apply Scalar.add_unsigned_spec <;> simp only [Scalar.max, *]
+
+@[cepspec] theorem U64.add_spec {x y : U64} (hmax : x.val + y.val ≤ U64.max) :
+  ∃ z, x + y = ret z ∧ z.val = x.val + y.val := by
+  apply Scalar.add_unsigned_spec <;> simp only [Scalar.max, *]
+
+@[cepspec] theorem U128.add_spec {x y : U128} (hmax : x.val + y.val ≤ U128.max) :
+  ∃ z, x + y = ret z ∧ z.val = x.val + y.val := by
+  apply Scalar.add_unsigned_spec <;> simp only [Scalar.max, *]
+
+-- Generic theorem - shouldn't be used much
+@[cpspec]
+theorem Scalar.sub_spec {ty} {x y : Scalar ty}
+  (hmin : Scalar.min ty ≤ x.val - y.val)
+  (hmax : x.val - y.val ≤ Scalar.max ty) :
+  ∃ z, x - y = ret z ∧ z.val = x.val - y.val := by
+  simp [HSub.hSub, sub, Sub.sub]
+  simp [tryMk]
+  split
+  . simp [pure]
+    rfl
+  . tauto
+
+theorem Scalar.sub_unsigned_spec {ty} (s: ¬ ty.isSigned) {x y : Scalar ty}
+  (hmin : Scalar.min ty ≤ x.val - y.val) :
+  ∃ z, x - y = ret z ∧ z.val = x.val - y.val := by
+  have : x.val - y.val ≤ Scalar.max ty := by
+    have hx := x.hmin
+    have hxm := x.hmax
+    have hy := y.hmin
+    cases ty <;> simp [min, max] at * <;> linarith
+  intros
+  apply sub_spec <;> assumption
+
+/- Fine-grained theorems -/
+@[cepspec] theorem Usize.sub_spec {x y : Usize} (hmin : Usize.min ≤ x.val - y.val) :
+  ∃ z, x - y = ret z ∧ z.val = x.val - y.val := by
+  apply Scalar.sub_unsigned_spec <;> simp only [Scalar.min, *]
+
+@[cepspec] theorem U8.sub_spec {x y : U8} (hmin : U8.min ≤ x.val - y.val) :
+  ∃ z, x - y = ret z ∧ z.val = x.val - y.val := by
+  apply Scalar.sub_unsigned_spec <;> simp only [Scalar.min, *]
+
+@[cepspec] theorem U16.sub_spec {x y : U16} (hmin : U16.min ≤ x.val - y.val) :
+  ∃ z, x - y = ret z ∧ z.val = x.val - y.val := by
+  apply Scalar.sub_unsigned_spec <;> simp only [Scalar.min, *]
+
+@[cepspec] theorem U32.sub_spec {x y : U32} (hmin : U32.min ≤ x.val - y.val) :
+  ∃ z, x - y = ret z ∧ z.val = x.val - y.val := by
+  apply Scalar.sub_unsigned_spec <;> simp only [Scalar.min, *]
+
+@[cepspec] theorem U64.sub_spec {x y : U64} (hmin : U64.min ≤ x.val - y.val) :
+  ∃ z, x - y = ret z ∧ z.val = x.val - y.val := by
+  apply Scalar.sub_unsigned_spec <;> simp only [Scalar.min, *]
+
+@[cepspec] theorem U128.sub_spec {x y : U128} (hmin : U128.min ≤ x.val - y.val) :
+  ∃ z, x - y = ret z ∧ z.val = x.val - y.val := by
+  apply Scalar.sub_unsigned_spec <;> simp only [Scalar.min, *]
+
+-- Generic theorem - shouldn't be used much
+theorem Scalar.mul_spec {ty} {x y : Scalar ty}
+  (hmin : Scalar.min ty ≤ x.val * y.val)
+  (hmax : x.val * y.val ≤ Scalar.max ty) :
+  ∃ z, x * y = ret z ∧ z.val = x.val * y.val := by
+  simp [HMul.hMul, mul, Mul.mul]
+  simp [tryMk]
+  split
+  . simp [pure]
+    rfl
+  . tauto
+
+theorem Scalar.mul_unsigned_spec {ty} (s: ¬ ty.isSigned) {x y : Scalar ty}
+  (hmax : x.val * y.val ≤ Scalar.max ty) :
+  ∃ z, x * y = ret z ∧ z.val = x.val * y.val := by
+  have : Scalar.min ty ≤ x.val * y.val := by
+    have hx := x.hmin
+    have hy := y.hmin
+    cases ty <;> simp at * <;> apply mul_nonneg hx hy
+  apply mul_spec <;> assumption
+
+/- Fine-grained theorems -/
+@[cepspec] theorem Usize.mul_spec {x y : Usize} (hmax : x.val * y.val ≤ Usize.max) :
+  ∃ z, x * y = ret z ∧ z.val = x.val * y.val := by
+  apply Scalar.mul_unsigned_spec <;> simp only [Scalar.max, *]
+
+@[cepspec] theorem U8.mul_spec {x y : U8} (hmax : x.val * y.val ≤ U8.max) :
+  ∃ z, x * y = ret z ∧ z.val = x.val * y.val := by
+  apply Scalar.mul_unsigned_spec <;> simp only [Scalar.max, *]
+
+@[cepspec] theorem U16.mul_spec {x y : U16} (hmax : x.val * y.val ≤ U16.max) :
+  ∃ z, x * y = ret z ∧ z.val = x.val * y.val := by
+  apply Scalar.mul_unsigned_spec <;> simp only [Scalar.max, *]
+
+@[cepspec] theorem U32.mul_spec {x y : U32} (hmax : x.val * y.val ≤ U32.max) :
+  ∃ z, x * y = ret z ∧ z.val = x.val * y.val := by
+  apply Scalar.mul_unsigned_spec <;> simp only [Scalar.max, *]
+
+@[cepspec] theorem U64.mul_spec {x y : U64} (hmax : x.val * y.val ≤ U64.max) :
+  ∃ z, x * y = ret z ∧ z.val = x.val * y.val := by
+  apply Scalar.mul_unsigned_spec <;> simp only [Scalar.max, *]
+
+@[cepspec] theorem U128.mul_spec {x y : U128} (hmax : x.val * y.val ≤ U128.max) :
+  ∃ z, x * y = ret z ∧ z.val = x.val * y.val := by
+  apply Scalar.mul_unsigned_spec <;> simp only [Scalar.max, *]
+
+-- Generic theorem - shouldn't be used much
+@[cpspec]
+theorem Scalar.div_spec {ty} {x y : Scalar ty}
+  (hnz : y.val ≠ 0)
+  (hmin : Scalar.min ty ≤ scalar_div x.val y.val)
+  (hmax : scalar_div x.val y.val ≤ Scalar.max ty) :
+  ∃ z, x / y = ret z ∧ z.val = scalar_div x.val y.val := by
+  simp [HDiv.hDiv, div, Div.div]
+  simp [tryMk, *]
+  simp [pure]
+  rfl
+
+theorem Scalar.div_unsigned_spec {ty} (s: ¬ ty.isSigned) (x : Scalar ty) {y : Scalar ty}
+  (hnz : y.val ≠ 0) :
+  ∃ z, x / y = ret z ∧ z.val = x.val / y.val := by
+  have h : Scalar.min ty = 0 := by cases ty <;> simp at *
+  have hx := x.hmin
+  have hy := y.hmin
+  simp [h] at hx hy
+  have hmin : 0 ≤ x.val / y.val := Int.ediv_nonneg hx hy
+  have hmax : x.val / y.val ≤ Scalar.max ty := by
+    have := Int.ediv_le_self y.val hx
+    have := x.hmax
+    linarith
+  have hs := @div_spec ty x y hnz
+  simp [*] at hs
+  apply hs
+
+/- Fine-grained theorems -/
+@[cepspec] theorem Usize.div_spec (x : Usize) {y : Usize} (hnz : y.val ≠ 0) :
+  ∃ z, x / y = ret z ∧ z.val = x.val / y.val := by
+  apply Scalar.div_unsigned_spec <;> simp [*]
+
+@[cepspec] theorem U8.div_spec (x : U8) {y : U8} (hnz : y.val ≠ 0) :
+  ∃ z, x / y = ret z ∧ z.val = x.val / y.val := by
+  apply Scalar.div_unsigned_spec <;> simp [Scalar.max, *]
+
+@[cepspec] theorem U16.div_spec (x : U16) {y : U16} (hnz : y.val ≠ 0) :
+  ∃ z, x / y = ret z ∧ z.val = x.val / y.val := by
+  apply Scalar.div_unsigned_spec <;> simp [Scalar.max, *]
+
+@[cepspec] theorem U32.div_spec (x : U32) {y : U32} (hnz : y.val ≠ 0) :
+  ∃ z, x / y = ret z ∧ z.val = x.val / y.val := by
+  apply Scalar.div_unsigned_spec <;> simp [Scalar.max, *]
+
+@[cepspec] theorem U64.div_spec (x : U64) {y : U64} (hnz : y.val ≠ 0) :
+  ∃ z, x / y = ret z ∧ z.val = x.val / y.val := by
+  apply Scalar.div_unsigned_spec <;> simp [Scalar.max, *]
+
+@[cepspec] theorem U128.div_spec (x : U128) {y : U128} (hnz : y.val ≠ 0) :
+  ∃ z, x / y = ret z ∧ z.val = x.val / y.val := by
+  apply Scalar.div_unsigned_spec <;> simp [Scalar.max, *]
+
+-- Generic theorem - shouldn't be used much
+@[cpspec]
+theorem Scalar.rem_spec {ty} {x y : Scalar ty}
+  (hnz : y.val ≠ 0)
+  (hmin : Scalar.min ty ≤ scalar_rem x.val y.val)
+  (hmax : scalar_rem x.val y.val ≤ Scalar.max ty) :
+  ∃ z, x % y = ret z ∧ z.val = scalar_rem x.val y.val := by
+  simp [HMod.hMod, rem]
+  simp [tryMk, *]
+  simp [pure]
+  rfl
+
+theorem Scalar.rem_unsigned_spec {ty} (s: ¬ ty.isSigned) (x : Scalar ty) {y : Scalar ty}
+  (hnz : y.val ≠ 0) :
+  ∃ z, x % y = ret z ∧ z.val = x.val % y.val := by
+  have h : Scalar.min ty = 0 := by cases ty <;> simp at *
+  have hx := x.hmin
+  have hy := y.hmin
+  simp [h] at hx hy
+  have hmin : 0 ≤ x.val % y.val := Int.emod_nonneg x.val hnz
+  have hmax : x.val % y.val ≤ Scalar.max ty := by
+    have h : 0 < y.val := by int_tac
+    have h := Int.emod_lt_of_pos x.val h
+    have := y.hmax
+    linarith
+  have hs := @rem_spec ty x y hnz
+  simp [*] at hs
+  simp [*]
+
+@[cepspec] theorem Usize.rem_spec (x : Usize) {y : Usize} (hnz : y.val ≠ 0) :
+  ∃ z, x % y = ret z ∧ z.val = x.val % y.val := by
+  apply Scalar.rem_unsigned_spec <;> simp [*]
+
+@[cepspec] theorem U8.rem_spec (x : U8) {y : U8} (hnz : y.val ≠ 0) :
+  ∃ z, x % y = ret z ∧ z.val = x.val % y.val := by
+  apply Scalar.rem_unsigned_spec <;> simp [Scalar.max, *]
+
+@[cepspec] theorem U16.rem_spec (x : U16) {y : U16} (hnz : y.val ≠ 0) :
+  ∃ z, x % y = ret z ∧ z.val = x.val % y.val := by
+  apply Scalar.rem_unsigned_spec <;> simp [Scalar.max, *]
+
+@[cepspec] theorem U32.rem_spec (x : U32) {y : U32} (hnz : y.val ≠ 0) :
+  ∃ z, x % y = ret z ∧ z.val = x.val % y.val := by
+  apply Scalar.rem_unsigned_spec <;> simp [Scalar.max, *]
+
+@[cepspec] theorem U64.rem_spec (x : U64) {y : U64} (hnz : y.val ≠ 0) :
+  ∃ z, x % y = ret z ∧ z.val = x.val % y.val := by
+  apply Scalar.rem_unsigned_spec <;> simp [Scalar.max, *]
+
+@[cepspec] theorem U128.rem_spec (x : U128) {y : U128} (hnz : y.val ≠ 0) :
+  ∃ z, x % y = ret z ∧ z.val = x.val % y.val := by
+  apply Scalar.rem_unsigned_spec <;> simp [Scalar.max, *]
+
+-- ofIntCore
+-- TODO: typeclass?
+def Isize.ofIntCore := @Scalar.ofIntCore .Isize
+def I8.ofIntCore    := @Scalar.ofIntCore .I8
+def I16.ofIntCore   := @Scalar.ofIntCore .I16
+def I32.ofIntCore   := @Scalar.ofIntCore .I32
+def I64.ofIntCore   := @Scalar.ofIntCore .I64
+def I128.ofIntCore  := @Scalar.ofIntCore .I128
+def Usize.ofIntCore := @Scalar.ofIntCore .Usize
+def U8.ofIntCore    := @Scalar.ofIntCore .U8
+def U16.ofIntCore   := @Scalar.ofIntCore .U16
+def U32.ofIntCore   := @Scalar.ofIntCore .U32
+def U64.ofIntCore   := @Scalar.ofIntCore .U64
+def U128.ofIntCore  := @Scalar.ofIntCore .U128
+
+--  ofInt
+-- TODO: typeclass?
+def Isize.ofInt := @Scalar.ofInt .Isize
+def I8.ofInt    := @Scalar.ofInt .I8
+def I16.ofInt   := @Scalar.ofInt .I16
+def I32.ofInt   := @Scalar.ofInt .I32
+def I64.ofInt   := @Scalar.ofInt .I64
+def I128.ofInt  := @Scalar.ofInt .I128
+def Usize.ofInt := @Scalar.ofInt .Usize
+def U8.ofInt    := @Scalar.ofInt .U8
+def U16.ofInt   := @Scalar.ofInt .U16
+def U32.ofInt   := @Scalar.ofInt .U32
+def U64.ofInt   := @Scalar.ofInt .U64
+def U128.ofInt  := @Scalar.ofInt .U128
+
+-- TODO: factor those lemmas out
+@[simp] theorem Scalar.ofInt_val_eq {ty} (h : Scalar.min ty ≤ x ∧ x ≤ Scalar.max ty) : (Scalar.ofInt x h).val = x := by
+  simp [Scalar.ofInt, Scalar.ofIntCore]
+
+@[simp] theorem Isize.ofInt_val_eq (h : Scalar.min ScalarTy.Isize ≤ x ∧ x ≤ Scalar.max ScalarTy.Isize) : (Isize.ofInt x h).val = x := by
+  apply Scalar.ofInt_val_eq h
+
+@[simp] theorem I8.ofInt_val_eq (h : Scalar.min ScalarTy.I8 ≤ x ∧ x ≤ Scalar.max ScalarTy.I8) : (I8.ofInt x h).val = x := by
+  apply Scalar.ofInt_val_eq h
+
+@[simp] theorem I16.ofInt_val_eq (h : Scalar.min ScalarTy.I16 ≤ x ∧ x ≤ Scalar.max ScalarTy.I16) : (I16.ofInt x h).val = x := by
+  apply Scalar.ofInt_val_eq h
+
+@[simp] theorem I32.ofInt_val_eq (h : Scalar.min ScalarTy.I32 ≤ x ∧ x ≤ Scalar.max ScalarTy.I32) : (I32.ofInt x h).val = x := by
+  apply Scalar.ofInt_val_eq h
+
+@[simp] theorem I64.ofInt_val_eq (h : Scalar.min ScalarTy.I64 ≤ x ∧ x ≤ Scalar.max ScalarTy.I64) : (I64.ofInt x h).val = x := by
+  apply Scalar.ofInt_val_eq h
+
+@[simp] theorem I128.ofInt_val_eq (h : Scalar.min ScalarTy.I128 ≤ x ∧ x ≤ Scalar.max ScalarTy.I128) : (I128.ofInt x h).val = x := by
+  apply Scalar.ofInt_val_eq h
+
+@[simp] theorem Usize.ofInt_val_eq (h : Scalar.min ScalarTy.Usize ≤ x ∧ x ≤ Scalar.max ScalarTy.Usize) : (Usize.ofInt x h).val = x := by
+  apply Scalar.ofInt_val_eq h
+
+@[simp] theorem U8.ofInt_val_eq (h : Scalar.min ScalarTy.U8 ≤ x ∧ x ≤ Scalar.max ScalarTy.U8) : (U8.ofInt x h).val = x := by
+  apply Scalar.ofInt_val_eq h
+
+@[simp] theorem U16.ofInt_val_eq (h : Scalar.min ScalarTy.U16 ≤ x ∧ x ≤ Scalar.max ScalarTy.U16) : (U16.ofInt x h).val = x := by
+  apply Scalar.ofInt_val_eq h
+
+@[simp] theorem U32.ofInt_val_eq (h : Scalar.min ScalarTy.U32 ≤ x ∧ x ≤ Scalar.max ScalarTy.U32) : (U32.ofInt x h).val = x := by
+  apply Scalar.ofInt_val_eq h
+
+@[simp] theorem U64.ofInt_val_eq (h : Scalar.min ScalarTy.U64 ≤ x ∧ x ≤ Scalar.max ScalarTy.U64) : (U64.ofInt x h).val = x := by
+  apply Scalar.ofInt_val_eq h
+
+@[simp] theorem U128.ofInt_val_eq (h : Scalar.min ScalarTy.U128 ≤ x ∧ x ≤ Scalar.max ScalarTy.U128) : (U128.ofInt x h).val = x := by
+  apply Scalar.ofInt_val_eq h
+
+
+-- Comparisons
+instance {ty} : LT (Scalar ty) where
+  lt a b := LT.lt a.val b.val
+
+instance {ty} : LE (Scalar ty) where le a b := LE.le a.val b.val
+
+instance Scalar.decLt {ty} (a b : Scalar ty) : Decidable (LT.lt a b) := Int.decLt ..
+instance Scalar.decLe {ty} (a b : Scalar ty) : Decidable (LE.le a b) := Int.decLe ..
+
+theorem Scalar.eq_of_val_eq {ty} : ∀ {i j : Scalar ty}, Eq i.val j.val → Eq i j
+  | ⟨_, _, _⟩, ⟨_, _, _⟩, rfl => rfl
+
+theorem Scalar.val_eq_of_eq {ty} {i j : Scalar ty} (h : Eq i j) : Eq i.val j.val :=
+  h ▸ rfl
+
+theorem Scalar.ne_of_val_ne {ty} {i j : Scalar ty} (h : Not (Eq i.val j.val)) : Not (Eq i j) :=
+  fun h' => absurd (val_eq_of_eq h') h
+
+instance (ty : ScalarTy) : DecidableEq (Scalar ty) :=
+  fun i j =>
+    match decEq i.val j.val with
+    | isTrue h  => isTrue (Scalar.eq_of_val_eq h)
+    | isFalse h => isFalse (Scalar.ne_of_val_ne h)
+
+/- Remark: we can't write the following instance because of restrictions about
+   the type class parameters (`ty` doesn't appear in the return type, which is
+   forbidden):
+
+   ```
+   instance Scalar.cast (ty : ScalarTy) : Coe (Scalar ty) Int where coe := λ v => v.val
+   ```
+ -/
+def Scalar.toInt {ty} (n : Scalar ty) : Int := n.val
+
+-- -- We now define a type class that subsumes the various machine integer types, so
+-- -- as to write a concise definition for scalar_cast, rather than exhaustively
+-- -- enumerating all of the possible pairs. We remark that Rust has sane semantics
+-- -- and fails if a cast operation would involve a truncation or modulo.
+
+-- class MachineInteger (t: Type) where
+--   size: Nat
+--   val: t -> Fin size
+--   ofNatCore: (n:Nat) -> LT.lt n size -> t
+
+-- set_option hygiene false in
+-- run_cmd
+--   for typeName in [`UInt8, `UInt16, `UInt32, `UInt64, `USize].map Lean.mkIdent do
+--   Lean.Elab.Command.elabCommand (← `(
+--     namespace $typeName
+--     instance: MachineInteger $typeName where
+--       size := size
+--       val := val
+--       ofNatCore := ofNatCore
+--     end $typeName
+--   ))
+
+-- -- Aeneas only instantiates the destination type (`src` is implicit). We rely on
+-- -- Lean to infer `src`.
+
+-- def scalar_cast { src: Type } (dst: Type) [ MachineInteger src ] [ MachineInteger dst ] (x: src): Result dst :=
+--   if h: MachineInteger.val x < MachineInteger.size dst then
+--     .ret (MachineInteger.ofNatCore (MachineInteger.val x).val h)
+--   else
+--     .fail integerOverflow
+
+end Primitives
diff --git a/backends/lean/Base/Primitives/Vec.lean b/backends/lean/Base/Primitives/Vec.lean
new file mode 100644
index 00000000..a09d6ac2
--- /dev/null
+++ b/backends/lean/Base/Primitives/Vec.lean
@@ -0,0 +1,145 @@
+import Lean
+import Lean.Meta.Tactic.Simp
+import Init.Data.List.Basic
+import Mathlib.Tactic.RunCmd
+import Mathlib.Tactic.Linarith
+import Base.IList
+import Base.Primitives.Scalar
+import Base.Arith
+import Base.Progress.Base
+
+namespace Primitives
+
+open Result Error
+
+-------------
+-- VECTORS --
+-------------
+
+def Vec (α : Type u) := { l : List α // l.length ≤ Usize.max }
+
+-- TODO: do we really need it? It should be with Subtype by default
+instance Vec.cast (a : Type u): Coe (Vec a) (List a)  where coe := λ v => v.val
+
+instance (a : Type u) : Arith.HasIntProp (Vec a) where
+  prop_ty := λ v => 0 ≤ v.val.len ∧ v.val.len ≤ Scalar.max ScalarTy.Usize
+  prop := λ ⟨ _, l ⟩ => by simp[Scalar.max, List.len_eq_length, *]
+
+@[simp]
+abbrev Vec.length {α : Type u} (v : Vec α) : Int := v.val.len
+
+@[simp]
+abbrev Vec.v {α : Type u} (v : Vec α) : List α := v.val
+
+example {a: Type u} (v : Vec a) : v.length ≤ Scalar.max ScalarTy.Usize := by
+  scalar_tac
+
+def Vec.new (α : Type u): Vec α := ⟨ [], by apply Scalar.cMax_suffices .Usize; simp ⟩
+
+-- TODO: very annoying that the α is an explicit parameter
+def Vec.len (α : Type u) (v : Vec α) : Usize :=
+  Usize.ofIntCore v.val.len (by scalar_tac) (by scalar_tac)
+
+@[simp]
+theorem Vec.len_val {α : Type u} (v : Vec α) : (Vec.len α v).val = v.length :=
+  by rfl
+
+-- This shouldn't be used
+def Vec.push_fwd (α : Type u) (_ : Vec α) (_ : α) : Unit := ()
+
+-- This is actually the backward function
+def Vec.push (α : Type u) (v : Vec α) (x : α) : Result (Vec α)
+  :=
+  let nlen := List.length v.val + 1
+  if h : nlen ≤ U32.max || nlen ≤ Usize.max then
+    have h : nlen ≤ Usize.max := by
+      simp [Usize.max] at *
+      have hm := Usize.refined_max.property
+      cases h <;> cases hm <;> simp [U32.max, U64.max] at * <;> try linarith
+    return ⟨ List.concat v.val x, by simp at *; assumption ⟩
+  else
+    fail maximumSizeExceeded
+
+-- This shouldn't be used
+def Vec.insert_fwd (α : Type u) (v: Vec α) (i: Usize) (_: α) : Result Unit :=
+  if i.val < v.length then
+    .ret ()
+  else
+    .fail arrayOutOfBounds
+
+-- This is actually the backward function
+def Vec.insert (α : Type u) (v: Vec α) (i: Usize) (x: α) : Result (Vec α) :=
+  if i.val < v.length then
+    .ret ⟨ v.val.update i.val x, by have := v.property; simp [*] ⟩
+  else
+    .fail arrayOutOfBounds
+
+@[pspec]
+theorem Vec.insert_spec {α : Type u} (v: Vec α) (i: Usize) (x: α)
+  (hbound : i.val < v.length) :
+  ∃ nv, v.insert α i x = ret nv ∧ nv.val = v.val.update i.val x := by
+  simp [insert, *]
+
+def Vec.index (α : Type u) (v: Vec α) (i: Usize) : Result α :=
+  match v.val.indexOpt i.val with
+  | none => fail .arrayOutOfBounds
+  | some x => ret x
+
+/- In the theorems below: we don't always need the `∃ ..`, but we use one
+   so that `progress` introduces an opaque variable and an equality. This
+   helps control the context.
+ -/
+
+@[pspec]
+theorem Vec.index_spec {α : Type u} [Inhabited α] (v: Vec α) (i: Usize)
+  (hbound : i.val < v.length) :
+  ∃ x, v.index α i = ret x ∧ x = v.val.index i.val := by
+  simp only [index]
+  -- TODO: dependent rewrite
+  have h := List.indexOpt_eq_index v.val i.val (by scalar_tac) (by simp [*])
+  simp [*]
+
+-- This shouldn't be used
+def Vec.index_back (α : Type u) (v: Vec α) (i: Usize) (_: α) : Result Unit :=
+  if i.val < List.length v.val then
+    .ret ()
+  else
+    .fail arrayOutOfBounds
+
+def Vec.index_mut (α : Type u) (v: Vec α) (i: Usize) : Result α :=
+  match v.val.indexOpt i.val with
+  | none => fail .arrayOutOfBounds
+  | some x => ret x
+
+@[pspec]
+theorem Vec.index_mut_spec {α : Type u} [Inhabited α] (v: Vec α) (i: Usize)
+  (hbound : i.val < v.length) :
+  ∃ x, v.index_mut α i = ret x ∧ x = v.val.index i.val := by
+  simp only [index_mut]
+  -- TODO: dependent rewrite
+  have h := List.indexOpt_eq_index v.val i.val (by scalar_tac) (by simp [*])
+  simp [*]
+
+instance {α : Type u} (p : Vec α → Prop) : Arith.HasIntProp (Subtype p) where
+  prop_ty := λ x => p x
+  prop := λ x => x.property
+
+def Vec.index_mut_back (α : Type u) (v: Vec α) (i: Usize) (x: α) : Result (Vec α) :=
+  match v.val.indexOpt i.val with
+  | none => fail .arrayOutOfBounds
+  | some _ =>
+    .ret ⟨ v.val.update i.val x, by have := v.property; simp [*] ⟩
+
+@[pspec]
+theorem Vec.index_mut_back_spec {α : Type u} (v: Vec α) (i: Usize) (x : α)
+  (hbound : i.val < v.length) :
+  ∃ nv, v.index_mut_back α i x = ret nv ∧
+  nv.val = v.val.update i.val x
+  := by
+  simp only [index_mut_back]
+  have h := List.indexOpt_bounds v.val i.val
+  split
+  . simp_all [length]; cases h <;> scalar_tac
+  . simp_all
+
+end Primitives
diff --git a/backends/lean/Base/Progress.lean b/backends/lean/Base/Progress.lean
new file mode 100644
index 00000000..d812b896
--- /dev/null
+++ b/backends/lean/Base/Progress.lean
@@ -0,0 +1 @@
+import Base.Progress.Progress
diff --git a/backends/lean/Base/Progress/Base.lean b/backends/lean/Base/Progress/Base.lean
new file mode 100644
index 00000000..6f820a84
--- /dev/null
+++ b/backends/lean/Base/Progress/Base.lean
@@ -0,0 +1,316 @@
+import Lean
+import Std.Lean.HashSet
+import Base.Utils
+import Base.Primitives.Base
+
+namespace Progress
+
+open Lean Elab Term Meta
+open Utils
+
+-- We can't define and use trace classes in the same file
+initialize registerTraceClass `Progress
+
+/- # Progress tactic -/
+
+structure PSpecDesc where
+  -- The universally quantified variables
+  fvars : Array Expr
+  -- The existentially quantified variables
+  evars : Array Expr
+  -- The function
+  fExpr : Expr
+  fName : Name
+  -- The function arguments
+  fLevels : List Level
+  args : Array Expr
+  -- The universally quantified variables which appear in the function arguments
+  argsFVars : Array FVarId
+  -- The returned value
+  ret : Expr
+  -- The postcondition (if there is)
+  post : Option Expr
+
+section Methods
+  variable [MonadLiftT MetaM m] [MonadControlT MetaM m] [Monad m] [MonadOptions m]
+  variable [MonadTrace m] [MonadLiftT IO m] [MonadRef m] [AddMessageContext m]
+  variable [MonadError m]
+  variable {a : Type}
+
+  /- Analyze a pspec theorem to decompose its arguments.
+
+     PSpec theorems should be of the following shape:
+     ```
+     ∀ x1 ... xn, H1 → ... Hn → ∃ y1 ... ym. f x1 ... xn = .ret ... ∧ Post1 ∧ ... ∧ Postk
+     ```
+
+     The continuation `k` receives the following inputs:
+     - universally quantified variables
+     - assumptions
+     - existentially quantified variables
+     - function name
+     - function arguments
+     - return
+     - postconditions
+
+     TODO: generalize for when we do inductive proofs
+  -/
+  partial
+  def withPSpec [Inhabited (m a)] [Nonempty (m a)] (th : Expr) (k : PSpecDesc → m a)
+    (sanityChecks : Bool := false) :
+    m a := do
+    trace[Progress] "Proposition: {th}"
+    -- Dive into the quantified variables and the assumptions
+    forallTelescope th.consumeMData fun fvars th => do
+    trace[Progress] "Universally quantified arguments and assumptions: {fvars}"
+    -- Dive into the existentials
+    existsTelescope th.consumeMData fun evars th => do
+    trace[Progress] "Existentials: {evars}"
+    trace[Progress] "Proposition after stripping the quantifiers: {th}"
+    -- Take the first conjunct
+    let (th, post) ← optSplitConj th.consumeMData
+    trace[Progress] "After splitting the conjunction:\n- eq: {th}\n- post: {post}"
+    -- Destruct the equality
+    let (mExpr, ret) ← destEq th.consumeMData
+    trace[Progress] "After splitting the equality:\n- lhs: {th}\n- rhs: {ret}"
+    -- Destruct the monadic application to dive into the bind, if necessary (this
+    -- is for when we use `withPSpec` inside of the `progress` tactic), and
+    -- destruct the application to get the function name
+    mExpr.consumeMData.withApp fun mf margs => do
+    trace[Progress] "After stripping the arguments of the monad expression:\n- mf: {mf}\n- margs: {margs}"
+    let (fExpr, f, args) ← do
+      if mf.isConst ∧ mf.constName = ``Bind.bind then do
+        -- Dive into the bind
+        let fExpr := (margs.get! 4).consumeMData
+        fExpr.withApp fun f args => pure (fExpr, f, args)
+      else pure (mExpr, mf, margs)
+    trace[Progress] "After stripping the arguments of the function call:\n- f: {f}\n- args: {args}"
+    if ¬ f.isConst then throwError "Not a constant: {f}"
+    -- Compute the set of universally quantified variables which appear in the function arguments
+    let allArgsFVars ← args.foldlM (fun hs arg => getFVarIds arg hs) HashSet.empty
+    -- Sanity check
+    if sanityChecks then
+      -- All the variables which appear in the inputs given to the function are
+      -- universally quantified (in particular, they are not *existentially* quantified)
+      let fvarsSet : HashSet FVarId := HashSet.ofArray (fvars.map (fun x => x.fvarId!))
+      let filtArgsFVars := allArgsFVars.toArray.filter (fun fvar => ¬ fvarsSet.contains fvar)
+      if ¬ filtArgsFVars.isEmpty then
+        let filtArgsFVars := filtArgsFVars.map (fun fvarId => Expr.fvar fvarId)
+        throwError "Some of the function inputs are not universally quantified: {filtArgsFVars}"
+    let argsFVars := fvars.map (fun x => x.fvarId!)
+    let argsFVars := argsFVars.filter (fun fvar => allArgsFVars.contains fvar)
+    -- Return
+    trace[Progress] "Function: {f.constName!}";
+    let thDesc := {
+      fvars := fvars
+      evars := evars
+      fExpr
+      fName := f.constName!
+      fLevels := f.constLevels!
+      args := args
+      argsFVars
+      ret := ret
+      post := post
+    }
+    k thDesc
+
+end Methods
+
+def getPSpecFunName (th : Expr) : MetaM Name :=
+  withPSpec th (fun d => do pure d.fName) true
+
+def getPSpecClassFunNames (th : Expr) : MetaM (Name × Name) :=
+  withPSpec th (fun d => do
+    let arg0 := d.args.get! 0
+    arg0.withApp fun f _ => do
+    if ¬ f.isConst then throwError "Not a constant: {f}"
+    pure (d.fName, f.constName)
+    ) true
+
+def getPSpecClassFunNameArg (th : Expr) : MetaM (Name × Expr) :=
+  withPSpec th (fun d => do
+    let arg0 := d.args.get! 0
+    pure (d.fName, arg0)
+    ) true
+
+-- "Regular" pspec attribute
+structure PSpecAttr where
+  attr : AttributeImpl
+  ext  : MapDeclarationExtension Name
+  deriving Inhabited
+
+/- pspec attribute for type classes: we use the name of the type class to
+   lookup another map. We use the *first* argument of the type class to lookup
+   into this second map.
+
+   Example:
+   ========
+   We use type classes for addition. For instance, the addition between two
+   U32 is written (without syntactic sugar) as `HAdd.add (Scalar ty) x y`. As a consequence,
+   we store the theorem through the bindings: HAdd.add → Scalar → ...
+
+   SH: TODO: this (and `PSpecClassExprAttr`) is a bit ad-hoc. For now it works for the
+   specs of the scalar operations, which is what I really need, but I'm not sure it
+   applies well to other situations. A better way would probably to use type classes, but
+   I couldn't get them to work on those cases. It is worth retrying.
+-/
+structure PSpecClassAttr where
+  attr : AttributeImpl
+  ext  : MapDeclarationExtension (NameMap Name)
+  deriving Inhabited
+
+/- Same as `PSpecClassAttr` but we use the full first argument (it works when it
+   is a constant). -/
+structure PSpecClassExprAttr where
+  attr : AttributeImpl
+  ext  : MapDeclarationExtension (HashMap Expr Name)
+  deriving Inhabited
+
+-- TODO: the original function doesn't define correctly the `addImportedFn`. Do a PR?
+def mkMapDeclarationExtension [Inhabited α] (name : Name := by exact decl_name%) : IO (MapDeclarationExtension α) :=
+  registerSimplePersistentEnvExtension {
+    name          := name,
+    addImportedFn := fun a => a.foldl (fun s a => a.foldl (fun s (k, v) => s.insert k v) s) RBMap.empty,
+    addEntryFn    := fun s n => s.insert n.1 n.2 ,
+    toArrayFn     := fun es => es.toArray.qsort (fun a b => Name.quickLt a.1 b.1)
+  }
+
+/- The persistent map from function to pspec theorems. -/
+initialize pspecAttr : PSpecAttr ← do
+  let ext ← mkMapDeclarationExtension `pspecMap
+  let attrImpl : AttributeImpl := {
+    name := `pspec
+    descr := "Marks theorems to use with the `progress` tactic"
+    add := fun thName stx attrKind => do
+      Attribute.Builtin.ensureNoArgs stx
+      -- TODO: use the attribute kind
+      unless attrKind == AttributeKind.global do
+        throwError "invalid attribute 'pspec', must be global"
+      -- Lookup the theorem
+      let env ← getEnv
+      let thDecl := env.constants.find! thName
+      let fName ← MetaM.run' (getPSpecFunName thDecl.type)
+      trace[Progress] "Registering spec theorem for {fName}"
+      let env := ext.addEntry env (fName, thName)
+      setEnv env
+      pure ()
+  }
+  registerBuiltinAttribute attrImpl
+  pure { attr := attrImpl, ext := ext }
+
+/- The persistent map from type classes to pspec theorems -/
+initialize pspecClassAttr : PSpecClassAttr ← do
+  let ext : MapDeclarationExtension (NameMap Name) ← mkMapDeclarationExtension `pspecClassMap
+  let attrImpl : AttributeImpl  := {
+    name := `cpspec
+    descr := "Marks theorems to use for type classes with the `progress` tactic"
+    add := fun thName stx attrKind => do
+      Attribute.Builtin.ensureNoArgs stx
+      -- TODO: use the attribute kind
+      unless attrKind == AttributeKind.global do
+        throwError "invalid attribute 'cpspec', must be global"
+      -- Lookup the theorem
+      let env ← getEnv
+      let thDecl := env.constants.find! thName
+      let (fName, argName) ← MetaM.run' (getPSpecClassFunNames thDecl.type)
+      trace[Progress] "Registering class spec theorem for ({fName}, {argName})"
+      -- Update the entry if there is one, add an entry if there is none
+      let env :=
+        match (ext.getState (← getEnv)).find? fName with
+        | none =>
+          let m := RBMap.ofList [(argName, thName)]
+          ext.addEntry env (fName, m)
+        | some m =>
+          let m := m.insert argName thName
+          ext.addEntry env (fName, m)
+      setEnv env
+      pure ()
+  }
+  registerBuiltinAttribute attrImpl
+  pure { attr := attrImpl, ext := ext }
+
+/- The 2nd persistent map from type classes to pspec theorems -/
+initialize pspecClassExprAttr : PSpecClassExprAttr ← do
+  let ext : MapDeclarationExtension (HashMap Expr Name) ← mkMapDeclarationExtension `pspecClassExprMap
+  let attrImpl : AttributeImpl  := {
+    name := `cepspec
+    descr := "Marks theorems to use for type classes with the `progress` tactic"
+    add := fun thName stx attrKind => do
+      Attribute.Builtin.ensureNoArgs stx
+      -- TODO: use the attribute kind
+      unless attrKind == AttributeKind.global do
+        throwError "invalid attribute 'cpspec', must be global"
+      -- Lookup the theorem
+      let env ← getEnv
+      let thDecl := env.constants.find! thName
+      let (fName, arg) ← MetaM.run' (getPSpecClassFunNameArg thDecl.type)
+      -- Sanity check: no variables appear in the argument
+      MetaM.run' do
+        let fvars ← getFVarIds arg
+        if ¬ fvars.isEmpty then throwError "The first argument ({arg}) contains variables"
+      -- We store two bindings:
+      -- - arg to theorem name
+      -- - reduced arg to theorem name
+      let rarg ← MetaM.run' (reduceAll arg)
+      trace[Progress] "Registering class spec theorem for ({fName}, {arg}) and ({fName}, {rarg})"
+      -- Update the entry if there is one, add an entry if there is none
+      let env :=
+        match (ext.getState (← getEnv)).find? fName with
+        | none =>
+          let m := HashMap.ofList [(arg, thName), (rarg, thName)]
+          ext.addEntry env (fName, m)
+        | some m =>
+          let m := m.insert arg thName
+          let m := m.insert rarg thName
+          ext.addEntry env (fName, m)
+      setEnv env
+      pure ()
+  }
+  registerBuiltinAttribute attrImpl
+  pure { attr := attrImpl, ext := ext }
+
+
+def PSpecAttr.find? (s : PSpecAttr) (name : Name) : MetaM (Option Name) := do
+  return (s.ext.getState (← getEnv)).find? name
+
+def PSpecClassAttr.find? (s : PSpecClassAttr) (className argName : Name) : MetaM (Option Name) := do
+  match (s.ext.getState (← getEnv)).find? className with
+  | none => return none
+  | some map => return map.find? argName
+
+def PSpecClassExprAttr.find? (s : PSpecClassExprAttr) (className : Name) (arg : Expr) : MetaM (Option Name) := do
+  match (s.ext.getState (← getEnv)).find? className with
+  | none => return none
+  | some map => return map.find? arg
+
+def PSpecAttr.getState (s : PSpecAttr) : MetaM (NameMap Name) := do
+  pure (s.ext.getState (← getEnv))
+
+def PSpecClassAttr.getState (s : PSpecClassAttr) : MetaM (NameMap (NameMap Name)) := do
+  pure (s.ext.getState (← getEnv))
+
+def PSpecClassExprAttr.getState (s : PSpecClassExprAttr) : MetaM (NameMap (HashMap Expr Name)) := do
+  pure (s.ext.getState (← getEnv))
+
+def showStoredPSpec : MetaM Unit := do
+  let st ← pspecAttr.getState
+  let s := st.toList.foldl (fun s (f, th) => f!"{s}\n{f} → {th}") f!""
+  IO.println s
+
+def showStoredPSpecClass : MetaM Unit := do
+  let st ← pspecClassAttr.getState
+  let s := st.toList.foldl (fun s (f, m) =>
+    let ms := m.toList.foldl (fun s (f, th) =>
+      f!"{s}\n  {f} → {th}") f!""
+    f!"{s}\n{f} → [{ms}]") f!""
+  IO.println s
+
+def showStoredPSpecExprClass : MetaM Unit := do
+  let st ← pspecClassExprAttr.getState
+  let s := st.toList.foldl (fun s (f, m) =>
+    let ms := m.toList.foldl (fun s (f, th) =>
+      f!"{s}\n  {f} → {th}") f!""
+    f!"{s}\n{f} → [{ms}]") f!""
+  IO.println s
+
+end Progress
diff --git a/backends/lean/Base/Progress/Progress.lean b/backends/lean/Base/Progress/Progress.lean
new file mode 100644
index 00000000..6a4729dc
--- /dev/null
+++ b/backends/lean/Base/Progress/Progress.lean
@@ -0,0 +1,377 @@
+import Lean
+import Base.Arith
+import Base.Progress.Base
+import Base.Primitives -- TODO: remove?
+
+namespace Progress
+
+open Lean Elab Term Meta Tactic
+open Utils
+
+inductive TheoremOrLocal where
+| Theorem (thName : Name)
+| Local (asm : LocalDecl)
+
+instance : ToMessageData TheoremOrLocal where
+  toMessageData := λ x => match x with | .Theorem thName => m!"{thName}" | .Local asm => m!"{asm.userName}"
+
+/- Type to propagate the errors of `progressWith`.
+   We need this because we use the exceptions to backtrack, when trying to
+   use the assumptions for instance. When there is actually an error we want
+   to propagate to the user, we return it. -/
+inductive ProgressError
+| Ok
+| Error (msg : MessageData)
+deriving Inhabited
+
+def progressWith (fExpr : Expr) (th : TheoremOrLocal)
+  (keep : Option Name) (ids : Array (Option Name)) (splitPost : Bool)
+  (asmTac : TacticM Unit) : TacticM ProgressError := do
+  /- Apply the theorem
+     We try to match the theorem with the goal
+     In order to do so, we introduce meta-variables for all the parameters
+     (i.e., quantified variables and assumpions), and unify those with the goal.
+     Remark: we do not introduce meta-variables for the quantified variables
+     which don't appear in the function arguments (we want to let them
+     quantified).
+     We also make sure that all the meta variables which appear in the
+     function arguments have been instantiated
+   -/
+  let env ← getEnv
+  let thTy ← do
+    match th with
+    | .Theorem thName =>
+      let thDecl := env.constants.find! thName
+      -- We have to introduce fresh meta-variables for the universes already
+      let ul : List (Name × Level) ←
+        thDecl.levelParams.mapM (λ x => do pure (x, ← mkFreshLevelMVar))
+      let ulMap : HashMap Name Level := HashMap.ofList ul
+      let thTy := thDecl.type.instantiateLevelParamsCore (λ x => ulMap.find! x)
+      pure thTy
+    | .Local asmDecl => pure asmDecl.type
+  trace[Progress] "Looked up theorem/assumption type: {thTy}"
+  -- TODO: the tactic fails if we uncomment withNewMCtxDepth
+  -- withNewMCtxDepth do
+  let (mvars, binders, thExBody) ← forallMetaTelescope thTy
+  trace[Progress] "After stripping foralls: {thExBody}"
+  -- Introduce the existentially quantified variables and the post-condition
+  -- in the context
+  let thBody ←
+    existsTelescope thExBody.consumeMData fun _evars thBody => do
+    trace[Progress] "After stripping existentials: {thBody}"
+    let (thBody, _) ← optSplitConj thBody
+    trace[Progress] "After splitting the conjunction: {thBody}"
+    let (thBody, _) ← destEq thBody
+    trace[Progress] "After splitting equality: {thBody}"
+    -- There shouldn't be any existential variables in thBody
+    pure thBody.consumeMData
+  -- Match the body with the target
+  trace[Progress] "Matching:\n- body:\n{thBody}\n- target:\n{fExpr}"
+  let ok ← isDefEq thBody fExpr
+  if ¬ ok then throwError "Could not unify the theorem with the target:\n- theorem: {thBody}\n- target: {fExpr}"
+  let mgoal ← Tactic.getMainGoal
+  postprocessAppMVars `progress mgoal mvars binders true true
+  Term.synthesizeSyntheticMVarsNoPostponing
+  let thBody ← instantiateMVars thBody
+  trace[Progress] "thBody (after instantiation): {thBody}"
+  -- Add the instantiated theorem to the assumptions (we apply it on the metavariables).
+  let th ← do
+    match th with
+    | .Theorem thName => mkAppOptM thName (mvars.map some)
+    | .Local decl => mkAppOptM' (mkFVar decl.fvarId) (mvars.map some)
+  let asmName ← do match keep with | none => mkFreshAnonPropUserName | some n => do pure n
+  let thTy ← inferType th
+  let thAsm ← Utils.addDeclTac asmName th thTy (asLet := false)
+  withMainContext do -- The context changed - TODO: remove once addDeclTac is updated
+  let ngoal ← getMainGoal
+  trace[Progress] "current goal: {ngoal}"
+  trace[Progress] "current goal: {← ngoal.isAssigned}"
+  -- The assumption should be of the shape:
+  -- `∃ x1 ... xn, f args = ... ∧ ...`
+  -- We introduce the existentially quantified variables and split the top-most
+  -- conjunction if there is one. We use the provided `ids` list to name the
+  -- introduced variables.
+  let res ← splitAllExistsTac thAsm ids.toList fun h ids => do
+    -- Split the conjunctions.
+    -- For the conjunctions, we split according once to separate the equality `f ... = .ret ...`
+    -- from the postcondition, if there is, then continue to split the postcondition if there
+    -- are remaining ids.
+    let splitEqAndPost (k : Expr → Option Expr → List (Option Name) → TacticM ProgressError) : TacticM ProgressError := do
+      if ← isConj (← inferType h) then do
+        let hName := (← h.fvarId!.getDecl).userName
+        let (optIds, ids) ← do
+          match ids with
+          | [] => do pure (some (hName, ← mkFreshAnonPropUserName), [])
+          | none :: ids => do pure (some (hName, ← mkFreshAnonPropUserName), ids)
+          | some id :: ids => do pure (some (hName, id), ids)
+        splitConjTac h optIds (fun hEq hPost => k hEq (some hPost) ids)
+      else k h none ids
+    -- Simplify the target by using the equality and some monad simplifications,
+    -- then continue splitting the post-condition
+    splitEqAndPost fun hEq hPost ids => do
+    trace[Progress] "eq and post:\n{hEq} : {← inferType hEq}\n{hPost}"
+    simpAt [] [``Primitives.bind_tc_ret, ``Primitives.bind_tc_fail, ``Primitives.bind_tc_div]
+           [hEq.fvarId!] (.targets #[] true)
+    -- Clear the equality, unless the user requests not to do so
+    let mgoal ← do
+      if keep.isSome then getMainGoal
+      else do
+        let mgoal ← getMainGoal
+        mgoal.tryClearMany #[hEq.fvarId!]
+    setGoals (mgoal :: (← getUnsolvedGoals))
+    trace[Progress] "Goal after splitting eq and post and simplifying the target: {mgoal}"
+    -- Continue splitting following the post following the user's instructions
+    match hPost with
+    | none =>
+      -- Sanity check
+      if ¬ ids.isEmpty then
+        return (.Error m!"Too many ids provided ({ids}): there is no postcondition to split")
+      else return .Ok
+    | some hPost => do
+      let rec splitPostWithIds (prevId : Name) (hPost : Expr) (ids0 : List (Option Name)) : TacticM ProgressError := do
+        match ids0 with
+        | [] =>
+          /- We used all the user provided ids.
+             Split the remaining conjunctions by using fresh ids if the user
+             instructed to fully split the post-condition, otherwise stop -/
+          if splitPost then
+            splitFullConjTac true hPost (λ _ => pure .Ok)
+          else pure .Ok
+        | nid :: ids => do
+          trace[Progress] "Splitting post: {← inferType hPost}"
+          -- Split
+          let nid ← do
+            match nid with
+            | none => mkFreshAnonPropUserName
+            | some nid => pure nid
+          trace[Progress] "\n- prevId: {prevId}\n- nid: {nid}\n- remaining ids: {ids}"
+          if ← isConj (← inferType hPost) then
+            splitConjTac hPost (some (prevId, nid)) (λ _ nhPost => splitPostWithIds nid nhPost ids)
+          else return (.Error m!"Too many ids provided ({ids0}) not enough conjuncts to split in the postcondition")
+      let curPostId := (← hPost.fvarId!.getDecl).userName
+      splitPostWithIds curPostId hPost ids
+  match res with
+  | .Error _ => return res -- Can we get there? We're using "return"
+  | .Ok =>
+    -- Update the set of goals
+    let curGoals ← getUnsolvedGoals
+    let newGoals := mvars.map Expr.mvarId!
+    let newGoals ← newGoals.filterM fun mvar => not <$> mvar.isAssigned
+    trace[Progress] "new goals: {newGoals}"
+    setGoals newGoals.toList
+    allGoals asmTac
+    let newGoals ← getUnsolvedGoals
+    setGoals (newGoals ++ curGoals)
+    trace[Progress] "progress: replaced the goals"
+    --
+    pure .Ok
+
+-- Small utility: if `args` is not empty, return the name of the app in the first
+-- arg, if it is a const.
+def getFirstArgAppName (args : Array Expr) : MetaM (Option Name) := do
+  if args.size = 0 then pure none
+  else
+    (args.get! 0).withApp fun f _ => do
+    if f.isConst then pure (some f.constName)
+    else pure none
+
+def getFirstArg (args : Array Expr) : Option Expr := do
+  if args.size = 0 then none
+  else some (args.get! 0)
+
+/- Helper: try to lookup a theorem and apply it, or continue with another tactic
+   if it fails -/
+def tryLookupApply (keep : Option Name) (ids : Array (Option Name)) (splitPost : Bool)
+  (asmTac : TacticM Unit) (fExpr : Expr)
+  (kind : String) (th : Option TheoremOrLocal) (x : TacticM Unit) : TacticM Unit := do
+  let res ← do
+    match th with
+    | none =>
+      trace[Progress] "Could not find a {kind}"
+      pure none
+    | some th => do
+      trace[Progress] "Lookuped up {kind}: {th}"
+      -- Apply the theorem
+      let res ← do
+        try
+          let res ← progressWith fExpr th keep ids splitPost asmTac
+          pure (some res)
+        catch _ => none
+  match res with
+  | some .Ok => return ()
+  | some (.Error msg) => throwError msg
+  | none => x
+
+-- The array of ids are identifiers to use when introducing fresh variables
+def progressAsmsOrLookupTheorem (keep : Option Name) (withTh : Option TheoremOrLocal)
+  (ids : Array (Option Name)) (splitPost : Bool) (asmTac : TacticM Unit) : TacticM Unit := do
+  withMainContext do
+  -- Retrieve the goal
+  let mgoal ← Tactic.getMainGoal
+  let goalTy ← mgoal.getType
+  trace[Progress] "goal: {goalTy}"
+  -- Dive into the goal to lookup the theorem
+  let (fExpr, fName, args) ← do
+    withPSpec goalTy fun desc =>
+    -- TODO: check that no quantified variables in the arguments
+    pure (desc.fExpr, desc.fName, desc.args)
+  trace[Progress] "Function: {fName}"
+  -- If the user provided a theorem/assumption: use it.
+  -- Otherwise, lookup one.
+  match withTh with
+  | some th => do
+    match ← progressWith fExpr th keep ids splitPost asmTac with
+    | .Ok => return ()
+    | .Error msg => throwError msg
+  | none =>
+    -- Try all the assumptions one by one and if it fails try to lookup a theorem.
+    let ctx ← Lean.MonadLCtx.getLCtx
+    let decls ← ctx.getDecls
+    for decl in decls.reverse do
+      trace[Progress] "Trying assumption: {decl.userName} : {decl.type}"
+      let res ← do try progressWith fExpr (.Local decl) keep ids splitPost asmTac catch _ => continue
+      match res with
+      | .Ok => return ()
+      | .Error msg => throwError msg
+    -- It failed: try to lookup a theorem
+    -- TODO: use a list of theorems, and try them one by one?
+    trace[Progress] "No assumption succeeded: trying to lookup a theorem"
+    let pspec ← do
+      let thName ← pspecAttr.find? fName
+      pure (thName.map fun th => .Theorem th)
+    tryLookupApply keep ids splitPost asmTac fExpr "pspec theorem" pspec do
+    -- It failed: try to lookup a *class* expr spec theorem (those are more
+    -- specific than class spec theorems)
+    let pspecClassExpr ← do
+      match getFirstArg args with
+      | none => pure none
+      | some arg => do
+        let thName ← pspecClassExprAttr.find? fName arg
+        pure (thName.map fun th => .Theorem th)
+    tryLookupApply keep ids splitPost asmTac fExpr "pspec class expr theorem" pspecClassExpr do
+    -- It failed: try to lookup a *class* spec theorem
+    let pspecClass ← do
+      match ← getFirstArgAppName args with
+      | none => pure none
+      | some argName => do
+        let thName ← pspecClassAttr.find? fName argName
+        pure (thName.map fun th => .Theorem th)
+    tryLookupApply keep ids splitPost asmTac fExpr "pspec class theorem" pspecClass do
+    -- Try a recursive call - we try the assumptions of kind "auxDecl"
+    let ctx ← Lean.MonadLCtx.getLCtx
+    let decls ← ctx.getAllDecls
+    let decls := decls.filter (λ decl => match decl.kind with
+      | .default | .implDetail => false | .auxDecl => true)
+    for decl in decls.reverse do
+      trace[Progress] "Trying recursive assumption: {decl.userName} : {decl.type}"
+      let res ← do try progressWith fExpr (.Local decl) keep ids splitPost asmTac catch _ => continue
+      match res with
+      | .Ok => return ()
+      | .Error msg => throwError msg
+    -- Nothing worked: failed
+    throwError "Progress failed"
+
+syntax progressArgs := ("keep" (ident <|> "_"))? ("with" ident)? ("as" " ⟨ " (ident <|> "_"),* " .."? " ⟩")?
+
+def evalProgress (args : TSyntax `Progress.progressArgs) : TacticM Unit := do
+  let args := args.raw
+  -- Process the arguments to retrieve the identifiers to use
+  trace[Progress] "Progress arguments: {args}"
+  let (keepArg, withArg, asArgs) ←
+    match args.getArgs.toList with
+    | [keepArg, withArg, asArgs] => do pure (keepArg, withArg, asArgs)
+    | _ => throwError "Unexpected: invalid arguments"
+  let keep : Option Name ← do
+    trace[Progress] "Keep arg: {keepArg}"
+    let args := keepArg.getArgs
+    if args.size > 0 then do
+      trace[Progress] "Keep args: {args}"
+      let arg := args.get! 1
+      trace[Progress] "Keep arg: {arg}"
+      if arg.isIdent then pure (some arg.getId)
+      else do pure (some (← mkFreshAnonPropUserName))
+    else do pure none
+  trace[Progress] "Keep: {keep}"
+  let withArg ← do
+    let withArg := withArg.getArgs
+    if withArg.size > 0 then
+      let id := withArg.get! 1
+      trace[Progress] "With arg: {id}"
+      -- Attempt to lookup a local declaration
+      match (← getLCtx).findFromUserName? id.getId with
+      | some decl => do
+        trace[Progress] "With arg: local decl"
+        pure (some (.Local decl))
+      | none => do
+        -- Not a local declaration: should be a theorem
+        trace[Progress] "With arg: theorem"
+        addCompletionInfo <| CompletionInfo.id id id.getId (danglingDot := false) {} none
+        let cs ← resolveGlobalConstWithInfos id
+        match cs with
+        | [] => throwError "Could not find theorem {id}"
+        | id :: _ =>
+          pure (some (.Theorem id))
+    else pure none
+  let ids :=
+    let args := asArgs.getArgs
+    let args := (args.get! 2).getSepArgs
+    args.map (λ s => if s.isIdent then some s.getId else none)
+  trace[Progress] "User-provided ids: {ids}"
+  let splitPost : Bool :=
+    let args := asArgs.getArgs
+    (args.get! 3).getArgs.size > 0
+  trace[Progress] "Split post: {splitPost}"
+  /- For scalarTac we have a fast track: if the goal is not a linear
+     arithmetic goal, we skip (note that otherwise, scalarTac would try
+     to prove a contradiction) -/
+  let scalarTac : TacticM Unit := do
+    if ← Arith.goalIsLinearInt then
+      -- Also: we don't try to split the goal if it is a conjunction
+      -- (it shouldn't be)
+      Arith.scalarTac false
+    else
+      throwError "Not a linear arithmetic goal"
+  progressAsmsOrLookupTheorem keep withArg ids splitPost (
+    withMainContext do
+    trace[Progress] "trying to solve assumption: {← getMainGoal}"
+    firstTac [assumptionTac, scalarTac])
+  trace[Diverge] "Progress done"
+
+elab "progress" args:progressArgs : tactic =>
+  evalProgress args
+
+namespace Test
+  open Primitives Result
+
+  set_option trace.Progress true
+  set_option pp.rawOnError true
+
+  #eval showStoredPSpec
+  #eval showStoredPSpecClass
+
+  example {ty} {x y : Scalar ty}
+    (hmin : Scalar.min ty ≤ x.val + y.val)
+    (hmax : x.val + y.val ≤ Scalar.max ty) :
+    ∃ z, x + y = ret z ∧ z.val = x.val + y.val := by
+    progress keep _ as ⟨ z, h1 .. ⟩
+    simp [*, h1]
+
+  example {ty} {x y : Scalar ty}
+    (hmin : Scalar.min ty ≤ x.val + y.val)
+    (hmax : x.val + y.val ≤ Scalar.max ty) :
+    ∃ z, x + y = ret z ∧ z.val = x.val + y.val := by
+    progress keep h with Scalar.add_spec as ⟨ z ⟩
+    simp [*, h]
+
+  /- Checking that universe instantiation works: the original spec uses
+     `α : Type u` where u is quantified, while here we use `α : Type 0` -/
+  example {α : Type} (v: Vec α) (i: Usize) (x : α)
+    (hbounds : i.val < v.length) :
+    ∃ nv, v.index_mut_back α i x = ret nv ∧
+    nv.val = v.val.update i.val x := by
+    progress
+    simp [*]
+
+end Test
+
+end Progress
diff --git a/backends/lean/Base/Utils.lean b/backends/lean/Base/Utils.lean
new file mode 100644
index 00000000..1f8f1455
--- /dev/null
+++ b/backends/lean/Base/Utils.lean
@@ -0,0 +1,640 @@
+import Lean
+import Mathlib.Tactic.Core
+import Mathlib.Tactic.LeftRight
+import Base.UtilsBase
+
+/-
+Mathlib tactics:
+- rcases: https://leanprover-community.github.io/mathlib_docs/tactics.html#rcases
+- split_ifs: https://leanprover-community.github.io/mathlib_docs/tactics.html#split_ifs
+- norm_num: https://leanprover-community.github.io/mathlib_docs/tactics.html#norm_num
+- should we use linarith or omega?
+- hint: https://leanprover-community.github.io/mathlib_docs/tactics.html#hint
+- classical: https://leanprover-community.github.io/mathlib_docs/tactics.html#classical
+-/
+
+/-
+TODO:
+- we want an easier to use cases:
+  - keeps in the goal an equation of the shape: `t = case`
+  - if called on Prop terms, uses Classical.em
+  Actually, the cases from mathlib seems already quite powerful
+  (https://leanprover-community.github.io/mathlib_docs/tactics.html#cases)
+  For instance: cases h : e
+  Also: **casesm**
+- better split tactic
+- we need conversions to operate on the head of applications.
+  Actually, something like this works:
+  ```
+  conv at Hl =>
+    apply congr_fun
+    simp [fix_fuel_P]
+  ```
+  Maybe we need a rpt ... ; focus?
+- simplifier/rewriter have a strange behavior sometimes
+-/
+
+
+namespace List
+
+  -- TODO: I could not find this function??
+  @[simp] def flatten {a : Type u} : List (List a) → List a
+  | [] => []
+  | x :: ls => x ++ flatten ls
+
+end List
+
+-- TODO: move?
+@[simp]
+theorem neq_imp {α : Type u} {x y : α} (h : ¬ x = y) : ¬ y = x := by intro; simp_all
+
+namespace Lean
+
+namespace LocalContext
+
+  open Lean Lean.Elab Command Term Lean.Meta
+
+  -- Small utility: return the list of declarations in the context, from
+  -- the last to the first.
+  def getAllDecls (lctx : Lean.LocalContext) : MetaM (List Lean.LocalDecl) :=
+    lctx.foldrM (fun d ls => do let d ← instantiateLocalDeclMVars d; pure (d :: ls)) []
+
+  -- Return the list of declarations in the context, but filter the
+  -- declarations which are considered as implementation details
+  def getDecls (lctx : Lean.LocalContext) : MetaM (List Lean.LocalDecl) := do
+    let ls ← lctx.getAllDecls
+    pure (ls.filter (fun d => not d.isImplementationDetail))
+
+end LocalContext
+
+end Lean
+
+namespace Utils
+
+open Lean Elab Term Meta Tactic
+
+-- Useful helper to explore definitions and figure out the variant
+-- of their sub-expressions.
+def explore_term (incr : String) (e : Expr) : MetaM Unit :=
+  match e with
+  | .bvar _ => do logInfo m!"{incr}bvar: {e}"; return ()
+  | .fvar _ => do logInfo m!"{incr}fvar: {e}"; return ()
+  | .mvar _ => do logInfo m!"{incr}mvar: {e}"; return ()
+  | .sort _ => do logInfo m!"{incr}sort: {e}"; return ()
+  | .const _ _ => do logInfo m!"{incr}const: {e}"; return ()
+  | .app fn arg => do
+    logInfo m!"{incr}app: {e}"
+    explore_term (incr ++ "  ") fn
+    explore_term (incr ++ "  ") arg
+  | .lam _bName bTy body _binfo => do
+    logInfo m!"{incr}lam: {e}"
+    explore_term (incr ++ "  ") bTy
+    explore_term (incr ++ "  ") body
+  | .forallE _bName bTy body _bInfo => do
+    logInfo m!"{incr}forallE: {e}"
+    explore_term (incr ++ "  ") bTy
+    explore_term (incr ++ "  ") body
+  | .letE _dName ty val body _nonDep => do
+    logInfo m!"{incr}letE: {e}"
+    explore_term (incr ++ "  ") ty
+    explore_term (incr ++ "  ") val
+    explore_term (incr ++ "  ") body
+  | .lit _ => do logInfo m!"{incr}lit: {e}"; return ()
+  | .mdata _ e => do
+    logInfo m!"{incr}mdata: {e}"
+    explore_term (incr ++ "  ") e
+  | .proj _ _ struct => do
+    logInfo m!"{incr}proj: {e}"
+    explore_term (incr ++ "  ") struct
+
+def explore_decl (n : Name) : TermElabM Unit := do
+  logInfo m!"Name: {n}"
+  let env ← getEnv
+  let decl := env.constants.find! n
+  match decl with
+  | .defnInfo val =>
+     logInfo m!"About to explore defn: {decl.name}"
+     logInfo m!"# Type:"
+     explore_term "" val.type
+     logInfo m!"# Value:"
+     explore_term "" val.value
+  | .axiomInfo _  => throwError m!"axiom: {n}"
+  | .thmInfo _    => throwError m!"thm: {n}"
+  | .opaqueInfo _ => throwError m!"opaque: {n}"
+  | .quotInfo _   => throwError m!"quot: {n}"
+  | .inductInfo _ => throwError m!"induct: {n}"
+  | .ctorInfo _   => throwError m!"ctor: {n}"
+  | .recInfo _    => throwError m!"rec: {n}"
+
+syntax (name := printDecl) "print_decl " ident : command
+
+open Lean.Elab.Command
+
+@[command_elab printDecl] def elabPrintDecl : CommandElab := fun stx => do
+  liftTermElabM do
+    let id := stx[1]
+    addCompletionInfo <| CompletionInfo.id id id.getId (danglingDot := false) {} none
+    let cs ← resolveGlobalConstWithInfos id
+    explore_decl cs[0]!
+
+private def test1 : Nat := 0
+private def test2 (x : Nat) : Nat := x
+print_decl test1
+print_decl test2
+
+def printDecls (decls : List LocalDecl) : MetaM Unit := do
+  let decls ← decls.foldrM (λ decl msg => do
+    pure (m!"\n{decl.toExpr} : {← inferType decl.toExpr}" ++ msg)) m!""
+  logInfo m!"# Ctx decls:{decls}"
+
+-- Small utility: print all the declarations in the context (including the "implementation details")
+elab "print_all_ctx_decls" : tactic => do
+  let ctx ← Lean.MonadLCtx.getLCtx
+  let decls ← ctx.getAllDecls
+  printDecls decls
+
+-- Small utility: print all declarations in the context
+elab "print_ctx_decls" : tactic => do
+  let ctx ← Lean.MonadLCtx.getLCtx
+  let decls ← ctx.getDecls
+  printDecls decls
+
+-- A map visitor function for expressions (adapted from `AbstractNestedProofs.visit`)
+-- The continuation takes as parameters:
+-- - the current depth of the expression (useful for printing/debugging)
+-- - the expression to explore
+partial def mapVisit (k : Nat → Expr → MetaM Expr) (e : Expr) : MetaM Expr := do
+  let mapVisitBinders (xs : Array Expr) (k2 : MetaM Expr) : MetaM Expr := do
+    let localInstances ← getLocalInstances
+    let mut lctx ← getLCtx
+    for x in xs do
+      let xFVarId := x.fvarId!
+      let localDecl ← xFVarId.getDecl
+      let type      ← mapVisit k localDecl.type
+      let localDecl := localDecl.setType type
+      let localDecl ← match localDecl.value? with
+         | some value => let value ← mapVisit k value; pure <| localDecl.setValue value
+         | none       => pure localDecl
+      lctx :=lctx.modifyLocalDecl xFVarId fun _ => localDecl
+    withLCtx lctx localInstances k2
+  -- TODO: use a cache? (Lean.checkCache)
+  let rec visit (i : Nat) (e : Expr) : MetaM Expr := do
+    -- Explore
+    let e ← k i e
+    match e with
+    | .bvar _
+    | .fvar _
+    | .mvar _
+    | .sort _
+    | .lit _
+    | .const _ _ => pure e
+    | .app .. => do e.withApp fun f args => return mkAppN f (← args.mapM (visit (i + 1)))
+    | .lam .. =>
+      lambdaLetTelescope e fun xs b =>
+        mapVisitBinders xs do mkLambdaFVars xs (← visit (i + 1) b) (usedLetOnly := false)
+    | .forallE .. => do
+      forallTelescope e fun xs b => mapVisitBinders xs do mkForallFVars xs (← visit (i + 1) b)
+    | .letE .. => do
+      lambdaLetTelescope e fun xs b => mapVisitBinders xs do
+        mkLambdaFVars xs (← visit (i + 1) b) (usedLetOnly := false)
+    | .mdata _ b => return e.updateMData! (← visit (i + 1) b)
+    | .proj _ _ b => return e.updateProj! (← visit (i + 1) b)
+  visit 0 e
+
+-- Generate a fresh user name for an anonymous proposition to introduce in the
+-- assumptions
+def mkFreshAnonPropUserName := mkFreshUserName `_
+
+section Methods
+  variable [MonadLiftT MetaM m] [MonadControlT MetaM m] [Monad m] [MonadError m]
+  variable {a : Type}
+
+  /- Like `lambdaTelescopeN` but only destructs a fixed number of lambdas -/
+  def lambdaTelescopeN (e : Expr) (n : Nat) (k : Array Expr → Expr → m a) : m a :=
+    lambdaTelescope e fun xs body => do
+    if xs.size < n then throwError "lambdaTelescopeN: not enough lambdas"
+    let xs := xs.extract 0 n
+    let ys := xs.extract n xs.size
+    let body ← liftMetaM (mkLambdaFVars ys body)
+    k xs body
+
+  /- Like `lambdaTelescope`, but only destructs one lambda
+     TODO: is there an equivalent of this function somewhere in the
+     standard library? -/
+  def lambdaOne (e : Expr) (k : Expr → Expr → m a) : m a :=
+    lambdaTelescopeN e 1 λ xs b => k (xs.get! 0) b
+
+  def isExists (e : Expr) : Bool := e.getAppFn.isConstOf ``Exists ∧ e.getAppNumArgs = 2
+
+  -- Remark: Lean doesn't find the inhabited and nonempty instances if we don'
+  -- put them explicitely in the signature
+  partial def existsTelescopeProcess [Inhabited (m a)] [Nonempty (m a)]
+    (fvars : Array Expr) (e : Expr) (k : Array Expr → Expr → m a) : m a := do
+    -- Attempt to deconstruct an existential
+    if isExists e then do
+      let p := e.appArg!
+      lambdaOne p fun x ne =>
+      existsTelescopeProcess (fvars.push x) ne k
+    else
+      -- No existential: call the continuation
+      k fvars e
+
+  def existsTelescope [Inhabited (m a)] [Nonempty (m a)] (e : Expr) (k : Array Expr → Expr → m a) : m a := do
+    existsTelescopeProcess #[] e k
+
+end Methods
+
+-- TODO: this should take a continuation
+def addDeclTac (name : Name) (val : Expr) (type : Expr) (asLet : Bool) : TacticM Expr :=
+  -- I don't think we need that
+  withMainContext do
+  -- Insert the new declaration
+  let withDecl := if asLet then withLetDecl name type val else withLocalDeclD name type
+  withDecl fun nval => do
+    -- For debugging
+    let lctx ← Lean.MonadLCtx.getLCtx
+    let fid := nval.fvarId!
+    let decl := lctx.get! fid
+    trace[Arith] "  new decl: \"{decl.userName}\" ({nval}) : {decl.type} := {decl.value}"
+    --
+    -- Tranform the main goal `?m0` to `let x = nval in ?m1`
+    let mvarId ← getMainGoal
+    let newMVar ← mkFreshExprSyntheticOpaqueMVar (← mvarId.getType)
+    let newVal ← mkLetFVars #[nval] newMVar
+    -- There are two cases:
+    -- - asLet is true: newVal is `let $name := $val in $newMVar`
+    -- - asLet is false: ewVal is `λ $name => $newMVar`
+    --   We need to apply it to `val`
+    let newVal := if asLet then newVal else mkAppN newVal #[val]
+    -- Assign the main goal and update the current goal
+    mvarId.assign newVal
+    let goals ← getUnsolvedGoals
+    setGoals (newMVar.mvarId! :: goals)
+    -- Return the new value - note: we are in the *new* context, created
+    -- after the declaration was added, so it will persist
+    pure nval
+
+def addDeclTacSyntax (name : Name) (val : Syntax) (asLet : Bool) : TacticM Unit :=
+  -- I don't think we need that
+  withMainContext do
+  --
+  let val ← Term.elabTerm val .none
+  let type ← inferType val
+  -- In some situations, the type will be left as a metavariable (for instance,
+  -- if the term is `3`, Lean has the choice between `Nat` and `Int` and will
+  -- not choose): we force the instantiation of the meta-variable
+  synthesizeSyntheticMVarsUsingDefault
+  --
+  let _ ← addDeclTac name val type asLet
+
+elab "custom_let " n:ident " := " v:term : tactic => do
+  addDeclTacSyntax n.getId v (asLet := true)
+
+elab "custom_have " n:ident " := " v:term : tactic =>
+  addDeclTacSyntax n.getId v (asLet := false)
+
+example : Nat := by
+  custom_let x := 4
+  custom_have y := 4
+  apply y
+
+example (x : Bool) : Nat := by
+  cases x <;> custom_let x := 3 <;> apply x
+
+-- Repeatedly apply a tactic
+partial def repeatTac (tac : TacticM Unit) : TacticM Unit := do
+  try
+    tac
+    allGoals (focus (repeatTac tac))
+  -- TODO: does this restore the state?
+  catch _ => pure ()
+
+def firstTac (tacl : List (TacticM Unit)) : TacticM Unit := do
+  match tacl with
+  | [] => pure ()
+  | tac :: tacl =>
+    -- Should use try ... catch or Lean.observing?
+    -- Generally speaking we should use Lean.observing? to restore the state,
+    -- but with tactics the try ... catch variant seems to work
+    try do
+      tac
+      -- Check that there are no remaining goals
+      let gl ← Tactic.getUnsolvedGoals
+      if ¬ gl.isEmpty then throwError "tactic failed"
+    catch _ => firstTac tacl
+/-    let res ← Lean.observing? do
+      tac
+      -- Check that there are no remaining goals
+      let gl ← Tactic.getUnsolvedGoals
+      if ¬ gl.isEmpty then throwError "tactic failed"
+    match res with
+    | some _ => pure ()
+    | none => firstTac tacl -/
+
+-- Taken from Lean.Elab.evalAssumption
+def assumptionTac : TacticM Unit :=
+  liftMetaTactic fun mvarId => do mvarId.assumption; pure []
+
+def isConj (e : Expr) : MetaM Bool :=
+  e.consumeMData.withApp fun f args => pure (f.isConstOf ``And ∧ args.size = 2)
+
+-- Return the first conjunct if the expression is a conjunction, or the
+-- expression itself otherwise. Also return the second conjunct if it is a
+-- conjunction.
+def optSplitConj (e : Expr) : MetaM (Expr × Option Expr) := do
+  e.consumeMData.withApp fun f args =>
+  if f.isConstOf ``And ∧ args.size = 2 then pure (args.get! 0, some (args.get! 1))
+  else pure (e, none)
+
+-- Split the goal if it is a conjunction
+def splitConjTarget : TacticM Unit := do
+  withMainContext do
+  let g ← getMainTarget
+  trace[Utils] "splitConjTarget: goal: {g}"
+  -- The tactic was initially implemened with `_root_.Lean.MVarId.apply`
+  -- but it tended to mess the goal by unfolding terms, even when it failed
+  let (l, r) ← optSplitConj g
+  match r with
+  | none => do throwError "The goal is not a conjunction"
+  | some r => do
+    let lmvar ← mkFreshExprSyntheticOpaqueMVar l
+    let rmvar ← mkFreshExprSyntheticOpaqueMVar r
+    let and_intro ← mkAppM ``And.intro #[lmvar, rmvar]
+    let g ← getMainGoal
+    g.assign and_intro
+    let goals ← getUnsolvedGoals
+    setGoals (lmvar.mvarId! :: rmvar.mvarId! :: goals)
+
+-- Destruct an equaliy and return the two sides
+def destEq (e : Expr) : MetaM (Expr × Expr) := do
+  e.withApp fun f args =>
+  if f.isConstOf ``Eq ∧ args.size = 3 then pure (args.get! 1, args.get! 2)
+  else throwError "Not an equality: {e}"
+
+-- Return the set of FVarIds in the expression
+partial def getFVarIds (e : Expr) (hs : HashSet FVarId := HashSet.empty) : MetaM (HashSet FVarId) := do
+  e.withApp fun body args => do
+  let hs := if body.isFVar then hs.insert body.fvarId! else hs
+  args.foldlM (fun hs arg => getFVarIds arg hs) hs
+
+-- Tactic to split on a disjunction.
+-- The expression `h` should be an fvar.
+-- TODO: there must be simpler. Use use _root_.Lean.MVarId.cases for instance
+def splitDisjTac (h : Expr) (kleft kright : TacticM Unit) : TacticM Unit := do
+  trace[Arith] "assumption on which to split: {h}"
+  -- Retrieve the main goal
+  withMainContext do
+  let goalType ← getMainTarget
+  let hDecl := (← getLCtx).get! h.fvarId!
+  let hName := hDecl.userName
+  -- Case disjunction
+  let hTy ← inferType h
+  hTy.withApp fun f xs => do
+  trace[Arith] "as app: {f} {xs}"
+  -- Sanity check
+  if ¬ (f.isConstOf ``Or ∧ xs.size = 2) then throwError "Invalid argument to splitDisjTac"
+  let a := xs.get! 0
+  let b := xs.get! 1
+  -- Introduce the new goals
+  -- Returns:
+  -- - the match branch
+  -- - a fresh new mvar id
+  let mkGoal (hTy : Expr) (nGoalName : String) : MetaM (Expr × MVarId) := do
+    -- Introduce a variable for the assumption (`a` or `b`). Note that we reuse
+    -- the name of the assumption we split.
+    withLocalDeclD hName hTy fun var => do
+    -- The new goal
+    let mgoal ← mkFreshExprSyntheticOpaqueMVar goalType (tag := Name.mkSimple nGoalName)
+    -- Clear the assumption that we split
+    let mgoal ← mgoal.mvarId!.tryClearMany #[h.fvarId!]
+    -- The branch expression
+    let branch ← mkLambdaFVars #[var] (mkMVar mgoal)
+    pure (branch, mgoal)
+  let (inl, mleft) ← mkGoal a "left"
+  let (inr, mright) ← mkGoal b "right"
+  trace[Arith] "left: {inl}: {mleft}"
+  trace[Arith] "right: {inr}: {mright}"
+  -- Create the match expression
+  withLocalDeclD (← mkFreshAnonPropUserName) hTy fun hVar => do
+  let motive ← mkLambdaFVars #[hVar] goalType
+  let casesExpr ← mkAppOptM ``Or.casesOn #[a, b, motive, h, inl, inr]
+  let mgoal ← getMainGoal
+  trace[Arith] "goals: {← getUnsolvedGoals}"
+  trace[Arith] "main goal: {mgoal}"
+  mgoal.assign casesExpr
+  let goals ← getUnsolvedGoals
+  -- Focus on the left
+  setGoals [mleft]
+  withMainContext kleft
+  let leftGoals ← getUnsolvedGoals
+  -- Focus on the right
+  setGoals [mright]
+  withMainContext kright
+  let rightGoals ← getUnsolvedGoals
+  -- Put all the goals back
+  setGoals (leftGoals ++ rightGoals ++ goals)
+  trace[Arith] "new goals: {← getUnsolvedGoals}"
+
+elab "split_disj " n:ident : tactic => do
+  withMainContext do
+  let decl ← Lean.Meta.getLocalDeclFromUserName n.getId
+  let fvar := mkFVar decl.fvarId
+  splitDisjTac fvar (fun _ => pure ()) (fun _ => pure ())
+
+example (x y : Int) (h0 : x ≤ y ∨ x ≥ y) : x ≤ y ∨ x ≥ y := by
+  split_disj h0
+  . left; assumption
+  . right; assumption
+
+
+-- Tactic to split on an exists.
+-- `h` must be an FVar
+def splitExistsTac (h : Expr) (optId : Option Name) (k : Expr → Expr → TacticM α) : TacticM α := do
+  withMainContext do
+  let goal ←  getMainGoal
+  let hTy ← inferType h
+  if isExists hTy then do
+    -- Try to use the user-provided names
+    let altVarNames ← do
+      let hDecl ← h.fvarId!.getDecl
+      let id ← do
+        match optId with
+        | none => mkFreshUserName `x
+        | some id => pure id
+      pure #[{ varNames := [id, hDecl.userName] }]
+    let newGoals ← goal.cases h.fvarId! altVarNames
+    -- There should be exactly one goal
+    match newGoals.toList with
+    | [ newGoal ] =>
+      -- Set the new goal
+      let goals ← getUnsolvedGoals
+      setGoals (newGoal.mvarId :: goals)
+      -- There should be exactly two fields
+      let fields := newGoal.fields
+      withMainContext do
+      k (fields.get! 0) (fields.get! 1)
+    | _ =>
+      throwError "Unreachable"
+  else
+    throwError "Not a conjunction"
+
+-- TODO: move
+def listTryPopHead (ls : List α) : Option α × List α :=
+  match ls with
+  | [] => (none, ls)
+  | hd :: tl => (some hd, tl)
+
+/- Destruct all the existentials appearing in `h`, and introduce them as variables
+   in the context.
+
+   If `ids` is not empty, we use it to name the introduced variables. We
+   transmit the stripped expression and the remaining ids to the continuation.
+ -/
+partial def splitAllExistsTac [Inhabited α] (h : Expr) (ids : List (Option Name)) (k : Expr → List (Option Name) → TacticM α) : TacticM α := do
+  try
+    let (optId, ids) :=
+      match ids with
+      | [] => (none, [])
+      | x :: ids => (x, ids)
+    splitExistsTac h optId (fun _ body => splitAllExistsTac body ids k)
+  catch _ => k h ids
+
+-- Tactic to split on a conjunction.
+def splitConjTac (h : Expr) (optIds : Option (Name × Name)) (k : Expr → Expr → TacticM α)  : TacticM α := do
+  withMainContext do
+  let goal ←  getMainGoal
+  let hTy ← inferType h
+  if ← isConj hTy then do
+    -- Try to use the user-provided names
+    let altVarNames ←
+      match optIds with
+      | none => do
+        let id0 ← mkFreshAnonPropUserName
+        let id1 ← mkFreshAnonPropUserName
+        pure #[{ varNames := [id0, id1] }]
+      | some (id0, id1) => do
+        pure #[{ varNames := [id0, id1] }]
+    let newGoals ← goal.cases h.fvarId! altVarNames
+    -- There should be exactly one goal
+    match newGoals.toList with
+    | [ newGoal ] =>
+      -- Set the new goal
+      let goals ← getUnsolvedGoals
+      setGoals (newGoal.mvarId :: goals)
+      -- There should be exactly two fields
+      let fields := newGoal.fields
+      withMainContext do
+      k (fields.get! 0) (fields.get! 1)
+    | _ =>
+      throwError "Unreachable"
+  else
+    throwError "Not a conjunction"
+
+-- Tactic to fully split a conjunction
+partial def splitFullConjTacAux [Inhabited α] [Nonempty α] (keepCurrentName : Bool) (l : List Expr) (h : Expr) (k : List Expr → TacticM α)  : TacticM α := do
+  try
+    let ids ← do
+      if keepCurrentName then do
+        let cur := (← h.fvarId!.getDecl).userName
+        let nid ← mkFreshAnonPropUserName
+        pure (some (cur, nid))
+      else
+        pure none
+    splitConjTac h ids (λ h1 h2 =>
+      splitFullConjTacAux keepCurrentName l h1 (λ l1 =>
+        splitFullConjTacAux keepCurrentName l1 h2 (λ l2 =>
+          k l2)))
+  catch _ =>
+    k (h :: l)
+
+-- Tactic to fully split a conjunction
+-- `keepCurrentName`: if `true`, then the first conjunct has the name of the original assumption
+def splitFullConjTac [Inhabited α] [Nonempty α] (keepCurrentName : Bool) (h : Expr) (k : List Expr → TacticM α)  : TacticM α := do
+  splitFullConjTacAux keepCurrentName [] h (λ l => k l.reverse)
+
+syntax optAtArgs := ("at" ident)?
+def elabOptAtArgs (args : TSyntax `Utils.optAtArgs) : TacticM (Option Expr) := do
+  withMainContext do
+  let args := (args.raw.getArgs.get! 0).getArgs
+  if args.size > 0 then do
+    let n := (args.get! 1).getId
+    let decl ← Lean.Meta.getLocalDeclFromUserName n
+    let fvar := mkFVar decl.fvarId
+    pure (some fvar)
+  else
+    pure none
+
+elab "split_conj" args:optAtArgs : tactic => do
+  withMainContext do
+  match ← elabOptAtArgs args with
+  | some fvar => do
+    trace[Utils] "split at {fvar}"
+    splitConjTac fvar none (fun _ _ =>  pure ())
+  | none => do
+    trace[Utils] "split goal"
+    splitConjTarget
+
+elab "split_conjs" args:optAtArgs : tactic => do
+  withMainContext do
+  match ← elabOptAtArgs args with
+  | some fvar =>
+    trace[Utils] "split at {fvar}"
+    splitFullConjTac false fvar (fun _ =>  pure ())
+  | none =>
+    trace[Utils] "split goal"
+    repeatTac splitConjTarget
+
+elab "split_existsl" " at " n:ident : tactic => do
+  withMainContext do
+  let decl ← Lean.Meta.getLocalDeclFromUserName n.getId
+  let fvar := mkFVar decl.fvarId
+  splitAllExistsTac fvar [] (fun _ _ => pure ())
+
+example (h : a ∧ b) : a := by
+  split_existsl at h
+  split_conj at h
+  assumption
+
+example (h : ∃ x y z, x + y + z ≥ 0) : ∃ x, x ≥ 0 := by
+  split_existsl at h
+  rename_i x y z
+  exists x + y + z
+
+/- Call the simp tactic.
+   The initialization of the context is adapted from Tactic.elabSimpArgs.
+   Something very annoying is that there is no function which allows to
+   initialize a simp context without doing an elaboration - as a consequence
+   we write our own here. -/
+def simpAt (declsToUnfold : List Name) (thms : List Name) (hypsToUse : List FVarId)
+  (loc : Tactic.Location) :
+  Tactic.TacticM Unit := do
+  -- Initialize with the builtin simp theorems
+  let simpThms ← Tactic.simpOnlyBuiltins.foldlM (·.addConst ·) ({} : SimpTheorems)
+  -- Add the equational theorem for the declarations to unfold
+  let simpThms ←
+    declsToUnfold.foldlM (fun thms decl => thms.addDeclToUnfold decl) simpThms
+  -- Add the hypotheses and the rewriting theorems
+  let simpThms ←
+    hypsToUse.foldlM (fun thms fvarId =>
+      -- post: TODO: don't know what that is
+      -- inv: invert the equality
+      thms.add (.fvar fvarId) #[] (mkFVar fvarId) (post := false) (inv := false)
+      -- thms.eraseCore (.fvar fvar)
+      ) simpThms
+  -- Add the rewriting theorems to use
+  let simpThms ←
+    thms.foldlM (fun thms thmName => do
+      let info ← getConstInfo thmName
+      if (← isProp info.type) then
+        -- post: TODO: don't know what that is
+        -- inv: invert the equality
+        thms.addConst thmName (post := false) (inv := false)
+      else
+        throwError "Not a proposition: {thmName}"
+      ) simpThms
+  let congrTheorems ← getSimpCongrTheorems
+  let ctx : Simp.Context := { simpTheorems := #[simpThms], congrTheorems }
+  -- Apply the simplifier
+  let _ ← Tactic.simpLocation ctx (discharge? := .none) loc
+
+end Utils
diff --git a/backends/lean/Primitives.lean b/backends/lean/Primitives.lean
deleted file mode 100644
index 4a66a453..00000000
--- a/backends/lean/Primitives.lean
+++ /dev/null
@@ -1,583 +0,0 @@
-import Lean
-import Lean.Meta.Tactic.Simp
-import Init.Data.List.Basic
-import Mathlib.Tactic.RunCmd
-
---------------------
--- ASSERT COMMAND --
---------------------
-
-open Lean Elab Command Term Meta
-
-syntax (name := assert) "#assert" term: command
-
-@[command_elab assert]
-unsafe
-def assertImpl : CommandElab := fun (_stx: Syntax) => do
-  runTermElabM (fun _ => do
-    let r ← evalTerm Bool (mkConst ``Bool) _stx[1]
-    if not r then
-      logInfo "Assertion failed for: "
-      logInfo _stx[1]
-      logError "Expression reduced to false"
-    pure ())
-
-#eval 2 == 2
-#assert (2 == 2)
-
--------------
--- PRELUDE --
--------------
-
--- Results & monadic combinators
-
-inductive Error where
-   | assertionFailure: Error
-   | integerOverflow: Error
-   | divisionByZero: Error
-   | arrayOutOfBounds: Error
-   | maximumSizeExceeded: Error
-   | panic: Error
-deriving Repr, BEq
-
-open Error
-
-inductive Result (α : Type u) where
-  | ret (v: α): Result α
-  | fail (e: Error): Result α
-deriving Repr, BEq
-
-open Result
-
-instance Result_Inhabited (α : Type u) : Inhabited (Result α) :=
-  Inhabited.mk (fail panic)
-
-/- HELPERS -/
-
-def ret? {α: Type} (r: Result α): Bool :=
-  match r with
-  | Result.ret _ => true
-  | Result.fail _ => false
-
-def massert (b:Bool) : Result Unit :=
-  if b then .ret () else fail assertionFailure
-
-def eval_global {α: Type} (x: Result α) (_: ret? x): α :=
-  match x with
-  | Result.fail _ => by contradiction
-  | Result.ret x => x
-
-/- DO-DSL SUPPORT -/
-
-def bind (x: Result α) (f: α -> Result β) : Result β :=
-  match x with
-  | ret v  => f v 
-  | fail v => fail v
-
--- Allows using Result in do-blocks
-instance : Bind Result where
-  bind := bind
-
--- Allows using return x in do-blocks
-instance : Pure Result where
-  pure := fun x => ret x
-
-/- CUSTOM-DSL SUPPORT -/
-
--- Let-binding the Result of a monadic operation is oftentimes not sufficient,
--- because we may need a hypothesis for equational reasoning in the scope. We
--- rely on subtype, and a custom let-binding operator, in effect recreating our
--- own variant of the do-dsl
-
-def Result.attach {α: Type} (o : Result α): Result { x : α // o = ret x } :=
-  match o with
-  | .ret x => .ret ⟨x, rfl⟩
-  | .fail e => .fail e
-
-macro "let" e:term " ⟵ " f:term : doElem =>
-  `(doElem| let ⟨$e, h⟩ ← Result.attach $f)
-
--- TODO: any way to factorize both definitions?
-macro "let" e:term " <-- " f:term : doElem =>
-  `(doElem| let ⟨$e, h⟩ ← Result.attach $f)
-
--- We call the hypothesis `h`, in effect making it unavailable to the user
--- (because too much shadowing). But in practice, once can use the French single
--- quote notation (input with f< and f>), where `‹ h ›` finds a suitable
--- hypothesis in the context, this is equivalent to `have x: h := by assumption in x`
-#eval do
-  let y <-- .ret (0: Nat)
-  let _: y = 0 := by cases ‹ ret 0 = ret y › ; decide
-  let r: { x: Nat // x = 0 } := ⟨ y, by assumption ⟩
-  .ret r
-
-----------------------
--- MACHINE INTEGERS --
-----------------------
-
--- We redefine our machine integers types.
-
--- For Isize/Usize, we reuse `getNumBits` from `USize`. You cannot reduce `getNumBits`
--- using the simplifier, meaning that proofs do not depend on the compile-time value of
--- USize.size. (Lean assumes 32 or 64-bit platforms, and Rust doesn't really support, at
--- least officially, 16-bit microcontrollers, so this seems like a fine design decision
--- for now.)
-
--- Note from Chris Bailey: "If there's more than one salient property of your
--- definition then the subtyping strategy might get messy, and the property part
--- of a subtype is less discoverable by the simplifier or tactics like
--- library_search." So, we will not add refinements on the return values of the
--- operations defined on Primitives, but will rather rely on custom lemmas to
--- invert on possible return values of the primitive operations.
-
--- Machine integer constants, done via `ofNatCore`, which requires a proof that
--- the `Nat` fits within the desired integer type. We provide a custom tactic.
-
-open System.Platform.getNumBits
-
--- TODO: is there a way of only importing System.Platform.getNumBits?
---
-@[simp] def size_num_bits : Nat := (System.Platform.getNumBits ()).val
-
--- Remark: Lean seems to use < for the comparisons with the upper bounds by convention.
--- We keep the F* convention for now.
-@[simp] def Isize.min : Int := - (HPow.hPow 2 (size_num_bits - 1))
-@[simp] def Isize.max : Int := (HPow.hPow 2 (size_num_bits - 1)) - 1
-@[simp] def I8.min    : Int := - (HPow.hPow 2 7)
-@[simp] def I8.max    : Int := HPow.hPow 2 7 - 1
-@[simp] def I16.min   : Int := - (HPow.hPow 2 15)
-@[simp] def I16.max   : Int := HPow.hPow 2 15 - 1
-@[simp] def I32.min   : Int := -(HPow.hPow 2 31)
-@[simp] def I32.max   : Int := HPow.hPow 2 31 - 1
-@[simp] def I64.min   : Int := -(HPow.hPow 2 63)
-@[simp] def I64.max   : Int := HPow.hPow 2 63 - 1
-@[simp] def I128.min  : Int := -(HPow.hPow 2 127)
-@[simp] def I128.max  : Int := HPow.hPow 2 127 - 1
-@[simp] def Usize.min : Int := 0
-@[simp] def Usize.max : Int := HPow.hPow 2 size_num_bits - 1
-@[simp] def U8.min    : Int := 0
-@[simp] def U8.max    : Int := HPow.hPow 2 8 - 1
-@[simp] def U16.min   : Int := 0
-@[simp] def U16.max   : Int := HPow.hPow 2 16 - 1
-@[simp] def U32.min   : Int := 0
-@[simp] def U32.max   : Int := HPow.hPow 2 32 - 1
-@[simp] def U64.min   : Int := 0
-@[simp] def U64.max   : Int := HPow.hPow 2 64 - 1
-@[simp] def U128.min  : Int := 0
-@[simp] def U128.max  : Int := HPow.hPow 2 128 - 1
-
-#assert (I8.min   == -128)
-#assert (I8.max   == 127)
-#assert (I16.min  == -32768)
-#assert (I16.max  == 32767)
-#assert (I32.min  == -2147483648)
-#assert (I32.max  == 2147483647)
-#assert (I64.min  == -9223372036854775808)
-#assert (I64.max  == 9223372036854775807)
-#assert (I128.min == -170141183460469231731687303715884105728)
-#assert (I128.max == 170141183460469231731687303715884105727)
-#assert (U8.min   == 0)
-#assert (U8.max   == 255)
-#assert (U16.min  == 0)
-#assert (U16.max  == 65535)
-#assert (U32.min  == 0)
-#assert (U32.max  == 4294967295)
-#assert (U64.min  == 0)
-#assert (U64.max  == 18446744073709551615)
-#assert (U128.min == 0)
-#assert (U128.max == 340282366920938463463374607431768211455)
-
-inductive ScalarTy :=
-| Isize
-| I8
-| I16
-| I32
-| I64
-| I128
-| Usize
-| U8
-| U16
-| U32
-| U64
-| U128
-
-def Scalar.min (ty : ScalarTy) : Int :=
-  match ty with
-  | .Isize => Isize.min
-  | .I8    => I8.min
-  | .I16   => I16.min
-  | .I32   => I32.min
-  | .I64   => I64.min
-  | .I128  => I128.min
-  | .Usize => Usize.min
-  | .U8    => U8.min
-  | .U16   => U16.min
-  | .U32   => U32.min
-  | .U64   => U64.min
-  | .U128  => U128.min
-
-def Scalar.max (ty : ScalarTy) : Int :=
-  match ty with
-  | .Isize => Isize.max
-  | .I8    => I8.max
-  | .I16   => I16.max
-  | .I32   => I32.max
-  | .I64   => I64.max
-  | .I128  => I128.max
-  | .Usize => Usize.max
-  | .U8    => U8.max
-  | .U16   => U16.max
-  | .U32   => U32.max
-  | .U64   => U64.max
-  | .U128  => U128.max
-
--- "Conservative" bounds
--- We use those because we can't compare to the isize bounds (which can't
--- reduce at compile-time). Whenever we perform an arithmetic operation like
--- addition we need to check that the result is in bounds: we first compare
--- to the conservative bounds, which reduce, then compare to the real bounds.
--- This is useful for the various #asserts that we want to reduce at
--- type-checking time.
-def Scalar.cMin (ty : ScalarTy) : Int :=
-  match ty with
-  | .Isize => I32.min
-  | _ => Scalar.min ty
-
-def Scalar.cMax (ty : ScalarTy) : Int :=
-  match ty with
-  | .Isize => I32.max
-  | .Usize => U32.max
-  | _ => Scalar.max ty
-
-theorem Scalar.cMin_bound ty : Scalar.min ty <= Scalar.cMin ty := by sorry
-theorem Scalar.cMax_bound ty : Scalar.min ty <= Scalar.cMin ty := by sorry
-
-structure Scalar (ty : ScalarTy) where
-  val : Int
-  hmin : Scalar.min ty <= val
-  hmax : val <= Scalar.max ty
-
-theorem Scalar.bound_suffices (ty : ScalarTy) (x : Int) :
-  Scalar.cMin ty <= x && x <= Scalar.cMax ty ->
-  (decide (Scalar.min ty ≤ x) && decide (x ≤ Scalar.max ty)) = true
-  := by sorry
-
-def Scalar.ofIntCore {ty : ScalarTy} (x : Int)
-  (hmin : Scalar.min ty <= x) (hmax : x <= Scalar.max ty) : Scalar ty :=
-  { val := x, hmin := hmin, hmax := hmax }
-
-def Scalar.ofInt {ty : ScalarTy} (x : Int)
-  (h : Scalar.min ty <= x && x <= Scalar.max ty) : Scalar ty :=
-  let hmin: Scalar.min ty <= x := by sorry
-  let hmax: x <= Scalar.max ty := by sorry
-  Scalar.ofIntCore x hmin hmax
-
--- Further thoughts: look at what has been done here:
--- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/Fin/Basic.lean
--- and
--- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/UInt.lean
--- which both contain a fair amount of reasoning already!
-def Scalar.tryMk (ty : ScalarTy) (x : Int) : Result (Scalar ty) :=
-  -- TODO: write this with only one if then else
-  if hmin_cons: Scalar.cMin ty <= x || Scalar.min ty <= x then
-    if hmax_cons: x <= Scalar.cMax ty || x <= Scalar.max ty then
-      let hmin: Scalar.min ty <= x := by sorry
-      let hmax: x <= Scalar.max ty := by sorry
-      return Scalar.ofIntCore x hmin hmax
-    else fail integerOverflow
-  else fail integerOverflow
-
-def Scalar.neg {ty : ScalarTy} (x : Scalar ty) : Result (Scalar ty) := Scalar.tryMk ty (- x.val)
-
-def Scalar.div {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
-  if y.val != 0 then Scalar.tryMk ty (x.val / y.val) else fail divisionByZero
-
--- Checking that the % operation in Lean computes the same as the remainder operation in Rust
-#assert 1 % 2 = (1:Int)
-#assert (-1) % 2 = -1
-#assert 1 % (-2) = 1
-#assert (-1) % (-2) = -1
-
-def Scalar.rem {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
-  if y.val != 0 then Scalar.tryMk ty (x.val % y.val) else fail divisionByZero
-
-def Scalar.add {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
-  Scalar.tryMk ty (x.val + y.val)
-
-def Scalar.sub {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
-  Scalar.tryMk ty (x.val - y.val)
-
-def Scalar.mul {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
-  Scalar.tryMk ty (x.val * y.val)
-
--- TODO: instances of +, -, * etc. for scalars
-
--- Cast an integer from a [src_ty] to a [tgt_ty]
--- TODO: check the semantics of casts in Rust
-def Scalar.cast {src_ty : ScalarTy} (tgt_ty : ScalarTy) (x : Scalar src_ty) : Result (Scalar tgt_ty) :=
-  Scalar.tryMk tgt_ty x.val
-
--- The scalar types
--- We declare the definitions as reducible so that Lean can unfold them (useful
--- for type class resolution for instance).
-@[reducible] def Isize := Scalar .Isize
-@[reducible] def I8    := Scalar .I8
-@[reducible] def I16   := Scalar .I16
-@[reducible] def I32   := Scalar .I32
-@[reducible] def I64   := Scalar .I64
-@[reducible] def I128  := Scalar .I128
-@[reducible] def Usize := Scalar .Usize
-@[reducible] def U8    := Scalar .U8
-@[reducible] def U16   := Scalar .U16
-@[reducible] def U32   := Scalar .U32
-@[reducible] def U64   := Scalar .U64
-@[reducible] def U128  := Scalar .U128
-
--- TODO: below: not sure this is the best way.
--- Should we rather overload operations like +, -, etc.?
--- Also, it is possible to automate the generation of those definitions
--- with macros (but would it be a good idea? It would be less easy to
--- read the file, which is not supposed to change a lot)
-
--- Negation
-
-/--
-Remark: there is no heterogeneous negation in the Lean prelude: we thus introduce
-one here.
-
-The notation typeclass for heterogeneous addition.
-This enables the notation `- a : β` where `a : α`.
--/
-class HNeg (α : Type u) (β : outParam (Type v)) where
-  /-- `- a` computes the negation of `a`.
-  The meaning of this notation is type-dependent. -/
-  hNeg : α → β
-
-prefix:75  "-"   => HNeg.hNeg
-
-instance : HNeg Isize (Result Isize) where hNeg x := Scalar.neg x
-instance : HNeg I8 (Result I8) where hNeg x := Scalar.neg x
-instance : HNeg I16 (Result I16) where hNeg x := Scalar.neg x
-instance : HNeg I32 (Result I32) where hNeg x := Scalar.neg x
-instance : HNeg I64 (Result I64) where hNeg x := Scalar.neg x
-instance : HNeg I128 (Result I128) where hNeg x := Scalar.neg x
-
--- Addition
-instance {ty} : HAdd (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
-  hAdd x y := Scalar.add x y
-
--- Substraction
-instance {ty} : HSub (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
-  hSub x y := Scalar.sub x y
-
--- Multiplication
-instance {ty} : HMul (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
-  hMul x y := Scalar.mul x y
-
--- Division
-instance {ty} : HDiv (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
-  hDiv x y := Scalar.div x y
-
--- Remainder
-instance {ty} : HMod (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
-  hMod x y := Scalar.rem x y
-
--- ofIntCore
--- TODO: typeclass?
-def Isize.ofIntCore := @Scalar.ofIntCore .Isize
-def I8.ofIntCore    := @Scalar.ofIntCore .I8
-def I16.ofIntCore   := @Scalar.ofIntCore .I16
-def I32.ofIntCore   := @Scalar.ofIntCore .I32
-def I64.ofIntCore   := @Scalar.ofIntCore .I64
-def I128.ofIntCore  := @Scalar.ofIntCore .I128
-def Usize.ofIntCore := @Scalar.ofIntCore .Usize
-def U8.ofIntCore    := @Scalar.ofIntCore .U8
-def U16.ofIntCore   := @Scalar.ofIntCore .U16
-def U32.ofIntCore   := @Scalar.ofIntCore .U32
-def U64.ofIntCore   := @Scalar.ofIntCore .U64
-def U128.ofIntCore  := @Scalar.ofIntCore .U128
-
---  ofInt
--- TODO: typeclass?
-def Isize.ofInt := @Scalar.ofInt .Isize
-def I8.ofInt    := @Scalar.ofInt .I8
-def I16.ofInt   := @Scalar.ofInt .I16
-def I32.ofInt   := @Scalar.ofInt .I32
-def I64.ofInt   := @Scalar.ofInt .I64
-def I128.ofInt  := @Scalar.ofInt .I128
-def Usize.ofInt := @Scalar.ofInt .Usize
-def U8.ofInt    := @Scalar.ofInt .U8
-def U16.ofInt   := @Scalar.ofInt .U16
-def U32.ofInt   := @Scalar.ofInt .U32
-def U64.ofInt   := @Scalar.ofInt .U64
-def U128.ofInt  := @Scalar.ofInt .U128
-
--- Comparisons
-instance {ty} : LT (Scalar ty) where
-  lt a b := LT.lt a.val b.val
-
-instance {ty} : LE (Scalar ty) where le a b := LE.le a.val b.val
-
-instance Scalar.decLt {ty} (a b : Scalar ty) : Decidable (LT.lt a b) := Int.decLt ..
-instance Scalar.decLe {ty} (a b : Scalar ty) : Decidable (LE.le a b) := Int.decLe ..
-
-theorem Scalar.eq_of_val_eq {ty} : ∀ {i j : Scalar ty}, Eq i.val j.val → Eq i j
-  | ⟨_, _, _⟩, ⟨_, _, _⟩, rfl => rfl
-
-theorem Scalar.val_eq_of_eq {ty} {i j : Scalar ty} (h : Eq i j) : Eq i.val j.val :=
-  h ▸ rfl
-
-theorem Scalar.ne_of_val_ne {ty} {i j : Scalar ty} (h : Not (Eq i.val j.val)) : Not (Eq i j) :=
-  fun h' => absurd (val_eq_of_eq h') h
-
-instance (ty : ScalarTy) : DecidableEq (Scalar ty) :=
-  fun i j =>
-    match decEq i.val j.val with
-    | isTrue h  => isTrue (Scalar.eq_of_val_eq h)
-    | isFalse h => isFalse (Scalar.ne_of_val_ne h)
-
-def Scalar.toInt {ty} (n : Scalar ty) : Int := n.val
-
--- Tactic to prove that integers are in bounds
-syntax "intlit" : tactic
-
-macro_rules
-  | `(tactic| intlit) => `(tactic| apply Scalar.bound_suffices ; decide)
-
--- -- We now define a type class that subsumes the various machine integer types, so
--- -- as to write a concise definition for scalar_cast, rather than exhaustively
--- -- enumerating all of the possible pairs. We remark that Rust has sane semantics
--- -- and fails if a cast operation would involve a truncation or modulo.
-
--- class MachineInteger (t: Type) where
---   size: Nat
---   val: t -> Fin size
---   ofNatCore: (n:Nat) -> LT.lt n size -> t
-
--- set_option hygiene false in
--- run_cmd
---   for typeName in [`UInt8, `UInt16, `UInt32, `UInt64, `USize].map Lean.mkIdent do
---   Lean.Elab.Command.elabCommand (← `(
---     namespace $typeName
---     instance: MachineInteger $typeName where
---       size := size
---       val := val
---       ofNatCore := ofNatCore
---     end $typeName
---   ))
-
--- -- Aeneas only instantiates the destination type (`src` is implicit). We rely on
--- -- Lean to infer `src`.
-
--- def scalar_cast { src: Type } (dst: Type) [ MachineInteger src ] [ MachineInteger dst ] (x: src): Result dst :=
---   if h: MachineInteger.val x < MachineInteger.size dst then
---     .ret (MachineInteger.ofNatCore (MachineInteger.val x).val h)
---   else
---     .fail integerOverflow
-
--------------
--- VECTORS --
--------------
-
-def Vec (α : Type u) := { l : List α // List.length l <= Usize.max }
-
-def vec_new (α : Type u): Vec α := ⟨ [], by sorry ⟩
-
-def vec_len (α : Type u) (v : Vec α) : Usize :=
-  let ⟨ v, l ⟩ := v
-  Usize.ofIntCore (List.length v) (by sorry) l
- 
-def vec_push_fwd (α : Type u) (_ : Vec α) (_ : α) : Unit := ()
-
-def vec_push_back (α : Type u) (v : Vec α) (x : α) : Result (Vec α)
-  :=
-  if h : List.length v.val <= U32.max || List.length v.val <= Usize.max then
-    return ⟨ List.concat v.val x, by sorry ⟩
-  else
-    fail maximumSizeExceeded
-
-def vec_insert_fwd (α : Type u) (v: Vec α) (i: Usize) (_: α): Result Unit :=
-  if i.val < List.length v.val then
-    .ret ()
-  else
-    .fail arrayOutOfBounds
-
-def vec_insert_back (α : Type u) (v: Vec α) (i: Usize) (x: α): Result (Vec α) :=
-  if i.val < List.length v.val then
-    -- TODO: maybe we should redefine a list library which uses integers
-    -- (instead of natural numbers)
-    let i : Nat :=
-      match i.val with
-      | .ofNat n => n
-      | .negSucc n => by sorry -- TODO: we can't get here
-    let isLt: i < USize.size := by sorry
-    let i : Fin USize.size := { val := i, isLt := isLt }
-    .ret ⟨ List.set v.val i.val x, by
-      have h: List.length v.val <= Usize.max := v.property
-      rewrite [ List.length_set v.val i.val x ]
-      assumption
-    ⟩
-  else
-    .fail arrayOutOfBounds
-
-def vec_index_fwd (α : Type u) (v: Vec α) (i: Usize): Result α :=
-  if i.val < List.length v.val then
-    let i : Nat :=
-      match i.val with
-      | .ofNat n => n
-      | .negSucc n => by sorry -- TODO: we can't get here
-    let isLt: i < USize.size := by sorry
-    let i : Fin USize.size := { val := i, isLt := isLt }
-    let h: i < List.length v.val := by sorry
-    .ret (List.get v.val ⟨i.val, h⟩)
-  else
-    .fail arrayOutOfBounds
-
-def vec_index_back (α : Type u) (v: Vec α) (i: Usize) (_: α): Result Unit :=
-  if i.val < List.length v.val then
-    .ret ()
-  else
-    .fail arrayOutOfBounds
-
-def vec_index_mut_fwd (α : Type u) (v: Vec α) (i: Usize): Result α :=
-  if i.val < List.length v.val then
-    let i : Nat :=
-      match i.val with
-      | .ofNat n => n
-      | .negSucc n => by sorry -- TODO: we can't get here
-    let isLt: i < USize.size := by sorry
-    let i : Fin USize.size := { val := i, isLt := isLt }
-    let h: i < List.length v.val := by sorry
-    .ret (List.get v.val ⟨i.val, h⟩)
-  else
-    .fail arrayOutOfBounds
-
-def vec_index_mut_back (α : Type u) (v: Vec α) (i: Usize) (x: α): Result (Vec α) :=
-  if i.val < List.length v.val then
-    let i : Nat :=
-      match i.val with
-      | .ofNat n => n
-      | .negSucc n => by sorry -- TODO: we can't get here
-    let isLt: i < USize.size := by sorry
-    let i : Fin USize.size := { val := i, isLt := isLt }
-    .ret ⟨ List.set v.val i.val x, by
-      have h: List.length v.val <= Usize.max := v.property
-      rewrite [ List.length_set v.val i.val x ]
-      assumption
-    ⟩
-  else
-    .fail arrayOutOfBounds
-
-----------
--- MISC --
-----------
-
-def mem_replace_fwd (a : Type) (x : a) (_ : a) : a :=
-  x
-
-def mem_replace_back (a : Type) (_ : a) (y : a) : a :=
-  y
-
-/-- Aeneas-translated function -- useful to reduce non-recursive definitions.
- Use with `simp [ aeneas ]` -/
-register_simp_attr aeneas
diff --git a/backends/lean/lake-manifest.json b/backends/lean/lake-manifest.json
index 7b23fc19..5a089838 100644
--- a/backends/lean/lake-manifest.json
+++ b/backends/lean/lake-manifest.json
@@ -2,26 +2,38 @@
  "packagesDir": "lake-packages",
  "packages":
  [{"git":
+   {"url": "https://github.com/EdAyers/ProofWidgets4",
+    "subDir?": null,
+    "rev": "c43db94a8f495dad37829e9d7ad65483d68c86b8",
+    "name": "proofwidgets",
+    "inputRev?": "v0.0.11"}},
+  {"git":
+   {"url": "https://github.com/mhuisi/lean4-cli.git",
+    "subDir?": null,
+    "rev": "5a858c32963b6b19be0d477a30a1f4b6c120be7e",
+    "name": "Cli",
+    "inputRev?": "nightly"}},
+  {"git":
    {"url": "https://github.com/leanprover-community/mathlib4.git",
     "subDir?": null,
-    "rev": "f89ee53085b8aad0bacd3bc94d7ef4b8d9aba643",
+    "rev": "fa05951a270fef2873666c46f138e90338cd48d6",
     "name": "mathlib",
     "inputRev?": null}},
   {"git":
    {"url": "https://github.com/gebner/quote4",
     "subDir?": null,
-    "rev": "2412c4fdf4a8b689f4467618e5e7b371ae5014aa",
+    "rev": "c0d9516f44d07feee01c1103c8f2f7c24a822b55",
     "name": "Qq",
     "inputRev?": "master"}},
   {"git":
    {"url": "https://github.com/JLimperg/aesop",
     "subDir?": null,
-    "rev": "7fe9ecd9339b0e1796e89d243b776849c305c690",
+    "rev": "f04538ab6ad07642368cf11d2702acc0a9b4bcee",
     "name": "aesop",
     "inputRev?": "master"}},
   {"git":
    {"url": "https://github.com/leanprover/std4",
     "subDir?": null,
-    "rev": "24897887905b3a1254b244369f5dd2cf6174b0ee",
+    "rev": "dff883c55395438ae2a5c65ad5ddba084b600feb",
     "name": "std",
     "inputRev?": "main"}}]}
diff --git a/backends/lean/lakefile.lean b/backends/lean/lakefile.lean
index 9633e1e8..21a4a332 100644
--- a/backends/lean/lakefile.lean
+++ b/backends/lean/lakefile.lean
@@ -1,10 +1,11 @@
 import Lake
 open Lake DSL
 
+-- Important: mathlib imports std4 and quote4: we mustn't add a `require std4` line
 require mathlib from git
   "https://github.com/leanprover-community/mathlib4.git"
 
 package «base» {}
 
 @[default_target]
-lean_lib «Primitives» {}
+lean_lib «Base» {}
diff --git a/backends/lean/lean-toolchain b/backends/lean/lean-toolchain
new file mode 100644
index 00000000..334c5053
--- /dev/null
+++ b/backends/lean/lean-toolchain
@@ -0,0 +1 @@
+leanprover/lean4:nightly-2023-07-12
\ No newline at end of file
diff --git a/compiler/Config.ml b/compiler/Config.ml
index ce9b0e0c..0475899c 100644
--- a/compiler/Config.ml
+++ b/compiler/Config.ml
@@ -162,6 +162,11 @@ let backward_no_state_update = ref false
  *)
 let split_files = ref true
 
+(** For Lean, controls whether we generate a lakefile or not.
+
+ *)
+let lean_gen_lakefile = ref false
+
 (** If true, treat the unit functions (function taking no inputs and returning
     no outputs) as unit tests: evaluate them with the interpreter and check that
     they don't panic.
@@ -292,3 +297,21 @@ let filter_useless_monadic_calls = ref true
       dynamically check for that).
  *)
 let filter_useless_functions = ref true
+
+(** Obsolete. TODO: remove.
+
+    For Lean we used to parameterize the entire development by a section variable
+    called opaque_defs, of type OpaqueDefs.
+  *)
+let wrap_opaque_in_sig = ref false
+
+(** Use short names for the record fields.
+
+    Some backends can't disambiguate records when their field names have collisions.
+    When this happens, we use long names, by which we concatenate the record
+    names with the field names, and check whether there are name collisions.
+
+    For backends which can disambiguate records (typically by using the typing
+    information), we use short names (i.e., the original field names).
+ *)
+let record_fields_short_names = ref false
diff --git a/compiler/Driver.ml b/compiler/Driver.ml
index 2ff9e295..166ef11b 100644
--- a/compiler/Driver.ml
+++ b/compiler/Driver.ml
@@ -107,6 +107,9 @@ let () =
         Arg.Clear check_invariants,
         " Deactivate the invariant sanity checks performed at every evaluation \
          step. Dramatically increases speed." );
+      ( "-lean-default-lakefile",
+        Arg.Clear lean_gen_lakefile,
+        " Generate a default lakefile.lean (Lean only)" );
     ]
   in
 
@@ -130,6 +133,9 @@ let () =
     (not !use_fuel)
     || (not !extract_decreases_clauses)
        && not !extract_template_decreases_clauses);
+  if !lean_gen_lakefile && not (!backend = Lean) then
+    log#error
+      "The -lean-default-lakefile option is valid only for the Lean backend";
 
   (* Check that the user specified a backend *)
   let _ =
@@ -157,7 +163,9 @@ let () =
         (* We don't support fuel for the Lean backend *)
         if !use_fuel then (
           log#error "The Lean backend doesn't support the -use-fuel option";
-          fail ())
+          fail ());
+        (* Lean can disambiguate the field names *)
+        record_fields_short_names := true
     | HOL4 ->
         (* We don't support fuel for the HOL4 backend *)
         if !use_fuel then (
diff --git a/compiler/Extract.ml b/compiler/Extract.ml
index d624d9ca..b16f9639 100644
--- a/compiler/Extract.ml
+++ b/compiler/Extract.ml
@@ -300,23 +300,40 @@ let assumed_variants () : (assumed_ty * VariantId.id * string) list =
         (Option, option_none_id, "NONE");
       ]
 
-let assumed_llbc_functions :
+let assumed_llbc_functions () :
     (A.assumed_fun_id * T.RegionGroupId.id option * string) list =
   let rg0 = Some T.RegionGroupId.zero in
-  [
-    (Replace, None, "mem_replace_fwd");
-    (Replace, rg0, "mem_replace_back");
-    (VecNew, None, "vec_new");
-    (VecPush, None, "vec_push_fwd") (* Shouldn't be used *);
-    (VecPush, rg0, "vec_push_back");
-    (VecInsert, None, "vec_insert_fwd") (* Shouldn't be used *);
-    (VecInsert, rg0, "vec_insert_back");
-    (VecLen, None, "vec_len");
-    (VecIndex, None, "vec_index_fwd");
-    (VecIndex, rg0, "vec_index_back") (* shouldn't be used *);
-    (VecIndexMut, None, "vec_index_mut_fwd");
-    (VecIndexMut, rg0, "vec_index_mut_back");
-  ]
+  match !backend with
+  | FStar | Coq | HOL4 ->
+      [
+        (Replace, None, "mem_replace_fwd");
+        (Replace, rg0, "mem_replace_back");
+        (VecNew, None, "vec_new");
+        (VecPush, None, "vec_push_fwd") (* Shouldn't be used *);
+        (VecPush, rg0, "vec_push_back");
+        (VecInsert, None, "vec_insert_fwd") (* Shouldn't be used *);
+        (VecInsert, rg0, "vec_insert_back");
+        (VecLen, None, "vec_len");
+        (VecIndex, None, "vec_index_fwd");
+        (VecIndex, rg0, "vec_index_back") (* shouldn't be used *);
+        (VecIndexMut, None, "vec_index_mut_fwd");
+        (VecIndexMut, rg0, "vec_index_mut_back");
+      ]
+  | Lean ->
+      [
+        (Replace, None, "mem.replace");
+        (Replace, rg0, "mem.replace_back");
+        (VecNew, None, "Vec.new");
+        (VecPush, None, "Vec.push_fwd") (* Shouldn't be used *);
+        (VecPush, rg0, "Vec.push");
+        (VecInsert, None, "Vec.insert_fwd") (* Shouldn't be used *);
+        (VecInsert, rg0, "Vec.insert");
+        (VecLen, None, "Vec.len");
+        (VecIndex, None, "Vec.index");
+        (VecIndex, rg0, "Vec.index_back") (* shouldn't be used *);
+        (VecIndexMut, None, "Vec.index_mut");
+        (VecIndexMut, rg0, "Vec.index_mut_back");
+      ]
 
 let assumed_pure_functions () : (pure_assumed_fun_id * string) list =
   match !backend with
@@ -344,7 +361,7 @@ let names_map_init () : names_map_init =
     assumed_adts = assumed_adts ();
     assumed_structs;
     assumed_variants = assumed_variants ();
-    assumed_llbc_functions;
+    assumed_llbc_functions = assumed_llbc_functions ();
     assumed_pure_functions = assumed_pure_functions ();
   }
 
@@ -505,10 +522,10 @@ let fun_decl_kind_to_qualif (kind : decl_kind) : string option =
   | Lean -> (
       match kind with
       | SingleNonRec -> Some "def"
-      | SingleRec -> Some "def"
-      | MutRecFirst -> Some "mutual def"
-      | MutRecInner -> Some "def"
-      | MutRecLast -> Some "def"
+      | SingleRec -> Some "divergent def"
+      | MutRecFirst -> Some "mutual divergent def"
+      | MutRecInner -> Some "divergent def"
+      | MutRecLast -> Some "divergent def"
       | Assumed -> Some "axiom"
       | Declared -> Some "axiom")
   | HOL4 -> None
@@ -601,34 +618,48 @@ let mk_formatter (ctx : trans_ctx) (crate_name : string)
     | FStar | Lean | HOL4 -> name
     | Coq -> capitalize_first_letter name
   in
-  let type_name name = type_name_to_snake_case name ^ "_t" in
+  let type_name name =
+    match !backend with
+    | FStar | Coq | HOL4 -> type_name_to_snake_case name ^ "_t"
+    | Lean -> String.concat "." (get_type_name name)
+  in
   let field_name (def_name : name) (field_id : FieldId.id)
       (field_name : string option) : string =
-    let def_name = type_name_to_snake_case def_name ^ "_" in
-    match field_name with
-    | Some field_name -> def_name ^ field_name
-    | None -> def_name ^ FieldId.to_string field_id
+    let field_name =
+      match field_name with
+      | Some field_name -> field_name
+      | None -> FieldId.to_string field_id
+    in
+    if !Config.record_fields_short_names then field_name
+    else
+      let def_name = type_name_to_snake_case def_name ^ "_" in
+      def_name ^ field_name
   in
   let variant_name (def_name : name) (variant : string) : string =
-    let variant = to_camel_case variant in
-    if variant_concatenate_type_name then
-      type_name_to_camel_case def_name ^ variant
-    else variant
+    match !backend with
+    | FStar | Coq | HOL4 ->
+        let variant = to_camel_case variant in
+        if variant_concatenate_type_name then
+          type_name_to_camel_case def_name ^ variant
+        else variant
+    | Lean -> variant
   in
   let struct_constructor (basename : name) : string =
     let tname = type_name basename in
     let prefix =
-      match !backend with FStar -> "Mk" | Lean | Coq | HOL4 -> "mk"
+      match !backend with FStar -> "Mk" | Coq | HOL4 -> "mk" | Lean -> ""
+    in
+    let suffix =
+      match !backend with FStar | Coq | HOL4 -> "" | Lean -> ".mk"
     in
-    prefix ^ tname
+    prefix ^ tname ^ suffix
   in
-  let get_fun_name = get_name in
-  let fun_name_to_snake_case (fname : fun_name) : string =
-    let fname = get_fun_name fname in
-    (* Converting to snake case should be a no-op, but it doesn't cost much *)
-    let fname = List.map to_snake_case fname in
-    (* Concatenate the elements *)
-    String.concat "_" fname
+  let get_fun_name fname =
+    let fname = get_name fname in
+    (* TODO: don't convert to snake case for Coq, HOL4, F* *)
+    match !backend with
+    | FStar | Coq | HOL4 -> String.concat "_" (List.map to_snake_case fname)
+    | Lean -> String.concat "." fname
   in
   let global_name (name : global_name) : string =
     (* Converting to snake case also lowercases the letters (in Rust, global
@@ -639,7 +670,7 @@ let mk_formatter (ctx : trans_ctx) (crate_name : string)
   let fun_name (fname : fun_name) (num_loops : int) (loop_id : LoopId.id option)
       (num_rgs : int) (rg : region_group_info option) (filter_info : bool * int)
       : string =
-    let fname = fun_name_to_snake_case fname in
+    let fname = get_fun_name fname in
     (* Compute the suffix *)
     let suffix = default_fun_suffix num_loops loop_id num_rgs rg filter_info in
     (* Concatenate *)
@@ -648,7 +679,7 @@ let mk_formatter (ctx : trans_ctx) (crate_name : string)
 
   let termination_measure_name (_fid : A.FunDeclId.id) (fname : fun_name)
       (num_loops : int) (loop_id : LoopId.id option) : string =
-    let fname = fun_name_to_snake_case fname in
+    let fname = get_fun_name fname in
     let lp_suffix = default_fun_loop_suffix num_loops loop_id in
     (* Compute the suffix *)
     let suffix =
@@ -663,7 +694,7 @@ let mk_formatter (ctx : trans_ctx) (crate_name : string)
 
   let decreases_proof_name (_fid : A.FunDeclId.id) (fname : fun_name)
       (num_loops : int) (loop_id : LoopId.id option) : string =
-    let fname = fun_name_to_snake_case fname in
+    let fname = get_fun_name fname in
     let lp_suffix = default_fun_loop_suffix num_loops loop_id in
     (* Compute the suffix *)
     let suffix =
@@ -678,7 +709,7 @@ let mk_formatter (ctx : trans_ctx) (crate_name : string)
   let opaque_pre () =
     match !Config.backend with
     | FStar | Coq | HOL4 -> ""
-    | Lean -> "opaque_defs."
+    | Lean -> if !Config.wrap_opaque_in_sig then "opaque_defs." else ""
   in
 
   let var_basename (_varset : StringSet.t) (basename : string option) (ty : ty)
@@ -789,7 +820,7 @@ let mk_formatter (ctx : trans_ctx) (crate_name : string)
               F.pp_print_string fmt ")";
               F.pp_print_string fmt ")")
             else Z.pp_print fmt sv.value;
-            F.pp_print_string fmt " (by intlit))")
+            F.pp_print_string fmt ")")
     | Bool b ->
         let b =
           match !backend with
@@ -1007,6 +1038,11 @@ let end_type_decl_group (fmt : F.formatter) (is_rec : bool)
 let unit_name () =
   match !backend with Lean -> "Unit" | Coq | FStar | HOL4 -> "unit"
 
+(** Small helper *)
+let extract_arrow (fmt : F.formatter) () : unit =
+  if !Config.backend = Lean then F.pp_print_string fmt "→"
+  else F.pp_print_string fmt "->"
+
 (** [inside] constrols whether we should add parentheses or not around type
     applications (if [true] we add parentheses).
 
@@ -1100,7 +1136,7 @@ let rec extract_ty (ctx : extraction_ctx) (fmt : F.formatter)
       if inside then F.pp_print_string fmt "(";
       extract_rec false arg_ty;
       F.pp_print_space fmt ();
-      F.pp_print_string fmt "->";
+      extract_arrow fmt ();
       F.pp_print_space fmt ();
       extract_rec false ret_ty;
       if inside then F.pp_print_string fmt ")"
@@ -1188,7 +1224,7 @@ let extract_type_decl_variant (ctx : extraction_ctx) (fmt : F.formatter)
     (* Print the arrow [->] *)
     if !backend <> HOL4 then (
       F.pp_print_space fmt ();
-      F.pp_print_string fmt "->");
+      extract_arrow fmt ());
     (* Close the field box *)
     F.pp_close_box fmt ();
     (* Return *)
@@ -1326,7 +1362,8 @@ let extract_type_decl_struct_body (ctx : extraction_ctx) (fmt : F.formatter)
       F.pp_print_string fmt (unit_name ()))
     else if !backend = Lean && fields = [] then ()
       (* If the definition is recursive, we may need to extract it as an inductive
-         (instead of a record) *)
+         (instead of a record). We start with the "normal" case: we extract it
+         as a record. *)
     else if (not is_rec) || (!backend <> Coq && !backend <> Lean) then (
       if !backend <> Lean then F.pp_print_space fmt ();
       (* If Coq: print the constructor name *)
@@ -1379,7 +1416,14 @@ let extract_type_decl_struct_body (ctx : extraction_ctx) (fmt : F.formatter)
          a group of mutually recursive types: we extract it as an inductive type *)
       assert (is_rec && (!backend = Coq || !backend = Lean));
       let with_opaque_pre = false in
-      let cons_name = ctx_get_struct with_opaque_pre (AdtId def.def_id) ctx in
+      (* Small trick: in Lean we use namespaces, meaning we don't need to prefix
+         the constructor name with the name of the type at definition site,
+         i.e., instead of generating `inductive Foo := | MkFoo ...` like in Coq
+         we generate `inductive Foo := | mk ... *)
+      let cons_name =
+        if !backend = Lean then "mk"
+        else ctx_get_struct with_opaque_pre (AdtId def.def_id) ctx
+      in
       let def_name = ctx_get_local_type with_opaque_pre def.def_id ctx in
       extract_type_decl_variant ctx fmt type_decl_group def_name type_params
         cons_name fields)
@@ -1387,16 +1431,26 @@ let extract_type_decl_struct_body (ctx : extraction_ctx) (fmt : F.formatter)
   ()
 
 (** Extract a nestable, muti-line comment *)
-let extract_comment (fmt : F.formatter) (s : string) : unit =
-  match !backend with
-  | Coq | FStar | HOL4 ->
-      F.pp_print_string fmt "(** ";
-      F.pp_print_string fmt s;
-      F.pp_print_string fmt " *)"
-  | Lean ->
-      F.pp_print_string fmt "/- ";
+let extract_comment (fmt : F.formatter) (sl : string list) : unit =
+  (* Delimiters, space after we break a line *)
+  let ld, space, rd =
+    match !backend with
+    | Coq | FStar | HOL4 -> ("(** ", 4, " *)")
+    | Lean -> ("/- ", 3, " -/")
+  in
+  F.pp_open_vbox fmt space;
+  F.pp_print_string fmt ld;
+  (match sl with
+  | [] -> ()
+  | s :: sl ->
       F.pp_print_string fmt s;
-      F.pp_print_string fmt " -/"
+      List.iter
+        (fun s ->
+          F.pp_print_space fmt ();
+          F.pp_print_string fmt s)
+        sl);
+  F.pp_print_string fmt rd;
+  F.pp_close_box fmt ()
 
 (** Extract a type declaration.
 
@@ -1436,7 +1490,7 @@ let extract_type_decl_gen (ctx : extraction_ctx) (fmt : F.formatter)
   if !backend <> HOL4 || not (decl_is_first_from_group kind) then
     F.pp_print_break fmt 0 0;
   (* Print a comment to link the extracted type to its original rust definition *)
-  extract_comment fmt ("[" ^ Print.name_to_string def.name ^ "]");
+  extract_comment fmt [ "[" ^ Print.name_to_string def.name ^ "]" ];
   F.pp_print_break fmt 0 0;
   (* Open a box for the definition, so that whenever possible it gets printed on
    * one line. Note however that in the case of Lean line breaks are important
@@ -1833,7 +1887,7 @@ let extract_state_type (fmt : F.formatter) (ctx : extraction_ctx)
   (* Add a break before *)
   F.pp_print_break fmt 0 0;
   (* Print a comment  *)
-  extract_comment fmt "The state type used in the state-error monad";
+  extract_comment fmt [ "The state type used in the state-error monad" ];
   F.pp_print_break fmt 0 0;
   (* Open a box for the definition, so that whenever possible it gets printed on
    * one line *)
@@ -1950,14 +2004,17 @@ let extract_global_decl_register_names (ctx : extraction_ctx)
     Note that patterns can introduce new variables: we thus return an extraction
     context updated with new bindings.
 
+    [is_single_pat]: are we extracting a single pattern (a pattern for a let-binding
+    or a lambda).
+
     TODO: we don't need something very generic anymore (some definitions used
     to be polymorphic).
  *)
 let extract_adt_g_value
     (extract_value : extraction_ctx -> bool -> 'v -> extraction_ctx)
-    (fmt : F.formatter) (ctx : extraction_ctx) (inside : bool)
-    (variant_id : VariantId.id option) (field_values : 'v list) (ty : ty) :
-    extraction_ctx =
+    (fmt : F.formatter) (ctx : extraction_ctx) (is_single_pat : bool)
+    (inside : bool) (variant_id : VariantId.id option) (field_values : 'v list)
+    (ty : ty) : extraction_ctx =
   match ty with
   | Adt (Tuple, type_args) ->
       (* Tuple *)
@@ -1982,36 +2039,57 @@ let extract_adt_g_value
         ctx)
   | Adt (adt_id, _) ->
       (* "Regular" ADT *)
-      (* We print something of the form: [Cons field0 ... fieldn].
-       * We could update the code to print something of the form:
-       * [{ field0=...; ...; fieldn=...; }] in case of structures.
-       *)
-      let cons =
-        (* The ADT shouldn't be opaque *)
-        let with_opaque_pre = false in
-        match variant_id with
-        | Some vid -> (
-            (* In the case of Lean, we might have to add the type name as a prefix *)
-            match (!backend, adt_id) with
-            | Lean, Assumed _ ->
-                ctx_get_type with_opaque_pre adt_id ctx
-                ^ "."
-                ^ ctx_get_variant adt_id vid ctx
-            | _ -> ctx_get_variant adt_id vid ctx)
-        | None -> ctx_get_struct with_opaque_pre adt_id ctx
-      in
-      let use_parentheses = inside && field_values <> [] in
-      if use_parentheses then F.pp_print_string fmt "(";
-      F.pp_print_string fmt cons;
-      let ctx =
-        Collections.List.fold_left
-          (fun ctx v ->
-            F.pp_print_space fmt ();
-            extract_value ctx true v)
-          ctx field_values
-      in
-      if use_parentheses then F.pp_print_string fmt ")";
-      ctx
+
+      (* If we are generating a pattern for a let-binding and we target Lean,
+         the syntax is: `let ⟨ x0, ..., xn ⟩ := ...`.
+
+         Otherwise, it is: `let Cons x0 ... xn = ...`
+      *)
+      if is_single_pat && !Config.backend = Lean then (
+        F.pp_print_string fmt "⟨";
+        F.pp_print_space fmt ();
+        let ctx =
+          Collections.List.fold_left_link
+            (fun _ ->
+              F.pp_print_string fmt ",";
+              F.pp_print_space fmt ())
+            (fun ctx v -> extract_value ctx true v)
+            ctx field_values
+        in
+        F.pp_print_space fmt ();
+        F.pp_print_string fmt "⟩";
+        ctx)
+      else
+        (* We print something of the form: [Cons field0 ... fieldn].
+         * We could update the code to print something of the form:
+         * [{ field0=...; ...; fieldn=...; }] in case of structures.
+         *)
+        let cons =
+          (* The ADT shouldn't be opaque *)
+          let with_opaque_pre = false in
+          match variant_id with
+          | Some vid -> (
+              (* In the case of Lean, we might have to add the type name as a prefix *)
+              match (!backend, adt_id) with
+              | Lean, Assumed _ ->
+                  ctx_get_type with_opaque_pre adt_id ctx
+                  ^ "."
+                  ^ ctx_get_variant adt_id vid ctx
+              | _ -> ctx_get_variant adt_id vid ctx)
+          | None -> ctx_get_struct with_opaque_pre adt_id ctx
+        in
+        let use_parentheses = inside && field_values <> [] in
+        if use_parentheses then F.pp_print_string fmt "(";
+        F.pp_print_string fmt cons;
+        let ctx =
+          Collections.List.fold_left
+            (fun ctx v ->
+              F.pp_print_space fmt ();
+              extract_value ctx true v)
+            ctx field_values
+        in
+        if use_parentheses then F.pp_print_string fmt ")";
+        ctx
   | _ -> raise (Failure "Inconsistent typed value")
 
 (* Extract globals in the same way as variables *)
@@ -2026,7 +2104,7 @@ let extract_global (ctx : extraction_ctx) (fmt : F.formatter)
     updated with new bindings.
  *)
 let rec extract_typed_pattern (ctx : extraction_ctx) (fmt : F.formatter)
-    (inside : bool) (v : typed_pattern) : extraction_ctx =
+    (is_let : bool) (inside : bool) (v : typed_pattern) : extraction_ctx =
   match v.value with
   | PatConstant cv ->
       ctx.fmt.extract_primitive_value fmt inside cv;
@@ -2042,8 +2120,10 @@ let rec extract_typed_pattern (ctx : extraction_ctx) (fmt : F.formatter)
       F.pp_print_string fmt "_";
       ctx
   | PatAdt av ->
-      let extract_value ctx inside v = extract_typed_pattern ctx fmt inside v in
-      extract_adt_g_value extract_value fmt ctx inside av.variant_id
+      let extract_value ctx inside v =
+        extract_typed_pattern ctx fmt is_let inside v
+      in
+      extract_adt_g_value extract_value fmt ctx is_let inside av.variant_id
         av.field_values v.ty
 
 (** [inside]: controls the introduction of parentheses. See [extract_ty]
@@ -2173,12 +2253,13 @@ and extract_adt_cons (ctx : extraction_ctx) (fmt : F.formatter) (inside : bool)
     (adt_cons : adt_cons_id) (type_args : ty list) (args : texpression list) :
     unit =
   let e_ty = Adt (adt_cons.adt_id, type_args) in
+  let is_single_pat = false in
   let _ =
     extract_adt_g_value
       (fun ctx inside e ->
         extract_texpression ctx fmt inside e;
         ctx)
-      fmt ctx inside adt_cons.variant_id args e_ty
+      fmt ctx is_single_pat inside adt_cons.variant_id args e_ty
   in
   ()
 
@@ -2226,11 +2307,12 @@ and extract_Abs (ctx : extraction_ctx) (fmt : F.formatter) (inside : bool)
     List.fold_left
       (fun ctx x ->
         F.pp_print_space fmt ();
-        extract_typed_pattern ctx fmt true x)
+        extract_typed_pattern ctx fmt true true x)
       ctx xl
   in
   F.pp_print_space fmt ();
-  F.pp_print_string fmt "->";
+  if !backend = Lean then F.pp_print_string fmt "=>"
+  else F.pp_print_string fmt "->";
   F.pp_print_space fmt ();
   (* Print the body *)
   extract_texpression ctx fmt false e;
@@ -2295,7 +2377,7 @@ and extract_lets (ctx : extraction_ctx) (fmt : F.formatter) (inside : bool)
        * TODO: cleanup
        * *)
       if monadic && (!backend = Coq || !backend = HOL4) then (
-        let ctx = extract_typed_pattern ctx fmt true lv in
+        let ctx = extract_typed_pattern ctx fmt true true lv in
         F.pp_print_space fmt ();
         let arrow =
           match !backend with
@@ -2321,15 +2403,13 @@ and extract_lets (ctx : extraction_ctx) (fmt : F.formatter) (inside : bool)
         else (
           F.pp_print_string fmt "let";
           F.pp_print_space fmt ());
-        let ctx = extract_typed_pattern ctx fmt true lv in
+        let ctx = extract_typed_pattern ctx fmt true true lv in
         F.pp_print_space fmt ();
         let eq =
           match !backend with
           | FStar -> "="
           | Coq -> ":="
-          | Lean ->
-              (* TODO: switch to ⟵ once issues are fixed *)
-              if monadic then "←" else ":="
+          | Lean -> if monadic then "←" else ":="
           | HOL4 -> if monadic then "<-" else "="
         in
         F.pp_print_string fmt eq;
@@ -2409,7 +2489,7 @@ and extract_Switch (ctx : extraction_ctx) (fmt : F.formatter) (_inside : bool)
       (* Open a box for the [if e] *)
       F.pp_open_hovbox fmt ctx.indent_incr;
       F.pp_print_string fmt "if";
-      if !backend = Lean then F.pp_print_string fmt " h:";
+      if !backend = Lean && ctx.use_dep_ite then F.pp_print_string fmt " h:";
       F.pp_print_space fmt ();
       let scrut_inside = PureUtils.texpression_requires_parentheses scrut in
       extract_texpression ctx fmt scrut_inside scrut;
@@ -2470,7 +2550,7 @@ and extract_Switch (ctx : extraction_ctx) (fmt : F.formatter) (_inside : bool)
         match !backend with
         | FStar -> "begin match"
         | Coq -> "match"
-        | Lean -> "match h:"
+        | Lean -> if ctx.use_dep_ite then "match h:" else "match"
         | HOL4 ->
             (* We're being extra safe in the case of HOL4 *)
             "(case"
@@ -2497,7 +2577,7 @@ and extract_Switch (ctx : extraction_ctx) (fmt : F.formatter) (_inside : bool)
         (* Print the pattern *)
         F.pp_print_string fmt "|";
         F.pp_print_space fmt ();
-        let ctx = extract_typed_pattern ctx fmt false br.pat in
+        let ctx = extract_typed_pattern ctx fmt false false br.pat in
         F.pp_print_space fmt ();
         let arrow =
           match !backend with FStar -> "->" | Coq | Lean | HOL4 -> "=>"
@@ -2689,7 +2769,7 @@ let extract_fun_parameters (space : bool ref) (ctx : extraction_ctx)
             (* Open a box for the input parameter *)
             F.pp_open_hovbox fmt 0;
             F.pp_print_string fmt "(";
-            let ctx = extract_typed_pattern ctx fmt false lv in
+            let ctx = extract_typed_pattern ctx fmt true false lv in
             F.pp_print_space fmt ();
             F.pp_print_string fmt ":";
             F.pp_print_space fmt ();
@@ -2714,7 +2794,7 @@ let extract_fun_input_parameters_types (ctx : extraction_ctx)
     let inside = false in
     extract_ty ctx fmt TypeDeclId.Set.empty inside ty;
     F.pp_print_space fmt ();
-    F.pp_print_string fmt "->";
+    extract_arrow fmt ();
     F.pp_print_space fmt ()
   in
   List.iter extract_param def.signature.inputs
@@ -2752,7 +2832,7 @@ let extract_template_fstar_decreases_clause (ctx : extraction_ctx)
   F.pp_print_break fmt 0 0;
   (* Print a comment to link the extracted type to its original rust definition *)
   extract_comment fmt
-    ("[" ^ Print.fun_name_to_string def.basename ^ "]: decreases clause");
+    [ "[" ^ Print.fun_name_to_string def.basename ^ "]: decreases clause" ];
   F.pp_print_space fmt ();
   (* Open a box for the definition, so that whenever possible it gets printed on
    * one line *)
@@ -2814,7 +2894,7 @@ let extract_template_lean_termination_and_decreasing (ctx : extraction_ctx)
   F.pp_print_break fmt 0 0;
   (* Print a comment to link the extracted type to its original rust definition *)
   extract_comment fmt
-    ("[" ^ Print.fun_name_to_string def.basename ^ "]: termination measure");
+    [ "[" ^ Print.fun_name_to_string def.basename ^ "]: termination measure" ];
   F.pp_print_space fmt ();
   (* Open a box for the definition, so that whenever possible it gets printed on
    * one line *)
@@ -2868,7 +2948,7 @@ let extract_template_lean_termination_and_decreasing (ctx : extraction_ctx)
   (* syntax <def_name> term ... term : tactic *)
   F.pp_print_break fmt 0 0;
   extract_comment fmt
-    ("[" ^ Print.fun_name_to_string def.basename ^ "]: decreases_by tactic");
+    [ "[" ^ Print.fun_name_to_string def.basename ^ "]: decreases_by tactic" ];
   F.pp_print_space fmt ();
   F.pp_open_hvbox fmt 0;
   F.pp_print_string fmt "syntax \"";
@@ -2897,6 +2977,40 @@ let extract_template_lean_termination_and_decreasing (ctx : extraction_ctx)
   F.pp_close_box fmt ();
   F.pp_print_break fmt 0 0
 
+let extract_fun_comment (ctx : extraction_ctx) (fmt : F.formatter)
+    (def : fun_decl) : unit =
+  let { keep_fwd; num_backs } =
+    PureUtils.RegularFunIdMap.find
+      (A.Regular def.def_id, def.loop_id, def.back_id)
+      ctx.fun_name_info
+  in
+  let comment_pre = "[" ^ Print.fun_name_to_string def.basename ^ "]: " in
+  let comment =
+    let loop_comment =
+      match def.loop_id with
+      | None -> ""
+      | Some id -> "loop " ^ LoopId.to_string id ^ ": "
+    in
+    let fwd_back_comment =
+      match def.back_id with
+      | None -> [ "forward function" ]
+      | Some id ->
+          (* Check if there is only one backward function, and no forward function *)
+          if (not keep_fwd) && num_backs = 1 then
+            [
+              "merged forward/backward function";
+              "(there is a single backward function, and the forward function \
+               returns ())";
+            ]
+          else [ "backward function " ^ T.RegionGroupId.to_string id ]
+    in
+    match fwd_back_comment with
+    | [] -> raise (Failure "Unreachable")
+    | [ s ] -> [ comment_pre ^ loop_comment ^ s ]
+    | s :: sl -> (comment_pre ^ loop_comment ^ s) :: sl
+  in
+  extract_comment fmt comment
+
 (** Extract a function declaration.
 
     This function is for all function declarations and all backends **at the exception**
@@ -2916,8 +3030,8 @@ let extract_fun_decl_gen (ctx : extraction_ctx) (fmt : F.formatter)
   (* Add a break before *)
   if !backend <> HOL4 || not (decl_is_first_from_group kind) then
     F.pp_print_break fmt 0 0;
-  (* Print a comment to link the extracted type to its original rust definition *)
-  extract_comment fmt ("[" ^ Print.fun_name_to_string def.basename ^ "]");
+  (* Print a comment to link the extracted definition to its original rust definition *)
+  extract_fun_comment ctx fmt def;
   F.pp_print_space fmt ();
   (* Open two boxes for the definition, so that whenever possible it gets printed on
    * one line and indents are correct *)
@@ -2939,8 +3053,11 @@ let extract_fun_decl_gen (ctx : extraction_ctx) (fmt : F.formatter)
   let use_forall = is_opaque_coq && def.signature.type_params <> [] in
   (* Print the qualifier ("assume", etc.).
 
-     For Lean: we generate a record of assumed functions *)
-  (if not (!backend = Lean && (kind = Assumed || kind = Declared)) then
+     if `wrap_opaque_in_sig`: we generate a record of assumed funcions.
+     TODO: this is obsolete.
+  *)
+  (if not (!Config.wrap_opaque_in_sig && (kind = Assumed || kind = Declared))
+   then
      let qualif = ctx.fmt.fun_decl_kind_to_qualif kind in
      match qualif with
      | Some qualif ->
@@ -3034,7 +3151,7 @@ let extract_fun_decl_gen (ctx : extraction_ctx) (fmt : F.formatter)
         List.fold_left
           (fun ctx (lv : typed_pattern) ->
             F.pp_print_space fmt ();
-            let ctx = extract_typed_pattern ctx fmt false lv in
+            let ctx = extract_typed_pattern ctx fmt true false lv in
             ctx)
           ctx inputs_lvs
       in
@@ -3168,6 +3285,8 @@ let extract_fun_decl_hol4_opaque (ctx : extraction_ctx) (fmt : F.formatter)
   F.pp_print_break fmt 0 0;
   (* Open a box for the whole definition *)
   F.pp_open_hvbox fmt ctx.indent_incr;
+  (* Print a comment to link the extracted definition to its original rust definition *)
+  extract_fun_comment ctx fmt def;
   (* Generate: `val _ = new_constant ("...",` *)
   F.pp_print_string fmt ("val _ = new_constant (\"" ^ def_name ^ "\",");
   F.pp_print_space fmt ();
@@ -3343,7 +3462,7 @@ let extract_global_decl (ctx : extraction_ctx) (fmt : F.formatter)
 
   (* Add a break then the name of the corresponding LLBC declaration *)
   F.pp_print_break fmt 0 0;
-  extract_comment fmt ("[" ^ Print.global_name_to_string global.name ^ "]");
+  extract_comment fmt [ "[" ^ Print.global_name_to_string global.name ^ "]" ];
   F.pp_print_space fmt ();
 
   let with_opaque_pre = false in
@@ -3417,7 +3536,7 @@ let extract_unit_test_if_unit_fun (ctx : extraction_ctx) (fmt : F.formatter)
     F.pp_print_break fmt 0 0;
     (* Print a comment *)
     extract_comment fmt
-      ("Unit test for [" ^ Print.fun_name_to_string def.basename ^ "]");
+      [ "Unit test for [" ^ Print.fun_name_to_string def.basename ^ "]" ];
     F.pp_print_space fmt ();
     (* Open a box for the test *)
     F.pp_open_hovbox fmt ctx.indent_incr;
diff --git a/compiler/ExtractBase.ml b/compiler/ExtractBase.ml
index 0a5d7df2..655bb033 100644
--- a/compiler/ExtractBase.ml
+++ b/compiler/ExtractBase.ml
@@ -240,7 +240,9 @@ type formatter = {
           - loop identifier, if this is for a loop
        *)
   opaque_pre : unit -> string;
-      (** The prefix to use for opaque definitions.
+      (** TODO: obsolete, remove.
+
+          The prefix to use for opaque definitions.
 
           We need this because for some backends like Lean and Coq, we group
           opaque definitions in module signatures, meaning that using those
@@ -414,7 +416,7 @@ module IdSet = Collections.MakeSet (IdOrderedType)
 
     We use it for lookups (during the translation) and to check for name clashes.
 
-    [id_to_string] is for debugging.
+    [id_to_name] is for debugging.
   *)
 type names_map = {
   id_to_name : string IdMap.t;
@@ -425,7 +427,9 @@ type names_map = {
        *)
   names_set : StringSet.t;
   opaque_ids : IdSet.t;
-      (** The set of opaque definitions.
+      (** TODO: this is obsolete. Remove.
+
+          The set of opaque definitions.
 
           See {!formatter.opaque_pre} for detailed explanations about why
           we need to know which definitions are opaque to compute names.
@@ -486,6 +490,20 @@ let names_map_add_function (id_to_string : id -> string) (is_opaque : bool)
     (fid : fun_id) (name : string) (nm : names_map) : names_map =
   names_map_add id_to_string is_opaque (FunId fid) name nm
 
+(** The unsafe names map stores mappings from identifiers to names which might
+    collide. For some backends and some names, it might be acceptable to have
+    collisions. For instance, in Lean, different records can have fields with
+    the same name because Lean uses the typing information to resolve the
+    ambiguities.
+
+    This map complements the {!names_map}, which checks for collisions.
+  *)
+type unsafe_names_map = { id_to_name : string IdMap.t }
+
+let unsafe_names_map_add (id : id) (name : string) (nm : unsafe_names_map) :
+    unsafe_names_map =
+  { id_to_name = IdMap.add id name nm.id_to_name }
+
 (** Make a (variable) basename unique (by adding an index).
 
     We do this in an inefficient manner (by testing all indices starting from
@@ -518,6 +536,8 @@ let basename_to_unique (names_set : StringSet.t)
   in
   if StringSet.mem basename names_set then gen 0 else basename
 
+type fun_name_info = { keep_fwd : bool; num_backs : int }
+
 (** Extraction context.
 
     Note that the extraction context contains information coming from the
@@ -528,6 +548,11 @@ let basename_to_unique (names_set : StringSet.t)
 type extraction_ctx = {
   trans_ctx : trans_ctx;
   names_map : names_map;
+      (** The map for id to names, where we forbid name collisions
+          (ex.: we always forbid function name collisions). *)
+  unsafe_names_map : unsafe_names_map;
+      (** The map for id to names, where we allow name collisions
+          (ex.: we might allow record field name collisions). *)
   fmt : formatter;
   indent_incr : int;
       (** The indent increment we insert whenever we need to indent more *)
@@ -539,6 +564,25 @@ type extraction_ctx = {
           use it.
           Also see {!names_map.opaque_ids}.
        *)
+  use_dep_ite : bool;
+      (** For Lean: do we use dependent-if then else expressions?
+
+          Example:
+          {[
+            if h: b then ... else ...
+            -- ^^
+            -- makes the if then else dependent
+          ]}
+        *)
+  fun_name_info : fun_name_info PureUtils.RegularFunIdMap.t;
+      (** Information used to filter and name functions - we use it
+          to print comments in the generated code, to help link
+          the generated code to the original code (information such
+          as: "this function is the backward function of ...", or
+          "this function is the merged forward/backward function of ..."
+          in case a Rust function only has one backward translation
+          and we filter the forward function because it returns unit.
+        *)
 }
 
 (** Debugging function, used when communicating name collisions to the user,
@@ -667,23 +711,42 @@ let id_to_string (id : id) (ctx : extraction_ctx) : string =
   | TypeVarId id -> "type_var_id: " ^ TypeVarId.to_string id
   | VarId id -> "var_id: " ^ VarId.to_string id
 
+(** We might not check for collisions for some specific ids (ex.: field names) *)
+let allow_collisions (id : id) : bool =
+  match id with
+  | FieldId (_, _) -> !Config.record_fields_short_names
+  | _ -> false
+
 let ctx_add (is_opaque : bool) (id : id) (name : string) (ctx : extraction_ctx)
     : extraction_ctx =
-  (* The id_to_string function to print nice debugging messages if there are
-   * collisions *)
-  let id_to_string (id : id) : string = id_to_string id ctx in
-  let names_map = names_map_add id_to_string is_opaque id name ctx.names_map in
-  { ctx with names_map }
+  (* We do not use the same name map if we allow/disallow collisions *)
+  if allow_collisions id then (
+    assert (not is_opaque);
+    {
+      ctx with
+      unsafe_names_map = unsafe_names_map_add id name ctx.unsafe_names_map;
+    })
+  else
+    (* The id_to_string function to print nice debugging messages if there are
+     * collisions *)
+    let id_to_string (id : id) : string = id_to_string id ctx in
+    let names_map =
+      names_map_add id_to_string is_opaque id name ctx.names_map
+    in
+    { ctx with names_map }
 
 (** [with_opaque_pre]: if [true] and the definition is opaque, add the opaque prefix *)
 let ctx_get (with_opaque_pre : bool) (id : id) (ctx : extraction_ctx) : string =
-  match IdMap.find_opt id ctx.names_map.id_to_name with
-  | Some s ->
-      let is_opaque = IdSet.mem id ctx.names_map.opaque_ids in
-      if with_opaque_pre && is_opaque then ctx.fmt.opaque_pre () ^ s else s
-  | None ->
-      log#serror ("Could not find: " ^ id_to_string id ctx);
-      raise Not_found
+  (* We do not use the same name map if we allow/disallow collisions *)
+  if allow_collisions id then IdMap.find id ctx.unsafe_names_map.id_to_name
+  else
+    match IdMap.find_opt id ctx.names_map.id_to_name with
+    | Some s ->
+        let is_opaque = IdSet.mem id ctx.names_map.opaque_ids in
+        if with_opaque_pre && is_opaque then ctx.fmt.opaque_pre () ^ s else s
+    | None ->
+        log#serror ("Could not find: " ^ id_to_string id ctx);
+        raise Not_found
 
 let ctx_get_global (with_opaque_pre : bool) (id : A.GlobalDeclId.id)
     (ctx : extraction_ctx) : string =
@@ -918,9 +981,15 @@ let ctx_add_fun_decl (trans_group : bool * pure_fun_translation)
     ctx.fmt.fun_name def.basename def.num_loops def.loop_id num_rgs rg_info
       (keep_fwd, num_backs)
   in
-  ctx_add is_opaque
-    (FunId (FromLlbc (A.Regular def_id, def.loop_id, def.back_id)))
-    def_name ctx
+  let fun_id = (A.Regular def_id, def.loop_id, def.back_id) in
+  let ctx = ctx_add is_opaque (FunId (FromLlbc fun_id)) def_name ctx in
+  (* Add the name info *)
+  {
+    ctx with
+    fun_name_info =
+      PureUtils.RegularFunIdMap.add fun_id { keep_fwd; num_backs }
+        ctx.fun_name_info;
+  }
 
 type names_map_init = {
   keywords : string list;
@@ -1041,13 +1110,24 @@ let default_fun_suffix (num_loops : int) (loop_id : LoopId.id option)
      definitions (in particular between type and function definitions).
   *)
   let rg_suff =
+    (* TODO: make all the backends match what is done for Lean *)
     match rg with
-    | None -> "_fwd"
+    | None -> (
+        match !Config.backend with
+        | FStar | Coq | HOL4 -> "_fwd"
+        | Lean ->
+            (* In order to avoid name conflicts:
+             * - if the forward is eliminated, we add the suffix "_fwd" (it won't be used)
+             * - otherwise, no suffix (because the backward functions will have a suffix)
+             *)
+            if num_backs = 1 && not keep_fwd then "_fwd" else "")
     | Some rg ->
         assert (num_region_groups > 0 && num_backs > 0);
         if num_backs = 1 then
           (* Exactly one backward function *)
-          if not keep_fwd then "_fwd_back" else "_back"
+          match !Config.backend with
+          | FStar | Coq | HOL4 -> if not keep_fwd then "_fwd_back" else "_back"
+          | Lean -> if not keep_fwd then "" else "_back"
         else if
           (* Several region groups/backward functions:
              - if all the regions in the group have names, we use those names
diff --git a/compiler/Pure.ml b/compiler/Pure.ml
index 4a00dfb2..b251a005 100644
--- a/compiler/Pure.ml
+++ b/compiler/Pure.ml
@@ -18,16 +18,19 @@ module GlobalDeclId = A.GlobalDeclId
     (they monotonically increase across functions) while in {!module:Pure} we want
     the indices to start at 0 for every function.
  *)
-module LoopId = IdGen ()
+module LoopId =
+IdGen ()
 
 type loop_id = LoopId.id [@@deriving show, ord]
 
 (** We give an identifier to every phase of the synthesis (forward, backward
     for group of regions 0, etc.) *)
-module SynthPhaseId = IdGen ()
+module SynthPhaseId =
+IdGen ()
 
 (** Pay attention to the fact that we also define a {!E.VarId} module in Values *)
-module VarId = IdGen ()
+module VarId =
+IdGen ()
 
 type integer_type = T.integer_type [@@deriving show, ord]
 
@@ -723,6 +726,7 @@ type fun_sig_info = {
  *)
 type fun_sig = {
   type_params : type_var list;
+      (** TODO: we should analyse the signature to make the type parameters implicit whenever possible *)
   inputs : ty list;
       (** The input types.
 
diff --git a/compiler/Translate.ml b/compiler/Translate.ml
index 75fc7fe9..c5f7df92 100644
--- a/compiler/Translate.ml
+++ b/compiler/Translate.ml
@@ -750,18 +750,17 @@ let extract_definitions (fmt : Format.formatter) (config : gen_config)
   if config.extract_state_type && config.extract_fun_decls then
     export_state_type ();
 
-  (* For Lean, we parameterize the entire development by a section variable
-     called opaque_defs, of type OpaqueDefs. The code below emits the type
-     definition for OpaqueDefs, which is a structure, in which each field is one
-     of the functions marked as Opaque. We emit the `structure ...` bit here,
-     then rely on `extract_fun_decl` to be aware of this, and skip the keyword
-     (e.g. "axiom" or "val") so as to generate valid syntax for records.
-
-     We also generate such a structure only if there actually are opaque
-     definitions.
-  *)
+  (* Obsolete: (TODO: remove) For Lean we parameterize the entire development by a section
+     variable called opaque_defs, of type OpaqueDefs. The code below emits the type
+     definition for OpaqueDefs, which is a structure, in which each field is one of the
+     functions marked as Opaque. We emit the `structure ...` bit here, then rely on
+     `extract_fun_decl` to be aware of this, and skip the keyword (e.g. "axiom" or "val")
+     so as to generate valid syntax for records.
+
+     We also generate such a structure only if there actually are opaque definitions. *)
   let wrap_in_sig =
-    config.extract_opaque && config.extract_fun_decls && !Config.backend = Lean
+    config.extract_opaque && config.extract_fun_decls
+    && !Config.wrap_opaque_in_sig
     &&
     let _, opaque_funs = module_has_opaque_decls ctx in
     opaque_funs
@@ -783,11 +782,22 @@ let extract_definitions (fmt : Format.formatter) (config : gen_config)
 
   if wrap_in_sig then Format.pp_close_box fmt ()
 
-let extract_file (config : gen_config) (ctx : gen_ctx) (filename : string)
-    (rust_module_name : string) (module_name : string) (custom_msg : string)
-    (custom_imports : string list) (custom_includes : string list) : unit =
+type extract_file_info = {
+  filename : string;
+  namespace : string;
+  in_namespace : bool;
+  crate_name : string;
+  rust_module_name : string;
+  module_name : string;
+  custom_msg : string;
+  custom_imports : string list;
+  custom_includes : string list;
+}
+
+let extract_file (config : gen_config) (ctx : gen_ctx) (fi : extract_file_info)
+    : unit =
   (* Open the file and create the formatter *)
-  let out = open_out filename in
+  let out = open_out fi.filename in
   let fmt = Format.formatter_of_out_channel out in
 
   (* Print the headers.
@@ -801,19 +811,22 @@ let extract_file (config : gen_config) (ctx : gen_ctx) (filename : string)
   (match !Config.backend with
   | Lean ->
       Printf.fprintf out "-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS\n";
-      Printf.fprintf out "-- [%s]%s\n" rust_module_name custom_msg
+      Printf.fprintf out "-- [%s]%s\n" fi.rust_module_name fi.custom_msg
   | Coq | FStar | HOL4 ->
       Printf.fprintf out
         "(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)\n";
-      Printf.fprintf out "(** [%s]%s *)\n" rust_module_name custom_msg);
+      Printf.fprintf out "(** [%s]%s *)\n" fi.rust_module_name fi.custom_msg);
+  (* Generate the imports *)
   (match !Config.backend with
   | FStar ->
-      Printf.fprintf out "module %s\n" module_name;
+      Printf.fprintf out "module %s\n" fi.module_name;
       Printf.fprintf out "open Primitives\n";
       (* Add the custom imports *)
-      List.iter (fun m -> Printf.fprintf out "open %s\n" m) custom_imports;
+      List.iter (fun m -> Printf.fprintf out "open %s\n" m) fi.custom_imports;
       (* Add the custom includes *)
-      List.iter (fun m -> Printf.fprintf out "include %s\n" m) custom_includes;
+      List.iter
+        (fun m -> Printf.fprintf out "include %s\n" m)
+        fi.custom_includes;
       (* Z3 options - note that we use fuel 1 because it its useful for the decrease clauses *)
       Printf.fprintf out "\n#set-options \"--z3rlimit 50 --fuel 1 --ifuel 1\"\n"
   | Coq ->
@@ -825,24 +838,29 @@ let extract_file (config : gen_config) (ctx : gen_ctx) (filename : string)
       (* Add the custom imports *)
       List.iter
         (fun m -> Printf.fprintf out "Require Import %s.\n" m)
-        custom_imports;
+        fi.custom_imports;
       (* Add the custom includes *)
       List.iter
         (fun m ->
           Printf.fprintf out "Require Export %s.\n" m;
           Printf.fprintf out "Import %s.\n" m)
-        custom_includes;
-      Printf.fprintf out "Module %s.\n" module_name
+        fi.custom_includes;
+      Printf.fprintf out "Module %s.\n" fi.module_name
   | Lean ->
-      Printf.fprintf out "import Base.Primitives\n";
+      Printf.fprintf out "import Base\n";
       (* Add the custom imports *)
-      List.iter (fun m -> Printf.fprintf out "import %s\n" m) custom_imports;
+      List.iter (fun m -> Printf.fprintf out "import %s\n" m) fi.custom_imports;
       (* Add the custom includes *)
-      List.iter (fun m -> Printf.fprintf out "import %s\n" m) custom_includes
+      List.iter (fun m -> Printf.fprintf out "import %s\n" m) fi.custom_includes;
+      (* Always open the Primitives namespace *)
+      Printf.fprintf out "open Primitives\n";
+      (* If we are inside the namespace: declare it, otherwise: open it *)
+      if fi.in_namespace then Printf.fprintf out "namespace %s\n" fi.namespace
+      else Printf.fprintf out "open %s\n" fi.namespace
   | HOL4 ->
       Printf.fprintf out "open primitivesLib divDefLib\n";
       (* Add the custom imports and includes *)
-      let imports = custom_imports @ custom_includes in
+      let imports = fi.custom_imports @ fi.custom_includes in
       (* The imports are a list of module names: we need to add a "Theory" suffix *)
       let imports = List.map (fun s -> s ^ "Theory") imports in
       if imports <> [] then
@@ -850,7 +868,7 @@ let extract_file (config : gen_config) (ctx : gen_ctx) (filename : string)
         Printf.fprintf out "open %s\n\n" imports
       else Printf.fprintf out "\n";
       (* Initialize the theory *)
-      Printf.fprintf out "val _ = new_theory \"%s\"\n\n" module_name);
+      Printf.fprintf out "val _ = new_theory \"%s\"\n\n" fi.module_name);
   (* From now onwards, we use the formatter *)
   (* Set the margin *)
   Format.pp_set_margin fmt 80;
@@ -867,12 +885,13 @@ let extract_file (config : gen_config) (ctx : gen_ctx) (filename : string)
 
   (* Close the module *)
   (match !Config.backend with
-  | FStar | Lean -> ()
+  | FStar -> ()
+  | Lean -> if fi.in_namespace then Printf.fprintf out "end %s\n" fi.namespace
   | HOL4 -> Printf.fprintf out "val _ = export_theory ()\n"
-  | Coq -> Printf.fprintf out "End %s .\n" module_name);
+  | Coq -> Printf.fprintf out "End %s .\n" fi.module_name);
 
   (* Some logging *)
-  log#linfo (lazy ("Generated: " ^ filename));
+  log#linfo (lazy ("Generated: " ^ fi.filename));
 
   (* Flush and close the file *)
   close_out out
@@ -891,18 +910,24 @@ let translate_crate (filename : string) (dest_dir : string) (crate : A.crate) :
        prefixed with the type name to prevent collisions *)
     match !Config.backend with Coq | FStar | HOL4 -> true | Lean -> false
   in
+  (* Initialize the names map (we insert the names of the "primitives"
+     declarations, and insert the names of the local declarations later) *)
   let mk_formatter_and_names_map = Extract.mk_formatter_and_names_map in
   let fmt, names_map =
     mk_formatter_and_names_map trans_ctx crate.name
       variant_concatenate_type_name
   in
+  (* Put everything in the context *)
   let ctx =
     {
       ExtractBase.trans_ctx;
       names_map;
+      unsafe_names_map = { id_to_name = ExtractBase.IdMap.empty };
       fmt;
       indent_incr = 2;
       use_opaque_pre = !Config.split_files;
+      use_dep_ite = !Config.backend = Lean && !Config.extract_decreases_clauses;
+      fun_name_info = PureUtils.RegularFunIdMap.empty;
     }
   in
 
@@ -968,7 +993,7 @@ let translate_crate (filename : string) (dest_dir : string) (crate : A.crate) :
   (* Open the output file *)
   (* First compute the filename by replacing the extension and converting the
    * case (rust module names are snake case) *)
-  let module_name, extract_filebasename =
+  let namespace, crate_name, extract_filebasename =
     match Filename.chop_suffix_opt ~suffix:".llbc" filename with
     | None ->
         (* Note that we already checked the suffix upon opening the file *)
@@ -977,14 +1002,20 @@ let translate_crate (filename : string) (dest_dir : string) (crate : A.crate) :
         (* Retrieve the file basename *)
         let basename = Filename.basename filename in
         (* Convert the case *)
-        let module_name = StringUtils.to_camel_case basename in
-        let module_name =
+        let crate_name = StringUtils.to_camel_case basename in
+        let crate_name =
           if !Config.backend = HOL4 then
-            StringUtils.lowercase_first_letter module_name
-          else module_name
+            StringUtils.lowercase_first_letter crate_name
+          else crate_name
+        in
+        (* We use the raw crate name for the namespaces *)
+        let namespace =
+          match !Config.backend with
+          | FStar | Coq | HOL4 -> crate.name
+          | Lean -> crate.name
         in
         (* Concatenate *)
-        (module_name, Filename.concat dest_dir module_name)
+        (namespace, crate_name, Filename.concat dest_dir crate_name)
   in
 
   (* Put the translated definitions in maps *)
@@ -1019,11 +1050,10 @@ let translate_crate (filename : string) (dest_dir : string) (crate : A.crate) :
      create more directories *)
   if !Config.backend = Lean then (
     let ( ^^ ) = Filename.concat in
-    mkdir_if (dest_dir ^^ "Base");
-    if !Config.split_files then mkdir_if (dest_dir ^^ module_name);
+    if !Config.split_files then mkdir_if (dest_dir ^^ crate_name);
     if needs_clauses_module then (
       assert !Config.split_files;
-      mkdir_if (dest_dir ^^ module_name ^^ "Clauses")));
+      mkdir_if (dest_dir ^^ crate_name ^^ "Clauses")));
 
   (* Copy the "Primitives" file, if necessary *)
   let _ =
@@ -1033,7 +1063,7 @@ let translate_crate (filename : string) (dest_dir : string) (crate : A.crate) :
       match !Config.backend with
       | FStar -> Some ("/backends/fstar/Primitives.fst", "Primitives.fst")
       | Coq -> Some ("/backends/coq/Primitives.v", "Primitives.v")
-      | Lean -> Some ("/backends/lean/Primitives.lean", "Base/Primitives.lean")
+      | Lean -> None
       | HOL4 -> None
     in
     match primitives_src_dest with
@@ -1117,6 +1147,7 @@ let translate_crate (filename : string) (dest_dir : string) (crate : A.crate) :
 
      (* Extract the types *)
      (* If there are opaque types, we extract in an interface *)
+     (* TODO: for Lean and Coq: generate a template file *)
      let types_filename_ext =
        match !Config.backend with
        | FStar -> if has_opaque_types then ".fsti" else ".fst"
@@ -1127,7 +1158,7 @@ let translate_crate (filename : string) (dest_dir : string) (crate : A.crate) :
      let types_filename =
        extract_filebasename ^ file_delimiter ^ "Types" ^ types_filename_ext
      in
-     let types_module = module_name ^ module_delimiter ^ "Types" in
+     let types_module = crate_name ^ module_delimiter ^ "Types" in
      let types_config =
        {
          base_gen_config with
@@ -1137,8 +1168,20 @@ let translate_crate (filename : string) (dest_dir : string) (crate : A.crate) :
          interface = has_opaque_types;
        }
      in
-     extract_file types_config gen_ctx types_filename crate.A.name types_module
-       ": type definitions" [] [];
+     let file_info =
+       {
+         filename = types_filename;
+         namespace;
+         in_namespace = true;
+         crate_name;
+         rust_module_name = crate.A.name;
+         module_name = types_module;
+         custom_msg = ": type definitions";
+         custom_imports = [];
+         custom_includes = [];
+       }
+     in
+     extract_file types_config gen_ctx file_info;
 
      (* Extract the template clauses *)
      (if needs_clauses_module && !Config.extract_template_decreases_clauses then
@@ -1147,33 +1190,49 @@ let translate_crate (filename : string) (dest_dir : string) (crate : A.crate) :
           ^ "Template" ^ ext
         in
         let template_clauses_module =
-          module_name ^ module_delimiter ^ "Clauses" ^ module_delimiter
+          crate_name ^ module_delimiter ^ "Clauses" ^ module_delimiter
           ^ "Template"
         in
         let template_clauses_config =
           { base_gen_config with extract_template_decreases_clauses = true }
         in
-        extract_file template_clauses_config gen_ctx template_clauses_filename
-          crate.A.name template_clauses_module
-          ": templates for the decreases clauses" [ types_module ] []);
+        let file_info =
+          {
+            filename = template_clauses_filename;
+            namespace;
+            in_namespace = true;
+            crate_name;
+            rust_module_name = crate.A.name;
+            module_name = template_clauses_module;
+            custom_msg = ": templates for the decreases clauses";
+            custom_imports = [ types_module ];
+            custom_includes = [];
+          }
+        in
+        extract_file template_clauses_config gen_ctx file_info);
 
      (* Extract the opaque functions, if needed *)
      let opaque_funs_module =
        if has_opaque_funs then (
+         (* In the case of Lean we generate a template file *)
+         let module_suffix, opaque_imported_suffix, custom_msg =
+           match !Config.backend with
+           | FStar | Coq | HOL4 ->
+               ("Opaque", "Opaque", ": external function declarations")
+           | Lean ->
+               ( "FunsExternal_Template",
+                 "FunsExternal",
+                 ": external functions.\n\
+                  -- This is a template file: rename it to \
+                  \"FunsExternal.lean\" and fill the holes." )
+         in
          let opaque_filename =
-           extract_filebasename ^ file_delimiter ^ "Opaque" ^ opaque_ext
+           extract_filebasename ^ file_delimiter ^ module_suffix ^ opaque_ext
          in
-         let opaque_module = module_name ^ module_delimiter ^ "Opaque" in
+         let opaque_module = crate_name ^ module_delimiter ^ module_suffix in
          let opaque_imported_module =
-           (* In the case of Lean, we declare an interface (a record) containing
-              the opaque definitions, and we leave it to the user to provide an
-              instance of this module.
-
-              TODO: do the same for Coq.
-              TODO: do the same for the type definitions.
-           *)
            if !Config.backend = Lean then
-             module_name ^ module_delimiter ^ "ExternalFuns"
+             crate_name ^ module_delimiter ^ opaque_imported_suffix
            else opaque_module
          in
          let opaque_config =
@@ -1191,15 +1250,28 @@ let translate_crate (filename : string) (dest_dir : string) (crate : A.crate) :
              extract_ctx = { gen_ctx.extract_ctx with use_opaque_pre = false };
            }
          in
-         extract_file opaque_config gen_ctx opaque_filename crate.A.name
-           opaque_module ": opaque function definitions" [] [ types_module ];
+         let file_info =
+           {
+             filename = opaque_filename;
+             namespace;
+             in_namespace = false;
+             crate_name;
+             rust_module_name = crate.A.name;
+             module_name = opaque_module;
+             custom_msg;
+             custom_imports = [];
+             custom_includes = [ types_module ];
+           }
+         in
+         extract_file opaque_config gen_ctx file_info;
+         (* Return the additional dependencies *)
          [ opaque_imported_module ])
        else []
      in
 
      (* Extract the functions *)
      let fun_filename = extract_filebasename ^ file_delimiter ^ "Funs" ^ ext in
-     let fun_module = module_name ^ module_delimiter ^ "Funs" in
+     let fun_module = crate_name ^ module_delimiter ^ "Funs" in
      let fun_config =
        {
          base_gen_config with
@@ -1213,12 +1285,24 @@ let translate_crate (filename : string) (dest_dir : string) (crate : A.crate) :
          let clauses_submodule =
            if !Config.backend = Lean then module_delimiter ^ "Clauses" else ""
          in
-         [ module_name ^ clauses_submodule ^ module_delimiter ^ "Clauses" ]
+         [ crate_name ^ clauses_submodule ^ module_delimiter ^ "Clauses" ]
        else []
      in
-     extract_file fun_config gen_ctx fun_filename crate.A.name fun_module
-       ": function definitions" []
-       ([ types_module ] @ opaque_funs_module @ clauses_module))
+     let file_info =
+       {
+         filename = fun_filename;
+         namespace;
+         in_namespace = true;
+         crate_name;
+         rust_module_name = crate.A.name;
+         module_name = fun_module;
+         custom_msg = ": function definitions";
+         custom_imports = [];
+         custom_includes =
+           [ types_module ] @ opaque_funs_module @ clauses_module;
+       }
+     in
+     extract_file fun_config gen_ctx file_info)
    else
      let gen_config =
        {
@@ -1235,10 +1319,21 @@ let translate_crate (filename : string) (dest_dir : string) (crate : A.crate) :
          test_trans_unit_functions = !Config.test_trans_unit_functions;
        }
      in
+     let file_info =
+       {
+         filename = extract_filebasename ^ ext;
+         namespace;
+         in_namespace = true;
+         crate_name;
+         rust_module_name = crate.A.name;
+         module_name = crate_name;
+         custom_msg = "";
+         custom_imports = [];
+         custom_includes = [];
+       }
+     in
      (* Add the extension for F* *)
-     let extract_filename = extract_filebasename ^ ext in
-     extract_file gen_config gen_ctx extract_filename crate.A.name module_name
-       "" [] []);
+     extract_file gen_config gen_ctx file_info);
 
   (* Generate the build file *)
   match !Config.backend with
@@ -1256,47 +1351,45 @@ let translate_crate (filename : string) (dest_dir : string) (crate : A.crate) :
        * different files.
        *)
       if !Config.split_files then (
-        let filename = Filename.concat dest_dir (module_name ^ ".lean") in
+        let filename = Filename.concat dest_dir (crate_name ^ ".lean") in
         let out = open_out filename in
         (* Write *)
-        Printf.fprintf out "import %s.Funs\n" module_name;
+        Printf.fprintf out "import %s.Funs\n" crate_name;
         (* Flush and close the file, log *)
         close_out out;
         log#linfo (lazy ("Generated: " ^ filename)));
 
       (*
-       * Generate the lakefile.lean file
+       * Generate the lakefile.lean file, if the user asks for it
        *)
+      if !Config.lean_gen_lakefile then (
+        (* Open the file *)
+        let filename = Filename.concat dest_dir "lakefile.lean" in
+        let out = open_out filename in
 
-      (* Open the file *)
-      let filename = Filename.concat dest_dir "lakefile.lean" in
-      let out = open_out filename in
-
-      (* Generate the content *)
-      Printf.fprintf out "import Lake\nopen Lake DSL\n\n";
-      Printf.fprintf out "require mathlib from git\n";
-      Printf.fprintf out
-        "  \"https://github.com/leanprover-community/mathlib4.git\"\n\n";
-
-      let package_name = StringUtils.to_snake_case module_name in
-      Printf.fprintf out "package «%s» {}\n\n" package_name;
-
-      Printf.fprintf out "lean_lib «Base» {}\n\n";
-
-      Printf.fprintf out "@[default_target]\nlean_lib «%s» {}\n" module_name;
-
-      (* No default target for now.
-         Format would be:
-         {[
-           @[default_target]
-           lean_exe «package_name» {
-             root := `Main
-           }
-         ]}
-      *)
+        (* Generate the content *)
+        Printf.fprintf out "import Lake\nopen Lake DSL\n\n";
+        Printf.fprintf out "require mathlib from git\n";
+        Printf.fprintf out
+          "  \"https://github.com/leanprover-community/mathlib4.git\"\n\n";
+
+        let package_name = StringUtils.to_snake_case crate_name in
+        Printf.fprintf out "package «%s» {}\n\n" package_name;
+
+        Printf.fprintf out "@[default_target]\nlean_lib «%s» {}\n" crate_name;
+
+        (* No default target for now.
+           Format would be:
+           {[
+             @[default_target]
+               lean_exe «package_name» {
+               root := `Main
+             }
+           ]}
+        *)
 
-      (* Flush and close the file *)
-      close_out out;
+        (* Flush and close the file *)
+        close_out out;
 
-      (* Logging *)
-      log#linfo (lazy ("Generated: " ^ filename))
+        (* Logging *)
+        log#linfo (lazy ("Generated: " ^ filename)))
diff --git a/tests/coq/betree/BetreeMain_Funs.v b/tests/coq/betree/BetreeMain_Funs.v
index 940b8650..86a9d5f2 100644
--- a/tests/coq/betree/BetreeMain_Funs.v
+++ b/tests/coq/betree/BetreeMain_Funs.v
@@ -10,7 +10,7 @@ Require Export BetreeMain_Opaque.
 Import BetreeMain_Opaque.
 Module BetreeMain_Funs.
 
-(** [betree_main::betree::load_internal_node] *)
+(** [betree_main::betree::load_internal_node]: forward function *)
 Definition betree_load_internal_node_fwd
   (id : u64) (st : state) :
   result (state * (Betree_list_t (u64 * Betree_message_t)))
@@ -18,7 +18,7 @@ Definition betree_load_internal_node_fwd
   betree_utils_load_internal_node_fwd id st
 .
 
-(** [betree_main::betree::store_internal_node] *)
+(** [betree_main::betree::store_internal_node]: forward function *)
 Definition betree_store_internal_node_fwd
   (id : u64) (content : Betree_list_t (u64 * Betree_message_t)) (st : state) :
   result (state * unit)
@@ -28,13 +28,13 @@ Definition betree_store_internal_node_fwd
   Return (st0, tt)
 .
 
-(** [betree_main::betree::load_leaf_node] *)
+(** [betree_main::betree::load_leaf_node]: forward function *)
 Definition betree_load_leaf_node_fwd
   (id : u64) (st : state) : result (state * (Betree_list_t (u64 * u64))) :=
   betree_utils_load_leaf_node_fwd id st
 .
 
-(** [betree_main::betree::store_leaf_node] *)
+(** [betree_main::betree::store_leaf_node]: forward function *)
 Definition betree_store_leaf_node_fwd
   (id : u64) (content : Betree_list_t (u64 * u64)) (st : state) :
   result (state * unit)
@@ -44,29 +44,29 @@ Definition betree_store_leaf_node_fwd
   Return (st0, tt)
 .
 
-(** [betree_main::betree::fresh_node_id] *)
+(** [betree_main::betree::fresh_node_id]: forward function *)
 Definition betree_fresh_node_id_fwd (counter : u64) : result u64 :=
   _ <- u64_add counter 1%u64; Return counter
 .
 
-(** [betree_main::betree::fresh_node_id] *)
+(** [betree_main::betree::fresh_node_id]: backward function 0 *)
 Definition betree_fresh_node_id_back (counter : u64) : result u64 :=
   u64_add counter 1%u64
 .
 
-(** [betree_main::betree::NodeIdCounter::{0}::new] *)
+(** [betree_main::betree::NodeIdCounter::{0}::new]: forward function *)
 Definition betree_node_id_counter_new_fwd : result Betree_node_id_counter_t :=
   Return {| Betree_node_id_counter_next_node_id := 0%u64 |}
 .
 
-(** [betree_main::betree::NodeIdCounter::{0}::fresh_id] *)
+(** [betree_main::betree::NodeIdCounter::{0}::fresh_id]: forward function *)
 Definition betree_node_id_counter_fresh_id_fwd
   (self : Betree_node_id_counter_t) : result u64 :=
   _ <- u64_add self.(Betree_node_id_counter_next_node_id) 1%u64;
   Return self.(Betree_node_id_counter_next_node_id)
 .
 
-(** [betree_main::betree::NodeIdCounter::{0}::fresh_id] *)
+(** [betree_main::betree::NodeIdCounter::{0}::fresh_id]: backward function 0 *)
 Definition betree_node_id_counter_fresh_id_back
   (self : Betree_node_id_counter_t) : result Betree_node_id_counter_t :=
   i <- u64_add self.(Betree_node_id_counter_next_node_id) 1%u64;
@@ -79,7 +79,7 @@ Definition core_num_u64_max_body : result u64 :=
 .
 Definition core_num_u64_max_c : u64 := core_num_u64_max_body%global.
 
-(** [betree_main::betree::upsert_update] *)
+(** [betree_main::betree::upsert_update]: forward function *)
 Definition betree_upsert_update_fwd
   (prev : option u64) (st : Betree_upsert_fun_state_t) : result u64 :=
   match prev with
@@ -99,7 +99,7 @@ Definition betree_upsert_update_fwd
   end
 .
 
-(** [betree_main::betree::List::{1}::len] *)
+(** [betree_main::betree::List::{1}::len]: forward function *)
 Fixpoint betree_list_len_fwd
   (T : Type) (n : nat) (self : Betree_list_t T) : result u64 :=
   match n with
@@ -112,7 +112,7 @@ Fixpoint betree_list_len_fwd
   end
 .
 
-(** [betree_main::betree::List::{1}::split_at] *)
+(** [betree_main::betree::List::{1}::split_at]: forward function *)
 Fixpoint betree_list_split_at_fwd
   (T : Type) (n : nat) (self : Betree_list_t T) (n0 : u64) :
   result ((Betree_list_t T) * (Betree_list_t T))
@@ -135,7 +135,8 @@ Fixpoint betree_list_split_at_fwd
   end
 .
 
-(** [betree_main::betree::List::{1}::push_front] *)
+(** [betree_main::betree::List::{1}::push_front]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ()) *)
 Definition betree_list_push_front_fwd_back
   (T : Type) (self : Betree_list_t T) (x : T) : result (Betree_list_t T) :=
   let tl := mem_replace_fwd (Betree_list_t T) self BetreeListNil in
@@ -143,7 +144,7 @@ Definition betree_list_push_front_fwd_back
   Return (BetreeListCons x l)
 .
 
-(** [betree_main::betree::List::{1}::pop_front] *)
+(** [betree_main::betree::List::{1}::pop_front]: forward function *)
 Definition betree_list_pop_front_fwd
   (T : Type) (self : Betree_list_t T) : result T :=
   let ls := mem_replace_fwd (Betree_list_t T) self BetreeListNil in
@@ -153,7 +154,7 @@ Definition betree_list_pop_front_fwd
   end
 .
 
-(** [betree_main::betree::List::{1}::pop_front] *)
+(** [betree_main::betree::List::{1}::pop_front]: backward function 0 *)
 Definition betree_list_pop_front_back
   (T : Type) (self : Betree_list_t T) : result (Betree_list_t T) :=
   let ls := mem_replace_fwd (Betree_list_t T) self BetreeListNil in
@@ -163,7 +164,7 @@ Definition betree_list_pop_front_back
   end
 .
 
-(** [betree_main::betree::List::{1}::hd] *)
+(** [betree_main::betree::List::{1}::hd]: forward function *)
 Definition betree_list_hd_fwd (T : Type) (self : Betree_list_t T) : result T :=
   match self with
   | BetreeListCons hd l => Return hd
@@ -171,7 +172,7 @@ Definition betree_list_hd_fwd (T : Type) (self : Betree_list_t T) : result T :=
   end
 .
 
-(** [betree_main::betree::List::{2}::head_has_key] *)
+(** [betree_main::betree::List::{2}::head_has_key]: forward function *)
 Definition betree_list_head_has_key_fwd
   (T : Type) (self : Betree_list_t (u64 * T)) (key : u64) : result bool :=
   match self with
@@ -180,7 +181,7 @@ Definition betree_list_head_has_key_fwd
   end
 .
 
-(** [betree_main::betree::List::{2}::partition_at_pivot] *)
+(** [betree_main::betree::List::{2}::partition_at_pivot]: forward function *)
 Fixpoint betree_list_partition_at_pivot_fwd
   (T : Type) (n : nat) (self : Betree_list_t (u64 * T)) (pivot : u64) :
   result ((Betree_list_t (u64 * T)) * (Betree_list_t (u64 * T)))
@@ -203,7 +204,7 @@ Fixpoint betree_list_partition_at_pivot_fwd
   end
 .
 
-(** [betree_main::betree::Leaf::{3}::split] *)
+(** [betree_main::betree::Leaf::{3}::split]: forward function *)
 Definition betree_leaf_split_fwd
   (n : nat) (self : Betree_leaf_t) (content : Betree_list_t (u64 * u64))
   (params : Betree_params_t) (node_id_cnt : Betree_node_id_counter_t)
@@ -236,7 +237,7 @@ Definition betree_leaf_split_fwd
   Return (st1, mkBetree_internal_t self.(Betree_leaf_id) pivot n0 n1)
 .
 
-(** [betree_main::betree::Leaf::{3}::split] *)
+(** [betree_main::betree::Leaf::{3}::split]: backward function 2 *)
 Definition betree_leaf_split_back
   (n : nat) (self : Betree_leaf_t) (content : Betree_list_t (u64 * u64))
   (params : Betree_params_t) (node_id_cnt : Betree_node_id_counter_t)
@@ -257,7 +258,7 @@ Definition betree_leaf_split_back
   betree_node_id_counter_fresh_id_back node_id_cnt0
 .
 
-(** [betree_main::betree::Node::{5}::lookup_in_bindings] *)
+(** [betree_main::betree::Node::{5}::lookup_in_bindings]: forward function *)
 Fixpoint betree_node_lookup_in_bindings_fwd
   (n : nat) (key : u64) (bindings : Betree_list_t (u64 * u64)) :
   result (option u64)
@@ -279,7 +280,7 @@ Fixpoint betree_node_lookup_in_bindings_fwd
   end
 .
 
-(** [betree_main::betree::Node::{5}::lookup_first_message_for_key] *)
+(** [betree_main::betree::Node::{5}::lookup_first_message_for_key]: forward function *)
 Fixpoint betree_node_lookup_first_message_for_key_fwd
   (n : nat) (key : u64) (msgs : Betree_list_t (u64 * Betree_message_t)) :
   result (Betree_list_t (u64 * Betree_message_t))
@@ -298,7 +299,7 @@ Fixpoint betree_node_lookup_first_message_for_key_fwd
   end
 .
 
-(** [betree_main::betree::Node::{5}::lookup_first_message_for_key] *)
+(** [betree_main::betree::Node::{5}::lookup_first_message_for_key]: backward function 0 *)
 Fixpoint betree_node_lookup_first_message_for_key_back
   (n : nat) (key : u64) (msgs : Betree_list_t (u64 * Betree_message_t))
   (ret : Betree_list_t (u64 * Betree_message_t)) :
@@ -321,7 +322,7 @@ Fixpoint betree_node_lookup_first_message_for_key_back
   end
 .
 
-(** [betree_main::betree::Node::{5}::apply_upserts] *)
+(** [betree_main::betree::Node::{5}::apply_upserts]: forward function *)
 Fixpoint betree_node_apply_upserts_fwd
   (n : nat) (msgs : Betree_list_t (u64 * Betree_message_t)) (prev : option u64)
   (key : u64) (st : state) :
@@ -353,7 +354,7 @@ Fixpoint betree_node_apply_upserts_fwd
   end
 .
 
-(** [betree_main::betree::Node::{5}::apply_upserts] *)
+(** [betree_main::betree::Node::{5}::apply_upserts]: backward function 0 *)
 Fixpoint betree_node_apply_upserts_back
   (n : nat) (msgs : Betree_list_t (u64 * Betree_message_t)) (prev : option u64)
   (key : u64) (st : state) :
@@ -383,7 +384,7 @@ Fixpoint betree_node_apply_upserts_back
   end
 .
 
-(** [betree_main::betree::Node::{5}::lookup] *)
+(** [betree_main::betree::Node::{5}::lookup]: forward function *)
 Fixpoint betree_node_lookup_fwd
   (n : nat) (self : Betree_node_t) (key : u64) (st : state) :
   result (state * (option u64))
@@ -455,7 +456,7 @@ Fixpoint betree_node_lookup_fwd
     end
   end
 
-(** [betree_main::betree::Node::{5}::lookup] *)
+(** [betree_main::betree::Node::{5}::lookup]: backward function 0 *)
 with betree_node_lookup_back
   (n : nat) (self : Betree_node_t) (key : u64) (st : state) :
   result Betree_node_t
@@ -524,7 +525,7 @@ with betree_node_lookup_back
     end
   end
 
-(** [betree_main::betree::Internal::{4}::lookup_in_children] *)
+(** [betree_main::betree::Internal::{4}::lookup_in_children]: forward function *)
 with betree_internal_lookup_in_children_fwd
   (n : nat) (self : Betree_internal_t) (key : u64) (st : state) :
   result (state * (option u64))
@@ -537,7 +538,7 @@ with betree_internal_lookup_in_children_fwd
     else betree_node_lookup_fwd n0 self.(Betree_internal_right) key st
   end
 
-(** [betree_main::betree::Internal::{4}::lookup_in_children] *)
+(** [betree_main::betree::Internal::{4}::lookup_in_children]: backward function 0 *)
 with betree_internal_lookup_in_children_back
   (n : nat) (self : Betree_internal_t) (key : u64) (st : state) :
   result Betree_internal_t
@@ -557,7 +558,7 @@ with betree_internal_lookup_in_children_back
   end
 .
 
-(** [betree_main::betree::Node::{5}::lookup_mut_in_bindings] *)
+(** [betree_main::betree::Node::{5}::lookup_mut_in_bindings]: forward function *)
 Fixpoint betree_node_lookup_mut_in_bindings_fwd
   (n : nat) (key : u64) (bindings : Betree_list_t (u64 * u64)) :
   result (Betree_list_t (u64 * u64))
@@ -576,7 +577,7 @@ Fixpoint betree_node_lookup_mut_in_bindings_fwd
   end
 .
 
-(** [betree_main::betree::Node::{5}::lookup_mut_in_bindings] *)
+(** [betree_main::betree::Node::{5}::lookup_mut_in_bindings]: backward function 0 *)
 Fixpoint betree_node_lookup_mut_in_bindings_back
   (n : nat) (key : u64) (bindings : Betree_list_t (u64 * u64))
   (ret : Betree_list_t (u64 * u64)) :
@@ -598,7 +599,8 @@ Fixpoint betree_node_lookup_mut_in_bindings_back
   end
 .
 
-(** [betree_main::betree::Node::{5}::apply_to_leaf] *)
+(** [betree_main::betree::Node::{5}::apply_to_leaf]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ()) *)
 Definition betree_node_apply_to_leaf_fwd_back
   (n : nat) (bindings : Betree_list_t (u64 * u64)) (key : u64)
   (new_msg : Betree_message_t) :
@@ -642,7 +644,8 @@ Definition betree_node_apply_to_leaf_fwd_back
     end
 .
 
-(** [betree_main::betree::Node::{5}::apply_messages_to_leaf] *)
+(** [betree_main::betree::Node::{5}::apply_messages_to_leaf]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ()) *)
 Fixpoint betree_node_apply_messages_to_leaf_fwd_back
   (n : nat) (bindings : Betree_list_t (u64 * u64))
   (new_msgs : Betree_list_t (u64 * Betree_message_t)) :
@@ -661,7 +664,8 @@ Fixpoint betree_node_apply_messages_to_leaf_fwd_back
   end
 .
 
-(** [betree_main::betree::Node::{5}::filter_messages_for_key] *)
+(** [betree_main::betree::Node::{5}::filter_messages_for_key]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ()) *)
 Fixpoint betree_node_filter_messages_for_key_fwd_back
   (n : nat) (key : u64) (msgs : Betree_list_t (u64 * Betree_message_t)) :
   result (Betree_list_t (u64 * Betree_message_t))
@@ -684,7 +688,7 @@ Fixpoint betree_node_filter_messages_for_key_fwd_back
   end
 .
 
-(** [betree_main::betree::Node::{5}::lookup_first_message_after_key] *)
+(** [betree_main::betree::Node::{5}::lookup_first_message_after_key]: forward function *)
 Fixpoint betree_node_lookup_first_message_after_key_fwd
   (n : nat) (key : u64) (msgs : Betree_list_t (u64 * Betree_message_t)) :
   result (Betree_list_t (u64 * Betree_message_t))
@@ -703,7 +707,7 @@ Fixpoint betree_node_lookup_first_message_after_key_fwd
   end
 .
 
-(** [betree_main::betree::Node::{5}::lookup_first_message_after_key] *)
+(** [betree_main::betree::Node::{5}::lookup_first_message_after_key]: backward function 0 *)
 Fixpoint betree_node_lookup_first_message_after_key_back
   (n : nat) (key : u64) (msgs : Betree_list_t (u64 * Betree_message_t))
   (ret : Betree_list_t (u64 * Betree_message_t)) :
@@ -726,7 +730,8 @@ Fixpoint betree_node_lookup_first_message_after_key_back
   end
 .
 
-(** [betree_main::betree::Node::{5}::apply_to_internal] *)
+(** [betree_main::betree::Node::{5}::apply_to_internal]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ()) *)
 Definition betree_node_apply_to_internal_fwd_back
   (n : nat) (msgs : Betree_list_t (u64 * Betree_message_t)) (key : u64)
   (new_msg : Betree_message_t) :
@@ -784,7 +789,8 @@ Definition betree_node_apply_to_internal_fwd_back
     betree_node_lookup_first_message_for_key_back n key msgs msgs1)
 .
 
-(** [betree_main::betree::Node::{5}::apply_messages_to_internal] *)
+(** [betree_main::betree::Node::{5}::apply_messages_to_internal]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ()) *)
 Fixpoint betree_node_apply_messages_to_internal_fwd_back
   (n : nat) (msgs : Betree_list_t (u64 * Betree_message_t))
   (new_msgs : Betree_list_t (u64 * Betree_message_t)) :
@@ -803,7 +809,7 @@ Fixpoint betree_node_apply_messages_to_internal_fwd_back
   end
 .
 
-(** [betree_main::betree::Node::{5}::apply_messages] *)
+(** [betree_main::betree::Node::{5}::apply_messages]: forward function *)
 Fixpoint betree_node_apply_messages_fwd
   (n : nat) (self : Betree_node_t) (params : Betree_params_t)
   (node_id_cnt : Betree_node_id_counter_t)
@@ -859,7 +865,7 @@ Fixpoint betree_node_apply_messages_fwd
     end
   end
 
-(** [betree_main::betree::Node::{5}::apply_messages] *)
+(** [betree_main::betree::Node::{5}::apply_messages]: backward function 0 *)
 with betree_node_apply_messages_back
   (n : nat) (self : Betree_node_t) (params : Betree_params_t)
   (node_id_cnt : Betree_node_id_counter_t)
@@ -915,7 +921,7 @@ with betree_node_apply_messages_back
     end
   end
 
-(** [betree_main::betree::Internal::{4}::flush] *)
+(** [betree_main::betree::Internal::{4}::flush]: forward function *)
 with betree_internal_flush_fwd
   (n : nat) (self : Betree_internal_t) (params : Betree_params_t)
   (node_id_cnt : Betree_node_id_counter_t)
@@ -963,7 +969,7 @@ with betree_internal_flush_fwd
       Return (st0, msgs_left))
   end
 
-(** [betree_main::betree::Internal::{4}::flush] *)
+(** [betree_main::betree::Internal::{4}::flush]: backward function 0 *)
 with betree_internal_flush_back
   (n : nat) (self : Betree_internal_t) (params : Betree_params_t)
   (node_id_cnt : Betree_node_id_counter_t)
@@ -1012,7 +1018,7 @@ with betree_internal_flush_back
   end
 .
 
-(** [betree_main::betree::Node::{5}::apply] *)
+(** [betree_main::betree::Node::{5}::apply]: forward function *)
 Definition betree_node_apply_fwd
   (n : nat) (self : Betree_node_t) (params : Betree_params_t)
   (node_id_cnt : Betree_node_id_counter_t) (key : u64)
@@ -1030,7 +1036,7 @@ Definition betree_node_apply_fwd
   Return (st0, tt)
 .
 
-(** [betree_main::betree::Node::{5}::apply] *)
+(** [betree_main::betree::Node::{5}::apply]: backward function 0 *)
 Definition betree_node_apply_back
   (n : nat) (self : Betree_node_t) (params : Betree_params_t)
   (node_id_cnt : Betree_node_id_counter_t) (key : u64)
@@ -1042,7 +1048,7 @@ Definition betree_node_apply_back
     (key, new_msg) l) st
 .
 
-(** [betree_main::betree::BeTree::{6}::new] *)
+(** [betree_main::betree::BeTree::{6}::new]: forward function *)
 Definition betree_be_tree_new_fwd
   (min_flush_size : u64) (split_size : u64) (st : state) :
   result (state * Betree_be_tree_t)
@@ -1065,7 +1071,7 @@ Definition betree_be_tree_new_fwd
     |})
 .
 
-(** [betree_main::betree::BeTree::{6}::apply] *)
+(** [betree_main::betree::BeTree::{6}::apply]: forward function *)
 Definition betree_be_tree_apply_fwd
   (n : nat) (self : Betree_be_tree_t) (key : u64) (msg : Betree_message_t)
   (st : state) :
@@ -1081,7 +1087,7 @@ Definition betree_be_tree_apply_fwd
   Return (st0, tt)
 .
 
-(** [betree_main::betree::BeTree::{6}::apply] *)
+(** [betree_main::betree::BeTree::{6}::apply]: backward function 0 *)
 Definition betree_be_tree_apply_back
   (n : nat) (self : Betree_be_tree_t) (key : u64) (msg : Betree_message_t)
   (st : state) :
@@ -1099,7 +1105,7 @@ Definition betree_be_tree_apply_back
     |}
 .
 
-(** [betree_main::betree::BeTree::{6}::insert] *)
+(** [betree_main::betree::BeTree::{6}::insert]: forward function *)
 Definition betree_be_tree_insert_fwd
   (n : nat) (self : Betree_be_tree_t) (key : u64) (value : u64) (st : state) :
   result (state * unit)
@@ -1110,7 +1116,7 @@ Definition betree_be_tree_insert_fwd
   Return (st0, tt)
 .
 
-(** [betree_main::betree::BeTree::{6}::insert] *)
+(** [betree_main::betree::BeTree::{6}::insert]: backward function 0 *)
 Definition betree_be_tree_insert_back
   (n : nat) (self : Betree_be_tree_t) (key : u64) (value : u64) (st : state) :
   result Betree_be_tree_t
@@ -1118,7 +1124,7 @@ Definition betree_be_tree_insert_back
   betree_be_tree_apply_back n self key (BetreeMessageInsert value) st
 .
 
-(** [betree_main::betree::BeTree::{6}::delete] *)
+(** [betree_main::betree::BeTree::{6}::delete]: forward function *)
 Definition betree_be_tree_delete_fwd
   (n : nat) (self : Betree_be_tree_t) (key : u64) (st : state) :
   result (state * unit)
@@ -1129,7 +1135,7 @@ Definition betree_be_tree_delete_fwd
   Return (st0, tt)
 .
 
-(** [betree_main::betree::BeTree::{6}::delete] *)
+(** [betree_main::betree::BeTree::{6}::delete]: backward function 0 *)
 Definition betree_be_tree_delete_back
   (n : nat) (self : Betree_be_tree_t) (key : u64) (st : state) :
   result Betree_be_tree_t
@@ -1137,7 +1143,7 @@ Definition betree_be_tree_delete_back
   betree_be_tree_apply_back n self key BetreeMessageDelete st
 .
 
-(** [betree_main::betree::BeTree::{6}::upsert] *)
+(** [betree_main::betree::BeTree::{6}::upsert]: forward function *)
 Definition betree_be_tree_upsert_fwd
   (n : nat) (self : Betree_be_tree_t) (key : u64)
   (upd : Betree_upsert_fun_state_t) (st : state) :
@@ -1149,7 +1155,7 @@ Definition betree_be_tree_upsert_fwd
   Return (st0, tt)
 .
 
-(** [betree_main::betree::BeTree::{6}::upsert] *)
+(** [betree_main::betree::BeTree::{6}::upsert]: backward function 0 *)
 Definition betree_be_tree_upsert_back
   (n : nat) (self : Betree_be_tree_t) (key : u64)
   (upd : Betree_upsert_fun_state_t) (st : state) :
@@ -1158,7 +1164,7 @@ Definition betree_be_tree_upsert_back
   betree_be_tree_apply_back n self key (BetreeMessageUpsert upd) st
 .
 
-(** [betree_main::betree::BeTree::{6}::lookup] *)
+(** [betree_main::betree::BeTree::{6}::lookup]: forward function *)
 Definition betree_be_tree_lookup_fwd
   (n : nat) (self : Betree_be_tree_t) (key : u64) (st : state) :
   result (state * (option u64))
@@ -1166,7 +1172,7 @@ Definition betree_be_tree_lookup_fwd
   betree_node_lookup_fwd n self.(Betree_be_tree_root) key st
 .
 
-(** [betree_main::betree::BeTree::{6}::lookup] *)
+(** [betree_main::betree::BeTree::{6}::lookup]: backward function 0 *)
 Definition betree_be_tree_lookup_back
   (n : nat) (self : Betree_be_tree_t) (key : u64) (st : state) :
   result Betree_be_tree_t
@@ -1180,7 +1186,7 @@ Definition betree_be_tree_lookup_back
     |}
 .
 
-(** [betree_main::main] *)
+(** [betree_main::main]: forward function *)
 Definition main_fwd : result unit :=
   Return tt.
 
diff --git a/tests/coq/betree/BetreeMain_Opaque.v b/tests/coq/betree/BetreeMain_Opaque.v
index 08ab530a..bd49500b 100644
--- a/tests/coq/betree/BetreeMain_Opaque.v
+++ b/tests/coq/betree/BetreeMain_Opaque.v
@@ -1,5 +1,5 @@
 (** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
-(** [betree_main]: opaque function definitions *)
+(** [betree_main]: external function declarations *)
 Require Import Primitives.
 Import Primitives.
 Require Import Coq.ZArith.ZArith.
@@ -8,29 +8,29 @@ Require Export BetreeMain_Types.
 Import BetreeMain_Types.
 Module BetreeMain_Opaque.
 
-(** [betree_main::betree_utils::load_internal_node] *)
+(** [betree_main::betree_utils::load_internal_node]: forward function *)
 Axiom betree_utils_load_internal_node_fwd
   : u64 -> state -> result (state * (Betree_list_t (u64 * Betree_message_t)))
 .
 
-(** [betree_main::betree_utils::store_internal_node] *)
+(** [betree_main::betree_utils::store_internal_node]: forward function *)
 Axiom betree_utils_store_internal_node_fwd
   :
   u64 -> Betree_list_t (u64 * Betree_message_t) -> state -> result (state *
     unit)
 .
 
-(** [betree_main::betree_utils::load_leaf_node] *)
+(** [betree_main::betree_utils::load_leaf_node]: forward function *)
 Axiom betree_utils_load_leaf_node_fwd
   : u64 -> state -> result (state * (Betree_list_t (u64 * u64)))
 .
 
-(** [betree_main::betree_utils::store_leaf_node] *)
+(** [betree_main::betree_utils::store_leaf_node]: forward function *)
 Axiom betree_utils_store_leaf_node_fwd
   : u64 -> Betree_list_t (u64 * u64) -> state -> result (state * unit)
 .
 
-(** [core::option::Option::{0}::unwrap] *)
+(** [core::option::Option::{0}::unwrap]: forward function *)
 Axiom core_option_option_unwrap_fwd :
   forall(T : Type), option T -> state -> result (state * T)
 .
diff --git a/tests/coq/betree/_CoqProject b/tests/coq/betree/_CoqProject
index e5a3f799..42c62421 100644
--- a/tests/coq/betree/_CoqProject
+++ b/tests/coq/betree/_CoqProject
@@ -3,7 +3,7 @@
 -arg -w
 -arg all
 
-Primitives.v
 BetreeMain_Types.v
+Primitives.v
 BetreeMain_Funs.v
 BetreeMain_Opaque.v
diff --git a/tests/coq/hashmap/Hashmap_Funs.v b/tests/coq/hashmap/Hashmap_Funs.v
index 6bc82677..c8630eb6 100644
--- a/tests/coq/hashmap/Hashmap_Funs.v
+++ b/tests/coq/hashmap/Hashmap_Funs.v
@@ -8,11 +8,11 @@ Require Export Hashmap_Types.
 Import Hashmap_Types.
 Module Hashmap_Funs.
 
-(** [hashmap::hash_key] *)
+(** [hashmap::hash_key]: forward function *)
 Definition hash_key_fwd (k : usize) : result usize :=
   Return k.
 
-(** [hashmap::HashMap::{0}::allocate_slots] *)
+(** [hashmap::HashMap::{0}::allocate_slots]: loop 0: forward function *)
 Fixpoint hash_map_allocate_slots_loop_fwd
   (T : Type) (n : nat) (slots : vec (List_t T)) (n0 : usize) :
   result (vec (List_t T))
@@ -29,7 +29,7 @@ Fixpoint hash_map_allocate_slots_loop_fwd
   end
 .
 
-(** [hashmap::HashMap::{0}::allocate_slots] *)
+(** [hashmap::HashMap::{0}::allocate_slots]: forward function *)
 Definition hash_map_allocate_slots_fwd
   (T : Type) (n : nat) (slots : vec (List_t T)) (n0 : usize) :
   result (vec (List_t T))
@@ -37,7 +37,7 @@ Definition hash_map_allocate_slots_fwd
   hash_map_allocate_slots_loop_fwd T n slots n0
 .
 
-(** [hashmap::HashMap::{0}::new_with_capacity] *)
+(** [hashmap::HashMap::{0}::new_with_capacity]: forward function *)
 Definition hash_map_new_with_capacity_fwd
   (T : Type) (n : nat) (capacity : usize) (max_load_dividend : usize)
   (max_load_divisor : usize) :
@@ -56,12 +56,13 @@ Definition hash_map_new_with_capacity_fwd
     |}
 .
 
-(** [hashmap::HashMap::{0}::new] *)
+(** [hashmap::HashMap::{0}::new]: forward function *)
 Definition hash_map_new_fwd (T : Type) (n : nat) : result (Hash_map_t T) :=
   hash_map_new_with_capacity_fwd T n 32%usize 4%usize 5%usize
 .
 
-(** [hashmap::HashMap::{0}::clear] *)
+(** [hashmap::HashMap::{0}::clear]: loop 0: merged forward/backward function
+    (there is a single backward function, and the forward function returns ()) *)
 Fixpoint hash_map_clear_loop_fwd_back
   (T : Type) (n : nat) (slots : vec (List_t T)) (i : usize) :
   result (vec (List_t T))
@@ -79,7 +80,8 @@ Fixpoint hash_map_clear_loop_fwd_back
   end
 .
 
-(** [hashmap::HashMap::{0}::clear] *)
+(** [hashmap::HashMap::{0}::clear]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ()) *)
 Definition hash_map_clear_fwd_back
   (T : Type) (n : nat) (self : Hash_map_t T) : result (Hash_map_t T) :=
   v <- hash_map_clear_loop_fwd_back T n self.(Hash_map_slots) 0%usize;
@@ -92,12 +94,12 @@ Definition hash_map_clear_fwd_back
     |}
 .
 
-(** [hashmap::HashMap::{0}::len] *)
+(** [hashmap::HashMap::{0}::len]: forward function *)
 Definition hash_map_len_fwd (T : Type) (self : Hash_map_t T) : result usize :=
   Return self.(Hash_map_num_entries)
 .
 
-(** [hashmap::HashMap::{0}::insert_in_list] *)
+(** [hashmap::HashMap::{0}::insert_in_list]: loop 0: forward function *)
 Fixpoint hash_map_insert_in_list_loop_fwd
   (T : Type) (n : nat) (key : usize) (value : T) (ls : List_t T) :
   result bool
@@ -115,7 +117,7 @@ Fixpoint hash_map_insert_in_list_loop_fwd
   end
 .
 
-(** [hashmap::HashMap::{0}::insert_in_list] *)
+(** [hashmap::HashMap::{0}::insert_in_list]: forward function *)
 Definition hash_map_insert_in_list_fwd
   (T : Type) (n : nat) (key : usize) (value : T) (ls : List_t T) :
   result bool
@@ -123,7 +125,7 @@ Definition hash_map_insert_in_list_fwd
   hash_map_insert_in_list_loop_fwd T n key value ls
 .
 
-(** [hashmap::HashMap::{0}::insert_in_list] *)
+(** [hashmap::HashMap::{0}::insert_in_list]: loop 0: backward function 0 *)
 Fixpoint hash_map_insert_in_list_loop_back
   (T : Type) (n : nat) (key : usize) (value : T) (ls : List_t T) :
   result (List_t T)
@@ -143,7 +145,7 @@ Fixpoint hash_map_insert_in_list_loop_back
   end
 .
 
-(** [hashmap::HashMap::{0}::insert_in_list] *)
+(** [hashmap::HashMap::{0}::insert_in_list]: backward function 0 *)
 Definition hash_map_insert_in_list_back
   (T : Type) (n : nat) (key : usize) (value : T) (ls : List_t T) :
   result (List_t T)
@@ -151,7 +153,8 @@ Definition hash_map_insert_in_list_back
   hash_map_insert_in_list_loop_back T n key value ls
 .
 
-(** [hashmap::HashMap::{0}::insert_no_resize] *)
+(** [hashmap::HashMap::{0}::insert_no_resize]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ()) *)
 Definition hash_map_insert_no_resize_fwd_back
   (T : Type) (n : nat) (self : Hash_map_t T) (key : usize) (value : T) :
   result (Hash_map_t T)
@@ -189,7 +192,8 @@ Definition hash_map_insert_no_resize_fwd_back
 Definition core_num_u32_max_body : result u32 := Return 4294967295%u32.
 Definition core_num_u32_max_c : u32 := core_num_u32_max_body%global.
 
-(** [hashmap::HashMap::{0}::move_elements_from_list] *)
+(** [hashmap::HashMap::{0}::move_elements_from_list]: loop 0: merged forward/backward function
+    (there is a single backward function, and the forward function returns ()) *)
 Fixpoint hash_map_move_elements_from_list_loop_fwd_back
   (T : Type) (n : nat) (ntable : Hash_map_t T) (ls : List_t T) :
   result (Hash_map_t T)
@@ -206,7 +210,8 @@ Fixpoint hash_map_move_elements_from_list_loop_fwd_back
   end
 .
 
-(** [hashmap::HashMap::{0}::move_elements_from_list] *)
+(** [hashmap::HashMap::{0}::move_elements_from_list]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ()) *)
 Definition hash_map_move_elements_from_list_fwd_back
   (T : Type) (n : nat) (ntable : Hash_map_t T) (ls : List_t T) :
   result (Hash_map_t T)
@@ -214,7 +219,8 @@ Definition hash_map_move_elements_from_list_fwd_back
   hash_map_move_elements_from_list_loop_fwd_back T n ntable ls
 .
 
-(** [hashmap::HashMap::{0}::move_elements] *)
+(** [hashmap::HashMap::{0}::move_elements]: loop 0: merged forward/backward function
+    (there is a single backward function, and the forward function returns ()) *)
 Fixpoint hash_map_move_elements_loop_fwd_back
   (T : Type) (n : nat) (ntable : Hash_map_t T) (slots : vec (List_t T))
   (i : usize) :
@@ -237,7 +243,8 @@ Fixpoint hash_map_move_elements_loop_fwd_back
   end
 .
 
-(** [hashmap::HashMap::{0}::move_elements] *)
+(** [hashmap::HashMap::{0}::move_elements]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ()) *)
 Definition hash_map_move_elements_fwd_back
   (T : Type) (n : nat) (ntable : Hash_map_t T) (slots : vec (List_t T))
   (i : usize) :
@@ -246,7 +253,8 @@ Definition hash_map_move_elements_fwd_back
   hash_map_move_elements_loop_fwd_back T n ntable slots i
 .
 
-(** [hashmap::HashMap::{0}::try_resize] *)
+(** [hashmap::HashMap::{0}::try_resize]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ()) *)
 Definition hash_map_try_resize_fwd_back
   (T : Type) (n : nat) (self : Hash_map_t T) : result (Hash_map_t T) :=
   max_usize <- scalar_cast U32 Usize core_num_u32_max_c;
@@ -278,7 +286,8 @@ Definition hash_map_try_resize_fwd_back
       |}
 .
 
-(** [hashmap::HashMap::{0}::insert] *)
+(** [hashmap::HashMap::{0}::insert]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ()) *)
 Definition hash_map_insert_fwd_back
   (T : Type) (n : nat) (self : Hash_map_t T) (key : usize) (value : T) :
   result (Hash_map_t T)
@@ -290,7 +299,7 @@ Definition hash_map_insert_fwd_back
   else Return self0
 .
 
-(** [hashmap::HashMap::{0}::contains_key_in_list] *)
+(** [hashmap::HashMap::{0}::contains_key_in_list]: loop 0: forward function *)
 Fixpoint hash_map_contains_key_in_list_loop_fwd
   (T : Type) (n : nat) (key : usize) (ls : List_t T) : result bool :=
   match n with
@@ -306,13 +315,13 @@ Fixpoint hash_map_contains_key_in_list_loop_fwd
   end
 .
 
-(** [hashmap::HashMap::{0}::contains_key_in_list] *)
+(** [hashmap::HashMap::{0}::contains_key_in_list]: forward function *)
 Definition hash_map_contains_key_in_list_fwd
   (T : Type) (n : nat) (key : usize) (ls : List_t T) : result bool :=
   hash_map_contains_key_in_list_loop_fwd T n key ls
 .
 
-(** [hashmap::HashMap::{0}::contains_key] *)
+(** [hashmap::HashMap::{0}::contains_key]: forward function *)
 Definition hash_map_contains_key_fwd
   (T : Type) (n : nat) (self : Hash_map_t T) (key : usize) : result bool :=
   hash <- hash_key_fwd key;
@@ -322,7 +331,7 @@ Definition hash_map_contains_key_fwd
   hash_map_contains_key_in_list_fwd T n key l
 .
 
-(** [hashmap::HashMap::{0}::get_in_list] *)
+(** [hashmap::HashMap::{0}::get_in_list]: loop 0: forward function *)
 Fixpoint hash_map_get_in_list_loop_fwd
   (T : Type) (n : nat) (key : usize) (ls : List_t T) : result T :=
   match n with
@@ -338,13 +347,13 @@ Fixpoint hash_map_get_in_list_loop_fwd
   end
 .
 
-(** [hashmap::HashMap::{0}::get_in_list] *)
+(** [hashmap::HashMap::{0}::get_in_list]: forward function *)
 Definition hash_map_get_in_list_fwd
   (T : Type) (n : nat) (key : usize) (ls : List_t T) : result T :=
   hash_map_get_in_list_loop_fwd T n key ls
 .
 
-(** [hashmap::HashMap::{0}::get] *)
+(** [hashmap::HashMap::{0}::get]: forward function *)
 Definition hash_map_get_fwd
   (T : Type) (n : nat) (self : Hash_map_t T) (key : usize) : result T :=
   hash <- hash_key_fwd key;
@@ -354,7 +363,7 @@ Definition hash_map_get_fwd
   hash_map_get_in_list_fwd T n key l
 .
 
-(** [hashmap::HashMap::{0}::get_mut_in_list] *)
+(** [hashmap::HashMap::{0}::get_mut_in_list]: loop 0: forward function *)
 Fixpoint hash_map_get_mut_in_list_loop_fwd
   (T : Type) (n : nat) (ls : List_t T) (key : usize) : result T :=
   match n with
@@ -370,13 +379,13 @@ Fixpoint hash_map_get_mut_in_list_loop_fwd
   end
 .
 
-(** [hashmap::HashMap::{0}::get_mut_in_list] *)
+(** [hashmap::HashMap::{0}::get_mut_in_list]: forward function *)
 Definition hash_map_get_mut_in_list_fwd
   (T : Type) (n : nat) (ls : List_t T) (key : usize) : result T :=
   hash_map_get_mut_in_list_loop_fwd T n ls key
 .
 
-(** [hashmap::HashMap::{0}::get_mut_in_list] *)
+(** [hashmap::HashMap::{0}::get_mut_in_list]: loop 0: backward function 0 *)
 Fixpoint hash_map_get_mut_in_list_loop_back
   (T : Type) (n : nat) (ls : List_t T) (key : usize) (ret : T) :
   result (List_t T)
@@ -396,7 +405,7 @@ Fixpoint hash_map_get_mut_in_list_loop_back
   end
 .
 
-(** [hashmap::HashMap::{0}::get_mut_in_list] *)
+(** [hashmap::HashMap::{0}::get_mut_in_list]: backward function 0 *)
 Definition hash_map_get_mut_in_list_back
   (T : Type) (n : nat) (ls : List_t T) (key : usize) (ret : T) :
   result (List_t T)
@@ -404,7 +413,7 @@ Definition hash_map_get_mut_in_list_back
   hash_map_get_mut_in_list_loop_back T n ls key ret
 .
 
-(** [hashmap::HashMap::{0}::get_mut] *)
+(** [hashmap::HashMap::{0}::get_mut]: forward function *)
 Definition hash_map_get_mut_fwd
   (T : Type) (n : nat) (self : Hash_map_t T) (key : usize) : result T :=
   hash <- hash_key_fwd key;
@@ -414,7 +423,7 @@ Definition hash_map_get_mut_fwd
   hash_map_get_mut_in_list_fwd T n l key
 .
 
-(** [hashmap::HashMap::{0}::get_mut] *)
+(** [hashmap::HashMap::{0}::get_mut]: backward function 0 *)
 Definition hash_map_get_mut_back
   (T : Type) (n : nat) (self : Hash_map_t T) (key : usize) (ret : T) :
   result (Hash_map_t T)
@@ -434,7 +443,7 @@ Definition hash_map_get_mut_back
     |}
 .
 
-(** [hashmap::HashMap::{0}::remove_from_list] *)
+(** [hashmap::HashMap::{0}::remove_from_list]: loop 0: forward function *)
 Fixpoint hash_map_remove_from_list_loop_fwd
   (T : Type) (n : nat) (key : usize) (ls : List_t T) : result (option T) :=
   match n with
@@ -455,13 +464,13 @@ Fixpoint hash_map_remove_from_list_loop_fwd
   end
 .
 
-(** [hashmap::HashMap::{0}::remove_from_list] *)
+(** [hashmap::HashMap::{0}::remove_from_list]: forward function *)
 Definition hash_map_remove_from_list_fwd
   (T : Type) (n : nat) (key : usize) (ls : List_t T) : result (option T) :=
   hash_map_remove_from_list_loop_fwd T n key ls
 .
 
-(** [hashmap::HashMap::{0}::remove_from_list] *)
+(** [hashmap::HashMap::{0}::remove_from_list]: loop 0: backward function 1 *)
 Fixpoint hash_map_remove_from_list_loop_back
   (T : Type) (n : nat) (key : usize) (ls : List_t T) : result (List_t T) :=
   match n with
@@ -484,13 +493,13 @@ Fixpoint hash_map_remove_from_list_loop_back
   end
 .
 
-(** [hashmap::HashMap::{0}::remove_from_list] *)
+(** [hashmap::HashMap::{0}::remove_from_list]: backward function 1 *)
 Definition hash_map_remove_from_list_back
   (T : Type) (n : nat) (key : usize) (ls : List_t T) : result (List_t T) :=
   hash_map_remove_from_list_loop_back T n key ls
 .
 
-(** [hashmap::HashMap::{0}::remove] *)
+(** [hashmap::HashMap::{0}::remove]: forward function *)
 Definition hash_map_remove_fwd
   (T : Type) (n : nat) (self : Hash_map_t T) (key : usize) :
   result (option T)
@@ -507,7 +516,7 @@ Definition hash_map_remove_fwd
   end
 .
 
-(** [hashmap::HashMap::{0}::remove] *)
+(** [hashmap::HashMap::{0}::remove]: backward function 0 *)
 Definition hash_map_remove_back
   (T : Type) (n : nat) (self : Hash_map_t T) (key : usize) :
   result (Hash_map_t T)
@@ -542,7 +551,7 @@ Definition hash_map_remove_back
   end
 .
 
-(** [hashmap::test1] *)
+(** [hashmap::test1]: forward function *)
 Definition test1_fwd (n : nat) : result unit :=
   hm <- hash_map_new_fwd u64 n;
   hm0 <- hash_map_insert_fwd_back u64 n hm 0%usize 42%u64;
diff --git a/tests/coq/hashmap/_CoqProject b/tests/coq/hashmap/_CoqProject
index daa9b2ba..7f80afbf 100644
--- a/tests/coq/hashmap/_CoqProject
+++ b/tests/coq/hashmap/_CoqProject
@@ -3,6 +3,6 @@
 -arg -w
 -arg all
 
-Primitives.v
 Hashmap_Types.v
+Primitives.v
 Hashmap_Funs.v
diff --git a/tests/coq/hashmap_on_disk/HashmapMain_Funs.v b/tests/coq/hashmap_on_disk/HashmapMain_Funs.v
index 2d1bcda6..1b7304cc 100644
--- a/tests/coq/hashmap_on_disk/HashmapMain_Funs.v
+++ b/tests/coq/hashmap_on_disk/HashmapMain_Funs.v
@@ -10,11 +10,11 @@ Require Export HashmapMain_Opaque.
 Import HashmapMain_Opaque.
 Module HashmapMain_Funs.
 
-(** [hashmap_main::hashmap::hash_key] *)
+(** [hashmap_main::hashmap::hash_key]: forward function *)
 Definition hashmap_hash_key_fwd (k : usize) : result usize :=
   Return k.
 
-(** [hashmap_main::hashmap::HashMap::{0}::allocate_slots] *)
+(** [hashmap_main::hashmap::HashMap::{0}::allocate_slots]: loop 0: forward function *)
 Fixpoint hashmap_hash_map_allocate_slots_loop_fwd
   (T : Type) (n : nat) (slots : vec (Hashmap_list_t T)) (n0 : usize) :
   result (vec (Hashmap_list_t T))
@@ -31,7 +31,7 @@ Fixpoint hashmap_hash_map_allocate_slots_loop_fwd
   end
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::allocate_slots] *)
+(** [hashmap_main::hashmap::HashMap::{0}::allocate_slots]: forward function *)
 Definition hashmap_hash_map_allocate_slots_fwd
   (T : Type) (n : nat) (slots : vec (Hashmap_list_t T)) (n0 : usize) :
   result (vec (Hashmap_list_t T))
@@ -39,7 +39,7 @@ Definition hashmap_hash_map_allocate_slots_fwd
   hashmap_hash_map_allocate_slots_loop_fwd T n slots n0
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::new_with_capacity] *)
+(** [hashmap_main::hashmap::HashMap::{0}::new_with_capacity]: forward function *)
 Definition hashmap_hash_map_new_with_capacity_fwd
   (T : Type) (n : nat) (capacity : usize) (max_load_dividend : usize)
   (max_load_divisor : usize) :
@@ -58,13 +58,14 @@ Definition hashmap_hash_map_new_with_capacity_fwd
     |}
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::new] *)
+(** [hashmap_main::hashmap::HashMap::{0}::new]: forward function *)
 Definition hashmap_hash_map_new_fwd
   (T : Type) (n : nat) : result (Hashmap_hash_map_t T) :=
   hashmap_hash_map_new_with_capacity_fwd T n 32%usize 4%usize 5%usize
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::clear] *)
+(** [hashmap_main::hashmap::HashMap::{0}::clear]: loop 0: merged forward/backward function
+    (there is a single backward function, and the forward function returns ()) *)
 Fixpoint hashmap_hash_map_clear_loop_fwd_back
   (T : Type) (n : nat) (slots : vec (Hashmap_list_t T)) (i : usize) :
   result (vec (Hashmap_list_t T))
@@ -82,7 +83,8 @@ Fixpoint hashmap_hash_map_clear_loop_fwd_back
   end
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::clear] *)
+(** [hashmap_main::hashmap::HashMap::{0}::clear]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ()) *)
 Definition hashmap_hash_map_clear_fwd_back
   (T : Type) (n : nat) (self : Hashmap_hash_map_t T) :
   result (Hashmap_hash_map_t T)
@@ -100,13 +102,13 @@ Definition hashmap_hash_map_clear_fwd_back
     |}
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::len] *)
+(** [hashmap_main::hashmap::HashMap::{0}::len]: forward function *)
 Definition hashmap_hash_map_len_fwd
   (T : Type) (self : Hashmap_hash_map_t T) : result usize :=
   Return self.(Hashmap_hash_map_num_entries)
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::insert_in_list] *)
+(** [hashmap_main::hashmap::HashMap::{0}::insert_in_list]: loop 0: forward function *)
 Fixpoint hashmap_hash_map_insert_in_list_loop_fwd
   (T : Type) (n : nat) (key : usize) (value : T) (ls : Hashmap_list_t T) :
   result bool
@@ -124,7 +126,7 @@ Fixpoint hashmap_hash_map_insert_in_list_loop_fwd
   end
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::insert_in_list] *)
+(** [hashmap_main::hashmap::HashMap::{0}::insert_in_list]: forward function *)
 Definition hashmap_hash_map_insert_in_list_fwd
   (T : Type) (n : nat) (key : usize) (value : T) (ls : Hashmap_list_t T) :
   result bool
@@ -132,7 +134,7 @@ Definition hashmap_hash_map_insert_in_list_fwd
   hashmap_hash_map_insert_in_list_loop_fwd T n key value ls
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::insert_in_list] *)
+(** [hashmap_main::hashmap::HashMap::{0}::insert_in_list]: loop 0: backward function 0 *)
 Fixpoint hashmap_hash_map_insert_in_list_loop_back
   (T : Type) (n : nat) (key : usize) (value : T) (ls : Hashmap_list_t T) :
   result (Hashmap_list_t T)
@@ -153,7 +155,7 @@ Fixpoint hashmap_hash_map_insert_in_list_loop_back
   end
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::insert_in_list] *)
+(** [hashmap_main::hashmap::HashMap::{0}::insert_in_list]: backward function 0 *)
 Definition hashmap_hash_map_insert_in_list_back
   (T : Type) (n : nat) (key : usize) (value : T) (ls : Hashmap_list_t T) :
   result (Hashmap_list_t T)
@@ -161,7 +163,8 @@ Definition hashmap_hash_map_insert_in_list_back
   hashmap_hash_map_insert_in_list_loop_back T n key value ls
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::insert_no_resize] *)
+(** [hashmap_main::hashmap::HashMap::{0}::insert_no_resize]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ()) *)
 Definition hashmap_hash_map_insert_no_resize_fwd_back
   (T : Type) (n : nat) (self : Hashmap_hash_map_t T) (key : usize) (value : T)
   :
@@ -207,7 +210,8 @@ Definition hashmap_hash_map_insert_no_resize_fwd_back
 Definition core_num_u32_max_body : result u32 := Return 4294967295%u32.
 Definition core_num_u32_max_c : u32 := core_num_u32_max_body%global.
 
-(** [hashmap_main::hashmap::HashMap::{0}::move_elements_from_list] *)
+(** [hashmap_main::hashmap::HashMap::{0}::move_elements_from_list]: loop 0: merged forward/backward function
+    (there is a single backward function, and the forward function returns ()) *)
 Fixpoint hashmap_hash_map_move_elements_from_list_loop_fwd_back
   (T : Type) (n : nat) (ntable : Hashmap_hash_map_t T) (ls : Hashmap_list_t T)
   :
@@ -225,7 +229,8 @@ Fixpoint hashmap_hash_map_move_elements_from_list_loop_fwd_back
   end
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::move_elements_from_list] *)
+(** [hashmap_main::hashmap::HashMap::{0}::move_elements_from_list]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ()) *)
 Definition hashmap_hash_map_move_elements_from_list_fwd_back
   (T : Type) (n : nat) (ntable : Hashmap_hash_map_t T) (ls : Hashmap_list_t T)
   :
@@ -234,7 +239,8 @@ Definition hashmap_hash_map_move_elements_from_list_fwd_back
   hashmap_hash_map_move_elements_from_list_loop_fwd_back T n ntable ls
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::move_elements] *)
+(** [hashmap_main::hashmap::HashMap::{0}::move_elements]: loop 0: merged forward/backward function
+    (there is a single backward function, and the forward function returns ()) *)
 Fixpoint hashmap_hash_map_move_elements_loop_fwd_back
   (T : Type) (n : nat) (ntable : Hashmap_hash_map_t T)
   (slots : vec (Hashmap_list_t T)) (i : usize) :
@@ -258,7 +264,8 @@ Fixpoint hashmap_hash_map_move_elements_loop_fwd_back
   end
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::move_elements] *)
+(** [hashmap_main::hashmap::HashMap::{0}::move_elements]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ()) *)
 Definition hashmap_hash_map_move_elements_fwd_back
   (T : Type) (n : nat) (ntable : Hashmap_hash_map_t T)
   (slots : vec (Hashmap_list_t T)) (i : usize) :
@@ -267,7 +274,8 @@ Definition hashmap_hash_map_move_elements_fwd_back
   hashmap_hash_map_move_elements_loop_fwd_back T n ntable slots i
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::try_resize] *)
+(** [hashmap_main::hashmap::HashMap::{0}::try_resize]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ()) *)
 Definition hashmap_hash_map_try_resize_fwd_back
   (T : Type) (n : nat) (self : Hashmap_hash_map_t T) :
   result (Hashmap_hash_map_t T)
@@ -302,7 +310,8 @@ Definition hashmap_hash_map_try_resize_fwd_back
       |}
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::insert] *)
+(** [hashmap_main::hashmap::HashMap::{0}::insert]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ()) *)
 Definition hashmap_hash_map_insert_fwd_back
   (T : Type) (n : nat) (self : Hashmap_hash_map_t T) (key : usize) (value : T)
   :
@@ -315,7 +324,7 @@ Definition hashmap_hash_map_insert_fwd_back
   else Return self0
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::contains_key_in_list] *)
+(** [hashmap_main::hashmap::HashMap::{0}::contains_key_in_list]: loop 0: forward function *)
 Fixpoint hashmap_hash_map_contains_key_in_list_loop_fwd
   (T : Type) (n : nat) (key : usize) (ls : Hashmap_list_t T) : result bool :=
   match n with
@@ -331,13 +340,13 @@ Fixpoint hashmap_hash_map_contains_key_in_list_loop_fwd
   end
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::contains_key_in_list] *)
+(** [hashmap_main::hashmap::HashMap::{0}::contains_key_in_list]: forward function *)
 Definition hashmap_hash_map_contains_key_in_list_fwd
   (T : Type) (n : nat) (key : usize) (ls : Hashmap_list_t T) : result bool :=
   hashmap_hash_map_contains_key_in_list_loop_fwd T n key ls
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::contains_key] *)
+(** [hashmap_main::hashmap::HashMap::{0}::contains_key]: forward function *)
 Definition hashmap_hash_map_contains_key_fwd
   (T : Type) (n : nat) (self : Hashmap_hash_map_t T) (key : usize) :
   result bool
@@ -349,7 +358,7 @@ Definition hashmap_hash_map_contains_key_fwd
   hashmap_hash_map_contains_key_in_list_fwd T n key l
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::get_in_list] *)
+(** [hashmap_main::hashmap::HashMap::{0}::get_in_list]: loop 0: forward function *)
 Fixpoint hashmap_hash_map_get_in_list_loop_fwd
   (T : Type) (n : nat) (key : usize) (ls : Hashmap_list_t T) : result T :=
   match n with
@@ -365,13 +374,13 @@ Fixpoint hashmap_hash_map_get_in_list_loop_fwd
   end
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::get_in_list] *)
+(** [hashmap_main::hashmap::HashMap::{0}::get_in_list]: forward function *)
 Definition hashmap_hash_map_get_in_list_fwd
   (T : Type) (n : nat) (key : usize) (ls : Hashmap_list_t T) : result T :=
   hashmap_hash_map_get_in_list_loop_fwd T n key ls
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::get] *)
+(** [hashmap_main::hashmap::HashMap::{0}::get]: forward function *)
 Definition hashmap_hash_map_get_fwd
   (T : Type) (n : nat) (self : Hashmap_hash_map_t T) (key : usize) :
   result T
@@ -383,7 +392,7 @@ Definition hashmap_hash_map_get_fwd
   hashmap_hash_map_get_in_list_fwd T n key l
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list] *)
+(** [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list]: loop 0: forward function *)
 Fixpoint hashmap_hash_map_get_mut_in_list_loop_fwd
   (T : Type) (n : nat) (ls : Hashmap_list_t T) (key : usize) : result T :=
   match n with
@@ -399,13 +408,13 @@ Fixpoint hashmap_hash_map_get_mut_in_list_loop_fwd
   end
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list] *)
+(** [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list]: forward function *)
 Definition hashmap_hash_map_get_mut_in_list_fwd
   (T : Type) (n : nat) (ls : Hashmap_list_t T) (key : usize) : result T :=
   hashmap_hash_map_get_mut_in_list_loop_fwd T n ls key
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list] *)
+(** [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list]: loop 0: backward function 0 *)
 Fixpoint hashmap_hash_map_get_mut_in_list_loop_back
   (T : Type) (n : nat) (ls : Hashmap_list_t T) (key : usize) (ret : T) :
   result (Hashmap_list_t T)
@@ -425,7 +434,7 @@ Fixpoint hashmap_hash_map_get_mut_in_list_loop_back
   end
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list] *)
+(** [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list]: backward function 0 *)
 Definition hashmap_hash_map_get_mut_in_list_back
   (T : Type) (n : nat) (ls : Hashmap_list_t T) (key : usize) (ret : T) :
   result (Hashmap_list_t T)
@@ -433,7 +442,7 @@ Definition hashmap_hash_map_get_mut_in_list_back
   hashmap_hash_map_get_mut_in_list_loop_back T n ls key ret
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::get_mut] *)
+(** [hashmap_main::hashmap::HashMap::{0}::get_mut]: forward function *)
 Definition hashmap_hash_map_get_mut_fwd
   (T : Type) (n : nat) (self : Hashmap_hash_map_t T) (key : usize) :
   result T
@@ -446,7 +455,7 @@ Definition hashmap_hash_map_get_mut_fwd
   hashmap_hash_map_get_mut_in_list_fwd T n l key
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::get_mut] *)
+(** [hashmap_main::hashmap::HashMap::{0}::get_mut]: backward function 0 *)
 Definition hashmap_hash_map_get_mut_back
   (T : Type) (n : nat) (self : Hashmap_hash_map_t T) (key : usize) (ret : T) :
   result (Hashmap_hash_map_t T)
@@ -470,7 +479,7 @@ Definition hashmap_hash_map_get_mut_back
     |}
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::remove_from_list] *)
+(** [hashmap_main::hashmap::HashMap::{0}::remove_from_list]: loop 0: forward function *)
 Fixpoint hashmap_hash_map_remove_from_list_loop_fwd
   (T : Type) (n : nat) (key : usize) (ls : Hashmap_list_t T) :
   result (option T)
@@ -495,7 +504,7 @@ Fixpoint hashmap_hash_map_remove_from_list_loop_fwd
   end
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::remove_from_list] *)
+(** [hashmap_main::hashmap::HashMap::{0}::remove_from_list]: forward function *)
 Definition hashmap_hash_map_remove_from_list_fwd
   (T : Type) (n : nat) (key : usize) (ls : Hashmap_list_t T) :
   result (option T)
@@ -503,7 +512,7 @@ Definition hashmap_hash_map_remove_from_list_fwd
   hashmap_hash_map_remove_from_list_loop_fwd T n key ls
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::remove_from_list] *)
+(** [hashmap_main::hashmap::HashMap::{0}::remove_from_list]: loop 0: backward function 1 *)
 Fixpoint hashmap_hash_map_remove_from_list_loop_back
   (T : Type) (n : nat) (key : usize) (ls : Hashmap_list_t T) :
   result (Hashmap_list_t T)
@@ -530,7 +539,7 @@ Fixpoint hashmap_hash_map_remove_from_list_loop_back
   end
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::remove_from_list] *)
+(** [hashmap_main::hashmap::HashMap::{0}::remove_from_list]: backward function 1 *)
 Definition hashmap_hash_map_remove_from_list_back
   (T : Type) (n : nat) (key : usize) (ls : Hashmap_list_t T) :
   result (Hashmap_list_t T)
@@ -538,7 +547,7 @@ Definition hashmap_hash_map_remove_from_list_back
   hashmap_hash_map_remove_from_list_loop_back T n key ls
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::remove] *)
+(** [hashmap_main::hashmap::HashMap::{0}::remove]: forward function *)
 Definition hashmap_hash_map_remove_fwd
   (T : Type) (n : nat) (self : Hashmap_hash_map_t T) (key : usize) :
   result (option T)
@@ -557,7 +566,7 @@ Definition hashmap_hash_map_remove_fwd
   end
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::remove] *)
+(** [hashmap_main::hashmap::HashMap::{0}::remove]: backward function 0 *)
 Definition hashmap_hash_map_remove_back
   (T : Type) (n : nat) (self : Hashmap_hash_map_t T) (key : usize) :
   result (Hashmap_hash_map_t T)
@@ -599,7 +608,7 @@ Definition hashmap_hash_map_remove_back
   end
 .
 
-(** [hashmap_main::hashmap::test1] *)
+(** [hashmap_main::hashmap::test1]: forward function *)
 Definition hashmap_test1_fwd (n : nat) : result unit :=
   hm <- hashmap_hash_map_new_fwd u64 n;
   hm0 <- hashmap_hash_map_insert_fwd_back u64 n hm 0%usize 42%u64;
@@ -636,7 +645,7 @@ Definition hashmap_test1_fwd (n : nat) : result unit :=
       end))
 .
 
-(** [hashmap_main::insert_on_disk] *)
+(** [hashmap_main::insert_on_disk]: forward function *)
 Definition insert_on_disk_fwd
   (n : nat) (key : usize) (value : u64) (st : state) : result (state * unit) :=
   p <- hashmap_utils_deserialize_fwd st;
@@ -647,7 +656,7 @@ Definition insert_on_disk_fwd
   Return (st1, tt)
 .
 
-(** [hashmap_main::main] *)
+(** [hashmap_main::main]: forward function *)
 Definition main_fwd : result unit :=
   Return tt.
 
diff --git a/tests/coq/hashmap_on_disk/HashmapMain_Opaque.v b/tests/coq/hashmap_on_disk/HashmapMain_Opaque.v
index 6152b94b..1ad9c697 100644
--- a/tests/coq/hashmap_on_disk/HashmapMain_Opaque.v
+++ b/tests/coq/hashmap_on_disk/HashmapMain_Opaque.v
@@ -1,5 +1,5 @@
 (** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
-(** [hashmap_main]: opaque function definitions *)
+(** [hashmap_main]: external function declarations *)
 Require Import Primitives.
 Import Primitives.
 Require Import Coq.ZArith.ZArith.
@@ -8,12 +8,12 @@ Require Export HashmapMain_Types.
 Import HashmapMain_Types.
 Module HashmapMain_Opaque.
 
-(** [hashmap_main::hashmap_utils::deserialize] *)
+(** [hashmap_main::hashmap_utils::deserialize]: forward function *)
 Axiom hashmap_utils_deserialize_fwd
   : state -> result (state * (Hashmap_hash_map_t u64))
 .
 
-(** [hashmap_main::hashmap_utils::serialize] *)
+(** [hashmap_main::hashmap_utils::serialize]: forward function *)
 Axiom hashmap_utils_serialize_fwd
   : Hashmap_hash_map_t u64 -> state -> result (state * unit)
 .
diff --git a/tests/coq/misc/Constants.v b/tests/coq/misc/Constants.v
index 6a5f2696..14c05c61 100644
--- a/tests/coq/misc/Constants.v
+++ b/tests/coq/misc/Constants.v
@@ -22,7 +22,7 @@ Definition x1_c : u32 := x1_body%global.
 Definition x2_body : result u32 := Return 3%u32.
 Definition x2_c : u32 := x2_body%global.
 
-(** [constants::incr] *)
+(** [constants::incr]: forward function *)
 Definition incr_fwd (n : u32) : result u32 :=
   u32_add n 1%u32.
 
@@ -30,7 +30,7 @@ Definition incr_fwd (n : u32) : result u32 :=
 Definition x3_body : result u32 := incr_fwd 32%u32.
 Definition x3_c : u32 := x3_body%global.
 
-(** [constants::mk_pair0] *)
+(** [constants::mk_pair0]: forward function *)
 Definition mk_pair0_fwd (x : u32) (y : u32) : result (u32 * u32) :=
   Return (x, y)
 .
@@ -42,7 +42,7 @@ Arguments mkPair_t {T1} {T2} _ _.
 Arguments Pair_x {T1} {T2}.
 Arguments Pair_y {T1} {T2}.
 
-(** [constants::mk_pair1] *)
+(** [constants::mk_pair1]: forward function *)
 Definition mk_pair1_fwd (x : u32) (y : u32) : result (Pair_t u32 u32) :=
   Return {| Pair_x := x; Pair_y := y |}
 .
@@ -71,7 +71,7 @@ Record Wrap_t (T : Type) := mkWrap_t { Wrap_val : T; }.
 Arguments mkWrap_t {T} _.
 Arguments Wrap_val {T}.
 
-(** [constants::Wrap::{0}::new] *)
+(** [constants::Wrap::{0}::new]: forward function *)
 Definition wrap_new_fwd (T : Type) (val : T) : result (Wrap_t T) :=
   Return {| Wrap_val := val |}
 .
@@ -80,7 +80,7 @@ Definition wrap_new_fwd (T : Type) (val : T) : result (Wrap_t T) :=
 Definition y_body : result (Wrap_t i32) := wrap_new_fwd i32 2%i32.
 Definition y_c : Wrap_t i32 := y_body%global.
 
-(** [constants::unwrap_y] *)
+(** [constants::unwrap_y]: forward function *)
 Definition unwrap_y_fwd : result i32 :=
   Return y_c.(Wrap_val).
 
@@ -92,11 +92,11 @@ Definition yval_c : i32 := yval_body%global.
 Definition get_z1_z1_body : result i32 := Return 3%i32.
 Definition get_z1_z1_c : i32 := get_z1_z1_body%global.
 
-(** [constants::get_z1] *)
+(** [constants::get_z1]: forward function *)
 Definition get_z1_fwd : result i32 :=
   Return get_z1_z1_c.
 
-(** [constants::add] *)
+(** [constants::add]: forward function *)
 Definition add_fwd (a : i32) (b : i32) : result i32 :=
   i32_add a b.
 
@@ -112,7 +112,7 @@ Definition q2_c : i32 := q2_body%global.
 Definition q3_body : result i32 := add_fwd q2_c 3%i32.
 Definition q3_c : i32 := q3_body%global.
 
-(** [constants::get_z2] *)
+(** [constants::get_z2]: forward function *)
 Definition get_z2_fwd : result i32 :=
   i <- get_z1_fwd; i0 <- add_fwd i q3_c; add_fwd q1_c i0
 .
diff --git a/tests/coq/misc/External_Funs.v b/tests/coq/misc/External_Funs.v
index 05dd8f2e..f18bbd1f 100644
--- a/tests/coq/misc/External_Funs.v
+++ b/tests/coq/misc/External_Funs.v
@@ -10,7 +10,7 @@ Require Export External_Opaque.
 Import External_Opaque.
 Module External_Funs.
 
-(** [external::swap] *)
+(** [external::swap]: forward function *)
 Definition swap_fwd
   (T : Type) (x : T) (y : T) (st : state) : result (state * unit) :=
   p <- core_mem_swap_fwd T x y st;
@@ -22,7 +22,7 @@ Definition swap_fwd
   Return (st2, tt)
 .
 
-(** [external::swap] *)
+(** [external::swap]: backward function 0 *)
 Definition swap_back
   (T : Type) (x : T) (y : T) (st : state) (st0 : state) :
   result (state * (T * T))
@@ -36,7 +36,7 @@ Definition swap_back
   Return (st0, (x0, y0))
 .
 
-(** [external::test_new_non_zero_u32] *)
+(** [external::test_new_non_zero_u32]: forward function *)
 Definition test_new_non_zero_u32_fwd
   (x : u32) (st : state) : result (state * Core_num_nonzero_non_zero_u32_t) :=
   p <- core_num_nonzero_non_zero_u32_new_fwd x st;
@@ -44,7 +44,7 @@ Definition test_new_non_zero_u32_fwd
   core_option_option_unwrap_fwd Core_num_nonzero_non_zero_u32_t opt st0
 .
 
-(** [external::test_vec] *)
+(** [external::test_vec]: forward function *)
 Definition test_vec_fwd : result unit :=
   let v := vec_new u32 in _ <- vec_push_back u32 v 0%u32; Return tt
 .
@@ -52,7 +52,7 @@ Definition test_vec_fwd : result unit :=
 (** Unit test for [external::test_vec] *)
 Check (test_vec_fwd )%return.
 
-(** [external::custom_swap] *)
+(** [external::custom_swap]: forward function *)
 Definition custom_swap_fwd
   (T : Type) (x : T) (y : T) (st : state) : result (state * T) :=
   p <- core_mem_swap_fwd T x y st;
@@ -64,7 +64,7 @@ Definition custom_swap_fwd
   Return (st2, x0)
 .
 
-(** [external::custom_swap] *)
+(** [external::custom_swap]: backward function 0 *)
 Definition custom_swap_back
   (T : Type) (x : T) (y : T) (st : state) (ret : T) (st0 : state) :
   result (state * (T * T))
@@ -78,13 +78,13 @@ Definition custom_swap_back
   Return (st0, (ret, y0))
 .
 
-(** [external::test_custom_swap] *)
+(** [external::test_custom_swap]: forward function *)
 Definition test_custom_swap_fwd
   (x : u32) (y : u32) (st : state) : result (state * unit) :=
   p <- custom_swap_fwd u32 x y st; let (st0, _) := p in Return (st0, tt)
 .
 
-(** [external::test_custom_swap] *)
+(** [external::test_custom_swap]: backward function 0 *)
 Definition test_custom_swap_back
   (x : u32) (y : u32) (st : state) (st0 : state) :
   result (state * (u32 * u32))
@@ -92,7 +92,7 @@ Definition test_custom_swap_back
   custom_swap_back u32 x y st 1%u32 st0
 .
 
-(** [external::test_swap_non_zero] *)
+(** [external::test_swap_non_zero]: forward function *)
 Definition test_swap_non_zero_fwd
   (x : u32) (st : state) : result (state * u32) :=
   p <- swap_fwd u32 x 0%u32 st;
diff --git a/tests/coq/misc/External_Opaque.v b/tests/coq/misc/External_Opaque.v
index d60251e0..1224f426 100644
--- a/tests/coq/misc/External_Opaque.v
+++ b/tests/coq/misc/External_Opaque.v
@@ -1,5 +1,5 @@
 (** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
-(** [external]: opaque function definitions *)
+(** [external]: external function declarations *)
 Require Import Primitives.
 Import Primitives.
 Require Import Coq.ZArith.ZArith.
@@ -8,27 +8,27 @@ Require Export External_Types.
 Import External_Types.
 Module External_Opaque.
 
-(** [core::mem::swap] *)
+(** [core::mem::swap]: forward function *)
 Axiom core_mem_swap_fwd :
   forall(T : Type), T -> T -> state -> result (state * unit)
 .
 
-(** [core::mem::swap] *)
+(** [core::mem::swap]: backward function 0 *)
 Axiom core_mem_swap_back0 :
   forall(T : Type), T -> T -> state -> state -> result (state * T)
 .
 
-(** [core::mem::swap] *)
+(** [core::mem::swap]: backward function 1 *)
 Axiom core_mem_swap_back1 :
   forall(T : Type), T -> T -> state -> state -> result (state * T)
 .
 
-(** [core::num::nonzero::NonZeroU32::{14}::new] *)
+(** [core::num::nonzero::NonZeroU32::{14}::new]: forward function *)
 Axiom core_num_nonzero_non_zero_u32_new_fwd
   : u32 -> state -> result (state * (option Core_num_nonzero_non_zero_u32_t))
 .
 
-(** [core::option::Option::{0}::unwrap] *)
+(** [core::option::Option::{0}::unwrap]: forward function *)
 Axiom core_option_option_unwrap_fwd :
   forall(T : Type), option T -> state -> result (state * T)
 .
diff --git a/tests/coq/misc/Loops.v b/tests/coq/misc/Loops.v
index a5cb3688..f17eb986 100644
--- a/tests/coq/misc/Loops.v
+++ b/tests/coq/misc/Loops.v
@@ -6,7 +6,7 @@ Require Import Coq.ZArith.ZArith.
 Local Open Scope Primitives_scope.
 Module Loops.
 
-(** [loops::sum] *)
+(** [loops::sum]: loop 0: forward function *)
 Fixpoint sum_loop_fwd (n : nat) (max : u32) (i : u32) (s : u32) : result u32 :=
   match n with
   | O => Fail_ OutOfFuel
@@ -17,12 +17,12 @@ Fixpoint sum_loop_fwd (n : nat) (max : u32) (i : u32) (s : u32) : result u32 :=
   end
 .
 
-(** [loops::sum] *)
+(** [loops::sum]: forward function *)
 Definition sum_fwd (n : nat) (max : u32) : result u32 :=
   sum_loop_fwd n max 0%u32 0%u32
 .
 
-(** [loops::sum_with_mut_borrows] *)
+(** [loops::sum_with_mut_borrows]: loop 0: forward function *)
 Fixpoint sum_with_mut_borrows_loop_fwd
   (n : nat) (max : u32) (mi : u32) (ms : u32) : result u32 :=
   match n with
@@ -37,12 +37,12 @@ Fixpoint sum_with_mut_borrows_loop_fwd
   end
 .
 
-(** [loops::sum_with_mut_borrows] *)
+(** [loops::sum_with_mut_borrows]: forward function *)
 Definition sum_with_mut_borrows_fwd (n : nat) (max : u32) : result u32 :=
   sum_with_mut_borrows_loop_fwd n max 0%u32 0%u32
 .
 
-(** [loops::sum_with_shared_borrows] *)
+(** [loops::sum_with_shared_borrows]: loop 0: forward function *)
 Fixpoint sum_with_shared_borrows_loop_fwd
   (n : nat) (max : u32) (i : u32) (s : u32) : result u32 :=
   match n with
@@ -57,12 +57,13 @@ Fixpoint sum_with_shared_borrows_loop_fwd
   end
 .
 
-(** [loops::sum_with_shared_borrows] *)
+(** [loops::sum_with_shared_borrows]: forward function *)
 Definition sum_with_shared_borrows_fwd (n : nat) (max : u32) : result u32 :=
   sum_with_shared_borrows_loop_fwd n max 0%u32 0%u32
 .
 
-(** [loops::clear] *)
+(** [loops::clear]: loop 0: merged forward/backward function
+    (there is a single backward function, and the forward function returns ()) *)
 Fixpoint clear_loop_fwd_back
   (n : nat) (v : vec u32) (i : usize) : result (vec u32) :=
   match n with
@@ -78,7 +79,8 @@ Fixpoint clear_loop_fwd_back
   end
 .
 
-(** [loops::clear] *)
+(** [loops::clear]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ()) *)
 Definition clear_fwd_back (n : nat) (v : vec u32) : result (vec u32) :=
   clear_loop_fwd_back n v 0%usize
 .
@@ -92,7 +94,7 @@ Inductive List_t (T : Type) :=
 Arguments ListCons {T} _ _.
 Arguments ListNil {T}.
 
-(** [loops::list_mem] *)
+(** [loops::list_mem]: loop 0: forward function *)
 Fixpoint list_mem_loop_fwd
   (n : nat) (x : u32) (ls : List_t u32) : result bool :=
   match n with
@@ -106,12 +108,12 @@ Fixpoint list_mem_loop_fwd
   end
 .
 
-(** [loops::list_mem] *)
+(** [loops::list_mem]: forward function *)
 Definition list_mem_fwd (n : nat) (x : u32) (ls : List_t u32) : result bool :=
   list_mem_loop_fwd n x ls
 .
 
-(** [loops::list_nth_mut_loop] *)
+(** [loops::list_nth_mut_loop]: loop 0: forward function *)
 Fixpoint list_nth_mut_loop_loop_fwd
   (T : Type) (n : nat) (ls : List_t T) (i : u32) : result T :=
   match n with
@@ -127,13 +129,13 @@ Fixpoint list_nth_mut_loop_loop_fwd
   end
 .
 
-(** [loops::list_nth_mut_loop] *)
+(** [loops::list_nth_mut_loop]: forward function *)
 Definition list_nth_mut_loop_fwd
   (T : Type) (n : nat) (ls : List_t T) (i : u32) : result T :=
   list_nth_mut_loop_loop_fwd T n ls i
 .
 
-(** [loops::list_nth_mut_loop] *)
+(** [loops::list_nth_mut_loop]: loop 0: backward function 0 *)
 Fixpoint list_nth_mut_loop_loop_back
   (T : Type) (n : nat) (ls : List_t T) (i : u32) (ret : T) :
   result (List_t T)
@@ -154,7 +156,7 @@ Fixpoint list_nth_mut_loop_loop_back
   end
 .
 
-(** [loops::list_nth_mut_loop] *)
+(** [loops::list_nth_mut_loop]: backward function 0 *)
 Definition list_nth_mut_loop_back
   (T : Type) (n : nat) (ls : List_t T) (i : u32) (ret : T) :
   result (List_t T)
@@ -162,7 +164,7 @@ Definition list_nth_mut_loop_back
   list_nth_mut_loop_loop_back T n ls i ret
 .
 
-(** [loops::list_nth_shared_loop] *)
+(** [loops::list_nth_shared_loop]: loop 0: forward function *)
 Fixpoint list_nth_shared_loop_loop_fwd
   (T : Type) (n : nat) (ls : List_t T) (i : u32) : result T :=
   match n with
@@ -178,13 +180,13 @@ Fixpoint list_nth_shared_loop_loop_fwd
   end
 .
 
-(** [loops::list_nth_shared_loop] *)
+(** [loops::list_nth_shared_loop]: forward function *)
 Definition list_nth_shared_loop_fwd
   (T : Type) (n : nat) (ls : List_t T) (i : u32) : result T :=
   list_nth_shared_loop_loop_fwd T n ls i
 .
 
-(** [loops::get_elem_mut] *)
+(** [loops::get_elem_mut]: loop 0: forward function *)
 Fixpoint get_elem_mut_loop_fwd
   (n : nat) (x : usize) (ls : List_t usize) : result usize :=
   match n with
@@ -198,14 +200,14 @@ Fixpoint get_elem_mut_loop_fwd
   end
 .
 
-(** [loops::get_elem_mut] *)
+(** [loops::get_elem_mut]: forward function *)
 Definition get_elem_mut_fwd
   (n : nat) (slots : vec (List_t usize)) (x : usize) : result usize :=
   l <- vec_index_mut_fwd (List_t usize) slots 0%usize;
   get_elem_mut_loop_fwd n x l
 .
 
-(** [loops::get_elem_mut] *)
+(** [loops::get_elem_mut]: loop 0: backward function 0 *)
 Fixpoint get_elem_mut_loop_back
   (n : nat) (x : usize) (ls : List_t usize) (ret : usize) :
   result (List_t usize)
@@ -223,7 +225,7 @@ Fixpoint get_elem_mut_loop_back
   end
 .
 
-(** [loops::get_elem_mut] *)
+(** [loops::get_elem_mut]: backward function 0 *)
 Definition get_elem_mut_back
   (n : nat) (slots : vec (List_t usize)) (x : usize) (ret : usize) :
   result (vec (List_t usize))
@@ -233,7 +235,7 @@ Definition get_elem_mut_back
   vec_index_mut_back (List_t usize) slots 0%usize l0
 .
 
-(** [loops::get_elem_shared] *)
+(** [loops::get_elem_shared]: loop 0: forward function *)
 Fixpoint get_elem_shared_loop_fwd
   (n : nat) (x : usize) (ls : List_t usize) : result usize :=
   match n with
@@ -247,30 +249,30 @@ Fixpoint get_elem_shared_loop_fwd
   end
 .
 
-(** [loops::get_elem_shared] *)
+(** [loops::get_elem_shared]: forward function *)
 Definition get_elem_shared_fwd
   (n : nat) (slots : vec (List_t usize)) (x : usize) : result usize :=
   l <- vec_index_fwd (List_t usize) slots 0%usize;
   get_elem_shared_loop_fwd n x l
 .
 
-(** [loops::id_mut] *)
+(** [loops::id_mut]: forward function *)
 Definition id_mut_fwd (T : Type) (ls : List_t T) : result (List_t T) :=
   Return ls
 .
 
-(** [loops::id_mut] *)
+(** [loops::id_mut]: backward function 0 *)
 Definition id_mut_back
   (T : Type) (ls : List_t T) (ret : List_t T) : result (List_t T) :=
   Return ret
 .
 
-(** [loops::id_shared] *)
+(** [loops::id_shared]: forward function *)
 Definition id_shared_fwd (T : Type) (ls : List_t T) : result (List_t T) :=
   Return ls
 .
 
-(** [loops::list_nth_mut_loop_with_id] *)
+(** [loops::list_nth_mut_loop_with_id]: loop 0: forward function *)
 Fixpoint list_nth_mut_loop_with_id_loop_fwd
   (T : Type) (n : nat) (i : u32) (ls : List_t T) : result T :=
   match n with
@@ -287,13 +289,13 @@ Fixpoint list_nth_mut_loop_with_id_loop_fwd
   end
 .
 
-(** [loops::list_nth_mut_loop_with_id] *)
+(** [loops::list_nth_mut_loop_with_id]: forward function *)
 Definition list_nth_mut_loop_with_id_fwd
   (T : Type) (n : nat) (ls : List_t T) (i : u32) : result T :=
   ls0 <- id_mut_fwd T ls; list_nth_mut_loop_with_id_loop_fwd T n i ls0
 .
 
-(** [loops::list_nth_mut_loop_with_id] *)
+(** [loops::list_nth_mut_loop_with_id]: loop 0: backward function 0 *)
 Fixpoint list_nth_mut_loop_with_id_loop_back
   (T : Type) (n : nat) (i : u32) (ls : List_t T) (ret : T) :
   result (List_t T)
@@ -314,7 +316,7 @@ Fixpoint list_nth_mut_loop_with_id_loop_back
   end
 .
 
-(** [loops::list_nth_mut_loop_with_id] *)
+(** [loops::list_nth_mut_loop_with_id]: backward function 0 *)
 Definition list_nth_mut_loop_with_id_back
   (T : Type) (n : nat) (ls : List_t T) (i : u32) (ret : T) :
   result (List_t T)
@@ -324,7 +326,7 @@ Definition list_nth_mut_loop_with_id_back
   id_mut_back T ls l
 .
 
-(** [loops::list_nth_shared_loop_with_id] *)
+(** [loops::list_nth_shared_loop_with_id]: loop 0: forward function *)
 Fixpoint list_nth_shared_loop_with_id_loop_fwd
   (T : Type) (n : nat) (i : u32) (ls : List_t T) : result T :=
   match n with
@@ -341,13 +343,13 @@ Fixpoint list_nth_shared_loop_with_id_loop_fwd
   end
 .
 
-(** [loops::list_nth_shared_loop_with_id] *)
+(** [loops::list_nth_shared_loop_with_id]: forward function *)
 Definition list_nth_shared_loop_with_id_fwd
   (T : Type) (n : nat) (ls : List_t T) (i : u32) : result T :=
   ls0 <- id_shared_fwd T ls; list_nth_shared_loop_with_id_loop_fwd T n i ls0
 .
 
-(** [loops::list_nth_mut_loop_pair] *)
+(** [loops::list_nth_mut_loop_pair]: loop 0: forward function *)
 Fixpoint list_nth_mut_loop_pair_loop_fwd
   (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) :
   result (T * T)
@@ -371,7 +373,7 @@ Fixpoint list_nth_mut_loop_pair_loop_fwd
   end
 .
 
-(** [loops::list_nth_mut_loop_pair] *)
+(** [loops::list_nth_mut_loop_pair]: forward function *)
 Definition list_nth_mut_loop_pair_fwd
   (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) :
   result (T * T)
@@ -379,7 +381,7 @@ Definition list_nth_mut_loop_pair_fwd
   list_nth_mut_loop_pair_loop_fwd T n ls0 ls1 i
 .
 
-(** [loops::list_nth_mut_loop_pair] *)
+(** [loops::list_nth_mut_loop_pair]: loop 0: backward function 0 *)
 Fixpoint list_nth_mut_loop_pair_loop_back'a
   (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) (ret : T) :
   result (List_t T)
@@ -404,7 +406,7 @@ Fixpoint list_nth_mut_loop_pair_loop_back'a
   end
 .
 
-(** [loops::list_nth_mut_loop_pair] *)
+(** [loops::list_nth_mut_loop_pair]: backward function 0 *)
 Definition list_nth_mut_loop_pair_back'a
   (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) (ret : T) :
   result (List_t T)
@@ -412,7 +414,7 @@ Definition list_nth_mut_loop_pair_back'a
   list_nth_mut_loop_pair_loop_back'a T n ls0 ls1 i ret
 .
 
-(** [loops::list_nth_mut_loop_pair] *)
+(** [loops::list_nth_mut_loop_pair]: loop 0: backward function 1 *)
 Fixpoint list_nth_mut_loop_pair_loop_back'b
   (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) (ret : T) :
   result (List_t T)
@@ -437,7 +439,7 @@ Fixpoint list_nth_mut_loop_pair_loop_back'b
   end
 .
 
-(** [loops::list_nth_mut_loop_pair] *)
+(** [loops::list_nth_mut_loop_pair]: backward function 1 *)
 Definition list_nth_mut_loop_pair_back'b
   (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) (ret : T) :
   result (List_t T)
@@ -445,7 +447,7 @@ Definition list_nth_mut_loop_pair_back'b
   list_nth_mut_loop_pair_loop_back'b T n ls0 ls1 i ret
 .
 
-(** [loops::list_nth_shared_loop_pair] *)
+(** [loops::list_nth_shared_loop_pair]: loop 0: forward function *)
 Fixpoint list_nth_shared_loop_pair_loop_fwd
   (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) :
   result (T * T)
@@ -469,7 +471,7 @@ Fixpoint list_nth_shared_loop_pair_loop_fwd
   end
 .
 
-(** [loops::list_nth_shared_loop_pair] *)
+(** [loops::list_nth_shared_loop_pair]: forward function *)
 Definition list_nth_shared_loop_pair_fwd
   (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) :
   result (T * T)
@@ -477,7 +479,7 @@ Definition list_nth_shared_loop_pair_fwd
   list_nth_shared_loop_pair_loop_fwd T n ls0 ls1 i
 .
 
-(** [loops::list_nth_mut_loop_pair_merge] *)
+(** [loops::list_nth_mut_loop_pair_merge]: loop 0: forward function *)
 Fixpoint list_nth_mut_loop_pair_merge_loop_fwd
   (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) :
   result (T * T)
@@ -501,7 +503,7 @@ Fixpoint list_nth_mut_loop_pair_merge_loop_fwd
   end
 .
 
-(** [loops::list_nth_mut_loop_pair_merge] *)
+(** [loops::list_nth_mut_loop_pair_merge]: forward function *)
 Definition list_nth_mut_loop_pair_merge_fwd
   (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) :
   result (T * T)
@@ -509,7 +511,7 @@ Definition list_nth_mut_loop_pair_merge_fwd
   list_nth_mut_loop_pair_merge_loop_fwd T n ls0 ls1 i
 .
 
-(** [loops::list_nth_mut_loop_pair_merge] *)
+(** [loops::list_nth_mut_loop_pair_merge]: loop 0: backward function 0 *)
 Fixpoint list_nth_mut_loop_pair_merge_loop_back
   (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32)
   (ret : (T * T)) :
@@ -536,7 +538,7 @@ Fixpoint list_nth_mut_loop_pair_merge_loop_back
   end
 .
 
-(** [loops::list_nth_mut_loop_pair_merge] *)
+(** [loops::list_nth_mut_loop_pair_merge]: backward function 0 *)
 Definition list_nth_mut_loop_pair_merge_back
   (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32)
   (ret : (T * T)) :
@@ -545,7 +547,7 @@ Definition list_nth_mut_loop_pair_merge_back
   list_nth_mut_loop_pair_merge_loop_back T n ls0 ls1 i ret
 .
 
-(** [loops::list_nth_shared_loop_pair_merge] *)
+(** [loops::list_nth_shared_loop_pair_merge]: loop 0: forward function *)
 Fixpoint list_nth_shared_loop_pair_merge_loop_fwd
   (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) :
   result (T * T)
@@ -569,7 +571,7 @@ Fixpoint list_nth_shared_loop_pair_merge_loop_fwd
   end
 .
 
-(** [loops::list_nth_shared_loop_pair_merge] *)
+(** [loops::list_nth_shared_loop_pair_merge]: forward function *)
 Definition list_nth_shared_loop_pair_merge_fwd
   (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) :
   result (T * T)
@@ -577,7 +579,7 @@ Definition list_nth_shared_loop_pair_merge_fwd
   list_nth_shared_loop_pair_merge_loop_fwd T n ls0 ls1 i
 .
 
-(** [loops::list_nth_mut_shared_loop_pair] *)
+(** [loops::list_nth_mut_shared_loop_pair]: loop 0: forward function *)
 Fixpoint list_nth_mut_shared_loop_pair_loop_fwd
   (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) :
   result (T * T)
@@ -601,7 +603,7 @@ Fixpoint list_nth_mut_shared_loop_pair_loop_fwd
   end
 .
 
-(** [loops::list_nth_mut_shared_loop_pair] *)
+(** [loops::list_nth_mut_shared_loop_pair]: forward function *)
 Definition list_nth_mut_shared_loop_pair_fwd
   (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) :
   result (T * T)
@@ -609,7 +611,7 @@ Definition list_nth_mut_shared_loop_pair_fwd
   list_nth_mut_shared_loop_pair_loop_fwd T n ls0 ls1 i
 .
 
-(** [loops::list_nth_mut_shared_loop_pair] *)
+(** [loops::list_nth_mut_shared_loop_pair]: loop 0: backward function 0 *)
 Fixpoint list_nth_mut_shared_loop_pair_loop_back
   (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) (ret : T) :
   result (List_t T)
@@ -634,7 +636,7 @@ Fixpoint list_nth_mut_shared_loop_pair_loop_back
   end
 .
 
-(** [loops::list_nth_mut_shared_loop_pair] *)
+(** [loops::list_nth_mut_shared_loop_pair]: backward function 0 *)
 Definition list_nth_mut_shared_loop_pair_back
   (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) (ret : T) :
   result (List_t T)
@@ -642,7 +644,7 @@ Definition list_nth_mut_shared_loop_pair_back
   list_nth_mut_shared_loop_pair_loop_back T n ls0 ls1 i ret
 .
 
-(** [loops::list_nth_mut_shared_loop_pair_merge] *)
+(** [loops::list_nth_mut_shared_loop_pair_merge]: loop 0: forward function *)
 Fixpoint list_nth_mut_shared_loop_pair_merge_loop_fwd
   (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) :
   result (T * T)
@@ -666,7 +668,7 @@ Fixpoint list_nth_mut_shared_loop_pair_merge_loop_fwd
   end
 .
 
-(** [loops::list_nth_mut_shared_loop_pair_merge] *)
+(** [loops::list_nth_mut_shared_loop_pair_merge]: forward function *)
 Definition list_nth_mut_shared_loop_pair_merge_fwd
   (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) :
   result (T * T)
@@ -674,7 +676,7 @@ Definition list_nth_mut_shared_loop_pair_merge_fwd
   list_nth_mut_shared_loop_pair_merge_loop_fwd T n ls0 ls1 i
 .
 
-(** [loops::list_nth_mut_shared_loop_pair_merge] *)
+(** [loops::list_nth_mut_shared_loop_pair_merge]: loop 0: backward function 0 *)
 Fixpoint list_nth_mut_shared_loop_pair_merge_loop_back
   (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) (ret : T) :
   result (List_t T)
@@ -700,7 +702,7 @@ Fixpoint list_nth_mut_shared_loop_pair_merge_loop_back
   end
 .
 
-(** [loops::list_nth_mut_shared_loop_pair_merge] *)
+(** [loops::list_nth_mut_shared_loop_pair_merge]: backward function 0 *)
 Definition list_nth_mut_shared_loop_pair_merge_back
   (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) (ret : T) :
   result (List_t T)
@@ -708,7 +710,7 @@ Definition list_nth_mut_shared_loop_pair_merge_back
   list_nth_mut_shared_loop_pair_merge_loop_back T n ls0 ls1 i ret
 .
 
-(** [loops::list_nth_shared_mut_loop_pair] *)
+(** [loops::list_nth_shared_mut_loop_pair]: loop 0: forward function *)
 Fixpoint list_nth_shared_mut_loop_pair_loop_fwd
   (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) :
   result (T * T)
@@ -732,7 +734,7 @@ Fixpoint list_nth_shared_mut_loop_pair_loop_fwd
   end
 .
 
-(** [loops::list_nth_shared_mut_loop_pair] *)
+(** [loops::list_nth_shared_mut_loop_pair]: forward function *)
 Definition list_nth_shared_mut_loop_pair_fwd
   (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) :
   result (T * T)
@@ -740,7 +742,7 @@ Definition list_nth_shared_mut_loop_pair_fwd
   list_nth_shared_mut_loop_pair_loop_fwd T n ls0 ls1 i
 .
 
-(** [loops::list_nth_shared_mut_loop_pair] *)
+(** [loops::list_nth_shared_mut_loop_pair]: loop 0: backward function 1 *)
 Fixpoint list_nth_shared_mut_loop_pair_loop_back
   (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) (ret : T) :
   result (List_t T)
@@ -765,7 +767,7 @@ Fixpoint list_nth_shared_mut_loop_pair_loop_back
   end
 .
 
-(** [loops::list_nth_shared_mut_loop_pair] *)
+(** [loops::list_nth_shared_mut_loop_pair]: backward function 1 *)
 Definition list_nth_shared_mut_loop_pair_back
   (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) (ret : T) :
   result (List_t T)
@@ -773,7 +775,7 @@ Definition list_nth_shared_mut_loop_pair_back
   list_nth_shared_mut_loop_pair_loop_back T n ls0 ls1 i ret
 .
 
-(** [loops::list_nth_shared_mut_loop_pair_merge] *)
+(** [loops::list_nth_shared_mut_loop_pair_merge]: loop 0: forward function *)
 Fixpoint list_nth_shared_mut_loop_pair_merge_loop_fwd
   (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) :
   result (T * T)
@@ -797,7 +799,7 @@ Fixpoint list_nth_shared_mut_loop_pair_merge_loop_fwd
   end
 .
 
-(** [loops::list_nth_shared_mut_loop_pair_merge] *)
+(** [loops::list_nth_shared_mut_loop_pair_merge]: forward function *)
 Definition list_nth_shared_mut_loop_pair_merge_fwd
   (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) :
   result (T * T)
@@ -805,7 +807,7 @@ Definition list_nth_shared_mut_loop_pair_merge_fwd
   list_nth_shared_mut_loop_pair_merge_loop_fwd T n ls0 ls1 i
 .
 
-(** [loops::list_nth_shared_mut_loop_pair_merge] *)
+(** [loops::list_nth_shared_mut_loop_pair_merge]: loop 0: backward function 0 *)
 Fixpoint list_nth_shared_mut_loop_pair_merge_loop_back
   (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) (ret : T) :
   result (List_t T)
@@ -831,7 +833,7 @@ Fixpoint list_nth_shared_mut_loop_pair_merge_loop_back
   end
 .
 
-(** [loops::list_nth_shared_mut_loop_pair_merge] *)
+(** [loops::list_nth_shared_mut_loop_pair_merge]: backward function 0 *)
 Definition list_nth_shared_mut_loop_pair_merge_back
   (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) (ret : T) :
   result (List_t T)
diff --git a/tests/coq/misc/NoNestedBorrows.v b/tests/coq/misc/NoNestedBorrows.v
index 96d62711..470a2cde 100644
--- a/tests/coq/misc/NoNestedBorrows.v
+++ b/tests/coq/misc/NoNestedBorrows.v
@@ -45,47 +45,47 @@ Inductive Sum_t (T1 T2 : Type) :=
 Arguments SumLeft {T1} {T2} _.
 Arguments SumRight {T1} {T2} _.
 
-(** [no_nested_borrows::neg_test] *)
+(** [no_nested_borrows::neg_test]: forward function *)
 Definition neg_test_fwd (x : i32) : result i32 :=
   i32_neg x.
 
-(** [no_nested_borrows::add_test] *)
+(** [no_nested_borrows::add_test]: forward function *)
 Definition add_test_fwd (x : u32) (y : u32) : result u32 :=
   u32_add x y.
 
-(** [no_nested_borrows::subs_test] *)
+(** [no_nested_borrows::subs_test]: forward function *)
 Definition subs_test_fwd (x : u32) (y : u32) : result u32 :=
   u32_sub x y.
 
-(** [no_nested_borrows::div_test] *)
+(** [no_nested_borrows::div_test]: forward function *)
 Definition div_test_fwd (x : u32) (y : u32) : result u32 :=
   u32_div x y.
 
-(** [no_nested_borrows::div_test1] *)
+(** [no_nested_borrows::div_test1]: forward function *)
 Definition div_test1_fwd (x : u32) : result u32 :=
   u32_div x 2%u32.
 
-(** [no_nested_borrows::rem_test] *)
+(** [no_nested_borrows::rem_test]: forward function *)
 Definition rem_test_fwd (x : u32) (y : u32) : result u32 :=
   u32_rem x y.
 
-(** [no_nested_borrows::cast_test] *)
+(** [no_nested_borrows::cast_test]: forward function *)
 Definition cast_test_fwd (x : u32) : result i32 :=
   scalar_cast U32 I32 x.
 
-(** [no_nested_borrows::test2] *)
+(** [no_nested_borrows::test2]: forward function *)
 Definition test2_fwd : result unit :=
   _ <- u32_add 23%u32 44%u32; Return tt.
 
 (** Unit test for [no_nested_borrows::test2] *)
 Check (test2_fwd )%return.
 
-(** [no_nested_borrows::get_max] *)
+(** [no_nested_borrows::get_max]: forward function *)
 Definition get_max_fwd (x : u32) (y : u32) : result u32 :=
   if x s>= y then Return x else Return y
 .
 
-(** [no_nested_borrows::test3] *)
+(** [no_nested_borrows::test3]: forward function *)
 Definition test3_fwd : result unit :=
   x <- get_max_fwd 4%u32 3%u32;
   y <- get_max_fwd 10%u32 11%u32;
@@ -96,7 +96,7 @@ Definition test3_fwd : result unit :=
 (** Unit test for [no_nested_borrows::test3] *)
 Check (test3_fwd )%return.
 
-(** [no_nested_borrows::test_neg1] *)
+(** [no_nested_borrows::test_neg1]: forward function *)
 Definition test_neg1_fwd : result unit :=
   y <- i32_neg 3%i32; if negb (y s= (-3)%i32) then Fail_ Failure else Return tt
 .
@@ -104,7 +104,7 @@ Definition test_neg1_fwd : result unit :=
 (** Unit test for [no_nested_borrows::test_neg1] *)
 Check (test_neg1_fwd )%return.
 
-(** [no_nested_borrows::refs_test1] *)
+(** [no_nested_borrows::refs_test1]: forward function *)
 Definition refs_test1_fwd : result unit :=
   if negb (1%i32 s= 1%i32) then Fail_ Failure else Return tt
 .
@@ -112,7 +112,7 @@ Definition refs_test1_fwd : result unit :=
 (** Unit test for [no_nested_borrows::refs_test1] *)
 Check (refs_test1_fwd )%return.
 
-(** [no_nested_borrows::refs_test2] *)
+(** [no_nested_borrows::refs_test2]: forward function *)
 Definition refs_test2_fwd : result unit :=
   if negb (2%i32 s= 2%i32)
   then Fail_ Failure
@@ -128,14 +128,14 @@ Definition refs_test2_fwd : result unit :=
 (** Unit test for [no_nested_borrows::refs_test2] *)
 Check (refs_test2_fwd )%return.
 
-(** [no_nested_borrows::test_list1] *)
+(** [no_nested_borrows::test_list1]: forward function *)
 Definition test_list1_fwd : result unit :=
   Return tt.
 
 (** Unit test for [no_nested_borrows::test_list1] *)
 Check (test_list1_fwd )%return.
 
-(** [no_nested_borrows::test_box1] *)
+(** [no_nested_borrows::test_box1]: forward function *)
 Definition test_box1_fwd : result unit :=
   let b := 1%i32 in
   let x := b in
@@ -145,21 +145,21 @@ Definition test_box1_fwd : result unit :=
 (** Unit test for [no_nested_borrows::test_box1] *)
 Check (test_box1_fwd )%return.
 
-(** [no_nested_borrows::copy_int] *)
+(** [no_nested_borrows::copy_int]: forward function *)
 Definition copy_int_fwd (x : i32) : result i32 :=
   Return x.
 
-(** [no_nested_borrows::test_unreachable] *)
+(** [no_nested_borrows::test_unreachable]: forward function *)
 Definition test_unreachable_fwd (b : bool) : result unit :=
   if b then Fail_ Failure else Return tt
 .
 
-(** [no_nested_borrows::test_panic] *)
+(** [no_nested_borrows::test_panic]: forward function *)
 Definition test_panic_fwd (b : bool) : result unit :=
   if b then Fail_ Failure else Return tt
 .
 
-(** [no_nested_borrows::test_copy_int] *)
+(** [no_nested_borrows::test_copy_int]: forward function *)
 Definition test_copy_int_fwd : result unit :=
   y <- copy_int_fwd 0%i32;
   if negb (0%i32 s= y) then Fail_ Failure else Return tt
@@ -168,12 +168,12 @@ Definition test_copy_int_fwd : result unit :=
 (** Unit test for [no_nested_borrows::test_copy_int] *)
 Check (test_copy_int_fwd )%return.
 
-(** [no_nested_borrows::is_cons] *)
+(** [no_nested_borrows::is_cons]: forward function *)
 Definition is_cons_fwd (T : Type) (l : List_t T) : result bool :=
   match l with | ListCons t l0 => Return true | ListNil => Return false end
 .
 
-(** [no_nested_borrows::test_is_cons] *)
+(** [no_nested_borrows::test_is_cons]: forward function *)
 Definition test_is_cons_fwd : result unit :=
   let l := ListNil in
   b <- is_cons_fwd i32 (ListCons 0%i32 l);
@@ -183,7 +183,7 @@ Definition test_is_cons_fwd : result unit :=
 (** Unit test for [no_nested_borrows::test_is_cons] *)
 Check (test_is_cons_fwd )%return.
 
-(** [no_nested_borrows::split_list] *)
+(** [no_nested_borrows::split_list]: forward function *)
 Definition split_list_fwd
   (T : Type) (l : List_t T) : result (T * (List_t T)) :=
   match l with
@@ -192,7 +192,7 @@ Definition split_list_fwd
   end
 .
 
-(** [no_nested_borrows::test_split_list] *)
+(** [no_nested_borrows::test_split_list]: forward function *)
 Definition test_split_list_fwd : result unit :=
   let l := ListNil in
   p <- split_list_fwd i32 (ListCons 0%i32 l);
@@ -203,18 +203,18 @@ Definition test_split_list_fwd : result unit :=
 (** Unit test for [no_nested_borrows::test_split_list] *)
 Check (test_split_list_fwd )%return.
 
-(** [no_nested_borrows::choose] *)
+(** [no_nested_borrows::choose]: forward function *)
 Definition choose_fwd (T : Type) (b : bool) (x : T) (y : T) : result T :=
   if b then Return x else Return y
 .
 
-(** [no_nested_borrows::choose] *)
+(** [no_nested_borrows::choose]: backward function 0 *)
 Definition choose_back
   (T : Type) (b : bool) (x : T) (y : T) (ret : T) : result (T * T) :=
   if b then Return (ret, y) else Return (x, ret)
 .
 
-(** [no_nested_borrows::choose_test] *)
+(** [no_nested_borrows::choose_test]: forward function *)
 Definition choose_test_fwd : result unit :=
   z <- choose_fwd i32 true 0%i32 0%i32;
   z0 <- i32_add z 1%i32;
@@ -231,7 +231,7 @@ Definition choose_test_fwd : result unit :=
 (** Unit test for [no_nested_borrows::choose_test] *)
 Check (choose_test_fwd )%return.
 
-(** [no_nested_borrows::test_char] *)
+(** [no_nested_borrows::test_char]: forward function *)
 Definition test_char_fwd : result char :=
   Return (char_of_byte Coq.Init.Byte.x61)
 .
@@ -253,7 +253,7 @@ Arguments NodeElemNil {T}.
 Arguments TreeLeaf {T} _.
 Arguments TreeNode {T} _ _ _.
 
-(** [no_nested_borrows::list_length] *)
+(** [no_nested_borrows::list_length]: forward function *)
 Fixpoint list_length_fwd (T : Type) (l : List_t T) : result u32 :=
   match l with
   | ListCons t l1 => i <- list_length_fwd T l1; u32_add 1%u32 i
@@ -261,7 +261,7 @@ Fixpoint list_length_fwd (T : Type) (l : List_t T) : result u32 :=
   end
 .
 
-(** [no_nested_borrows::list_nth_shared] *)
+(** [no_nested_borrows::list_nth_shared]: forward function *)
 Fixpoint list_nth_shared_fwd (T : Type) (l : List_t T) (i : u32) : result T :=
   match l with
   | ListCons x tl =>
@@ -272,7 +272,7 @@ Fixpoint list_nth_shared_fwd (T : Type) (l : List_t T) (i : u32) : result T :=
   end
 .
 
-(** [no_nested_borrows::list_nth_mut] *)
+(** [no_nested_borrows::list_nth_mut]: forward function *)
 Fixpoint list_nth_mut_fwd (T : Type) (l : List_t T) (i : u32) : result T :=
   match l with
   | ListCons x tl =>
@@ -283,7 +283,7 @@ Fixpoint list_nth_mut_fwd (T : Type) (l : List_t T) (i : u32) : result T :=
   end
 .
 
-(** [no_nested_borrows::list_nth_mut] *)
+(** [no_nested_borrows::list_nth_mut]: backward function 0 *)
 Fixpoint list_nth_mut_back
   (T : Type) (l : List_t T) (i : u32) (ret : T) : result (List_t T) :=
   match l with
@@ -298,7 +298,7 @@ Fixpoint list_nth_mut_back
   end
 .
 
-(** [no_nested_borrows::list_rev_aux] *)
+(** [no_nested_borrows::list_rev_aux]: forward function *)
 Fixpoint list_rev_aux_fwd
   (T : Type) (li : List_t T) (lo : List_t T) : result (List_t T) :=
   match li with
@@ -307,13 +307,14 @@ Fixpoint list_rev_aux_fwd
   end
 .
 
-(** [no_nested_borrows::list_rev] *)
+(** [no_nested_borrows::list_rev]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ()) *)
 Definition list_rev_fwd_back (T : Type) (l : List_t T) : result (List_t T) :=
   let li := mem_replace_fwd (List_t T) l ListNil in
   list_rev_aux_fwd T li ListNil
 .
 
-(** [no_nested_borrows::test_list_functions] *)
+(** [no_nested_borrows::test_list_functions]: forward function *)
 Definition test_list_functions_fwd : result unit :=
   let l := ListNil in
   let l0 := ListCons 2%i32 l in
@@ -350,61 +351,61 @@ Definition test_list_functions_fwd : result unit :=
 (** Unit test for [no_nested_borrows::test_list_functions] *)
 Check (test_list_functions_fwd )%return.
 
-(** [no_nested_borrows::id_mut_pair1] *)
+(** [no_nested_borrows::id_mut_pair1]: forward function *)
 Definition id_mut_pair1_fwd
   (T1 T2 : Type) (x : T1) (y : T2) : result (T1 * T2) :=
   Return (x, y)
 .
 
-(** [no_nested_borrows::id_mut_pair1] *)
+(** [no_nested_borrows::id_mut_pair1]: backward function 0 *)
 Definition id_mut_pair1_back
   (T1 T2 : Type) (x : T1) (y : T2) (ret : (T1 * T2)) : result (T1 * T2) :=
   let (t, t0) := ret in Return (t, t0)
 .
 
-(** [no_nested_borrows::id_mut_pair2] *)
+(** [no_nested_borrows::id_mut_pair2]: forward function *)
 Definition id_mut_pair2_fwd
   (T1 T2 : Type) (p : (T1 * T2)) : result (T1 * T2) :=
   let (t, t0) := p in Return (t, t0)
 .
 
-(** [no_nested_borrows::id_mut_pair2] *)
+(** [no_nested_borrows::id_mut_pair2]: backward function 0 *)
 Definition id_mut_pair2_back
   (T1 T2 : Type) (p : (T1 * T2)) (ret : (T1 * T2)) : result (T1 * T2) :=
   let (t, t0) := ret in Return (t, t0)
 .
 
-(** [no_nested_borrows::id_mut_pair3] *)
+(** [no_nested_borrows::id_mut_pair3]: forward function *)
 Definition id_mut_pair3_fwd
   (T1 T2 : Type) (x : T1) (y : T2) : result (T1 * T2) :=
   Return (x, y)
 .
 
-(** [no_nested_borrows::id_mut_pair3] *)
+(** [no_nested_borrows::id_mut_pair3]: backward function 0 *)
 Definition id_mut_pair3_back'a
   (T1 T2 : Type) (x : T1) (y : T2) (ret : T1) : result T1 :=
   Return ret
 .
 
-(** [no_nested_borrows::id_mut_pair3] *)
+(** [no_nested_borrows::id_mut_pair3]: backward function 1 *)
 Definition id_mut_pair3_back'b
   (T1 T2 : Type) (x : T1) (y : T2) (ret : T2) : result T2 :=
   Return ret
 .
 
-(** [no_nested_borrows::id_mut_pair4] *)
+(** [no_nested_borrows::id_mut_pair4]: forward function *)
 Definition id_mut_pair4_fwd
   (T1 T2 : Type) (p : (T1 * T2)) : result (T1 * T2) :=
   let (t, t0) := p in Return (t, t0)
 .
 
-(** [no_nested_borrows::id_mut_pair4] *)
+(** [no_nested_borrows::id_mut_pair4]: backward function 0 *)
 Definition id_mut_pair4_back'a
   (T1 T2 : Type) (p : (T1 * T2)) (ret : T1) : result T1 :=
   Return ret
 .
 
-(** [no_nested_borrows::id_mut_pair4] *)
+(** [no_nested_borrows::id_mut_pair4]: backward function 1 *)
 Definition id_mut_pair4_back'b
   (T1 T2 : Type) (p : (T1 * T2)) (ret : T2) : result T2 :=
   Return ret
@@ -420,17 +421,17 @@ mkStruct_with_tuple_t {
 Arguments mkStruct_with_tuple_t {T1} {T2} _.
 Arguments Struct_with_tuple_p {T1} {T2}.
 
-(** [no_nested_borrows::new_tuple1] *)
+(** [no_nested_borrows::new_tuple1]: forward function *)
 Definition new_tuple1_fwd : result (Struct_with_tuple_t u32 u32) :=
   Return {| Struct_with_tuple_p := (1%u32, 2%u32) |}
 .
 
-(** [no_nested_borrows::new_tuple2] *)
+(** [no_nested_borrows::new_tuple2]: forward function *)
 Definition new_tuple2_fwd : result (Struct_with_tuple_t i16 i16) :=
   Return {| Struct_with_tuple_p := (1%i16, 2%i16) |}
 .
 
-(** [no_nested_borrows::new_tuple3] *)
+(** [no_nested_borrows::new_tuple3]: forward function *)
 Definition new_tuple3_fwd : result (Struct_with_tuple_t u64 i64) :=
   Return {| Struct_with_tuple_p := (1%u64, 2%i64) |}
 .
@@ -445,12 +446,12 @@ mkStruct_with_pair_t {
 Arguments mkStruct_with_pair_t {T1} {T2} _.
 Arguments Struct_with_pair_p {T1} {T2}.
 
-(** [no_nested_borrows::new_pair1] *)
+(** [no_nested_borrows::new_pair1]: forward function *)
 Definition new_pair1_fwd : result (Struct_with_pair_t u32 u32) :=
   Return {| Struct_with_pair_p := {| Pair_x := 1%u32; Pair_y := 2%u32 |} |}
 .
 
-(** [no_nested_borrows::test_constants] *)
+(** [no_nested_borrows::test_constants]: forward function *)
 Definition test_constants_fwd : result unit :=
   swt <- new_tuple1_fwd;
   let (i, _) := swt.(Struct_with_tuple_p) in
@@ -476,34 +477,35 @@ Definition test_constants_fwd : result unit :=
 (** Unit test for [no_nested_borrows::test_constants] *)
 Check (test_constants_fwd )%return.
 
-(** [no_nested_borrows::test_weird_borrows1] *)
+(** [no_nested_borrows::test_weird_borrows1]: forward function *)
 Definition test_weird_borrows1_fwd : result unit :=
   Return tt.
 
 (** Unit test for [no_nested_borrows::test_weird_borrows1] *)
 Check (test_weird_borrows1_fwd )%return.
 
-(** [no_nested_borrows::test_mem_replace] *)
+(** [no_nested_borrows::test_mem_replace]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ()) *)
 Definition test_mem_replace_fwd_back (px : u32) : result u32 :=
   let y := mem_replace_fwd u32 px 1%u32 in
   if negb (y s= 0%u32) then Fail_ Failure else Return 2%u32
 .
 
-(** [no_nested_borrows::test_shared_borrow_bool1] *)
+(** [no_nested_borrows::test_shared_borrow_bool1]: forward function *)
 Definition test_shared_borrow_bool1_fwd (b : bool) : result u32 :=
   if b then Return 0%u32 else Return 1%u32
 .
 
-(** [no_nested_borrows::test_shared_borrow_bool2] *)
+(** [no_nested_borrows::test_shared_borrow_bool2]: forward function *)
 Definition test_shared_borrow_bool2_fwd : result u32 :=
   Return 0%u32.
 
-(** [no_nested_borrows::test_shared_borrow_enum1] *)
+(** [no_nested_borrows::test_shared_borrow_enum1]: forward function *)
 Definition test_shared_borrow_enum1_fwd (l : List_t u32) : result u32 :=
   match l with | ListCons i l0 => Return 1%u32 | ListNil => Return 0%u32 end
 .
 
-(** [no_nested_borrows::test_shared_borrow_enum2] *)
+(** [no_nested_borrows::test_shared_borrow_enum2]: forward function *)
 Definition test_shared_borrow_enum2_fwd : result u32 :=
   Return 0%u32.
 
diff --git a/tests/coq/misc/Paper.v b/tests/coq/misc/Paper.v
index 513bc749..0f854f31 100644
--- a/tests/coq/misc/Paper.v
+++ b/tests/coq/misc/Paper.v
@@ -6,11 +6,12 @@ Require Import Coq.ZArith.ZArith.
 Local Open Scope Primitives_scope.
 Module Paper.
 
-(** [paper::ref_incr] *)
+(** [paper::ref_incr]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ()) *)
 Definition ref_incr_fwd_back (x : i32) : result i32 :=
   i32_add x 1%i32.
 
-(** [paper::test_incr] *)
+(** [paper::test_incr]: forward function *)
 Definition test_incr_fwd : result unit :=
   x <- ref_incr_fwd_back 0%i32;
   if negb (x s= 1%i32) then Fail_ Failure else Return tt
@@ -19,18 +20,18 @@ Definition test_incr_fwd : result unit :=
 (** Unit test for [paper::test_incr] *)
 Check (test_incr_fwd )%return.
 
-(** [paper::choose] *)
+(** [paper::choose]: forward function *)
 Definition choose_fwd (T : Type) (b : bool) (x : T) (y : T) : result T :=
   if b then Return x else Return y
 .
 
-(** [paper::choose] *)
+(** [paper::choose]: backward function 0 *)
 Definition choose_back
   (T : Type) (b : bool) (x : T) (y : T) (ret : T) : result (T * T) :=
   if b then Return (ret, y) else Return (x, ret)
 .
 
-(** [paper::test_choose] *)
+(** [paper::test_choose]: forward function *)
 Definition test_choose_fwd : result unit :=
   z <- choose_fwd i32 true 0%i32 0%i32;
   z0 <- i32_add z 1%i32;
@@ -56,7 +57,7 @@ Inductive List_t (T : Type) :=
 Arguments ListCons {T} _ _.
 Arguments ListNil {T}.
 
-(** [paper::list_nth_mut] *)
+(** [paper::list_nth_mut]: forward function *)
 Fixpoint list_nth_mut_fwd (T : Type) (l : List_t T) (i : u32) : result T :=
   match l with
   | ListCons x tl =>
@@ -67,7 +68,7 @@ Fixpoint list_nth_mut_fwd (T : Type) (l : List_t T) (i : u32) : result T :=
   end
 .
 
-(** [paper::list_nth_mut] *)
+(** [paper::list_nth_mut]: backward function 0 *)
 Fixpoint list_nth_mut_back
   (T : Type) (l : List_t T) (i : u32) (ret : T) : result (List_t T) :=
   match l with
@@ -82,7 +83,7 @@ Fixpoint list_nth_mut_back
   end
 .
 
-(** [paper::sum] *)
+(** [paper::sum]: forward function *)
 Fixpoint sum_fwd (l : List_t i32) : result i32 :=
   match l with
   | ListCons x tl => i <- sum_fwd tl; i32_add x i
@@ -90,7 +91,7 @@ Fixpoint sum_fwd (l : List_t i32) : result i32 :=
   end
 .
 
-(** [paper::test_nth] *)
+(** [paper::test_nth]: forward function *)
 Definition test_nth_fwd : result unit :=
   let l := ListNil in
   let l0 := ListCons 3%i32 l in
@@ -105,7 +106,7 @@ Definition test_nth_fwd : result unit :=
 (** Unit test for [paper::test_nth] *)
 Check (test_nth_fwd )%return.
 
-(** [paper::call_choose] *)
+(** [paper::call_choose]: forward function *)
 Definition call_choose_fwd (p : (u32 * u32)) : result u32 :=
   let (px, py) := p in
   pz <- choose_fwd u32 true px py;
diff --git a/tests/coq/misc/PoloniusList.v b/tests/coq/misc/PoloniusList.v
index bd6df02e..e94b6dcb 100644
--- a/tests/coq/misc/PoloniusList.v
+++ b/tests/coq/misc/PoloniusList.v
@@ -15,7 +15,7 @@ Inductive List_t (T : Type) :=
 Arguments ListCons {T} _ _.
 Arguments ListNil {T}.
 
-(** [polonius_list::get_list_at_x] *)
+(** [polonius_list::get_list_at_x]: forward function *)
 Fixpoint get_list_at_x_fwd (ls : List_t u32) (x : u32) : result (List_t u32) :=
   match ls with
   | ListCons hd tl =>
@@ -24,7 +24,7 @@ Fixpoint get_list_at_x_fwd (ls : List_t u32) (x : u32) : result (List_t u32) :=
   end
 .
 
-(** [polonius_list::get_list_at_x] *)
+(** [polonius_list::get_list_at_x]: backward function 0 *)
 Fixpoint get_list_at_x_back
   (ls : List_t u32) (x : u32) (ret : List_t u32) : result (List_t u32) :=
   match ls with
diff --git a/tests/coq/misc/_CoqProject b/tests/coq/misc/_CoqProject
index 87dea3e6..db6c2742 100644
--- a/tests/coq/misc/_CoqProject
+++ b/tests/coq/misc/_CoqProject
@@ -3,12 +3,12 @@
 -arg -w
 -arg all
 
-Constants.v
-External_Types.v
-Primitives.v
 Loops.v
+Primitives.v
 External_Funs.v
+Constants.v
 PoloniusList.v
+External_Types.v
 NoNestedBorrows.v
 External_Opaque.v
 Paper.v
diff --git a/tests/fstar/betree/BetreeMain.Funs.fst b/tests/fstar/betree/BetreeMain.Funs.fst
index 0c868f47..f1bc1191 100644
--- a/tests/fstar/betree/BetreeMain.Funs.fst
+++ b/tests/fstar/betree/BetreeMain.Funs.fst
@@ -8,14 +8,14 @@ include BetreeMain.Clauses
 
 #set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
 
-(** [betree_main::betree::load_internal_node] *)
+(** [betree_main::betree::load_internal_node]: forward function *)
 let betree_load_internal_node_fwd
   (id : u64) (st : state) :
   result (state & (betree_list_t (u64 & betree_message_t)))
   =
   betree_utils_load_internal_node_fwd id st
 
-(** [betree_main::betree::store_internal_node] *)
+(** [betree_main::betree::store_internal_node]: forward function *)
 let betree_store_internal_node_fwd
   (id : u64) (content : betree_list_t (u64 & betree_message_t)) (st : state) :
   result (state & unit)
@@ -23,12 +23,12 @@ let betree_store_internal_node_fwd
   let* (st0, _) = betree_utils_store_internal_node_fwd id content st in
   Return (st0, ())
 
-(** [betree_main::betree::load_leaf_node] *)
+(** [betree_main::betree::load_leaf_node]: forward function *)
 let betree_load_leaf_node_fwd
   (id : u64) (st : state) : result (state & (betree_list_t (u64 & u64))) =
   betree_utils_load_leaf_node_fwd id st
 
-(** [betree_main::betree::store_leaf_node] *)
+(** [betree_main::betree::store_leaf_node]: forward function *)
 let betree_store_leaf_node_fwd
   (id : u64) (content : betree_list_t (u64 & u64)) (st : state) :
   result (state & unit)
@@ -36,25 +36,25 @@ let betree_store_leaf_node_fwd
   let* (st0, _) = betree_utils_store_leaf_node_fwd id content st in
   Return (st0, ())
 
-(** [betree_main::betree::fresh_node_id] *)
+(** [betree_main::betree::fresh_node_id]: forward function *)
 let betree_fresh_node_id_fwd (counter : u64) : result u64 =
   let* _ = u64_add counter 1 in Return counter
 
-(** [betree_main::betree::fresh_node_id] *)
+(** [betree_main::betree::fresh_node_id]: backward function 0 *)
 let betree_fresh_node_id_back (counter : u64) : result u64 =
   u64_add counter 1
 
-(** [betree_main::betree::NodeIdCounter::{0}::new] *)
+(** [betree_main::betree::NodeIdCounter::{0}::new]: forward function *)
 let betree_node_id_counter_new_fwd : result betree_node_id_counter_t =
   Return { betree_node_id_counter_next_node_id = 0 }
 
-(** [betree_main::betree::NodeIdCounter::{0}::fresh_id] *)
+(** [betree_main::betree::NodeIdCounter::{0}::fresh_id]: forward function *)
 let betree_node_id_counter_fresh_id_fwd
   (self : betree_node_id_counter_t) : result u64 =
   let* _ = u64_add self.betree_node_id_counter_next_node_id 1 in
   Return self.betree_node_id_counter_next_node_id
 
-(** [betree_main::betree::NodeIdCounter::{0}::fresh_id] *)
+(** [betree_main::betree::NodeIdCounter::{0}::fresh_id]: backward function 0 *)
 let betree_node_id_counter_fresh_id_back
   (self : betree_node_id_counter_t) : result betree_node_id_counter_t =
   let* i = u64_add self.betree_node_id_counter_next_node_id 1 in
@@ -64,7 +64,7 @@ let betree_node_id_counter_fresh_id_back
 let core_num_u64_max_body : result u64 = Return 18446744073709551615
 let core_num_u64_max_c : u64 = eval_global core_num_u64_max_body
 
-(** [betree_main::betree::upsert_update] *)
+(** [betree_main::betree::upsert_update]: forward function *)
 let betree_upsert_update_fwd
   (prev : option u64) (st : betree_upsert_fun_state_t) : result u64 =
   begin match prev with
@@ -83,7 +83,7 @@ let betree_upsert_update_fwd
     end
   end
 
-(** [betree_main::betree::List::{1}::len] *)
+(** [betree_main::betree::List::{1}::len]: forward function *)
 let rec betree_list_len_fwd
   (t : Type0) (self : betree_list_t t) :
   Tot (result u64) (decreases (betree_list_len_decreases t self))
@@ -93,7 +93,7 @@ let rec betree_list_len_fwd
   | BetreeListNil -> Return 0
   end
 
-(** [betree_main::betree::List::{1}::split_at] *)
+(** [betree_main::betree::List::{1}::split_at]: forward function *)
 let rec betree_list_split_at_fwd
   (t : Type0) (self : betree_list_t t) (n : u64) :
   Tot (result ((betree_list_t t) & (betree_list_t t)))
@@ -112,14 +112,15 @@ let rec betree_list_split_at_fwd
     | BetreeListNil -> Fail Failure
     end
 
-(** [betree_main::betree::List::{1}::push_front] *)
+(** [betree_main::betree::List::{1}::push_front]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ()) *)
 let betree_list_push_front_fwd_back
   (t : Type0) (self : betree_list_t t) (x : t) : result (betree_list_t t) =
   let tl = mem_replace_fwd (betree_list_t t) self BetreeListNil in
   let l = tl in
   Return (BetreeListCons x l)
 
-(** [betree_main::betree::List::{1}::pop_front] *)
+(** [betree_main::betree::List::{1}::pop_front]: forward function *)
 let betree_list_pop_front_fwd (t : Type0) (self : betree_list_t t) : result t =
   let ls = mem_replace_fwd (betree_list_t t) self BetreeListNil in
   begin match ls with
@@ -127,7 +128,7 @@ let betree_list_pop_front_fwd (t : Type0) (self : betree_list_t t) : result t =
   | BetreeListNil -> Fail Failure
   end
 
-(** [betree_main::betree::List::{1}::pop_front] *)
+(** [betree_main::betree::List::{1}::pop_front]: backward function 0 *)
 let betree_list_pop_front_back
   (t : Type0) (self : betree_list_t t) : result (betree_list_t t) =
   let ls = mem_replace_fwd (betree_list_t t) self BetreeListNil in
@@ -136,14 +137,14 @@ let betree_list_pop_front_back
   | BetreeListNil -> Fail Failure
   end
 
-(** [betree_main::betree::List::{1}::hd] *)
+(** [betree_main::betree::List::{1}::hd]: forward function *)
 let betree_list_hd_fwd (t : Type0) (self : betree_list_t t) : result t =
   begin match self with
   | BetreeListCons hd l -> Return hd
   | BetreeListNil -> Fail Failure
   end
 
-(** [betree_main::betree::List::{2}::head_has_key] *)
+(** [betree_main::betree::List::{2}::head_has_key]: forward function *)
 let betree_list_head_has_key_fwd
   (t : Type0) (self : betree_list_t (u64 & t)) (key : u64) : result bool =
   begin match self with
@@ -151,7 +152,7 @@ let betree_list_head_has_key_fwd
   | BetreeListNil -> Return false
   end
 
-(** [betree_main::betree::List::{2}::partition_at_pivot] *)
+(** [betree_main::betree::List::{2}::partition_at_pivot]: forward function *)
 let rec betree_list_partition_at_pivot_fwd
   (t : Type0) (self : betree_list_t (u64 & t)) (pivot : u64) :
   Tot (result ((betree_list_t (u64 & t)) & (betree_list_t (u64 & t))))
@@ -170,7 +171,7 @@ let rec betree_list_partition_at_pivot_fwd
   | BetreeListNil -> Return (BetreeListNil, BetreeListNil)
   end
 
-(** [betree_main::betree::Leaf::{3}::split] *)
+(** [betree_main::betree::Leaf::{3}::split]: forward function *)
 let betree_leaf_split_fwd
   (self : betree_leaf_t) (content : betree_list_t (u64 & u64))
   (params : betree_params_t) (node_id_cnt : betree_node_id_counter_t)
@@ -202,7 +203,7 @@ let betree_leaf_split_fwd
       betree_internal_right = n0
     })
 
-(** [betree_main::betree::Leaf::{3}::split] *)
+(** [betree_main::betree::Leaf::{3}::split]: backward function 2 *)
 let betree_leaf_split_back
   (self : betree_leaf_t) (content : betree_list_t (u64 & u64))
   (params : betree_params_t) (node_id_cnt : betree_node_id_counter_t)
@@ -221,7 +222,7 @@ let betree_leaf_split_back
   let* _ = betree_store_leaf_node_fwd id1 content1 st0 in
   betree_node_id_counter_fresh_id_back node_id_cnt0
 
-(** [betree_main::betree::Node::{5}::lookup_in_bindings] *)
+(** [betree_main::betree::Node::{5}::lookup_in_bindings]: forward function *)
 let rec betree_node_lookup_in_bindings_fwd
   (key : u64) (bindings : betree_list_t (u64 & u64)) :
   Tot (result (option u64))
@@ -239,7 +240,7 @@ let rec betree_node_lookup_in_bindings_fwd
   | BetreeListNil -> Return None
   end
 
-(** [betree_main::betree::Node::{5}::lookup_first_message_for_key] *)
+(** [betree_main::betree::Node::{5}::lookup_first_message_for_key]: forward function *)
 let rec betree_node_lookup_first_message_for_key_fwd
   (key : u64) (msgs : betree_list_t (u64 & betree_message_t)) :
   Tot (result (betree_list_t (u64 & betree_message_t)))
@@ -254,7 +255,7 @@ let rec betree_node_lookup_first_message_for_key_fwd
   | BetreeListNil -> Return BetreeListNil
   end
 
-(** [betree_main::betree::Node::{5}::lookup_first_message_for_key] *)
+(** [betree_main::betree::Node::{5}::lookup_first_message_for_key]: backward function 0 *)
 let rec betree_node_lookup_first_message_for_key_back
   (key : u64) (msgs : betree_list_t (u64 & betree_message_t))
   (ret : betree_list_t (u64 & betree_message_t)) :
@@ -273,7 +274,7 @@ let rec betree_node_lookup_first_message_for_key_back
   | BetreeListNil -> Return ret
   end
 
-(** [betree_main::betree::Node::{5}::apply_upserts] *)
+(** [betree_main::betree::Node::{5}::apply_upserts]: forward function *)
 let rec betree_node_apply_upserts_fwd
   (msgs : betree_list_t (u64 & betree_message_t)) (prev : option u64)
   (key : u64) (st : state) :
@@ -300,7 +301,7 @@ let rec betree_node_apply_upserts_fwd
         BetreeMessageInsert v) in
     Return (st0, v)
 
-(** [betree_main::betree::Node::{5}::apply_upserts] *)
+(** [betree_main::betree::Node::{5}::apply_upserts]: backward function 0 *)
 let rec betree_node_apply_upserts_back
   (msgs : betree_list_t (u64 & betree_message_t)) (prev : option u64)
   (key : u64) (st : state) :
@@ -325,7 +326,7 @@ let rec betree_node_apply_upserts_back
     betree_list_push_front_fwd_back (u64 & betree_message_t) msgs (key,
       BetreeMessageInsert v)
 
-(** [betree_main::betree::Node::{5}::lookup] *)
+(** [betree_main::betree::Node::{5}::lookup]: forward function *)
 let rec betree_node_lookup_fwd
   (self : betree_node_t) (key : u64) (st : state) :
   Tot (result (state & (option u64)))
@@ -388,7 +389,7 @@ let rec betree_node_lookup_fwd
     Return (st0, opt)
   end
 
-(** [betree_main::betree::Node::{5}::lookup] *)
+(** [betree_main::betree::Node::{5}::lookup]: backward function 0 *)
 and betree_node_lookup_back
   (self : betree_node_t) (key : u64) (st : state) :
   Tot (result betree_node_t)
@@ -450,7 +451,7 @@ and betree_node_lookup_back
     Return (BetreeNodeLeaf node)
   end
 
-(** [betree_main::betree::Internal::{4}::lookup_in_children] *)
+(** [betree_main::betree::Internal::{4}::lookup_in_children]: forward function *)
 and betree_internal_lookup_in_children_fwd
   (self : betree_internal_t) (key : u64) (st : state) :
   Tot (result (state & (option u64)))
@@ -460,7 +461,7 @@ and betree_internal_lookup_in_children_fwd
   then betree_node_lookup_fwd self.betree_internal_left key st
   else betree_node_lookup_fwd self.betree_internal_right key st
 
-(** [betree_main::betree::Internal::{4}::lookup_in_children] *)
+(** [betree_main::betree::Internal::{4}::lookup_in_children]: backward function 0 *)
 and betree_internal_lookup_in_children_back
   (self : betree_internal_t) (key : u64) (st : state) :
   Tot (result betree_internal_t)
@@ -474,7 +475,7 @@ and betree_internal_lookup_in_children_back
     let* n = betree_node_lookup_back self.betree_internal_right key st in
     Return { self with betree_internal_right = n }
 
-(** [betree_main::betree::Node::{5}::lookup_mut_in_bindings] *)
+(** [betree_main::betree::Node::{5}::lookup_mut_in_bindings]: forward function *)
 let rec betree_node_lookup_mut_in_bindings_fwd
   (key : u64) (bindings : betree_list_t (u64 & u64)) :
   Tot (result (betree_list_t (u64 & u64)))
@@ -489,7 +490,7 @@ let rec betree_node_lookup_mut_in_bindings_fwd
   | BetreeListNil -> Return BetreeListNil
   end
 
-(** [betree_main::betree::Node::{5}::lookup_mut_in_bindings] *)
+(** [betree_main::betree::Node::{5}::lookup_mut_in_bindings]: backward function 0 *)
 let rec betree_node_lookup_mut_in_bindings_back
   (key : u64) (bindings : betree_list_t (u64 & u64))
   (ret : betree_list_t (u64 & u64)) :
@@ -507,7 +508,8 @@ let rec betree_node_lookup_mut_in_bindings_back
   | BetreeListNil -> Return ret
   end
 
-(** [betree_main::betree::Node::{5}::apply_to_leaf] *)
+(** [betree_main::betree::Node::{5}::apply_to_leaf]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ()) *)
 let betree_node_apply_to_leaf_fwd_back
   (bindings : betree_list_t (u64 & u64)) (key : u64)
   (new_msg : betree_message_t) :
@@ -550,7 +552,8 @@ let betree_node_apply_to_leaf_fwd_back
       betree_node_lookup_mut_in_bindings_back key bindings bindings1
     end
 
-(** [betree_main::betree::Node::{5}::apply_messages_to_leaf] *)
+(** [betree_main::betree::Node::{5}::apply_messages_to_leaf]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ()) *)
 let rec betree_node_apply_messages_to_leaf_fwd_back
   (bindings : betree_list_t (u64 & u64))
   (new_msgs : betree_list_t (u64 & betree_message_t)) :
@@ -565,7 +568,8 @@ let rec betree_node_apply_messages_to_leaf_fwd_back
   | BetreeListNil -> Return bindings
   end
 
-(** [betree_main::betree::Node::{5}::filter_messages_for_key] *)
+(** [betree_main::betree::Node::{5}::filter_messages_for_key]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ()) *)
 let rec betree_node_filter_messages_for_key_fwd_back
   (key : u64) (msgs : betree_list_t (u64 & betree_message_t)) :
   Tot (result (betree_list_t (u64 & betree_message_t)))
@@ -584,7 +588,7 @@ let rec betree_node_filter_messages_for_key_fwd_back
   | BetreeListNil -> Return BetreeListNil
   end
 
-(** [betree_main::betree::Node::{5}::lookup_first_message_after_key] *)
+(** [betree_main::betree::Node::{5}::lookup_first_message_after_key]: forward function *)
 let rec betree_node_lookup_first_message_after_key_fwd
   (key : u64) (msgs : betree_list_t (u64 & betree_message_t)) :
   Tot (result (betree_list_t (u64 & betree_message_t)))
@@ -599,7 +603,7 @@ let rec betree_node_lookup_first_message_after_key_fwd
   | BetreeListNil -> Return BetreeListNil
   end
 
-(** [betree_main::betree::Node::{5}::lookup_first_message_after_key] *)
+(** [betree_main::betree::Node::{5}::lookup_first_message_after_key]: backward function 0 *)
 let rec betree_node_lookup_first_message_after_key_back
   (key : u64) (msgs : betree_list_t (u64 & betree_message_t))
   (ret : betree_list_t (u64 & betree_message_t)) :
@@ -618,7 +622,8 @@ let rec betree_node_lookup_first_message_after_key_back
   | BetreeListNil -> Return ret
   end
 
-(** [betree_main::betree::Node::{5}::apply_to_internal] *)
+(** [betree_main::betree::Node::{5}::apply_to_internal]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ()) *)
 let betree_node_apply_to_internal_fwd_back
   (msgs : betree_list_t (u64 & betree_message_t)) (key : u64)
   (new_msg : betree_message_t) :
@@ -678,7 +683,8 @@ let betree_node_apply_to_internal_fwd_back
         new_msg) in
     betree_node_lookup_first_message_for_key_back key msgs msgs1
 
-(** [betree_main::betree::Node::{5}::apply_messages_to_internal] *)
+(** [betree_main::betree::Node::{5}::apply_messages_to_internal]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ()) *)
 let rec betree_node_apply_messages_to_internal_fwd_back
   (msgs : betree_list_t (u64 & betree_message_t))
   (new_msgs : betree_list_t (u64 & betree_message_t)) :
@@ -693,7 +699,7 @@ let rec betree_node_apply_messages_to_internal_fwd_back
   | BetreeListNil -> Return msgs
   end
 
-(** [betree_main::betree::Node::{5}::apply_messages] *)
+(** [betree_main::betree::Node::{5}::apply_messages]: forward function *)
 let rec betree_node_apply_messages_fwd
   (self : betree_node_t) (params : betree_params_t)
   (node_id_cnt : betree_node_id_counter_t)
@@ -740,7 +746,7 @@ let rec betree_node_apply_messages_fwd
       Return (st1, ())
   end
 
-(** [betree_main::betree::Node::{5}::apply_messages] *)
+(** [betree_main::betree::Node::{5}::apply_messages]: backward function 0 *)
 and betree_node_apply_messages_back
   (self : betree_node_t) (params : betree_params_t)
   (node_id_cnt : betree_node_id_counter_t)
@@ -788,7 +794,7 @@ and betree_node_apply_messages_back
       Return (BetreeNodeLeaf { node with betree_leaf_size = len }, node_id_cnt)
   end
 
-(** [betree_main::betree::Internal::{4}::flush] *)
+(** [betree_main::betree::Internal::{4}::flush]: forward function *)
 and betree_internal_flush_fwd
   (self : betree_internal_t) (params : betree_params_t)
   (node_id_cnt : betree_node_id_counter_t)
@@ -830,7 +836,7 @@ and betree_internal_flush_fwd
         node_id_cnt msgs_right st in
     Return (st0, msgs_left)
 
-(** [betree_main::betree::Internal::{4}::flush] *)
+(** [betree_main::betree::Internal::{4}::flush]: backward function 0 *)
 and betree_internal_flush_back
   (self : betree_internal_t) (params : betree_params_t)
   (node_id_cnt : betree_node_id_counter_t)
@@ -868,7 +874,7 @@ and betree_internal_flush_back
         node_id_cnt msgs_right st in
     Return ({ self with betree_internal_right = n }, node_id_cnt0)
 
-(** [betree_main::betree::Node::{5}::apply] *)
+(** [betree_main::betree::Node::{5}::apply]: forward function *)
 let betree_node_apply_fwd
   (self : betree_node_t) (params : betree_params_t)
   (node_id_cnt : betree_node_id_counter_t) (key : u64)
@@ -884,7 +890,7 @@ let betree_node_apply_fwd
       (key, new_msg) l) st in
   Return (st0, ())
 
-(** [betree_main::betree::Node::{5}::apply] *)
+(** [betree_main::betree::Node::{5}::apply]: backward function 0 *)
 let betree_node_apply_back
   (self : betree_node_t) (params : betree_params_t)
   (node_id_cnt : betree_node_id_counter_t) (key : u64)
@@ -895,7 +901,7 @@ let betree_node_apply_back
   betree_node_apply_messages_back self params node_id_cnt (BetreeListCons (key,
     new_msg) l) st
 
-(** [betree_main::betree::BeTree::{6}::new] *)
+(** [betree_main::betree::BeTree::{6}::new]: forward function *)
 let betree_be_tree_new_fwd
   (min_flush_size : u64) (split_size : u64) (st : state) :
   result (state & betree_be_tree_t)
@@ -916,7 +922,7 @@ let betree_be_tree_new_fwd
         (BetreeNodeLeaf { betree_leaf_id = id; betree_leaf_size = 0 })
     })
 
-(** [betree_main::betree::BeTree::{6}::apply] *)
+(** [betree_main::betree::BeTree::{6}::apply]: forward function *)
 let betree_be_tree_apply_fwd
   (self : betree_be_tree_t) (key : u64) (msg : betree_message_t) (st : state) :
   result (state & unit)
@@ -929,7 +935,7 @@ let betree_be_tree_apply_fwd
       self.betree_be_tree_node_id_cnt key msg st in
   Return (st0, ())
 
-(** [betree_main::betree::BeTree::{6}::apply] *)
+(** [betree_main::betree::BeTree::{6}::apply]: backward function 0 *)
 let betree_be_tree_apply_back
   (self : betree_be_tree_t) (key : u64) (msg : betree_message_t) (st : state) :
   result betree_be_tree_t
@@ -940,7 +946,7 @@ let betree_be_tree_apply_back
   Return
     { self with betree_be_tree_node_id_cnt = nic; betree_be_tree_root = n }
 
-(** [betree_main::betree::BeTree::{6}::insert] *)
+(** [betree_main::betree::BeTree::{6}::insert]: forward function *)
 let betree_be_tree_insert_fwd
   (self : betree_be_tree_t) (key : u64) (value : u64) (st : state) :
   result (state & unit)
@@ -950,28 +956,28 @@ let betree_be_tree_insert_fwd
   let* _ = betree_be_tree_apply_back self key (BetreeMessageInsert value) st in
   Return (st0, ())
 
-(** [betree_main::betree::BeTree::{6}::insert] *)
+(** [betree_main::betree::BeTree::{6}::insert]: backward function 0 *)
 let betree_be_tree_insert_back
   (self : betree_be_tree_t) (key : u64) (value : u64) (st : state) :
   result betree_be_tree_t
   =
   betree_be_tree_apply_back self key (BetreeMessageInsert value) st
 
-(** [betree_main::betree::BeTree::{6}::delete] *)
+(** [betree_main::betree::BeTree::{6}::delete]: forward function *)
 let betree_be_tree_delete_fwd
   (self : betree_be_tree_t) (key : u64) (st : state) : result (state & unit) =
   let* (st0, _) = betree_be_tree_apply_fwd self key BetreeMessageDelete st in
   let* _ = betree_be_tree_apply_back self key BetreeMessageDelete st in
   Return (st0, ())
 
-(** [betree_main::betree::BeTree::{6}::delete] *)
+(** [betree_main::betree::BeTree::{6}::delete]: backward function 0 *)
 let betree_be_tree_delete_back
   (self : betree_be_tree_t) (key : u64) (st : state) :
   result betree_be_tree_t
   =
   betree_be_tree_apply_back self key BetreeMessageDelete st
 
-(** [betree_main::betree::BeTree::{6}::upsert] *)
+(** [betree_main::betree::BeTree::{6}::upsert]: forward function *)
 let betree_be_tree_upsert_fwd
   (self : betree_be_tree_t) (key : u64) (upd : betree_upsert_fun_state_t)
   (st : state) :
@@ -982,7 +988,7 @@ let betree_be_tree_upsert_fwd
   let* _ = betree_be_tree_apply_back self key (BetreeMessageUpsert upd) st in
   Return (st0, ())
 
-(** [betree_main::betree::BeTree::{6}::upsert] *)
+(** [betree_main::betree::BeTree::{6}::upsert]: backward function 0 *)
 let betree_be_tree_upsert_back
   (self : betree_be_tree_t) (key : u64) (upd : betree_upsert_fun_state_t)
   (st : state) :
@@ -990,14 +996,14 @@ let betree_be_tree_upsert_back
   =
   betree_be_tree_apply_back self key (BetreeMessageUpsert upd) st
 
-(** [betree_main::betree::BeTree::{6}::lookup] *)
+(** [betree_main::betree::BeTree::{6}::lookup]: forward function *)
 let betree_be_tree_lookup_fwd
   (self : betree_be_tree_t) (key : u64) (st : state) :
   result (state & (option u64))
   =
   betree_node_lookup_fwd self.betree_be_tree_root key st
 
-(** [betree_main::betree::BeTree::{6}::lookup] *)
+(** [betree_main::betree::BeTree::{6}::lookup]: backward function 0 *)
 let betree_be_tree_lookup_back
   (self : betree_be_tree_t) (key : u64) (st : state) :
   result betree_be_tree_t
@@ -1005,7 +1011,7 @@ let betree_be_tree_lookup_back
   let* n = betree_node_lookup_back self.betree_be_tree_root key st in
   Return { self with betree_be_tree_root = n }
 
-(** [betree_main::main] *)
+(** [betree_main::main]: forward function *)
 let main_fwd : result unit =
   Return ()
 
diff --git a/tests/fstar/betree/BetreeMain.Opaque.fsti b/tests/fstar/betree/BetreeMain.Opaque.fsti
index dc49601a..c33cf225 100644
--- a/tests/fstar/betree/BetreeMain.Opaque.fsti
+++ b/tests/fstar/betree/BetreeMain.Opaque.fsti
@@ -1,30 +1,30 @@
 (** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
-(** [betree_main]: opaque function definitions *)
+(** [betree_main]: external function declarations *)
 module BetreeMain.Opaque
 open Primitives
 include BetreeMain.Types
 
 #set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
 
-(** [betree_main::betree_utils::load_internal_node] *)
+(** [betree_main::betree_utils::load_internal_node]: forward function *)
 val betree_utils_load_internal_node_fwd
   : u64 -> state -> result (state & (betree_list_t (u64 & betree_message_t)))
 
-(** [betree_main::betree_utils::store_internal_node] *)
+(** [betree_main::betree_utils::store_internal_node]: forward function *)
 val betree_utils_store_internal_node_fwd
   :
   u64 -> betree_list_t (u64 & betree_message_t) -> state -> result (state &
     unit)
 
-(** [betree_main::betree_utils::load_leaf_node] *)
+(** [betree_main::betree_utils::load_leaf_node]: forward function *)
 val betree_utils_load_leaf_node_fwd
   : u64 -> state -> result (state & (betree_list_t (u64 & u64)))
 
-(** [betree_main::betree_utils::store_leaf_node] *)
+(** [betree_main::betree_utils::store_leaf_node]: forward function *)
 val betree_utils_store_leaf_node_fwd
   : u64 -> betree_list_t (u64 & u64) -> state -> result (state & unit)
 
-(** [core::option::Option::{0}::unwrap] *)
+(** [core::option::Option::{0}::unwrap]: forward function *)
 val core_option_option_unwrap_fwd
   (t : Type0) : option t -> state -> result (state & t)
 
diff --git a/tests/fstar/betree_back_stateful/BetreeMain.Funs.fst b/tests/fstar/betree_back_stateful/BetreeMain.Funs.fst
index c70bef08..12402fb4 100644
--- a/tests/fstar/betree_back_stateful/BetreeMain.Funs.fst
+++ b/tests/fstar/betree_back_stateful/BetreeMain.Funs.fst
@@ -8,14 +8,14 @@ include BetreeMain.Clauses
 
 #set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
 
-(** [betree_main::betree::load_internal_node] *)
+(** [betree_main::betree::load_internal_node]: forward function *)
 let betree_load_internal_node_fwd
   (id : u64) (st : state) :
   result (state & (betree_list_t (u64 & betree_message_t)))
   =
   betree_utils_load_internal_node_fwd id st
 
-(** [betree_main::betree::store_internal_node] *)
+(** [betree_main::betree::store_internal_node]: forward function *)
 let betree_store_internal_node_fwd
   (id : u64) (content : betree_list_t (u64 & betree_message_t)) (st : state) :
   result (state & unit)
@@ -23,12 +23,12 @@ let betree_store_internal_node_fwd
   let* (st0, _) = betree_utils_store_internal_node_fwd id content st in
   Return (st0, ())
 
-(** [betree_main::betree::load_leaf_node] *)
+(** [betree_main::betree::load_leaf_node]: forward function *)
 let betree_load_leaf_node_fwd
   (id : u64) (st : state) : result (state & (betree_list_t (u64 & u64))) =
   betree_utils_load_leaf_node_fwd id st
 
-(** [betree_main::betree::store_leaf_node] *)
+(** [betree_main::betree::store_leaf_node]: forward function *)
 let betree_store_leaf_node_fwd
   (id : u64) (content : betree_list_t (u64 & u64)) (st : state) :
   result (state & unit)
@@ -36,25 +36,25 @@ let betree_store_leaf_node_fwd
   let* (st0, _) = betree_utils_store_leaf_node_fwd id content st in
   Return (st0, ())
 
-(** [betree_main::betree::fresh_node_id] *)
+(** [betree_main::betree::fresh_node_id]: forward function *)
 let betree_fresh_node_id_fwd (counter : u64) : result u64 =
   let* _ = u64_add counter 1 in Return counter
 
-(** [betree_main::betree::fresh_node_id] *)
+(** [betree_main::betree::fresh_node_id]: backward function 0 *)
 let betree_fresh_node_id_back (counter : u64) : result u64 =
   u64_add counter 1
 
-(** [betree_main::betree::NodeIdCounter::{0}::new] *)
+(** [betree_main::betree::NodeIdCounter::{0}::new]: forward function *)
 let betree_node_id_counter_new_fwd : result betree_node_id_counter_t =
   Return { betree_node_id_counter_next_node_id = 0 }
 
-(** [betree_main::betree::NodeIdCounter::{0}::fresh_id] *)
+(** [betree_main::betree::NodeIdCounter::{0}::fresh_id]: forward function *)
 let betree_node_id_counter_fresh_id_fwd
   (self : betree_node_id_counter_t) : result u64 =
   let* _ = u64_add self.betree_node_id_counter_next_node_id 1 in
   Return self.betree_node_id_counter_next_node_id
 
-(** [betree_main::betree::NodeIdCounter::{0}::fresh_id] *)
+(** [betree_main::betree::NodeIdCounter::{0}::fresh_id]: backward function 0 *)
 let betree_node_id_counter_fresh_id_back
   (self : betree_node_id_counter_t) : result betree_node_id_counter_t =
   let* i = u64_add self.betree_node_id_counter_next_node_id 1 in
@@ -64,7 +64,7 @@ let betree_node_id_counter_fresh_id_back
 let core_num_u64_max_body : result u64 = Return 18446744073709551615
 let core_num_u64_max_c : u64 = eval_global core_num_u64_max_body
 
-(** [betree_main::betree::upsert_update] *)
+(** [betree_main::betree::upsert_update]: forward function *)
 let betree_upsert_update_fwd
   (prev : option u64) (st : betree_upsert_fun_state_t) : result u64 =
   begin match prev with
@@ -83,7 +83,7 @@ let betree_upsert_update_fwd
     end
   end
 
-(** [betree_main::betree::List::{1}::len] *)
+(** [betree_main::betree::List::{1}::len]: forward function *)
 let rec betree_list_len_fwd
   (t : Type0) (self : betree_list_t t) :
   Tot (result u64) (decreases (betree_list_len_decreases t self))
@@ -93,7 +93,7 @@ let rec betree_list_len_fwd
   | BetreeListNil -> Return 0
   end
 
-(** [betree_main::betree::List::{1}::split_at] *)
+(** [betree_main::betree::List::{1}::split_at]: forward function *)
 let rec betree_list_split_at_fwd
   (t : Type0) (self : betree_list_t t) (n : u64) :
   Tot (result ((betree_list_t t) & (betree_list_t t)))
@@ -112,14 +112,15 @@ let rec betree_list_split_at_fwd
     | BetreeListNil -> Fail Failure
     end
 
-(** [betree_main::betree::List::{1}::push_front] *)
+(** [betree_main::betree::List::{1}::push_front]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ()) *)
 let betree_list_push_front_fwd_back
   (t : Type0) (self : betree_list_t t) (x : t) : result (betree_list_t t) =
   let tl = mem_replace_fwd (betree_list_t t) self BetreeListNil in
   let l = tl in
   Return (BetreeListCons x l)
 
-(** [betree_main::betree::List::{1}::pop_front] *)
+(** [betree_main::betree::List::{1}::pop_front]: forward function *)
 let betree_list_pop_front_fwd (t : Type0) (self : betree_list_t t) : result t =
   let ls = mem_replace_fwd (betree_list_t t) self BetreeListNil in
   begin match ls with
@@ -127,7 +128,7 @@ let betree_list_pop_front_fwd (t : Type0) (self : betree_list_t t) : result t =
   | BetreeListNil -> Fail Failure
   end
 
-(** [betree_main::betree::List::{1}::pop_front] *)
+(** [betree_main::betree::List::{1}::pop_front]: backward function 0 *)
 let betree_list_pop_front_back
   (t : Type0) (self : betree_list_t t) : result (betree_list_t t) =
   let ls = mem_replace_fwd (betree_list_t t) self BetreeListNil in
@@ -136,14 +137,14 @@ let betree_list_pop_front_back
   | BetreeListNil -> Fail Failure
   end
 
-(** [betree_main::betree::List::{1}::hd] *)
+(** [betree_main::betree::List::{1}::hd]: forward function *)
 let betree_list_hd_fwd (t : Type0) (self : betree_list_t t) : result t =
   begin match self with
   | BetreeListCons hd l -> Return hd
   | BetreeListNil -> Fail Failure
   end
 
-(** [betree_main::betree::List::{2}::head_has_key] *)
+(** [betree_main::betree::List::{2}::head_has_key]: forward function *)
 let betree_list_head_has_key_fwd
   (t : Type0) (self : betree_list_t (u64 & t)) (key : u64) : result bool =
   begin match self with
@@ -151,7 +152,7 @@ let betree_list_head_has_key_fwd
   | BetreeListNil -> Return false
   end
 
-(** [betree_main::betree::List::{2}::partition_at_pivot] *)
+(** [betree_main::betree::List::{2}::partition_at_pivot]: forward function *)
 let rec betree_list_partition_at_pivot_fwd
   (t : Type0) (self : betree_list_t (u64 & t)) (pivot : u64) :
   Tot (result ((betree_list_t (u64 & t)) & (betree_list_t (u64 & t))))
@@ -170,7 +171,7 @@ let rec betree_list_partition_at_pivot_fwd
   | BetreeListNil -> Return (BetreeListNil, BetreeListNil)
   end
 
-(** [betree_main::betree::Leaf::{3}::split] *)
+(** [betree_main::betree::Leaf::{3}::split]: forward function *)
 let betree_leaf_split_fwd
   (self : betree_leaf_t) (content : betree_list_t (u64 & u64))
   (params : betree_params_t) (node_id_cnt : betree_node_id_counter_t)
@@ -202,7 +203,7 @@ let betree_leaf_split_fwd
       betree_internal_right = n0
     })
 
-(** [betree_main::betree::Leaf::{3}::split] *)
+(** [betree_main::betree::Leaf::{3}::split]: backward function 0 *)
 let betree_leaf_split_back0
   (self : betree_leaf_t) (content : betree_list_t (u64 & u64))
   (params : betree_params_t) (node_id_cnt : betree_node_id_counter_t)
@@ -221,7 +222,7 @@ let betree_leaf_split_back0
   let* _ = betree_store_leaf_node_fwd id1 content1 st1 in
   Return (st0, ())
 
-(** [betree_main::betree::Leaf::{3}::split] *)
+(** [betree_main::betree::Leaf::{3}::split]: backward function 1 *)
 let betree_leaf_split_back1
   (self : betree_leaf_t) (content : betree_list_t (u64 & u64))
   (params : betree_params_t) (node_id_cnt : betree_node_id_counter_t)
@@ -240,7 +241,7 @@ let betree_leaf_split_back1
   let* _ = betree_store_leaf_node_fwd id1 content1 st1 in
   Return (st0, ())
 
-(** [betree_main::betree::Leaf::{3}::split] *)
+(** [betree_main::betree::Leaf::{3}::split]: backward function 2 *)
 let betree_leaf_split_back2
   (self : betree_leaf_t) (content : betree_list_t (u64 & u64))
   (params : betree_params_t) (node_id_cnt : betree_node_id_counter_t)
@@ -260,7 +261,7 @@ let betree_leaf_split_back2
   let* node_id_cnt1 = betree_node_id_counter_fresh_id_back node_id_cnt0 in
   Return (st0, node_id_cnt1)
 
-(** [betree_main::betree::Node::{5}::lookup_in_bindings] *)
+(** [betree_main::betree::Node::{5}::lookup_in_bindings]: forward function *)
 let rec betree_node_lookup_in_bindings_fwd
   (key : u64) (bindings : betree_list_t (u64 & u64)) :
   Tot (result (option u64))
@@ -278,7 +279,7 @@ let rec betree_node_lookup_in_bindings_fwd
   | BetreeListNil -> Return None
   end
 
-(** [betree_main::betree::Node::{5}::lookup_first_message_for_key] *)
+(** [betree_main::betree::Node::{5}::lookup_first_message_for_key]: forward function *)
 let rec betree_node_lookup_first_message_for_key_fwd
   (key : u64) (msgs : betree_list_t (u64 & betree_message_t)) :
   Tot (result (betree_list_t (u64 & betree_message_t)))
@@ -293,7 +294,7 @@ let rec betree_node_lookup_first_message_for_key_fwd
   | BetreeListNil -> Return BetreeListNil
   end
 
-(** [betree_main::betree::Node::{5}::lookup_first_message_for_key] *)
+(** [betree_main::betree::Node::{5}::lookup_first_message_for_key]: backward function 0 *)
 let rec betree_node_lookup_first_message_for_key_back
   (key : u64) (msgs : betree_list_t (u64 & betree_message_t))
   (ret : betree_list_t (u64 & betree_message_t)) :
@@ -312,7 +313,7 @@ let rec betree_node_lookup_first_message_for_key_back
   | BetreeListNil -> Return ret
   end
 
-(** [betree_main::betree::Node::{5}::apply_upserts] *)
+(** [betree_main::betree::Node::{5}::apply_upserts]: forward function *)
 let rec betree_node_apply_upserts_fwd
   (msgs : betree_list_t (u64 & betree_message_t)) (prev : option u64)
   (key : u64) (st : state) :
@@ -339,7 +340,7 @@ let rec betree_node_apply_upserts_fwd
         BetreeMessageInsert v) in
     Return (st0, v)
 
-(** [betree_main::betree::Node::{5}::apply_upserts] *)
+(** [betree_main::betree::Node::{5}::apply_upserts]: backward function 0 *)
 let rec betree_node_apply_upserts_back
   (msgs : betree_list_t (u64 & betree_message_t)) (prev : option u64)
   (key : u64) (st : state) (st0 : state) :
@@ -366,7 +367,7 @@ let rec betree_node_apply_upserts_back
         BetreeMessageInsert v) in
     Return (st0, msgs0)
 
-(** [betree_main::betree::Node::{5}::lookup] *)
+(** [betree_main::betree::Node::{5}::lookup]: forward function *)
 let rec betree_node_lookup_fwd
   (self : betree_node_t) (key : u64) (st : state) :
   Tot (result (state & (option u64)))
@@ -430,7 +431,7 @@ let rec betree_node_lookup_fwd
     Return (st0, opt)
   end
 
-(** [betree_main::betree::Node::{5}::lookup] *)
+(** [betree_main::betree::Node::{5}::lookup]: backward function 0 *)
 and betree_node_lookup_back
   (self : betree_node_t) (key : u64) (st : state) (st0 : state) :
   Tot (result (state & betree_node_t))
@@ -495,7 +496,7 @@ and betree_node_lookup_back
     Return (st0, BetreeNodeLeaf node)
   end
 
-(** [betree_main::betree::Internal::{4}::lookup_in_children] *)
+(** [betree_main::betree::Internal::{4}::lookup_in_children]: forward function *)
 and betree_internal_lookup_in_children_fwd
   (self : betree_internal_t) (key : u64) (st : state) :
   Tot (result (state & (option u64)))
@@ -505,7 +506,7 @@ and betree_internal_lookup_in_children_fwd
   then betree_node_lookup_fwd self.betree_internal_left key st
   else betree_node_lookup_fwd self.betree_internal_right key st
 
-(** [betree_main::betree::Internal::{4}::lookup_in_children] *)
+(** [betree_main::betree::Internal::{4}::lookup_in_children]: backward function 0 *)
 and betree_internal_lookup_in_children_back
   (self : betree_internal_t) (key : u64) (st : state) (st0 : state) :
   Tot (result (state & betree_internal_t))
@@ -521,7 +522,7 @@ and betree_internal_lookup_in_children_back
       betree_node_lookup_back self.betree_internal_right key st st0 in
     Return (st1, { self with betree_internal_right = n })
 
-(** [betree_main::betree::Node::{5}::lookup_mut_in_bindings] *)
+(** [betree_main::betree::Node::{5}::lookup_mut_in_bindings]: forward function *)
 let rec betree_node_lookup_mut_in_bindings_fwd
   (key : u64) (bindings : betree_list_t (u64 & u64)) :
   Tot (result (betree_list_t (u64 & u64)))
@@ -536,7 +537,7 @@ let rec betree_node_lookup_mut_in_bindings_fwd
   | BetreeListNil -> Return BetreeListNil
   end
 
-(** [betree_main::betree::Node::{5}::lookup_mut_in_bindings] *)
+(** [betree_main::betree::Node::{5}::lookup_mut_in_bindings]: backward function 0 *)
 let rec betree_node_lookup_mut_in_bindings_back
   (key : u64) (bindings : betree_list_t (u64 & u64))
   (ret : betree_list_t (u64 & u64)) :
@@ -554,7 +555,8 @@ let rec betree_node_lookup_mut_in_bindings_back
   | BetreeListNil -> Return ret
   end
 
-(** [betree_main::betree::Node::{5}::apply_to_leaf] *)
+(** [betree_main::betree::Node::{5}::apply_to_leaf]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ()) *)
 let betree_node_apply_to_leaf_fwd_back
   (bindings : betree_list_t (u64 & u64)) (key : u64)
   (new_msg : betree_message_t) :
@@ -597,7 +599,8 @@ let betree_node_apply_to_leaf_fwd_back
       betree_node_lookup_mut_in_bindings_back key bindings bindings1
     end
 
-(** [betree_main::betree::Node::{5}::apply_messages_to_leaf] *)
+(** [betree_main::betree::Node::{5}::apply_messages_to_leaf]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ()) *)
 let rec betree_node_apply_messages_to_leaf_fwd_back
   (bindings : betree_list_t (u64 & u64))
   (new_msgs : betree_list_t (u64 & betree_message_t)) :
@@ -612,7 +615,8 @@ let rec betree_node_apply_messages_to_leaf_fwd_back
   | BetreeListNil -> Return bindings
   end
 
-(** [betree_main::betree::Node::{5}::filter_messages_for_key] *)
+(** [betree_main::betree::Node::{5}::filter_messages_for_key]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ()) *)
 let rec betree_node_filter_messages_for_key_fwd_back
   (key : u64) (msgs : betree_list_t (u64 & betree_message_t)) :
   Tot (result (betree_list_t (u64 & betree_message_t)))
@@ -631,7 +635,7 @@ let rec betree_node_filter_messages_for_key_fwd_back
   | BetreeListNil -> Return BetreeListNil
   end
 
-(** [betree_main::betree::Node::{5}::lookup_first_message_after_key] *)
+(** [betree_main::betree::Node::{5}::lookup_first_message_after_key]: forward function *)
 let rec betree_node_lookup_first_message_after_key_fwd
   (key : u64) (msgs : betree_list_t (u64 & betree_message_t)) :
   Tot (result (betree_list_t (u64 & betree_message_t)))
@@ -646,7 +650,7 @@ let rec betree_node_lookup_first_message_after_key_fwd
   | BetreeListNil -> Return BetreeListNil
   end
 
-(** [betree_main::betree::Node::{5}::lookup_first_message_after_key] *)
+(** [betree_main::betree::Node::{5}::lookup_first_message_after_key]: backward function 0 *)
 let rec betree_node_lookup_first_message_after_key_back
   (key : u64) (msgs : betree_list_t (u64 & betree_message_t))
   (ret : betree_list_t (u64 & betree_message_t)) :
@@ -665,7 +669,8 @@ let rec betree_node_lookup_first_message_after_key_back
   | BetreeListNil -> Return ret
   end
 
-(** [betree_main::betree::Node::{5}::apply_to_internal] *)
+(** [betree_main::betree::Node::{5}::apply_to_internal]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ()) *)
 let betree_node_apply_to_internal_fwd_back
   (msgs : betree_list_t (u64 & betree_message_t)) (key : u64)
   (new_msg : betree_message_t) :
@@ -725,7 +730,8 @@ let betree_node_apply_to_internal_fwd_back
         new_msg) in
     betree_node_lookup_first_message_for_key_back key msgs msgs1
 
-(** [betree_main::betree::Node::{5}::apply_messages_to_internal] *)
+(** [betree_main::betree::Node::{5}::apply_messages_to_internal]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ()) *)
 let rec betree_node_apply_messages_to_internal_fwd_back
   (msgs : betree_list_t (u64 & betree_message_t))
   (new_msgs : betree_list_t (u64 & betree_message_t)) :
@@ -740,7 +746,7 @@ let rec betree_node_apply_messages_to_internal_fwd_back
   | BetreeListNil -> Return msgs
   end
 
-(** [betree_main::betree::Node::{5}::apply_messages] *)
+(** [betree_main::betree::Node::{5}::apply_messages]: forward function *)
 let rec betree_node_apply_messages_fwd
   (self : betree_node_t) (params : betree_params_t)
   (node_id_cnt : betree_node_id_counter_t)
@@ -788,7 +794,7 @@ let rec betree_node_apply_messages_fwd
       Return (st1, ())
   end
 
-(** [betree_main::betree::Node::{5}::apply_messages] *)
+(** [betree_main::betree::Node::{5}::apply_messages]: backward function 0 *)
 and betree_node_apply_messages_back'a
   (self : betree_node_t) (params : betree_params_t)
   (node_id_cnt : betree_node_id_counter_t)
@@ -840,7 +846,7 @@ and betree_node_apply_messages_back'a
         node_id_cnt))
   end
 
-(** [betree_main::betree::Node::{5}::apply_messages] *)
+(** [betree_main::betree::Node::{5}::apply_messages]: backward function 1 *)
 and betree_node_apply_messages_back1
   (self : betree_node_t) (params : betree_params_t)
   (node_id_cnt : betree_node_id_counter_t)
@@ -889,7 +895,7 @@ and betree_node_apply_messages_back1
       Return (st0, ())
   end
 
-(** [betree_main::betree::Internal::{4}::flush] *)
+(** [betree_main::betree::Internal::{4}::flush]: forward function *)
 and betree_internal_flush_fwd
   (self : betree_internal_t) (params : betree_params_t)
   (node_id_cnt : betree_node_id_counter_t)
@@ -940,7 +946,7 @@ and betree_internal_flush_fwd
         node_id_cnt msgs_right st st1 in
     Return (st2, msgs_left)
 
-(** [betree_main::betree::Internal::{4}::flush] *)
+(** [betree_main::betree::Internal::{4}::flush]: backward function 0 *)
 and betree_internal_flush_back'a
   (self : betree_internal_t) (params : betree_params_t)
   (node_id_cnt : betree_node_id_counter_t)
@@ -994,7 +1000,7 @@ and betree_internal_flush_back'a
         node_id_cnt msgs_right st st2 in
     Return (st0, ({ self with betree_internal_right = n }, node_id_cnt0))
 
-(** [betree_main::betree::Internal::{4}::flush] *)
+(** [betree_main::betree::Internal::{4}::flush]: backward function 1 *)
 and betree_internal_flush_back1
   (self : betree_internal_t) (params : betree_params_t)
   (node_id_cnt : betree_node_id_counter_t)
@@ -1046,7 +1052,7 @@ and betree_internal_flush_back1
         node_id_cnt msgs_right st st2 in
     Return (st0, ())
 
-(** [betree_main::betree::Node::{5}::apply] *)
+(** [betree_main::betree::Node::{5}::apply]: forward function *)
 let betree_node_apply_fwd
   (self : betree_node_t) (params : betree_params_t)
   (node_id_cnt : betree_node_id_counter_t) (key : u64)
@@ -1063,7 +1069,7 @@ let betree_node_apply_fwd
   betree_node_apply_messages_back1 self params node_id_cnt (BetreeListCons
     (key, new_msg) l) st st1
 
-(** [betree_main::betree::Node::{5}::apply] *)
+(** [betree_main::betree::Node::{5}::apply]: backward function 0 *)
 let betree_node_apply_back'a
   (self : betree_node_t) (params : betree_params_t)
   (node_id_cnt : betree_node_id_counter_t) (key : u64)
@@ -1082,7 +1088,7 @@ let betree_node_apply_back'a
       (key, new_msg) l) st st2 in
   Return (st0, (self0, node_id_cnt0))
 
-(** [betree_main::betree::Node::{5}::apply] *)
+(** [betree_main::betree::Node::{5}::apply]: backward function 1 *)
 let betree_node_apply_back1
   (self : betree_node_t) (params : betree_params_t)
   (node_id_cnt : betree_node_id_counter_t) (key : u64)
@@ -1101,7 +1107,7 @@ let betree_node_apply_back1
       (key, new_msg) l) st st2 in
   Return (st0, ())
 
-(** [betree_main::betree::BeTree::{6}::new] *)
+(** [betree_main::betree::BeTree::{6}::new]: forward function *)
 let betree_be_tree_new_fwd
   (min_flush_size : u64) (split_size : u64) (st : state) :
   result (state & betree_be_tree_t)
@@ -1122,7 +1128,7 @@ let betree_be_tree_new_fwd
         (BetreeNodeLeaf { betree_leaf_id = id; betree_leaf_size = 0 })
     })
 
-(** [betree_main::betree::BeTree::{6}::apply] *)
+(** [betree_main::betree::BeTree::{6}::apply]: forward function *)
 let betree_be_tree_apply_fwd
   (self : betree_be_tree_t) (key : u64) (msg : betree_message_t) (st : state) :
   result (state & unit)
@@ -1137,7 +1143,7 @@ let betree_be_tree_apply_fwd
   betree_node_apply_back1 self.betree_be_tree_root self.betree_be_tree_params
     self.betree_be_tree_node_id_cnt key msg st st1
 
-(** [betree_main::betree::BeTree::{6}::apply] *)
+(** [betree_main::betree::BeTree::{6}::apply]: backward function 0 *)
 let betree_be_tree_apply_back
   (self : betree_be_tree_t) (key : u64) (msg : betree_message_t) (st : state)
   (st0 : state) :
@@ -1156,7 +1162,7 @@ let betree_be_tree_apply_back
   Return (st0,
     { self with betree_be_tree_node_id_cnt = nic; betree_be_tree_root = n })
 
-(** [betree_main::betree::BeTree::{6}::insert] *)
+(** [betree_main::betree::BeTree::{6}::insert]: forward function *)
 let betree_be_tree_insert_fwd
   (self : betree_be_tree_t) (key : u64) (value : u64) (st : state) :
   result (state & unit)
@@ -1167,7 +1173,7 @@ let betree_be_tree_insert_fwd
     betree_be_tree_apply_back self key (BetreeMessageInsert value) st st0 in
   Return (st1, ())
 
-(** [betree_main::betree::BeTree::{6}::insert] *)
+(** [betree_main::betree::BeTree::{6}::insert]: backward function 0 *)
 let betree_be_tree_insert_back
   (self : betree_be_tree_t) (key : u64) (value : u64) (st : state)
   (st0 : state) :
@@ -1179,7 +1185,7 @@ let betree_be_tree_insert_back
     betree_be_tree_apply_back self key (BetreeMessageInsert value) st st1 in
   Return (st0, self0)
 
-(** [betree_main::betree::BeTree::{6}::delete] *)
+(** [betree_main::betree::BeTree::{6}::delete]: forward function *)
 let betree_be_tree_delete_fwd
   (self : betree_be_tree_t) (key : u64) (st : state) : result (state & unit) =
   let* (st0, _) = betree_be_tree_apply_fwd self key BetreeMessageDelete st in
@@ -1187,7 +1193,7 @@ let betree_be_tree_delete_fwd
     in
   Return (st1, ())
 
-(** [betree_main::betree::BeTree::{6}::delete] *)
+(** [betree_main::betree::BeTree::{6}::delete]: backward function 0 *)
 let betree_be_tree_delete_back
   (self : betree_be_tree_t) (key : u64) (st : state) (st0 : state) :
   result (state & betree_be_tree_t)
@@ -1197,7 +1203,7 @@ let betree_be_tree_delete_back
     betree_be_tree_apply_back self key BetreeMessageDelete st st1 in
   Return (st0, self0)
 
-(** [betree_main::betree::BeTree::{6}::upsert] *)
+(** [betree_main::betree::BeTree::{6}::upsert]: forward function *)
 let betree_be_tree_upsert_fwd
   (self : betree_be_tree_t) (key : u64) (upd : betree_upsert_fun_state_t)
   (st : state) :
@@ -1209,7 +1215,7 @@ let betree_be_tree_upsert_fwd
     betree_be_tree_apply_back self key (BetreeMessageUpsert upd) st st0 in
   Return (st1, ())
 
-(** [betree_main::betree::BeTree::{6}::upsert] *)
+(** [betree_main::betree::BeTree::{6}::upsert]: backward function 0 *)
 let betree_be_tree_upsert_back
   (self : betree_be_tree_t) (key : u64) (upd : betree_upsert_fun_state_t)
   (st : state) (st0 : state) :
@@ -1221,14 +1227,14 @@ let betree_be_tree_upsert_back
     betree_be_tree_apply_back self key (BetreeMessageUpsert upd) st st1 in
   Return (st0, self0)
 
-(** [betree_main::betree::BeTree::{6}::lookup] *)
+(** [betree_main::betree::BeTree::{6}::lookup]: forward function *)
 let betree_be_tree_lookup_fwd
   (self : betree_be_tree_t) (key : u64) (st : state) :
   result (state & (option u64))
   =
   betree_node_lookup_fwd self.betree_be_tree_root key st
 
-(** [betree_main::betree::BeTree::{6}::lookup] *)
+(** [betree_main::betree::BeTree::{6}::lookup]: backward function 0 *)
 let betree_be_tree_lookup_back
   (self : betree_be_tree_t) (key : u64) (st : state) (st0 : state) :
   result (state & betree_be_tree_t)
@@ -1237,7 +1243,7 @@ let betree_be_tree_lookup_back
     in
   Return (st1, { self with betree_be_tree_root = n })
 
-(** [betree_main::main] *)
+(** [betree_main::main]: forward function *)
 let main_fwd : result unit =
   Return ()
 
diff --git a/tests/fstar/betree_back_stateful/BetreeMain.Opaque.fsti b/tests/fstar/betree_back_stateful/BetreeMain.Opaque.fsti
index dc49601a..c33cf225 100644
--- a/tests/fstar/betree_back_stateful/BetreeMain.Opaque.fsti
+++ b/tests/fstar/betree_back_stateful/BetreeMain.Opaque.fsti
@@ -1,30 +1,30 @@
 (** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
-(** [betree_main]: opaque function definitions *)
+(** [betree_main]: external function declarations *)
 module BetreeMain.Opaque
 open Primitives
 include BetreeMain.Types
 
 #set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
 
-(** [betree_main::betree_utils::load_internal_node] *)
+(** [betree_main::betree_utils::load_internal_node]: forward function *)
 val betree_utils_load_internal_node_fwd
   : u64 -> state -> result (state & (betree_list_t (u64 & betree_message_t)))
 
-(** [betree_main::betree_utils::store_internal_node] *)
+(** [betree_main::betree_utils::store_internal_node]: forward function *)
 val betree_utils_store_internal_node_fwd
   :
   u64 -> betree_list_t (u64 & betree_message_t) -> state -> result (state &
     unit)
 
-(** [betree_main::betree_utils::load_leaf_node] *)
+(** [betree_main::betree_utils::load_leaf_node]: forward function *)
 val betree_utils_load_leaf_node_fwd
   : u64 -> state -> result (state & (betree_list_t (u64 & u64)))
 
-(** [betree_main::betree_utils::store_leaf_node] *)
+(** [betree_main::betree_utils::store_leaf_node]: forward function *)
 val betree_utils_store_leaf_node_fwd
   : u64 -> betree_list_t (u64 & u64) -> state -> result (state & unit)
 
-(** [core::option::Option::{0}::unwrap] *)
+(** [core::option::Option::{0}::unwrap]: forward function *)
 val core_option_option_unwrap_fwd
   (t : Type0) : option t -> state -> result (state & t)
 
diff --git a/tests/fstar/hashmap/Hashmap.Funs.fst b/tests/fstar/hashmap/Hashmap.Funs.fst
index 44ad7463..950f1490 100644
--- a/tests/fstar/hashmap/Hashmap.Funs.fst
+++ b/tests/fstar/hashmap/Hashmap.Funs.fst
@@ -7,11 +7,11 @@ include Hashmap.Clauses
 
 #set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
 
-(** [hashmap::hash_key] *)
+(** [hashmap::hash_key]: forward function *)
 let hash_key_fwd (k : usize) : result usize =
   Return k
 
-(** [hashmap::HashMap::{0}::allocate_slots] *)
+(** [hashmap::HashMap::{0}::allocate_slots]: loop 0: forward function *)
 let rec hash_map_allocate_slots_loop_fwd
   (t : Type0) (slots : vec (list_t t)) (n : usize) :
   Tot (result (vec (list_t t)))
@@ -24,12 +24,12 @@ let rec hash_map_allocate_slots_loop_fwd
     hash_map_allocate_slots_loop_fwd t slots0 n0
   else Return slots
 
-(** [hashmap::HashMap::{0}::allocate_slots] *)
+(** [hashmap::HashMap::{0}::allocate_slots]: forward function *)
 let hash_map_allocate_slots_fwd
   (t : Type0) (slots : vec (list_t t)) (n : usize) : result (vec (list_t t)) =
   hash_map_allocate_slots_loop_fwd t slots n
 
-(** [hashmap::HashMap::{0}::new_with_capacity] *)
+(** [hashmap::HashMap::{0}::new_with_capacity]: forward function *)
 let hash_map_new_with_capacity_fwd
   (t : Type0) (capacity : usize) (max_load_dividend : usize)
   (max_load_divisor : usize) :
@@ -47,11 +47,12 @@ let hash_map_new_with_capacity_fwd
       hash_map_slots = slots
     }
 
-(** [hashmap::HashMap::{0}::new] *)
+(** [hashmap::HashMap::{0}::new]: forward function *)
 let hash_map_new_fwd (t : Type0) : result (hash_map_t t) =
   hash_map_new_with_capacity_fwd t 32 4 5
 
-(** [hashmap::HashMap::{0}::clear] *)
+(** [hashmap::HashMap::{0}::clear]: loop 0: merged forward/backward function
+    (there is a single backward function, and the forward function returns ()) *)
 let rec hash_map_clear_loop_fwd_back
   (t : Type0) (slots : vec (list_t t)) (i : usize) :
   Tot (result (vec (list_t t)))
@@ -65,17 +66,18 @@ let rec hash_map_clear_loop_fwd_back
     hash_map_clear_loop_fwd_back t slots0 i1
   else Return slots
 
-(** [hashmap::HashMap::{0}::clear] *)
+(** [hashmap::HashMap::{0}::clear]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ()) *)
 let hash_map_clear_fwd_back
   (t : Type0) (self : hash_map_t t) : result (hash_map_t t) =
   let* v = hash_map_clear_loop_fwd_back t self.hash_map_slots 0 in
   Return { self with hash_map_num_entries = 0; hash_map_slots = v }
 
-(** [hashmap::HashMap::{0}::len] *)
+(** [hashmap::HashMap::{0}::len]: forward function *)
 let hash_map_len_fwd (t : Type0) (self : hash_map_t t) : result usize =
   Return self.hash_map_num_entries
 
-(** [hashmap::HashMap::{0}::insert_in_list] *)
+(** [hashmap::HashMap::{0}::insert_in_list]: loop 0: forward function *)
 let rec hash_map_insert_in_list_loop_fwd
   (t : Type0) (key : usize) (value : t) (ls : list_t t) :
   Tot (result bool)
@@ -89,12 +91,12 @@ let rec hash_map_insert_in_list_loop_fwd
   | ListNil -> Return true
   end
 
-(** [hashmap::HashMap::{0}::insert_in_list] *)
+(** [hashmap::HashMap::{0}::insert_in_list]: forward function *)
 let hash_map_insert_in_list_fwd
   (t : Type0) (key : usize) (value : t) (ls : list_t t) : result bool =
   hash_map_insert_in_list_loop_fwd t key value ls
 
-(** [hashmap::HashMap::{0}::insert_in_list] *)
+(** [hashmap::HashMap::{0}::insert_in_list]: loop 0: backward function 0 *)
 let rec hash_map_insert_in_list_loop_back
   (t : Type0) (key : usize) (value : t) (ls : list_t t) :
   Tot (result (list_t t))
@@ -110,12 +112,13 @@ let rec hash_map_insert_in_list_loop_back
   | ListNil -> let l = ListNil in Return (ListCons key value l)
   end
 
-(** [hashmap::HashMap::{0}::insert_in_list] *)
+(** [hashmap::HashMap::{0}::insert_in_list]: backward function 0 *)
 let hash_map_insert_in_list_back
   (t : Type0) (key : usize) (value : t) (ls : list_t t) : result (list_t t) =
   hash_map_insert_in_list_loop_back t key value ls
 
-(** [hashmap::HashMap::{0}::insert_no_resize] *)
+(** [hashmap::HashMap::{0}::insert_no_resize]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ()) *)
 let hash_map_insert_no_resize_fwd_back
   (t : Type0) (self : hash_map_t t) (key : usize) (value : t) :
   result (hash_map_t t)
@@ -140,7 +143,8 @@ let hash_map_insert_no_resize_fwd_back
 let core_num_u32_max_body : result u32 = Return 4294967295
 let core_num_u32_max_c : u32 = eval_global core_num_u32_max_body
 
-(** [hashmap::HashMap::{0}::move_elements_from_list] *)
+(** [hashmap::HashMap::{0}::move_elements_from_list]: loop 0: merged forward/backward function
+    (there is a single backward function, and the forward function returns ()) *)
 let rec hash_map_move_elements_from_list_loop_fwd_back
   (t : Type0) (ntable : hash_map_t t) (ls : list_t t) :
   Tot (result (hash_map_t t))
@@ -153,12 +157,14 @@ let rec hash_map_move_elements_from_list_loop_fwd_back
   | ListNil -> Return ntable
   end
 
-(** [hashmap::HashMap::{0}::move_elements_from_list] *)
+(** [hashmap::HashMap::{0}::move_elements_from_list]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ()) *)
 let hash_map_move_elements_from_list_fwd_back
   (t : Type0) (ntable : hash_map_t t) (ls : list_t t) : result (hash_map_t t) =
   hash_map_move_elements_from_list_loop_fwd_back t ntable ls
 
-(** [hashmap::HashMap::{0}::move_elements] *)
+(** [hashmap::HashMap::{0}::move_elements]: loop 0: merged forward/backward function
+    (there is a single backward function, and the forward function returns ()) *)
 let rec hash_map_move_elements_loop_fwd_back
   (t : Type0) (ntable : hash_map_t t) (slots : vec (list_t t)) (i : usize) :
   Tot (result ((hash_map_t t) & (vec (list_t t))))
@@ -176,14 +182,16 @@ let rec hash_map_move_elements_loop_fwd_back
     hash_map_move_elements_loop_fwd_back t ntable0 slots0 i1
   else Return (ntable, slots)
 
-(** [hashmap::HashMap::{0}::move_elements] *)
+(** [hashmap::HashMap::{0}::move_elements]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ()) *)
 let hash_map_move_elements_fwd_back
   (t : Type0) (ntable : hash_map_t t) (slots : vec (list_t t)) (i : usize) :
   result ((hash_map_t t) & (vec (list_t t)))
   =
   hash_map_move_elements_loop_fwd_back t ntable slots i
 
-(** [hashmap::HashMap::{0}::try_resize] *)
+(** [hashmap::HashMap::{0}::try_resize]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ()) *)
 let hash_map_try_resize_fwd_back
   (t : Type0) (self : hash_map_t t) : result (hash_map_t t) =
   let* max_usize = scalar_cast U32 Usize core_num_u32_max_c in
@@ -206,7 +214,8 @@ let hash_map_try_resize_fwd_back
       }
   else Return { self with hash_map_max_load_factor = (i, i0) }
 
-(** [hashmap::HashMap::{0}::insert] *)
+(** [hashmap::HashMap::{0}::insert]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ()) *)
 let hash_map_insert_fwd_back
   (t : Type0) (self : hash_map_t t) (key : usize) (value : t) :
   result (hash_map_t t)
@@ -217,7 +226,7 @@ let hash_map_insert_fwd_back
   then hash_map_try_resize_fwd_back t self0
   else Return self0
 
-(** [hashmap::HashMap::{0}::contains_key_in_list] *)
+(** [hashmap::HashMap::{0}::contains_key_in_list]: loop 0: forward function *)
 let rec hash_map_contains_key_in_list_loop_fwd
   (t : Type0) (key : usize) (ls : list_t t) :
   Tot (result bool)
@@ -231,12 +240,12 @@ let rec hash_map_contains_key_in_list_loop_fwd
   | ListNil -> Return false
   end
 
-(** [hashmap::HashMap::{0}::contains_key_in_list] *)
+(** [hashmap::HashMap::{0}::contains_key_in_list]: forward function *)
 let hash_map_contains_key_in_list_fwd
   (t : Type0) (key : usize) (ls : list_t t) : result bool =
   hash_map_contains_key_in_list_loop_fwd t key ls
 
-(** [hashmap::HashMap::{0}::contains_key] *)
+(** [hashmap::HashMap::{0}::contains_key]: forward function *)
 let hash_map_contains_key_fwd
   (t : Type0) (self : hash_map_t t) (key : usize) : result bool =
   let* hash = hash_key_fwd key in
@@ -245,7 +254,7 @@ let hash_map_contains_key_fwd
   let* l = vec_index_fwd (list_t t) self.hash_map_slots hash_mod in
   hash_map_contains_key_in_list_fwd t key l
 
-(** [hashmap::HashMap::{0}::get_in_list] *)
+(** [hashmap::HashMap::{0}::get_in_list]: loop 0: forward function *)
 let rec hash_map_get_in_list_loop_fwd
   (t : Type0) (key : usize) (ls : list_t t) :
   Tot (result t) (decreases (hash_map_get_in_list_loop_decreases t key ls))
@@ -258,12 +267,12 @@ let rec hash_map_get_in_list_loop_fwd
   | ListNil -> Fail Failure
   end
 
-(** [hashmap::HashMap::{0}::get_in_list] *)
+(** [hashmap::HashMap::{0}::get_in_list]: forward function *)
 let hash_map_get_in_list_fwd
   (t : Type0) (key : usize) (ls : list_t t) : result t =
   hash_map_get_in_list_loop_fwd t key ls
 
-(** [hashmap::HashMap::{0}::get] *)
+(** [hashmap::HashMap::{0}::get]: forward function *)
 let hash_map_get_fwd
   (t : Type0) (self : hash_map_t t) (key : usize) : result t =
   let* hash = hash_key_fwd key in
@@ -272,7 +281,7 @@ let hash_map_get_fwd
   let* l = vec_index_fwd (list_t t) self.hash_map_slots hash_mod in
   hash_map_get_in_list_fwd t key l
 
-(** [hashmap::HashMap::{0}::get_mut_in_list] *)
+(** [hashmap::HashMap::{0}::get_mut_in_list]: loop 0: forward function *)
 let rec hash_map_get_mut_in_list_loop_fwd
   (t : Type0) (ls : list_t t) (key : usize) :
   Tot (result t) (decreases (hash_map_get_mut_in_list_loop_decreases t ls key))
@@ -285,12 +294,12 @@ let rec hash_map_get_mut_in_list_loop_fwd
   | ListNil -> Fail Failure
   end
 
-(** [hashmap::HashMap::{0}::get_mut_in_list] *)
+(** [hashmap::HashMap::{0}::get_mut_in_list]: forward function *)
 let hash_map_get_mut_in_list_fwd
   (t : Type0) (ls : list_t t) (key : usize) : result t =
   hash_map_get_mut_in_list_loop_fwd t ls key
 
-(** [hashmap::HashMap::{0}::get_mut_in_list] *)
+(** [hashmap::HashMap::{0}::get_mut_in_list]: loop 0: backward function 0 *)
 let rec hash_map_get_mut_in_list_loop_back
   (t : Type0) (ls : list_t t) (key : usize) (ret : t) :
   Tot (result (list_t t))
@@ -306,12 +315,12 @@ let rec hash_map_get_mut_in_list_loop_back
   | ListNil -> Fail Failure
   end
 
-(** [hashmap::HashMap::{0}::get_mut_in_list] *)
+(** [hashmap::HashMap::{0}::get_mut_in_list]: backward function 0 *)
 let hash_map_get_mut_in_list_back
   (t : Type0) (ls : list_t t) (key : usize) (ret : t) : result (list_t t) =
   hash_map_get_mut_in_list_loop_back t ls key ret
 
-(** [hashmap::HashMap::{0}::get_mut] *)
+(** [hashmap::HashMap::{0}::get_mut]: forward function *)
 let hash_map_get_mut_fwd
   (t : Type0) (self : hash_map_t t) (key : usize) : result t =
   let* hash = hash_key_fwd key in
@@ -320,7 +329,7 @@ let hash_map_get_mut_fwd
   let* l = vec_index_mut_fwd (list_t t) self.hash_map_slots hash_mod in
   hash_map_get_mut_in_list_fwd t l key
 
-(** [hashmap::HashMap::{0}::get_mut] *)
+(** [hashmap::HashMap::{0}::get_mut]: backward function 0 *)
 let hash_map_get_mut_back
   (t : Type0) (self : hash_map_t t) (key : usize) (ret : t) :
   result (hash_map_t t)
@@ -333,7 +342,7 @@ let hash_map_get_mut_back
   let* v = vec_index_mut_back (list_t t) self.hash_map_slots hash_mod l0 in
   Return { self with hash_map_slots = v }
 
-(** [hashmap::HashMap::{0}::remove_from_list] *)
+(** [hashmap::HashMap::{0}::remove_from_list]: loop 0: forward function *)
 let rec hash_map_remove_from_list_loop_fwd
   (t : Type0) (key : usize) (ls : list_t t) :
   Tot (result (option t))
@@ -352,12 +361,12 @@ let rec hash_map_remove_from_list_loop_fwd
   | ListNil -> Return None
   end
 
-(** [hashmap::HashMap::{0}::remove_from_list] *)
+(** [hashmap::HashMap::{0}::remove_from_list]: forward function *)
 let hash_map_remove_from_list_fwd
   (t : Type0) (key : usize) (ls : list_t t) : result (option t) =
   hash_map_remove_from_list_loop_fwd t key ls
 
-(** [hashmap::HashMap::{0}::remove_from_list] *)
+(** [hashmap::HashMap::{0}::remove_from_list]: loop 0: backward function 1 *)
 let rec hash_map_remove_from_list_loop_back
   (t : Type0) (key : usize) (ls : list_t t) :
   Tot (result (list_t t))
@@ -378,12 +387,12 @@ let rec hash_map_remove_from_list_loop_back
   | ListNil -> Return ListNil
   end
 
-(** [hashmap::HashMap::{0}::remove_from_list] *)
+(** [hashmap::HashMap::{0}::remove_from_list]: backward function 1 *)
 let hash_map_remove_from_list_back
   (t : Type0) (key : usize) (ls : list_t t) : result (list_t t) =
   hash_map_remove_from_list_loop_back t key ls
 
-(** [hashmap::HashMap::{0}::remove] *)
+(** [hashmap::HashMap::{0}::remove]: forward function *)
 let hash_map_remove_fwd
   (t : Type0) (self : hash_map_t t) (key : usize) : result (option t) =
   let* hash = hash_key_fwd key in
@@ -397,7 +406,7 @@ let hash_map_remove_fwd
     let* _ = usize_sub self.hash_map_num_entries 1 in Return (Some x0)
   end
 
-(** [hashmap::HashMap::{0}::remove] *)
+(** [hashmap::HashMap::{0}::remove]: backward function 0 *)
 let hash_map_remove_back
   (t : Type0) (self : hash_map_t t) (key : usize) : result (hash_map_t t) =
   let* hash = hash_key_fwd key in
@@ -417,7 +426,7 @@ let hash_map_remove_back
     Return { self with hash_map_num_entries = i0; hash_map_slots = v }
   end
 
-(** [hashmap::test1] *)
+(** [hashmap::test1]: forward function *)
 let test1_fwd : result unit =
   let* hm = hash_map_new_fwd u64 in
   let* hm0 = hash_map_insert_fwd_back u64 hm 0 42 in
diff --git a/tests/fstar/hashmap_on_disk/HashmapMain.Funs.fst b/tests/fstar/hashmap_on_disk/HashmapMain.Funs.fst
index e8cd54c1..f6d9c8cf 100644
--- a/tests/fstar/hashmap_on_disk/HashmapMain.Funs.fst
+++ b/tests/fstar/hashmap_on_disk/HashmapMain.Funs.fst
@@ -8,11 +8,11 @@ include HashmapMain.Clauses
 
 #set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
 
-(** [hashmap_main::hashmap::hash_key] *)
+(** [hashmap_main::hashmap::hash_key]: forward function *)
 let hashmap_hash_key_fwd (k : usize) : result usize =
   Return k
 
-(** [hashmap_main::hashmap::HashMap::{0}::allocate_slots] *)
+(** [hashmap_main::hashmap::HashMap::{0}::allocate_slots]: loop 0: forward function *)
 let rec hashmap_hash_map_allocate_slots_loop_fwd
   (t : Type0) (slots : vec (hashmap_list_t t)) (n : usize) :
   Tot (result (vec (hashmap_list_t t)))
@@ -25,14 +25,14 @@ let rec hashmap_hash_map_allocate_slots_loop_fwd
     hashmap_hash_map_allocate_slots_loop_fwd t slots0 n0
   else Return slots
 
-(** [hashmap_main::hashmap::HashMap::{0}::allocate_slots] *)
+(** [hashmap_main::hashmap::HashMap::{0}::allocate_slots]: forward function *)
 let hashmap_hash_map_allocate_slots_fwd
   (t : Type0) (slots : vec (hashmap_list_t t)) (n : usize) :
   result (vec (hashmap_list_t t))
   =
   hashmap_hash_map_allocate_slots_loop_fwd t slots n
 
-(** [hashmap_main::hashmap::HashMap::{0}::new_with_capacity] *)
+(** [hashmap_main::hashmap::HashMap::{0}::new_with_capacity]: forward function *)
 let hashmap_hash_map_new_with_capacity_fwd
   (t : Type0) (capacity : usize) (max_load_dividend : usize)
   (max_load_divisor : usize) :
@@ -50,11 +50,12 @@ let hashmap_hash_map_new_with_capacity_fwd
       hashmap_hash_map_slots = slots
     }
 
-(** [hashmap_main::hashmap::HashMap::{0}::new] *)
+(** [hashmap_main::hashmap::HashMap::{0}::new]: forward function *)
 let hashmap_hash_map_new_fwd (t : Type0) : result (hashmap_hash_map_t t) =
   hashmap_hash_map_new_with_capacity_fwd t 32 4 5
 
-(** [hashmap_main::hashmap::HashMap::{0}::clear] *)
+(** [hashmap_main::hashmap::HashMap::{0}::clear]: loop 0: merged forward/backward function
+    (there is a single backward function, and the forward function returns ()) *)
 let rec hashmap_hash_map_clear_loop_fwd_back
   (t : Type0) (slots : vec (hashmap_list_t t)) (i : usize) :
   Tot (result (vec (hashmap_list_t t)))
@@ -69,7 +70,8 @@ let rec hashmap_hash_map_clear_loop_fwd_back
     hashmap_hash_map_clear_loop_fwd_back t slots0 i1
   else Return slots
 
-(** [hashmap_main::hashmap::HashMap::{0}::clear] *)
+(** [hashmap_main::hashmap::HashMap::{0}::clear]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ()) *)
 let hashmap_hash_map_clear_fwd_back
   (t : Type0) (self : hashmap_hash_map_t t) : result (hashmap_hash_map_t t) =
   let* v = hashmap_hash_map_clear_loop_fwd_back t self.hashmap_hash_map_slots 0
@@ -77,12 +79,12 @@ let hashmap_hash_map_clear_fwd_back
   Return
     { self with hashmap_hash_map_num_entries = 0; hashmap_hash_map_slots = v }
 
-(** [hashmap_main::hashmap::HashMap::{0}::len] *)
+(** [hashmap_main::hashmap::HashMap::{0}::len]: forward function *)
 let hashmap_hash_map_len_fwd
   (t : Type0) (self : hashmap_hash_map_t t) : result usize =
   Return self.hashmap_hash_map_num_entries
 
-(** [hashmap_main::hashmap::HashMap::{0}::insert_in_list] *)
+(** [hashmap_main::hashmap::HashMap::{0}::insert_in_list]: loop 0: forward function *)
 let rec hashmap_hash_map_insert_in_list_loop_fwd
   (t : Type0) (key : usize) (value : t) (ls : hashmap_list_t t) :
   Tot (result bool)
@@ -96,12 +98,12 @@ let rec hashmap_hash_map_insert_in_list_loop_fwd
   | HashmapListNil -> Return true
   end
 
-(** [hashmap_main::hashmap::HashMap::{0}::insert_in_list] *)
+(** [hashmap_main::hashmap::HashMap::{0}::insert_in_list]: forward function *)
 let hashmap_hash_map_insert_in_list_fwd
   (t : Type0) (key : usize) (value : t) (ls : hashmap_list_t t) : result bool =
   hashmap_hash_map_insert_in_list_loop_fwd t key value ls
 
-(** [hashmap_main::hashmap::HashMap::{0}::insert_in_list] *)
+(** [hashmap_main::hashmap::HashMap::{0}::insert_in_list]: loop 0: backward function 0 *)
 let rec hashmap_hash_map_insert_in_list_loop_back
   (t : Type0) (key : usize) (value : t) (ls : hashmap_list_t t) :
   Tot (result (hashmap_list_t t))
@@ -118,14 +120,15 @@ let rec hashmap_hash_map_insert_in_list_loop_back
     let l = HashmapListNil in Return (HashmapListCons key value l)
   end
 
-(** [hashmap_main::hashmap::HashMap::{0}::insert_in_list] *)
+(** [hashmap_main::hashmap::HashMap::{0}::insert_in_list]: backward function 0 *)
 let hashmap_hash_map_insert_in_list_back
   (t : Type0) (key : usize) (value : t) (ls : hashmap_list_t t) :
   result (hashmap_list_t t)
   =
   hashmap_hash_map_insert_in_list_loop_back t key value ls
 
-(** [hashmap_main::hashmap::HashMap::{0}::insert_no_resize] *)
+(** [hashmap_main::hashmap::HashMap::{0}::insert_no_resize]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ()) *)
 let hashmap_hash_map_insert_no_resize_fwd_back
   (t : Type0) (self : hashmap_hash_map_t t) (key : usize) (value : t) :
   result (hashmap_hash_map_t t)
@@ -158,7 +161,8 @@ let hashmap_hash_map_insert_no_resize_fwd_back
 let core_num_u32_max_body : result u32 = Return 4294967295
 let core_num_u32_max_c : u32 = eval_global core_num_u32_max_body
 
-(** [hashmap_main::hashmap::HashMap::{0}::move_elements_from_list] *)
+(** [hashmap_main::hashmap::HashMap::{0}::move_elements_from_list]: loop 0: merged forward/backward function
+    (there is a single backward function, and the forward function returns ()) *)
 let rec hashmap_hash_map_move_elements_from_list_loop_fwd_back
   (t : Type0) (ntable : hashmap_hash_map_t t) (ls : hashmap_list_t t) :
   Tot (result (hashmap_hash_map_t t))
@@ -172,14 +176,16 @@ let rec hashmap_hash_map_move_elements_from_list_loop_fwd_back
   | HashmapListNil -> Return ntable
   end
 
-(** [hashmap_main::hashmap::HashMap::{0}::move_elements_from_list] *)
+(** [hashmap_main::hashmap::HashMap::{0}::move_elements_from_list]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ()) *)
 let hashmap_hash_map_move_elements_from_list_fwd_back
   (t : Type0) (ntable : hashmap_hash_map_t t) (ls : hashmap_list_t t) :
   result (hashmap_hash_map_t t)
   =
   hashmap_hash_map_move_elements_from_list_loop_fwd_back t ntable ls
 
-(** [hashmap_main::hashmap::HashMap::{0}::move_elements] *)
+(** [hashmap_main::hashmap::HashMap::{0}::move_elements]: loop 0: merged forward/backward function
+    (there is a single backward function, and the forward function returns ()) *)
 let rec hashmap_hash_map_move_elements_loop_fwd_back
   (t : Type0) (ntable : hashmap_hash_map_t t) (slots : vec (hashmap_list_t t))
   (i : usize) :
@@ -199,7 +205,8 @@ let rec hashmap_hash_map_move_elements_loop_fwd_back
     hashmap_hash_map_move_elements_loop_fwd_back t ntable0 slots0 i1
   else Return (ntable, slots)
 
-(** [hashmap_main::hashmap::HashMap::{0}::move_elements] *)
+(** [hashmap_main::hashmap::HashMap::{0}::move_elements]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ()) *)
 let hashmap_hash_map_move_elements_fwd_back
   (t : Type0) (ntable : hashmap_hash_map_t t) (slots : vec (hashmap_list_t t))
   (i : usize) :
@@ -207,7 +214,8 @@ let hashmap_hash_map_move_elements_fwd_back
   =
   hashmap_hash_map_move_elements_loop_fwd_back t ntable slots i
 
-(** [hashmap_main::hashmap::HashMap::{0}::try_resize] *)
+(** [hashmap_main::hashmap::HashMap::{0}::try_resize]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ()) *)
 let hashmap_hash_map_try_resize_fwd_back
   (t : Type0) (self : hashmap_hash_map_t t) : result (hashmap_hash_map_t t) =
   let* max_usize = scalar_cast U32 Usize core_num_u32_max_c in
@@ -231,7 +239,8 @@ let hashmap_hash_map_try_resize_fwd_back
       }
   else Return { self with hashmap_hash_map_max_load_factor = (i, i0) }
 
-(** [hashmap_main::hashmap::HashMap::{0}::insert] *)
+(** [hashmap_main::hashmap::HashMap::{0}::insert]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ()) *)
 let hashmap_hash_map_insert_fwd_back
   (t : Type0) (self : hashmap_hash_map_t t) (key : usize) (value : t) :
   result (hashmap_hash_map_t t)
@@ -242,7 +251,7 @@ let hashmap_hash_map_insert_fwd_back
   then hashmap_hash_map_try_resize_fwd_back t self0
   else Return self0
 
-(** [hashmap_main::hashmap::HashMap::{0}::contains_key_in_list] *)
+(** [hashmap_main::hashmap::HashMap::{0}::contains_key_in_list]: loop 0: forward function *)
 let rec hashmap_hash_map_contains_key_in_list_loop_fwd
   (t : Type0) (key : usize) (ls : hashmap_list_t t) :
   Tot (result bool)
@@ -256,12 +265,12 @@ let rec hashmap_hash_map_contains_key_in_list_loop_fwd
   | HashmapListNil -> Return false
   end
 
-(** [hashmap_main::hashmap::HashMap::{0}::contains_key_in_list] *)
+(** [hashmap_main::hashmap::HashMap::{0}::contains_key_in_list]: forward function *)
 let hashmap_hash_map_contains_key_in_list_fwd
   (t : Type0) (key : usize) (ls : hashmap_list_t t) : result bool =
   hashmap_hash_map_contains_key_in_list_loop_fwd t key ls
 
-(** [hashmap_main::hashmap::HashMap::{0}::contains_key] *)
+(** [hashmap_main::hashmap::HashMap::{0}::contains_key]: forward function *)
 let hashmap_hash_map_contains_key_fwd
   (t : Type0) (self : hashmap_hash_map_t t) (key : usize) : result bool =
   let* hash = hashmap_hash_key_fwd key in
@@ -271,7 +280,7 @@ let hashmap_hash_map_contains_key_fwd
     vec_index_fwd (hashmap_list_t t) self.hashmap_hash_map_slots hash_mod in
   hashmap_hash_map_contains_key_in_list_fwd t key l
 
-(** [hashmap_main::hashmap::HashMap::{0}::get_in_list] *)
+(** [hashmap_main::hashmap::HashMap::{0}::get_in_list]: loop 0: forward function *)
 let rec hashmap_hash_map_get_in_list_loop_fwd
   (t : Type0) (key : usize) (ls : hashmap_list_t t) :
   Tot (result t)
@@ -285,12 +294,12 @@ let rec hashmap_hash_map_get_in_list_loop_fwd
   | HashmapListNil -> Fail Failure
   end
 
-(** [hashmap_main::hashmap::HashMap::{0}::get_in_list] *)
+(** [hashmap_main::hashmap::HashMap::{0}::get_in_list]: forward function *)
 let hashmap_hash_map_get_in_list_fwd
   (t : Type0) (key : usize) (ls : hashmap_list_t t) : result t =
   hashmap_hash_map_get_in_list_loop_fwd t key ls
 
-(** [hashmap_main::hashmap::HashMap::{0}::get] *)
+(** [hashmap_main::hashmap::HashMap::{0}::get]: forward function *)
 let hashmap_hash_map_get_fwd
   (t : Type0) (self : hashmap_hash_map_t t) (key : usize) : result t =
   let* hash = hashmap_hash_key_fwd key in
@@ -300,7 +309,7 @@ let hashmap_hash_map_get_fwd
     vec_index_fwd (hashmap_list_t t) self.hashmap_hash_map_slots hash_mod in
   hashmap_hash_map_get_in_list_fwd t key l
 
-(** [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list] *)
+(** [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list]: loop 0: forward function *)
 let rec hashmap_hash_map_get_mut_in_list_loop_fwd
   (t : Type0) (ls : hashmap_list_t t) (key : usize) :
   Tot (result t)
@@ -314,12 +323,12 @@ let rec hashmap_hash_map_get_mut_in_list_loop_fwd
   | HashmapListNil -> Fail Failure
   end
 
-(** [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list] *)
+(** [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list]: forward function *)
 let hashmap_hash_map_get_mut_in_list_fwd
   (t : Type0) (ls : hashmap_list_t t) (key : usize) : result t =
   hashmap_hash_map_get_mut_in_list_loop_fwd t ls key
 
-(** [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list] *)
+(** [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list]: loop 0: backward function 0 *)
 let rec hashmap_hash_map_get_mut_in_list_loop_back
   (t : Type0) (ls : hashmap_list_t t) (key : usize) (ret : t) :
   Tot (result (hashmap_list_t t))
@@ -335,14 +344,14 @@ let rec hashmap_hash_map_get_mut_in_list_loop_back
   | HashmapListNil -> Fail Failure
   end
 
-(** [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list] *)
+(** [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list]: backward function 0 *)
 let hashmap_hash_map_get_mut_in_list_back
   (t : Type0) (ls : hashmap_list_t t) (key : usize) (ret : t) :
   result (hashmap_list_t t)
   =
   hashmap_hash_map_get_mut_in_list_loop_back t ls key ret
 
-(** [hashmap_main::hashmap::HashMap::{0}::get_mut] *)
+(** [hashmap_main::hashmap::HashMap::{0}::get_mut]: forward function *)
 let hashmap_hash_map_get_mut_fwd
   (t : Type0) (self : hashmap_hash_map_t t) (key : usize) : result t =
   let* hash = hashmap_hash_key_fwd key in
@@ -353,7 +362,7 @@ let hashmap_hash_map_get_mut_fwd
     in
   hashmap_hash_map_get_mut_in_list_fwd t l key
 
-(** [hashmap_main::hashmap::HashMap::{0}::get_mut] *)
+(** [hashmap_main::hashmap::HashMap::{0}::get_mut]: backward function 0 *)
 let hashmap_hash_map_get_mut_back
   (t : Type0) (self : hashmap_hash_map_t t) (key : usize) (ret : t) :
   result (hashmap_hash_map_t t)
@@ -370,7 +379,7 @@ let hashmap_hash_map_get_mut_back
       l0 in
   Return { self with hashmap_hash_map_slots = v }
 
-(** [hashmap_main::hashmap::HashMap::{0}::remove_from_list] *)
+(** [hashmap_main::hashmap::HashMap::{0}::remove_from_list]: loop 0: forward function *)
 let rec hashmap_hash_map_remove_from_list_loop_fwd
   (t : Type0) (key : usize) (ls : hashmap_list_t t) :
   Tot (result (option t))
@@ -391,12 +400,12 @@ let rec hashmap_hash_map_remove_from_list_loop_fwd
   | HashmapListNil -> Return None
   end
 
-(** [hashmap_main::hashmap::HashMap::{0}::remove_from_list] *)
+(** [hashmap_main::hashmap::HashMap::{0}::remove_from_list]: forward function *)
 let hashmap_hash_map_remove_from_list_fwd
   (t : Type0) (key : usize) (ls : hashmap_list_t t) : result (option t) =
   hashmap_hash_map_remove_from_list_loop_fwd t key ls
 
-(** [hashmap_main::hashmap::HashMap::{0}::remove_from_list] *)
+(** [hashmap_main::hashmap::HashMap::{0}::remove_from_list]: loop 0: backward function 1 *)
 let rec hashmap_hash_map_remove_from_list_loop_back
   (t : Type0) (key : usize) (ls : hashmap_list_t t) :
   Tot (result (hashmap_list_t t))
@@ -419,14 +428,14 @@ let rec hashmap_hash_map_remove_from_list_loop_back
   | HashmapListNil -> Return HashmapListNil
   end
 
-(** [hashmap_main::hashmap::HashMap::{0}::remove_from_list] *)
+(** [hashmap_main::hashmap::HashMap::{0}::remove_from_list]: backward function 1 *)
 let hashmap_hash_map_remove_from_list_back
   (t : Type0) (key : usize) (ls : hashmap_list_t t) :
   result (hashmap_list_t t)
   =
   hashmap_hash_map_remove_from_list_loop_back t key ls
 
-(** [hashmap_main::hashmap::HashMap::{0}::remove] *)
+(** [hashmap_main::hashmap::HashMap::{0}::remove]: forward function *)
 let hashmap_hash_map_remove_fwd
   (t : Type0) (self : hashmap_hash_map_t t) (key : usize) : result (option t) =
   let* hash = hashmap_hash_key_fwd key in
@@ -442,7 +451,7 @@ let hashmap_hash_map_remove_fwd
     let* _ = usize_sub self.hashmap_hash_map_num_entries 1 in Return (Some x0)
   end
 
-(** [hashmap_main::hashmap::HashMap::{0}::remove] *)
+(** [hashmap_main::hashmap::HashMap::{0}::remove]: backward function 0 *)
 let hashmap_hash_map_remove_back
   (t : Type0) (self : hashmap_hash_map_t t) (key : usize) :
   result (hashmap_hash_map_t t)
@@ -472,7 +481,7 @@ let hashmap_hash_map_remove_back
       }
   end
 
-(** [hashmap_main::hashmap::test1] *)
+(** [hashmap_main::hashmap::test1]: forward function *)
 let hashmap_test1_fwd : result unit =
   let* hm = hashmap_hash_map_new_fwd u64 in
   let* hm0 = hashmap_hash_map_insert_fwd_back u64 hm 0 42 in
@@ -511,7 +520,7 @@ let hashmap_test1_fwd : result unit =
 (** Unit test for [hashmap_main::hashmap::test1] *)
 let _ = assert_norm (hashmap_test1_fwd = Return ())
 
-(** [hashmap_main::insert_on_disk] *)
+(** [hashmap_main::insert_on_disk]: forward function *)
 let insert_on_disk_fwd
   (key : usize) (value : u64) (st : state) : result (state & unit) =
   let* (st0, hm) = hashmap_utils_deserialize_fwd st in
@@ -519,7 +528,7 @@ let insert_on_disk_fwd
   let* (st1, _) = hashmap_utils_serialize_fwd hm0 st0 in
   Return (st1, ())
 
-(** [hashmap_main::main] *)
+(** [hashmap_main::main]: forward function *)
 let main_fwd : result unit =
   Return ()
 
diff --git a/tests/fstar/hashmap_on_disk/HashmapMain.Opaque.fsti b/tests/fstar/hashmap_on_disk/HashmapMain.Opaque.fsti
index 6e54ea10..78a6c3ba 100644
--- a/tests/fstar/hashmap_on_disk/HashmapMain.Opaque.fsti
+++ b/tests/fstar/hashmap_on_disk/HashmapMain.Opaque.fsti
@@ -1,16 +1,16 @@
 (** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
-(** [hashmap_main]: opaque function definitions *)
+(** [hashmap_main]: external function declarations *)
 module HashmapMain.Opaque
 open Primitives
 include HashmapMain.Types
 
 #set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
 
-(** [hashmap_main::hashmap_utils::deserialize] *)
+(** [hashmap_main::hashmap_utils::deserialize]: forward function *)
 val hashmap_utils_deserialize_fwd
   : state -> result (state & (hashmap_hash_map_t u64))
 
-(** [hashmap_main::hashmap_utils::serialize] *)
+(** [hashmap_main::hashmap_utils::serialize]: forward function *)
 val hashmap_utils_serialize_fwd
   : hashmap_hash_map_t u64 -> state -> result (state & unit)
 
diff --git a/tests/fstar/misc/Constants.fst b/tests/fstar/misc/Constants.fst
index bf2f0b1b..aae997fa 100644
--- a/tests/fstar/misc/Constants.fst
+++ b/tests/fstar/misc/Constants.fst
@@ -21,7 +21,7 @@ let x1_c : u32 = eval_global x1_body
 let x2_body : result u32 = Return 3
 let x2_c : u32 = eval_global x2_body
 
-(** [constants::incr] *)
+(** [constants::incr]: forward function *)
 let incr_fwd (n : u32) : result u32 =
   u32_add n 1
 
@@ -29,14 +29,14 @@ let incr_fwd (n : u32) : result u32 =
 let x3_body : result u32 = incr_fwd 32
 let x3_c : u32 = eval_global x3_body
 
-(** [constants::mk_pair0] *)
+(** [constants::mk_pair0]: forward function *)
 let mk_pair0_fwd (x : u32) (y : u32) : result (u32 & u32) =
   Return (x, y)
 
 (** [constants::Pair] *)
 type pair_t (t1 t2 : Type0) = { pair_x : t1; pair_y : t2; }
 
-(** [constants::mk_pair1] *)
+(** [constants::mk_pair1]: forward function *)
 let mk_pair1_fwd (x : u32) (y : u32) : result (pair_t u32 u32) =
   Return { pair_x = x; pair_y = y }
 
@@ -59,7 +59,7 @@ let p3_c : pair_t u32 u32 = eval_global p3_body
 (** [constants::Wrap] *)
 type wrap_t (t : Type0) = { wrap_val : t; }
 
-(** [constants::Wrap::{0}::new] *)
+(** [constants::Wrap::{0}::new]: forward function *)
 let wrap_new_fwd (t : Type0) (val0 : t) : result (wrap_t t) =
   Return { wrap_val = val0 }
 
@@ -67,7 +67,7 @@ let wrap_new_fwd (t : Type0) (val0 : t) : result (wrap_t t) =
 let y_body : result (wrap_t i32) = wrap_new_fwd i32 2
 let y_c : wrap_t i32 = eval_global y_body
 
-(** [constants::unwrap_y] *)
+(** [constants::unwrap_y]: forward function *)
 let unwrap_y_fwd : result i32 =
   Return y_c.wrap_val
 
@@ -79,11 +79,11 @@ let yval_c : i32 = eval_global yval_body
 let get_z1_z1_body : result i32 = Return 3
 let get_z1_z1_c : i32 = eval_global get_z1_z1_body
 
-(** [constants::get_z1] *)
+(** [constants::get_z1]: forward function *)
 let get_z1_fwd : result i32 =
   Return get_z1_z1_c
 
-(** [constants::add] *)
+(** [constants::add]: forward function *)
 let add_fwd (a : i32) (b : i32) : result i32 =
   i32_add a b
 
@@ -99,7 +99,7 @@ let q2_c : i32 = eval_global q2_body
 let q3_body : result i32 = add_fwd q2_c 3
 let q3_c : i32 = eval_global q3_body
 
-(** [constants::get_z2] *)
+(** [constants::get_z2]: forward function *)
 let get_z2_fwd : result i32 =
   let* i = get_z1_fwd in let* i0 = add_fwd i q3_c in add_fwd q1_c i0
 
diff --git a/tests/fstar/misc/External.Funs.fst b/tests/fstar/misc/External.Funs.fst
index f70a9fc6..f118a2cf 100644
--- a/tests/fstar/misc/External.Funs.fst
+++ b/tests/fstar/misc/External.Funs.fst
@@ -7,14 +7,14 @@ include External.Opaque
 
 #set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
 
-(** [external::swap] *)
+(** [external::swap]: forward function *)
 let swap_fwd (t : Type0) (x : t) (y : t) (st : state) : result (state & unit) =
   let* (st0, _) = core_mem_swap_fwd t x y st in
   let* (st1, _) = core_mem_swap_back0 t x y st st0 in
   let* (st2, _) = core_mem_swap_back1 t x y st st1 in
   Return (st2, ())
 
-(** [external::swap] *)
+(** [external::swap]: backward function 0 *)
 let swap_back
   (t : Type0) (x : t) (y : t) (st : state) (st0 : state) :
   result (state & (t & t))
@@ -24,20 +24,20 @@ let swap_back
   let* (_, y0) = core_mem_swap_back1 t x y st st2 in
   Return (st0, (x0, y0))
 
-(** [external::test_new_non_zero_u32] *)
+(** [external::test_new_non_zero_u32]: forward function *)
 let test_new_non_zero_u32_fwd
   (x : u32) (st : state) : result (state & core_num_nonzero_non_zero_u32_t) =
   let* (st0, opt) = core_num_nonzero_non_zero_u32_new_fwd x st in
   core_option_option_unwrap_fwd core_num_nonzero_non_zero_u32_t opt st0
 
-(** [external::test_vec] *)
+(** [external::test_vec]: forward function *)
 let test_vec_fwd : result unit =
   let v = vec_new u32 in let* _ = vec_push_back u32 v 0 in Return ()
 
 (** Unit test for [external::test_vec] *)
 let _ = assert_norm (test_vec_fwd = Return ())
 
-(** [external::custom_swap] *)
+(** [external::custom_swap]: forward function *)
 let custom_swap_fwd
   (t : Type0) (x : t) (y : t) (st : state) : result (state & t) =
   let* (st0, _) = core_mem_swap_fwd t x y st in
@@ -45,7 +45,7 @@ let custom_swap_fwd
   let* (st2, _) = core_mem_swap_back1 t x y st st1 in
   Return (st2, x0)
 
-(** [external::custom_swap] *)
+(** [external::custom_swap]: backward function 0 *)
 let custom_swap_back
   (t : Type0) (x : t) (y : t) (st : state) (ret : t) (st0 : state) :
   result (state & (t & t))
@@ -55,19 +55,19 @@ let custom_swap_back
   let* (_, y0) = core_mem_swap_back1 t x y st st2 in
   Return (st0, (ret, y0))
 
-(** [external::test_custom_swap] *)
+(** [external::test_custom_swap]: forward function *)
 let test_custom_swap_fwd
   (x : u32) (y : u32) (st : state) : result (state & unit) =
   let* (st0, _) = custom_swap_fwd u32 x y st in Return (st0, ())
 
-(** [external::test_custom_swap] *)
+(** [external::test_custom_swap]: backward function 0 *)
 let test_custom_swap_back
   (x : u32) (y : u32) (st : state) (st0 : state) :
   result (state & (u32 & u32))
   =
   custom_swap_back u32 x y st 1 st0
 
-(** [external::test_swap_non_zero] *)
+(** [external::test_swap_non_zero]: forward function *)
 let test_swap_non_zero_fwd (x : u32) (st : state) : result (state & u32) =
   let* (st0, _) = swap_fwd u32 x 0 st in
   let* (st1, (x0, _)) = swap_back u32 x 0 st st0 in
diff --git a/tests/fstar/misc/External.Opaque.fsti b/tests/fstar/misc/External.Opaque.fsti
index 7d86405a..2e19f767 100644
--- a/tests/fstar/misc/External.Opaque.fsti
+++ b/tests/fstar/misc/External.Opaque.fsti
@@ -1,27 +1,27 @@
 (** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
-(** [external]: opaque function definitions *)
+(** [external]: external function declarations *)
 module External.Opaque
 open Primitives
 include External.Types
 
 #set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
 
-(** [core::mem::swap] *)
+(** [core::mem::swap]: forward function *)
 val core_mem_swap_fwd (t : Type0) : t -> t -> state -> result (state & unit)
 
-(** [core::mem::swap] *)
+(** [core::mem::swap]: backward function 0 *)
 val core_mem_swap_back0
   (t : Type0) : t -> t -> state -> state -> result (state & t)
 
-(** [core::mem::swap] *)
+(** [core::mem::swap]: backward function 1 *)
 val core_mem_swap_back1
   (t : Type0) : t -> t -> state -> state -> result (state & t)
 
-(** [core::num::nonzero::NonZeroU32::{14}::new] *)
+(** [core::num::nonzero::NonZeroU32::{14}::new]: forward function *)
 val core_num_nonzero_non_zero_u32_new_fwd
   : u32 -> state -> result (state & (option core_num_nonzero_non_zero_u32_t))
 
-(** [core::option::Option::{0}::unwrap] *)
+(** [core::option::Option::{0}::unwrap]: forward function *)
 val core_option_option_unwrap_fwd
   (t : Type0) : option t -> state -> result (state & t)
 
diff --git a/tests/fstar/misc/Loops.Funs.fst b/tests/fstar/misc/Loops.Funs.fst
index 7fe175e5..9a80f415 100644
--- a/tests/fstar/misc/Loops.Funs.fst
+++ b/tests/fstar/misc/Loops.Funs.fst
@@ -7,7 +7,7 @@ include Loops.Clauses
 
 #set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
 
-(** [loops::sum] *)
+(** [loops::sum]: loop 0: forward function *)
 let rec sum_loop_fwd
   (max : u32) (i : u32) (s : u32) :
   Tot (result u32) (decreases (sum_loop_decreases max i s))
@@ -16,11 +16,11 @@ let rec sum_loop_fwd
   then let* s0 = u32_add s i in let* i0 = u32_add i 1 in sum_loop_fwd max i0 s0
   else u32_mul s 2
 
-(** [loops::sum] *)
+(** [loops::sum]: forward function *)
 let sum_fwd (max : u32) : result u32 =
   sum_loop_fwd max 0 0
 
-(** [loops::sum_with_mut_borrows] *)
+(** [loops::sum_with_mut_borrows]: loop 0: forward function *)
 let rec sum_with_mut_borrows_loop_fwd
   (max : u32) (mi : u32) (ms : u32) :
   Tot (result u32) (decreases (sum_with_mut_borrows_loop_decreases max mi ms))
@@ -32,11 +32,11 @@ let rec sum_with_mut_borrows_loop_fwd
     sum_with_mut_borrows_loop_fwd max mi0 ms0
   else u32_mul ms 2
 
-(** [loops::sum_with_mut_borrows] *)
+(** [loops::sum_with_mut_borrows]: forward function *)
 let sum_with_mut_borrows_fwd (max : u32) : result u32 =
   sum_with_mut_borrows_loop_fwd max 0 0
 
-(** [loops::sum_with_shared_borrows] *)
+(** [loops::sum_with_shared_borrows]: loop 0: forward function *)
 let rec sum_with_shared_borrows_loop_fwd
   (max : u32) (i : u32) (s : u32) :
   Tot (result u32) (decreases (sum_with_shared_borrows_loop_decreases max i s))
@@ -48,11 +48,12 @@ let rec sum_with_shared_borrows_loop_fwd
     sum_with_shared_borrows_loop_fwd max i0 s0
   else u32_mul s 2
 
-(** [loops::sum_with_shared_borrows] *)
+(** [loops::sum_with_shared_borrows]: forward function *)
 let sum_with_shared_borrows_fwd (max : u32) : result u32 =
   sum_with_shared_borrows_loop_fwd max 0 0
 
-(** [loops::clear] *)
+(** [loops::clear]: loop 0: merged forward/backward function
+    (there is a single backward function, and the forward function returns ()) *)
 let rec clear_loop_fwd_back
   (v : vec u32) (i : usize) :
   Tot (result (vec u32)) (decreases (clear_loop_decreases v i))
@@ -65,11 +66,12 @@ let rec clear_loop_fwd_back
     clear_loop_fwd_back v0 i1
   else Return v
 
-(** [loops::clear] *)
+(** [loops::clear]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ()) *)
 let clear_fwd_back (v : vec u32) : result (vec u32) =
   clear_loop_fwd_back v 0
 
-(** [loops::list_mem] *)
+(** [loops::list_mem]: loop 0: forward function *)
 let rec list_mem_loop_fwd
   (x : u32) (ls : list_t u32) :
   Tot (result bool) (decreases (list_mem_loop_decreases x ls))
@@ -79,11 +81,11 @@ let rec list_mem_loop_fwd
   | ListNil -> Return false
   end
 
-(** [loops::list_mem] *)
+(** [loops::list_mem]: forward function *)
 let list_mem_fwd (x : u32) (ls : list_t u32) : result bool =
   list_mem_loop_fwd x ls
 
-(** [loops::list_nth_mut_loop] *)
+(** [loops::list_nth_mut_loop]: loop 0: forward function *)
 let rec list_nth_mut_loop_loop_fwd
   (t : Type0) (ls : list_t t) (i : u32) :
   Tot (result t) (decreases (list_nth_mut_loop_loop_decreases t ls i))
@@ -96,11 +98,11 @@ let rec list_nth_mut_loop_loop_fwd
   | ListNil -> Fail Failure
   end
 
-(** [loops::list_nth_mut_loop] *)
+(** [loops::list_nth_mut_loop]: forward function *)
 let list_nth_mut_loop_fwd (t : Type0) (ls : list_t t) (i : u32) : result t =
   list_nth_mut_loop_loop_fwd t ls i
 
-(** [loops::list_nth_mut_loop] *)
+(** [loops::list_nth_mut_loop]: loop 0: backward function 0 *)
 let rec list_nth_mut_loop_loop_back
   (t : Type0) (ls : list_t t) (i : u32) (ret : t) :
   Tot (result (list_t t)) (decreases (list_nth_mut_loop_loop_decreases t ls i))
@@ -116,12 +118,12 @@ let rec list_nth_mut_loop_loop_back
   | ListNil -> Fail Failure
   end
 
-(** [loops::list_nth_mut_loop] *)
+(** [loops::list_nth_mut_loop]: backward function 0 *)
 let list_nth_mut_loop_back
   (t : Type0) (ls : list_t t) (i : u32) (ret : t) : result (list_t t) =
   list_nth_mut_loop_loop_back t ls i ret
 
-(** [loops::list_nth_shared_loop] *)
+(** [loops::list_nth_shared_loop]: loop 0: forward function *)
 let rec list_nth_shared_loop_loop_fwd
   (t : Type0) (ls : list_t t) (i : u32) :
   Tot (result t) (decreases (list_nth_shared_loop_loop_decreases t ls i))
@@ -134,11 +136,11 @@ let rec list_nth_shared_loop_loop_fwd
   | ListNil -> Fail Failure
   end
 
-(** [loops::list_nth_shared_loop] *)
+(** [loops::list_nth_shared_loop]: forward function *)
 let list_nth_shared_loop_fwd (t : Type0) (ls : list_t t) (i : u32) : result t =
   list_nth_shared_loop_loop_fwd t ls i
 
-(** [loops::get_elem_mut] *)
+(** [loops::get_elem_mut]: loop 0: forward function *)
 let rec get_elem_mut_loop_fwd
   (x : usize) (ls : list_t usize) :
   Tot (result usize) (decreases (get_elem_mut_loop_decreases x ls))
@@ -148,12 +150,12 @@ let rec get_elem_mut_loop_fwd
   | ListNil -> Fail Failure
   end
 
-(** [loops::get_elem_mut] *)
+(** [loops::get_elem_mut]: forward function *)
 let get_elem_mut_fwd (slots : vec (list_t usize)) (x : usize) : result usize =
   let* l = vec_index_mut_fwd (list_t usize) slots 0 in
   get_elem_mut_loop_fwd x l
 
-(** [loops::get_elem_mut] *)
+(** [loops::get_elem_mut]: loop 0: backward function 0 *)
 let rec get_elem_mut_loop_back
   (x : usize) (ls : list_t usize) (ret : usize) :
   Tot (result (list_t usize)) (decreases (get_elem_mut_loop_decreases x ls))
@@ -166,7 +168,7 @@ let rec get_elem_mut_loop_back
   | ListNil -> Fail Failure
   end
 
-(** [loops::get_elem_mut] *)
+(** [loops::get_elem_mut]: backward function 0 *)
 let get_elem_mut_back
   (slots : vec (list_t usize)) (x : usize) (ret : usize) :
   result (vec (list_t usize))
@@ -175,7 +177,7 @@ let get_elem_mut_back
   let* l0 = get_elem_mut_loop_back x l ret in
   vec_index_mut_back (list_t usize) slots 0 l0
 
-(** [loops::get_elem_shared] *)
+(** [loops::get_elem_shared]: loop 0: forward function *)
 let rec get_elem_shared_loop_fwd
   (x : usize) (ls : list_t usize) :
   Tot (result usize) (decreases (get_elem_shared_loop_decreases x ls))
@@ -185,25 +187,25 @@ let rec get_elem_shared_loop_fwd
   | ListNil -> Fail Failure
   end
 
-(** [loops::get_elem_shared] *)
+(** [loops::get_elem_shared]: forward function *)
 let get_elem_shared_fwd
   (slots : vec (list_t usize)) (x : usize) : result usize =
   let* l = vec_index_fwd (list_t usize) slots 0 in get_elem_shared_loop_fwd x l
 
-(** [loops::id_mut] *)
+(** [loops::id_mut]: forward function *)
 let id_mut_fwd (t : Type0) (ls : list_t t) : result (list_t t) =
   Return ls
 
-(** [loops::id_mut] *)
+(** [loops::id_mut]: backward function 0 *)
 let id_mut_back
   (t : Type0) (ls : list_t t) (ret : list_t t) : result (list_t t) =
   Return ret
 
-(** [loops::id_shared] *)
+(** [loops::id_shared]: forward function *)
 let id_shared_fwd (t : Type0) (ls : list_t t) : result (list_t t) =
   Return ls
 
-(** [loops::list_nth_mut_loop_with_id] *)
+(** [loops::list_nth_mut_loop_with_id]: loop 0: forward function *)
 let rec list_nth_mut_loop_with_id_loop_fwd
   (t : Type0) (i : u32) (ls : list_t t) :
   Tot (result t) (decreases (list_nth_mut_loop_with_id_loop_decreases t i ls))
@@ -216,12 +218,12 @@ let rec list_nth_mut_loop_with_id_loop_fwd
   | ListNil -> Fail Failure
   end
 
-(** [loops::list_nth_mut_loop_with_id] *)
+(** [loops::list_nth_mut_loop_with_id]: forward function *)
 let list_nth_mut_loop_with_id_fwd
   (t : Type0) (ls : list_t t) (i : u32) : result t =
   let* ls0 = id_mut_fwd t ls in list_nth_mut_loop_with_id_loop_fwd t i ls0
 
-(** [loops::list_nth_mut_loop_with_id] *)
+(** [loops::list_nth_mut_loop_with_id]: loop 0: backward function 0 *)
 let rec list_nth_mut_loop_with_id_loop_back
   (t : Type0) (i : u32) (ls : list_t t) (ret : t) :
   Tot (result (list_t t))
@@ -238,14 +240,14 @@ let rec list_nth_mut_loop_with_id_loop_back
   | ListNil -> Fail Failure
   end
 
-(** [loops::list_nth_mut_loop_with_id] *)
+(** [loops::list_nth_mut_loop_with_id]: backward function 0 *)
 let list_nth_mut_loop_with_id_back
   (t : Type0) (ls : list_t t) (i : u32) (ret : t) : result (list_t t) =
   let* ls0 = id_mut_fwd t ls in
   let* l = list_nth_mut_loop_with_id_loop_back t i ls0 ret in
   id_mut_back t ls l
 
-(** [loops::list_nth_shared_loop_with_id] *)
+(** [loops::list_nth_shared_loop_with_id]: loop 0: forward function *)
 let rec list_nth_shared_loop_with_id_loop_fwd
   (t : Type0) (i : u32) (ls : list_t t) :
   Tot (result t)
@@ -259,13 +261,13 @@ let rec list_nth_shared_loop_with_id_loop_fwd
   | ListNil -> Fail Failure
   end
 
-(** [loops::list_nth_shared_loop_with_id] *)
+(** [loops::list_nth_shared_loop_with_id]: forward function *)
 let list_nth_shared_loop_with_id_fwd
   (t : Type0) (ls : list_t t) (i : u32) : result t =
   let* ls0 = id_shared_fwd t ls in
   list_nth_shared_loop_with_id_loop_fwd t i ls0
 
-(** [loops::list_nth_mut_loop_pair] *)
+(** [loops::list_nth_mut_loop_pair]: loop 0: forward function *)
 let rec list_nth_mut_loop_pair_loop_fwd
   (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) :
   Tot (result (t & t))
@@ -284,12 +286,12 @@ let rec list_nth_mut_loop_pair_loop_fwd
   | ListNil -> Fail Failure
   end
 
-(** [loops::list_nth_mut_loop_pair] *)
+(** [loops::list_nth_mut_loop_pair]: forward function *)
 let list_nth_mut_loop_pair_fwd
   (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) : result (t & t) =
   list_nth_mut_loop_pair_loop_fwd t ls0 ls1 i
 
-(** [loops::list_nth_mut_loop_pair] *)
+(** [loops::list_nth_mut_loop_pair]: loop 0: backward function 0 *)
 let rec list_nth_mut_loop_pair_loop_back'a
   (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) :
   Tot (result (list_t t))
@@ -310,14 +312,14 @@ let rec list_nth_mut_loop_pair_loop_back'a
   | ListNil -> Fail Failure
   end
 
-(** [loops::list_nth_mut_loop_pair] *)
+(** [loops::list_nth_mut_loop_pair]: backward function 0 *)
 let list_nth_mut_loop_pair_back'a
   (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) :
   result (list_t t)
   =
   list_nth_mut_loop_pair_loop_back'a t ls0 ls1 i ret
 
-(** [loops::list_nth_mut_loop_pair] *)
+(** [loops::list_nth_mut_loop_pair]: loop 0: backward function 1 *)
 let rec list_nth_mut_loop_pair_loop_back'b
   (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) :
   Tot (result (list_t t))
@@ -338,14 +340,14 @@ let rec list_nth_mut_loop_pair_loop_back'b
   | ListNil -> Fail Failure
   end
 
-(** [loops::list_nth_mut_loop_pair] *)
+(** [loops::list_nth_mut_loop_pair]: backward function 1 *)
 let list_nth_mut_loop_pair_back'b
   (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) :
   result (list_t t)
   =
   list_nth_mut_loop_pair_loop_back'b t ls0 ls1 i ret
 
-(** [loops::list_nth_shared_loop_pair] *)
+(** [loops::list_nth_shared_loop_pair]: loop 0: forward function *)
 let rec list_nth_shared_loop_pair_loop_fwd
   (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) :
   Tot (result (t & t))
@@ -365,12 +367,12 @@ let rec list_nth_shared_loop_pair_loop_fwd
   | ListNil -> Fail Failure
   end
 
-(** [loops::list_nth_shared_loop_pair] *)
+(** [loops::list_nth_shared_loop_pair]: forward function *)
 let list_nth_shared_loop_pair_fwd
   (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) : result (t & t) =
   list_nth_shared_loop_pair_loop_fwd t ls0 ls1 i
 
-(** [loops::list_nth_mut_loop_pair_merge] *)
+(** [loops::list_nth_mut_loop_pair_merge]: loop 0: forward function *)
 let rec list_nth_mut_loop_pair_merge_loop_fwd
   (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) :
   Tot (result (t & t))
@@ -390,12 +392,12 @@ let rec list_nth_mut_loop_pair_merge_loop_fwd
   | ListNil -> Fail Failure
   end
 
-(** [loops::list_nth_mut_loop_pair_merge] *)
+(** [loops::list_nth_mut_loop_pair_merge]: forward function *)
 let list_nth_mut_loop_pair_merge_fwd
   (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) : result (t & t) =
   list_nth_mut_loop_pair_merge_loop_fwd t ls0 ls1 i
 
-(** [loops::list_nth_mut_loop_pair_merge] *)
+(** [loops::list_nth_mut_loop_pair_merge]: loop 0: backward function 0 *)
 let rec list_nth_mut_loop_pair_merge_loop_back
   (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : (t & t)) :
   Tot (result ((list_t t) & (list_t t)))
@@ -417,14 +419,14 @@ let rec list_nth_mut_loop_pair_merge_loop_back
   | ListNil -> Fail Failure
   end
 
-(** [loops::list_nth_mut_loop_pair_merge] *)
+(** [loops::list_nth_mut_loop_pair_merge]: backward function 0 *)
 let list_nth_mut_loop_pair_merge_back
   (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : (t & t)) :
   result ((list_t t) & (list_t t))
   =
   list_nth_mut_loop_pair_merge_loop_back t ls0 ls1 i ret
 
-(** [loops::list_nth_shared_loop_pair_merge] *)
+(** [loops::list_nth_shared_loop_pair_merge]: loop 0: forward function *)
 let rec list_nth_shared_loop_pair_merge_loop_fwd
   (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) :
   Tot (result (t & t))
@@ -444,12 +446,12 @@ let rec list_nth_shared_loop_pair_merge_loop_fwd
   | ListNil -> Fail Failure
   end
 
-(** [loops::list_nth_shared_loop_pair_merge] *)
+(** [loops::list_nth_shared_loop_pair_merge]: forward function *)
 let list_nth_shared_loop_pair_merge_fwd
   (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) : result (t & t) =
   list_nth_shared_loop_pair_merge_loop_fwd t ls0 ls1 i
 
-(** [loops::list_nth_mut_shared_loop_pair] *)
+(** [loops::list_nth_mut_shared_loop_pair]: loop 0: forward function *)
 let rec list_nth_mut_shared_loop_pair_loop_fwd
   (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) :
   Tot (result (t & t))
@@ -469,12 +471,12 @@ let rec list_nth_mut_shared_loop_pair_loop_fwd
   | ListNil -> Fail Failure
   end
 
-(** [loops::list_nth_mut_shared_loop_pair] *)
+(** [loops::list_nth_mut_shared_loop_pair]: forward function *)
 let list_nth_mut_shared_loop_pair_fwd
   (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) : result (t & t) =
   list_nth_mut_shared_loop_pair_loop_fwd t ls0 ls1 i
 
-(** [loops::list_nth_mut_shared_loop_pair] *)
+(** [loops::list_nth_mut_shared_loop_pair]: loop 0: backward function 0 *)
 let rec list_nth_mut_shared_loop_pair_loop_back
   (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) :
   Tot (result (list_t t))
@@ -495,14 +497,14 @@ let rec list_nth_mut_shared_loop_pair_loop_back
   | ListNil -> Fail Failure
   end
 
-(** [loops::list_nth_mut_shared_loop_pair] *)
+(** [loops::list_nth_mut_shared_loop_pair]: backward function 0 *)
 let list_nth_mut_shared_loop_pair_back
   (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) :
   result (list_t t)
   =
   list_nth_mut_shared_loop_pair_loop_back t ls0 ls1 i ret
 
-(** [loops::list_nth_mut_shared_loop_pair_merge] *)
+(** [loops::list_nth_mut_shared_loop_pair_merge]: loop 0: forward function *)
 let rec list_nth_mut_shared_loop_pair_merge_loop_fwd
   (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) :
   Tot (result (t & t))
@@ -522,12 +524,12 @@ let rec list_nth_mut_shared_loop_pair_merge_loop_fwd
   | ListNil -> Fail Failure
   end
 
-(** [loops::list_nth_mut_shared_loop_pair_merge] *)
+(** [loops::list_nth_mut_shared_loop_pair_merge]: forward function *)
 let list_nth_mut_shared_loop_pair_merge_fwd
   (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) : result (t & t) =
   list_nth_mut_shared_loop_pair_merge_loop_fwd t ls0 ls1 i
 
-(** [loops::list_nth_mut_shared_loop_pair_merge] *)
+(** [loops::list_nth_mut_shared_loop_pair_merge]: loop 0: backward function 0 *)
 let rec list_nth_mut_shared_loop_pair_merge_loop_back
   (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) :
   Tot (result (list_t t))
@@ -549,14 +551,14 @@ let rec list_nth_mut_shared_loop_pair_merge_loop_back
   | ListNil -> Fail Failure
   end
 
-(** [loops::list_nth_mut_shared_loop_pair_merge] *)
+(** [loops::list_nth_mut_shared_loop_pair_merge]: backward function 0 *)
 let list_nth_mut_shared_loop_pair_merge_back
   (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) :
   result (list_t t)
   =
   list_nth_mut_shared_loop_pair_merge_loop_back t ls0 ls1 i ret
 
-(** [loops::list_nth_shared_mut_loop_pair] *)
+(** [loops::list_nth_shared_mut_loop_pair]: loop 0: forward function *)
 let rec list_nth_shared_mut_loop_pair_loop_fwd
   (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) :
   Tot (result (t & t))
@@ -576,12 +578,12 @@ let rec list_nth_shared_mut_loop_pair_loop_fwd
   | ListNil -> Fail Failure
   end
 
-(** [loops::list_nth_shared_mut_loop_pair] *)
+(** [loops::list_nth_shared_mut_loop_pair]: forward function *)
 let list_nth_shared_mut_loop_pair_fwd
   (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) : result (t & t) =
   list_nth_shared_mut_loop_pair_loop_fwd t ls0 ls1 i
 
-(** [loops::list_nth_shared_mut_loop_pair] *)
+(** [loops::list_nth_shared_mut_loop_pair]: loop 0: backward function 1 *)
 let rec list_nth_shared_mut_loop_pair_loop_back
   (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) :
   Tot (result (list_t t))
@@ -602,14 +604,14 @@ let rec list_nth_shared_mut_loop_pair_loop_back
   | ListNil -> Fail Failure
   end
 
-(** [loops::list_nth_shared_mut_loop_pair] *)
+(** [loops::list_nth_shared_mut_loop_pair]: backward function 1 *)
 let list_nth_shared_mut_loop_pair_back
   (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) :
   result (list_t t)
   =
   list_nth_shared_mut_loop_pair_loop_back t ls0 ls1 i ret
 
-(** [loops::list_nth_shared_mut_loop_pair_merge] *)
+(** [loops::list_nth_shared_mut_loop_pair_merge]: loop 0: forward function *)
 let rec list_nth_shared_mut_loop_pair_merge_loop_fwd
   (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) :
   Tot (result (t & t))
@@ -629,12 +631,12 @@ let rec list_nth_shared_mut_loop_pair_merge_loop_fwd
   | ListNil -> Fail Failure
   end
 
-(** [loops::list_nth_shared_mut_loop_pair_merge] *)
+(** [loops::list_nth_shared_mut_loop_pair_merge]: forward function *)
 let list_nth_shared_mut_loop_pair_merge_fwd
   (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) : result (t & t) =
   list_nth_shared_mut_loop_pair_merge_loop_fwd t ls0 ls1 i
 
-(** [loops::list_nth_shared_mut_loop_pair_merge] *)
+(** [loops::list_nth_shared_mut_loop_pair_merge]: loop 0: backward function 0 *)
 let rec list_nth_shared_mut_loop_pair_merge_loop_back
   (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) :
   Tot (result (list_t t))
@@ -656,7 +658,7 @@ let rec list_nth_shared_mut_loop_pair_merge_loop_back
   | ListNil -> Fail Failure
   end
 
-(** [loops::list_nth_shared_mut_loop_pair_merge] *)
+(** [loops::list_nth_shared_mut_loop_pair_merge]: backward function 0 *)
 let list_nth_shared_mut_loop_pair_merge_back
   (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) :
   result (list_t t)
diff --git a/tests/fstar/misc/NoNestedBorrows.fst b/tests/fstar/misc/NoNestedBorrows.fst
index 3770ab5d..d790bfa9 100644
--- a/tests/fstar/misc/NoNestedBorrows.fst
+++ b/tests/fstar/misc/NoNestedBorrows.fst
@@ -30,46 +30,46 @@ type sum_t (t1 t2 : Type0) =
 | SumLeft : t1 -> sum_t t1 t2
 | SumRight : t2 -> sum_t t1 t2
 
-(** [no_nested_borrows::neg_test] *)
+(** [no_nested_borrows::neg_test]: forward function *)
 let neg_test_fwd (x : i32) : result i32 =
   i32_neg x
 
-(** [no_nested_borrows::add_test] *)
+(** [no_nested_borrows::add_test]: forward function *)
 let add_test_fwd (x : u32) (y : u32) : result u32 =
   u32_add x y
 
-(** [no_nested_borrows::subs_test] *)
+(** [no_nested_borrows::subs_test]: forward function *)
 let subs_test_fwd (x : u32) (y : u32) : result u32 =
   u32_sub x y
 
-(** [no_nested_borrows::div_test] *)
+(** [no_nested_borrows::div_test]: forward function *)
 let div_test_fwd (x : u32) (y : u32) : result u32 =
   u32_div x y
 
-(** [no_nested_borrows::div_test1] *)
+(** [no_nested_borrows::div_test1]: forward function *)
 let div_test1_fwd (x : u32) : result u32 =
   u32_div x 2
 
-(** [no_nested_borrows::rem_test] *)
+(** [no_nested_borrows::rem_test]: forward function *)
 let rem_test_fwd (x : u32) (y : u32) : result u32 =
   u32_rem x y
 
-(** [no_nested_borrows::cast_test] *)
+(** [no_nested_borrows::cast_test]: forward function *)
 let cast_test_fwd (x : u32) : result i32 =
   scalar_cast U32 I32 x
 
-(** [no_nested_borrows::test2] *)
+(** [no_nested_borrows::test2]: forward function *)
 let test2_fwd : result unit =
   let* _ = u32_add 23 44 in Return ()
 
 (** Unit test for [no_nested_borrows::test2] *)
 let _ = assert_norm (test2_fwd = Return ())
 
-(** [no_nested_borrows::get_max] *)
+(** [no_nested_borrows::get_max]: forward function *)
 let get_max_fwd (x : u32) (y : u32) : result u32 =
   if x >= y then Return x else Return y
 
-(** [no_nested_borrows::test3] *)
+(** [no_nested_borrows::test3]: forward function *)
 let test3_fwd : result unit =
   let* x = get_max_fwd 4 3 in
   let* y = get_max_fwd 10 11 in
@@ -79,21 +79,21 @@ let test3_fwd : result unit =
 (** Unit test for [no_nested_borrows::test3] *)
 let _ = assert_norm (test3_fwd = Return ())
 
-(** [no_nested_borrows::test_neg1] *)
+(** [no_nested_borrows::test_neg1]: forward function *)
 let test_neg1_fwd : result unit =
   let* y = i32_neg 3 in if not (y = -3) then Fail Failure else Return ()
 
 (** Unit test for [no_nested_borrows::test_neg1] *)
 let _ = assert_norm (test_neg1_fwd = Return ())
 
-(** [no_nested_borrows::refs_test1] *)
+(** [no_nested_borrows::refs_test1]: forward function *)
 let refs_test1_fwd : result unit =
   if not (1 = 1) then Fail Failure else Return ()
 
 (** Unit test for [no_nested_borrows::refs_test1] *)
 let _ = assert_norm (refs_test1_fwd = Return ())
 
-(** [no_nested_borrows::refs_test2] *)
+(** [no_nested_borrows::refs_test2]: forward function *)
 let refs_test2_fwd : result unit =
   if not (2 = 2)
   then Fail Failure
@@ -108,47 +108,47 @@ let refs_test2_fwd : result unit =
 (** Unit test for [no_nested_borrows::refs_test2] *)
 let _ = assert_norm (refs_test2_fwd = Return ())
 
-(** [no_nested_borrows::test_list1] *)
+(** [no_nested_borrows::test_list1]: forward function *)
 let test_list1_fwd : result unit =
   Return ()
 
 (** Unit test for [no_nested_borrows::test_list1] *)
 let _ = assert_norm (test_list1_fwd = Return ())
 
-(** [no_nested_borrows::test_box1] *)
+(** [no_nested_borrows::test_box1]: forward function *)
 let test_box1_fwd : result unit =
   let b = 1 in let x = b in if not (x = 1) then Fail Failure else Return ()
 
 (** Unit test for [no_nested_borrows::test_box1] *)
 let _ = assert_norm (test_box1_fwd = Return ())
 
-(** [no_nested_borrows::copy_int] *)
+(** [no_nested_borrows::copy_int]: forward function *)
 let copy_int_fwd (x : i32) : result i32 =
   Return x
 
-(** [no_nested_borrows::test_unreachable] *)
+(** [no_nested_borrows::test_unreachable]: forward function *)
 let test_unreachable_fwd (b : bool) : result unit =
   if b then Fail Failure else Return ()
 
-(** [no_nested_borrows::test_panic] *)
+(** [no_nested_borrows::test_panic]: forward function *)
 let test_panic_fwd (b : bool) : result unit =
   if b then Fail Failure else Return ()
 
-(** [no_nested_borrows::test_copy_int] *)
+(** [no_nested_borrows::test_copy_int]: forward function *)
 let test_copy_int_fwd : result unit =
   let* y = copy_int_fwd 0 in if not (0 = y) then Fail Failure else Return ()
 
 (** Unit test for [no_nested_borrows::test_copy_int] *)
 let _ = assert_norm (test_copy_int_fwd = Return ())
 
-(** [no_nested_borrows::is_cons] *)
+(** [no_nested_borrows::is_cons]: forward function *)
 let is_cons_fwd (t : Type0) (l : list_t t) : result bool =
   begin match l with
   | ListCons x l0 -> Return true
   | ListNil -> Return false
   end
 
-(** [no_nested_borrows::test_is_cons] *)
+(** [no_nested_borrows::test_is_cons]: forward function *)
 let test_is_cons_fwd : result unit =
   let l = ListNil in
   let* b = is_cons_fwd i32 (ListCons 0 l) in
@@ -157,14 +157,14 @@ let test_is_cons_fwd : result unit =
 (** Unit test for [no_nested_borrows::test_is_cons] *)
 let _ = assert_norm (test_is_cons_fwd = Return ())
 
-(** [no_nested_borrows::split_list] *)
+(** [no_nested_borrows::split_list]: forward function *)
 let split_list_fwd (t : Type0) (l : list_t t) : result (t & (list_t t)) =
   begin match l with
   | ListCons hd tl -> Return (hd, tl)
   | ListNil -> Fail Failure
   end
 
-(** [no_nested_borrows::test_split_list] *)
+(** [no_nested_borrows::test_split_list]: forward function *)
 let test_split_list_fwd : result unit =
   let l = ListNil in
   let* p = split_list_fwd i32 (ListCons 0 l) in
@@ -174,16 +174,16 @@ let test_split_list_fwd : result unit =
 (** Unit test for [no_nested_borrows::test_split_list] *)
 let _ = assert_norm (test_split_list_fwd = Return ())
 
-(** [no_nested_borrows::choose] *)
+(** [no_nested_borrows::choose]: forward function *)
 let choose_fwd (t : Type0) (b : bool) (x : t) (y : t) : result t =
   if b then Return x else Return y
 
-(** [no_nested_borrows::choose] *)
+(** [no_nested_borrows::choose]: backward function 0 *)
 let choose_back
   (t : Type0) (b : bool) (x : t) (y : t) (ret : t) : result (t & t) =
   if b then Return (ret, y) else Return (x, ret)
 
-(** [no_nested_borrows::choose_test] *)
+(** [no_nested_borrows::choose_test]: forward function *)
 let choose_test_fwd : result unit =
   let* z = choose_fwd i32 true 0 0 in
   let* z0 = i32_add z 1 in
@@ -198,7 +198,7 @@ let choose_test_fwd : result unit =
 (** Unit test for [no_nested_borrows::choose_test] *)
 let _ = assert_norm (choose_test_fwd = Return ())
 
-(** [no_nested_borrows::test_char] *)
+(** [no_nested_borrows::test_char]: forward function *)
 let test_char_fwd : result char =
   Return 'a'
 
@@ -212,14 +212,14 @@ and tree_t (t : Type0) =
 | TreeLeaf : t -> tree_t t
 | TreeNode : t -> node_elem_t t -> tree_t t -> tree_t t
 
-(** [no_nested_borrows::list_length] *)
+(** [no_nested_borrows::list_length]: forward function *)
 let rec list_length_fwd (t : Type0) (l : list_t t) : result u32 =
   begin match l with
   | ListCons x l1 -> let* i = list_length_fwd t l1 in u32_add 1 i
   | ListNil -> Return 0
   end
 
-(** [no_nested_borrows::list_nth_shared] *)
+(** [no_nested_borrows::list_nth_shared]: forward function *)
 let rec list_nth_shared_fwd (t : Type0) (l : list_t t) (i : u32) : result t =
   begin match l with
   | ListCons x tl ->
@@ -229,7 +229,7 @@ let rec list_nth_shared_fwd (t : Type0) (l : list_t t) (i : u32) : result t =
   | ListNil -> Fail Failure
   end
 
-(** [no_nested_borrows::list_nth_mut] *)
+(** [no_nested_borrows::list_nth_mut]: forward function *)
 let rec list_nth_mut_fwd (t : Type0) (l : list_t t) (i : u32) : result t =
   begin match l with
   | ListCons x tl ->
@@ -239,7 +239,7 @@ let rec list_nth_mut_fwd (t : Type0) (l : list_t t) (i : u32) : result t =
   | ListNil -> Fail Failure
   end
 
-(** [no_nested_borrows::list_nth_mut] *)
+(** [no_nested_borrows::list_nth_mut]: backward function 0 *)
 let rec list_nth_mut_back
   (t : Type0) (l : list_t t) (i : u32) (ret : t) : result (list_t t) =
   begin match l with
@@ -253,7 +253,7 @@ let rec list_nth_mut_back
   | ListNil -> Fail Failure
   end
 
-(** [no_nested_borrows::list_rev_aux] *)
+(** [no_nested_borrows::list_rev_aux]: forward function *)
 let rec list_rev_aux_fwd
   (t : Type0) (li : list_t t) (lo : list_t t) : result (list_t t) =
   begin match li with
@@ -261,12 +261,13 @@ let rec list_rev_aux_fwd
   | ListNil -> Return lo
   end
 
-(** [no_nested_borrows::list_rev] *)
+(** [no_nested_borrows::list_rev]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ()) *)
 let list_rev_fwd_back (t : Type0) (l : list_t t) : result (list_t t) =
   let li = mem_replace_fwd (list_t t) l ListNil in
   list_rev_aux_fwd t li ListNil
 
-(** [no_nested_borrows::test_list_functions] *)
+(** [no_nested_borrows::test_list_functions]: forward function *)
 let test_list_functions_fwd : result unit =
   let l = ListNil in
   let l0 = ListCons 2 l in
@@ -302,48 +303,48 @@ let test_list_functions_fwd : result unit =
 (** Unit test for [no_nested_borrows::test_list_functions] *)
 let _ = assert_norm (test_list_functions_fwd = Return ())
 
-(** [no_nested_borrows::id_mut_pair1] *)
+(** [no_nested_borrows::id_mut_pair1]: forward function *)
 let id_mut_pair1_fwd (t1 t2 : Type0) (x : t1) (y : t2) : result (t1 & t2) =
   Return (x, y)
 
-(** [no_nested_borrows::id_mut_pair1] *)
+(** [no_nested_borrows::id_mut_pair1]: backward function 0 *)
 let id_mut_pair1_back
   (t1 t2 : Type0) (x : t1) (y : t2) (ret : (t1 & t2)) : result (t1 & t2) =
   let (x0, x1) = ret in Return (x0, x1)
 
-(** [no_nested_borrows::id_mut_pair2] *)
+(** [no_nested_borrows::id_mut_pair2]: forward function *)
 let id_mut_pair2_fwd (t1 t2 : Type0) (p : (t1 & t2)) : result (t1 & t2) =
   let (x, x0) = p in Return (x, x0)
 
-(** [no_nested_borrows::id_mut_pair2] *)
+(** [no_nested_borrows::id_mut_pair2]: backward function 0 *)
 let id_mut_pair2_back
   (t1 t2 : Type0) (p : (t1 & t2)) (ret : (t1 & t2)) : result (t1 & t2) =
   let (x, x0) = ret in Return (x, x0)
 
-(** [no_nested_borrows::id_mut_pair3] *)
+(** [no_nested_borrows::id_mut_pair3]: forward function *)
 let id_mut_pair3_fwd (t1 t2 : Type0) (x : t1) (y : t2) : result (t1 & t2) =
   Return (x, y)
 
-(** [no_nested_borrows::id_mut_pair3] *)
+(** [no_nested_borrows::id_mut_pair3]: backward function 0 *)
 let id_mut_pair3_back'a
   (t1 t2 : Type0) (x : t1) (y : t2) (ret : t1) : result t1 =
   Return ret
 
-(** [no_nested_borrows::id_mut_pair3] *)
+(** [no_nested_borrows::id_mut_pair3]: backward function 1 *)
 let id_mut_pair3_back'b
   (t1 t2 : Type0) (x : t1) (y : t2) (ret : t2) : result t2 =
   Return ret
 
-(** [no_nested_borrows::id_mut_pair4] *)
+(** [no_nested_borrows::id_mut_pair4]: forward function *)
 let id_mut_pair4_fwd (t1 t2 : Type0) (p : (t1 & t2)) : result (t1 & t2) =
   let (x, x0) = p in Return (x, x0)
 
-(** [no_nested_borrows::id_mut_pair4] *)
+(** [no_nested_borrows::id_mut_pair4]: backward function 0 *)
 let id_mut_pair4_back'a
   (t1 t2 : Type0) (p : (t1 & t2)) (ret : t1) : result t1 =
   Return ret
 
-(** [no_nested_borrows::id_mut_pair4] *)
+(** [no_nested_borrows::id_mut_pair4]: backward function 1 *)
 let id_mut_pair4_back'b
   (t1 t2 : Type0) (p : (t1 & t2)) (ret : t2) : result t2 =
   Return ret
@@ -351,15 +352,15 @@ let id_mut_pair4_back'b
 (** [no_nested_borrows::StructWithTuple] *)
 type struct_with_tuple_t (t1 t2 : Type0) = { struct_with_tuple_p : (t1 & t2); }
 
-(** [no_nested_borrows::new_tuple1] *)
+(** [no_nested_borrows::new_tuple1]: forward function *)
 let new_tuple1_fwd : result (struct_with_tuple_t u32 u32) =
   Return { struct_with_tuple_p = (1, 2) }
 
-(** [no_nested_borrows::new_tuple2] *)
+(** [no_nested_borrows::new_tuple2]: forward function *)
 let new_tuple2_fwd : result (struct_with_tuple_t i16 i16) =
   Return { struct_with_tuple_p = (1, 2) }
 
-(** [no_nested_borrows::new_tuple3] *)
+(** [no_nested_borrows::new_tuple3]: forward function *)
 let new_tuple3_fwd : result (struct_with_tuple_t u64 i64) =
   Return { struct_with_tuple_p = (1, 2) }
 
@@ -369,11 +370,11 @@ type struct_with_pair_t (t1 t2 : Type0) =
   struct_with_pair_p : pair_t t1 t2;
 }
 
-(** [no_nested_borrows::new_pair1] *)
+(** [no_nested_borrows::new_pair1]: forward function *)
 let new_pair1_fwd : result (struct_with_pair_t u32 u32) =
   Return { struct_with_pair_p = { pair_x = 1; pair_y = 2 } }
 
-(** [no_nested_borrows::test_constants] *)
+(** [no_nested_borrows::test_constants]: forward function *)
 let test_constants_fwd : result unit =
   let* swt = new_tuple1_fwd in
   let (i, _) = swt.struct_with_tuple_p in
@@ -398,31 +399,32 @@ let test_constants_fwd : result unit =
 (** Unit test for [no_nested_borrows::test_constants] *)
 let _ = assert_norm (test_constants_fwd = Return ())
 
-(** [no_nested_borrows::test_weird_borrows1] *)
+(** [no_nested_borrows::test_weird_borrows1]: forward function *)
 let test_weird_borrows1_fwd : result unit =
   Return ()
 
 (** Unit test for [no_nested_borrows::test_weird_borrows1] *)
 let _ = assert_norm (test_weird_borrows1_fwd = Return ())
 
-(** [no_nested_borrows::test_mem_replace] *)
+(** [no_nested_borrows::test_mem_replace]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ()) *)
 let test_mem_replace_fwd_back (px : u32) : result u32 =
   let y = mem_replace_fwd u32 px 1 in
   if not (y = 0) then Fail Failure else Return 2
 
-(** [no_nested_borrows::test_shared_borrow_bool1] *)
+(** [no_nested_borrows::test_shared_borrow_bool1]: forward function *)
 let test_shared_borrow_bool1_fwd (b : bool) : result u32 =
   if b then Return 0 else Return 1
 
-(** [no_nested_borrows::test_shared_borrow_bool2] *)
+(** [no_nested_borrows::test_shared_borrow_bool2]: forward function *)
 let test_shared_borrow_bool2_fwd : result u32 =
   Return 0
 
-(** [no_nested_borrows::test_shared_borrow_enum1] *)
+(** [no_nested_borrows::test_shared_borrow_enum1]: forward function *)
 let test_shared_borrow_enum1_fwd (l : list_t u32) : result u32 =
   begin match l with | ListCons i l0 -> Return 1 | ListNil -> Return 0 end
 
-(** [no_nested_borrows::test_shared_borrow_enum2] *)
+(** [no_nested_borrows::test_shared_borrow_enum2]: forward function *)
 let test_shared_borrow_enum2_fwd : result u32 =
   Return 0
 
diff --git a/tests/fstar/misc/Paper.fst b/tests/fstar/misc/Paper.fst
index 4ab31de3..e2d692c2 100644
--- a/tests/fstar/misc/Paper.fst
+++ b/tests/fstar/misc/Paper.fst
@@ -5,11 +5,12 @@ open Primitives
 
 #set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
 
-(** [paper::ref_incr] *)
+(** [paper::ref_incr]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ()) *)
 let ref_incr_fwd_back (x : i32) : result i32 =
   i32_add x 1
 
-(** [paper::test_incr] *)
+(** [paper::test_incr]: forward function *)
 let test_incr_fwd : result unit =
   let* x = ref_incr_fwd_back 0 in
   if not (x = 1) then Fail Failure else Return ()
@@ -17,16 +18,16 @@ let test_incr_fwd : result unit =
 (** Unit test for [paper::test_incr] *)
 let _ = assert_norm (test_incr_fwd = Return ())
 
-(** [paper::choose] *)
+(** [paper::choose]: forward function *)
 let choose_fwd (t : Type0) (b : bool) (x : t) (y : t) : result t =
   if b then Return x else Return y
 
-(** [paper::choose] *)
+(** [paper::choose]: backward function 0 *)
 let choose_back
   (t : Type0) (b : bool) (x : t) (y : t) (ret : t) : result (t & t) =
   if b then Return (ret, y) else Return (x, ret)
 
-(** [paper::test_choose] *)
+(** [paper::test_choose]: forward function *)
 let test_choose_fwd : result unit =
   let* z = choose_fwd i32 true 0 0 in
   let* z0 = i32_add z 1 in
@@ -46,7 +47,7 @@ type list_t (t : Type0) =
 | ListCons : t -> list_t t -> list_t t
 | ListNil : list_t t
 
-(** [paper::list_nth_mut] *)
+(** [paper::list_nth_mut]: forward function *)
 let rec list_nth_mut_fwd (t : Type0) (l : list_t t) (i : u32) : result t =
   begin match l with
   | ListCons x tl ->
@@ -56,7 +57,7 @@ let rec list_nth_mut_fwd (t : Type0) (l : list_t t) (i : u32) : result t =
   | ListNil -> Fail Failure
   end
 
-(** [paper::list_nth_mut] *)
+(** [paper::list_nth_mut]: backward function 0 *)
 let rec list_nth_mut_back
   (t : Type0) (l : list_t t) (i : u32) (ret : t) : result (list_t t) =
   begin match l with
@@ -70,14 +71,14 @@ let rec list_nth_mut_back
   | ListNil -> Fail Failure
   end
 
-(** [paper::sum] *)
+(** [paper::sum]: forward function *)
 let rec sum_fwd (l : list_t i32) : result i32 =
   begin match l with
   | ListCons x tl -> let* i = sum_fwd tl in i32_add x i
   | ListNil -> Return 0
   end
 
-(** [paper::test_nth] *)
+(** [paper::test_nth]: forward function *)
 let test_nth_fwd : result unit =
   let l = ListNil in
   let l0 = ListCons 3 l in
@@ -91,7 +92,7 @@ let test_nth_fwd : result unit =
 (** Unit test for [paper::test_nth] *)
 let _ = assert_norm (test_nth_fwd = Return ())
 
-(** [paper::call_choose] *)
+(** [paper::call_choose]: forward function *)
 let call_choose_fwd (p : (u32 & u32)) : result u32 =
   let (px, py) = p in
   let* pz = choose_fwd u32 true px py in
diff --git a/tests/fstar/misc/PoloniusList.fst b/tests/fstar/misc/PoloniusList.fst
index e2144487..79c86606 100644
--- a/tests/fstar/misc/PoloniusList.fst
+++ b/tests/fstar/misc/PoloniusList.fst
@@ -10,7 +10,7 @@ type list_t (t : Type0) =
 | ListCons : t -> list_t t -> list_t t
 | ListNil : list_t t
 
-(** [polonius_list::get_list_at_x] *)
+(** [polonius_list::get_list_at_x]: forward function *)
 let rec get_list_at_x_fwd (ls : list_t u32) (x : u32) : result (list_t u32) =
   begin match ls with
   | ListCons hd tl ->
@@ -18,7 +18,7 @@ let rec get_list_at_x_fwd (ls : list_t u32) (x : u32) : result (list_t u32) =
   | ListNil -> Return ListNil
   end
 
-(** [polonius_list::get_list_at_x] *)
+(** [polonius_list::get_list_at_x]: backward function 0 *)
 let rec get_list_at_x_back
   (ls : list_t u32) (x : u32) (ret : list_t u32) : result (list_t u32) =
   begin match ls with
diff --git a/tests/hol4/betree/betreeMain_FunsScript.sml b/tests/hol4/betree/betreeMain_FunsScript.sml
index df0c6a24..03ff2671 100644
--- a/tests/hol4/betree/betreeMain_FunsScript.sml
+++ b/tests/hol4/betree/betreeMain_FunsScript.sml
@@ -7,7 +7,7 @@ val _ = new_theory "betreeMain_Funs"
 
 
 val betree_load_internal_node_fwd_def = Define ‘
-  (** [betree_main::betree::load_internal_node] *)
+  (** [betree_main::betree::load_internal_node]: forward function *)
   betree_load_internal_node_fwd
     (id : u64) (st : state) :
     (state # (u64 # betree_message_t) betree_list_t) result
@@ -16,7 +16,7 @@ val betree_load_internal_node_fwd_def = Define ‘
 ’
 
 val betree_store_internal_node_fwd_def = Define ‘
-  (** [betree_main::betree::store_internal_node] *)
+  (** [betree_main::betree::store_internal_node]: forward function *)
   betree_store_internal_node_fwd
     (id : u64) (content : (u64 # betree_message_t) betree_list_t) (st : state)
     :
@@ -29,14 +29,14 @@ val betree_store_internal_node_fwd_def = Define ‘
 ’
 
 val betree_load_leaf_node_fwd_def = Define ‘
-  (** [betree_main::betree::load_leaf_node] *)
+  (** [betree_main::betree::load_leaf_node]: forward function *)
   betree_load_leaf_node_fwd
     (id : u64) (st : state) : (state # (u64 # u64) betree_list_t) result =
     betree_utils_load_leaf_node_fwd id st
 ’
 
 val betree_store_leaf_node_fwd_def = Define ‘
-  (** [betree_main::betree::store_leaf_node] *)
+  (** [betree_main::betree::store_leaf_node]: forward function *)
   betree_store_leaf_node_fwd
     (id : u64) (content : (u64 # u64) betree_list_t) (st : state) :
     (state # unit) result
@@ -48,7 +48,7 @@ val betree_store_leaf_node_fwd_def = Define ‘
 ’
 
 val betree_fresh_node_id_fwd_def = Define ‘
-  (** [betree_main::betree::fresh_node_id] *)
+  (** [betree_main::betree::fresh_node_id]: forward function *)
   betree_fresh_node_id_fwd (counter : u64) : u64 result =
     do
     _ <- u64_add counter (int_to_u64 1);
@@ -57,19 +57,19 @@ val betree_fresh_node_id_fwd_def = Define ‘
 ’
 
 val betree_fresh_node_id_back_def = Define ‘
-  (** [betree_main::betree::fresh_node_id] *)
+  (** [betree_main::betree::fresh_node_id]: backward function 0 *)
   betree_fresh_node_id_back (counter : u64) : u64 result =
     u64_add counter (int_to_u64 1)
 ’
 
 val betree_node_id_counter_new_fwd_def = Define ‘
-  (** [betree_main::betree::NodeIdCounter::{0}::new] *)
+  (** [betree_main::betree::NodeIdCounter::{0}::new]: forward function *)
   betree_node_id_counter_new_fwd : betree_node_id_counter_t result =
     Return (<| betree_node_id_counter_next_node_id := (int_to_u64 0) |>)
 ’
 
 val betree_node_id_counter_fresh_id_fwd_def = Define ‘
-  (** [betree_main::betree::NodeIdCounter::{0}::fresh_id] *)
+  (** [betree_main::betree::NodeIdCounter::{0}::fresh_id]: forward function *)
   betree_node_id_counter_fresh_id_fwd
     (self : betree_node_id_counter_t) : u64 result =
     do
@@ -79,7 +79,7 @@ val betree_node_id_counter_fresh_id_fwd_def = Define ‘
 ’
 
 val betree_node_id_counter_fresh_id_back_def = Define ‘
-  (** [betree_main::betree::NodeIdCounter::{0}::fresh_id] *)
+  (** [betree_main::betree::NodeIdCounter::{0}::fresh_id]: backward function 0 *)
   betree_node_id_counter_fresh_id_back
     (self : betree_node_id_counter_t) : betree_node_id_counter_t result =
     do
@@ -97,7 +97,7 @@ Definition core_num_u64_max_c_def:
 End
 
 val betree_upsert_update_fwd_def = Define ‘
-  (** [betree_main::betree::upsert_update] *)
+  (** [betree_main::betree::upsert_update]: forward function *)
   betree_upsert_update_fwd
     (prev : u64 option) (st : betree_upsert_fun_state_t) : u64 result =
     (case prev of
@@ -117,7 +117,7 @@ val betree_upsert_update_fwd_def = Define ‘
 ’
 
 val [betree_list_len_fwd_def] = DefineDiv ‘
-  (** [betree_main::betree::List::{1}::len] *)
+  (** [betree_main::betree::List::{1}::len]: forward function *)
   betree_list_len_fwd (self : 't betree_list_t) : u64 result =
     (case self of
     | BetreeListCons t tl =>
@@ -129,7 +129,7 @@ val [betree_list_len_fwd_def] = DefineDiv ‘
 ’
 
 val [betree_list_split_at_fwd_def] = DefineDiv ‘
-  (** [betree_main::betree::List::{1}::split_at] *)
+  (** [betree_main::betree::List::{1}::split_at]: forward function *)
   betree_list_split_at_fwd
     (self : 't betree_list_t) (n : u64) :
     ('t betree_list_t # 't betree_list_t) result
@@ -148,7 +148,8 @@ val [betree_list_split_at_fwd_def] = DefineDiv ‘
 ’
 
 val betree_list_push_front_fwd_back_def = Define ‘
-  (** [betree_main::betree::List::{1}::push_front] *)
+  (** [betree_main::betree::List::{1}::push_front]: merged forward/backward function
+      (there is a single backward function, and the forward function returns ()) *)
   betree_list_push_front_fwd_back
     (self : 't betree_list_t) (x : 't) : 't betree_list_t result =
     let tl = mem_replace_fwd self BetreeListNil in
@@ -157,7 +158,7 @@ val betree_list_push_front_fwd_back_def = Define ‘
 ’
 
 val betree_list_pop_front_fwd_def = Define ‘
-  (** [betree_main::betree::List::{1}::pop_front] *)
+  (** [betree_main::betree::List::{1}::pop_front]: forward function *)
   betree_list_pop_front_fwd (self : 't betree_list_t) : 't result =
     let ls = mem_replace_fwd self BetreeListNil in
     (case ls of
@@ -166,7 +167,7 @@ val betree_list_pop_front_fwd_def = Define ‘
 ’
 
 val betree_list_pop_front_back_def = Define ‘
-  (** [betree_main::betree::List::{1}::pop_front] *)
+  (** [betree_main::betree::List::{1}::pop_front]: backward function 0 *)
   betree_list_pop_front_back
     (self : 't betree_list_t) : 't betree_list_t result =
     let ls = mem_replace_fwd self BetreeListNil in
@@ -176,7 +177,7 @@ val betree_list_pop_front_back_def = Define ‘
 ’
 
 val betree_list_hd_fwd_def = Define ‘
-  (** [betree_main::betree::List::{1}::hd] *)
+  (** [betree_main::betree::List::{1}::hd]: forward function *)
   betree_list_hd_fwd (self : 't betree_list_t) : 't result =
     (case self of
     | BetreeListCons hd l => Return hd
@@ -184,7 +185,7 @@ val betree_list_hd_fwd_def = Define ‘
 ’
 
 val betree_list_head_has_key_fwd_def = Define ‘
-  (** [betree_main::betree::List::{2}::head_has_key] *)
+  (** [betree_main::betree::List::{2}::head_has_key]: forward function *)
   betree_list_head_has_key_fwd
     (self : (u64 # 't) betree_list_t) (key : u64) : bool result =
     (case self of
@@ -193,7 +194,7 @@ val betree_list_head_has_key_fwd_def = Define ‘
 ’
 
 val [betree_list_partition_at_pivot_fwd_def] = DefineDiv ‘
-  (** [betree_main::betree::List::{2}::partition_at_pivot] *)
+  (** [betree_main::betree::List::{2}::partition_at_pivot]: forward function *)
   betree_list_partition_at_pivot_fwd
     (self : (u64 # 't) betree_list_t) (pivot : u64) :
     ((u64 # 't) betree_list_t # (u64 # 't) betree_list_t) result
@@ -214,7 +215,7 @@ val [betree_list_partition_at_pivot_fwd_def] = DefineDiv ‘
 ’
 
 val betree_leaf_split_fwd_def = Define ‘
-  (** [betree_main::betree::Leaf::{3}::split] *)
+  (** [betree_main::betree::Leaf::{3}::split]: forward function *)
   betree_leaf_split_fwd
     (self : betree_leaf_t) (content : (u64 # u64) betree_list_t)
     (params : betree_params_t) (node_id_cnt : betree_node_id_counter_t)
@@ -256,7 +257,7 @@ val betree_leaf_split_fwd_def = Define ‘
 ’
 
 val betree_leaf_split_back_def = Define ‘
-  (** [betree_main::betree::Leaf::{3}::split] *)
+  (** [betree_main::betree::Leaf::{3}::split]: backward function 2 *)
   betree_leaf_split_back
     (self : betree_leaf_t) (content : (u64 # u64) betree_list_t)
     (params : betree_params_t) (node_id_cnt : betree_node_id_counter_t)
@@ -279,7 +280,7 @@ val betree_leaf_split_back_def = Define ‘
 ’
 
 val [betree_node_lookup_in_bindings_fwd_def] = DefineDiv ‘
-  (** [betree_main::betree::Node::{5}::lookup_in_bindings] *)
+  (** [betree_main::betree::Node::{5}::lookup_in_bindings]: forward function *)
   betree_node_lookup_in_bindings_fwd
     (key : u64) (bindings : (u64 # u64) betree_list_t) : u64 option result =
     (case bindings of
@@ -295,7 +296,7 @@ val [betree_node_lookup_in_bindings_fwd_def] = DefineDiv ‘
 ’
 
 val [betree_node_lookup_first_message_for_key_fwd_def] = DefineDiv ‘
-  (** [betree_main::betree::Node::{5}::lookup_first_message_for_key] *)
+  (** [betree_main::betree::Node::{5}::lookup_first_message_for_key]: forward function *)
   betree_node_lookup_first_message_for_key_fwd
     (key : u64) (msgs : (u64 # betree_message_t) betree_list_t) :
     (u64 # betree_message_t) betree_list_t result
@@ -310,7 +311,7 @@ val [betree_node_lookup_first_message_for_key_fwd_def] = DefineDiv ‘
 ’
 
 val [betree_node_lookup_first_message_for_key_back_def] = DefineDiv ‘
-  (** [betree_main::betree::Node::{5}::lookup_first_message_for_key] *)
+  (** [betree_main::betree::Node::{5}::lookup_first_message_for_key]: backward function 0 *)
   betree_node_lookup_first_message_for_key_back
     (key : u64) (msgs : (u64 # betree_message_t) betree_list_t)
     (ret : (u64 # betree_message_t) betree_list_t) :
@@ -331,7 +332,7 @@ val [betree_node_lookup_first_message_for_key_back_def] = DefineDiv ‘
 ’
 
 val [betree_node_apply_upserts_fwd_def] = DefineDiv ‘
-  (** [betree_main::betree::Node::{5}::apply_upserts] *)
+  (** [betree_main::betree::Node::{5}::apply_upserts]: forward function *)
   betree_node_apply_upserts_fwd
     (msgs : (u64 # betree_message_t) betree_list_t) (prev : u64 option)
     (key : u64) (st : state) :
@@ -364,7 +365,7 @@ val [betree_node_apply_upserts_fwd_def] = DefineDiv ‘
 ’
 
 val [betree_node_apply_upserts_back_def] = DefineDiv ‘
-  (** [betree_main::betree::Node::{5}::apply_upserts] *)
+  (** [betree_main::betree::Node::{5}::apply_upserts]: backward function 0 *)
   betree_node_apply_upserts_back
     (msgs : (u64 # betree_message_t) betree_list_t) (prev : u64 option)
     (key : u64) (st : state) :
@@ -396,7 +397,7 @@ val [betree_node_apply_upserts_back_def] = DefineDiv ‘
 ’
 
 val [betree_node_lookup_fwd_def, betree_node_lookup_back_def, betree_internal_lookup_in_children_fwd_def, betree_internal_lookup_in_children_back_def] = DefineDiv ‘
-  (** [betree_main::betree::Node::{5}::lookup] *)
+  (** [betree_main::betree::Node::{5}::lookup]: forward function *)
   (betree_node_lookup_fwd
      (self : betree_node_t) (key : u64) (st : state) :
      (state # u64 option) result
@@ -466,7 +467,7 @@ val [betree_node_lookup_fwd_def, betree_node_lookup_back_def, betree_internal_lo
       od))
   /\
   
-  (** [betree_main::betree::Node::{5}::lookup] *)
+  (** [betree_main::betree::Node::{5}::lookup]: backward function 0 *)
   (betree_node_lookup_back
      (self : betree_node_t) (key : u64) (st : state) : betree_node_t result =
     (case self of
@@ -534,7 +535,7 @@ val [betree_node_lookup_fwd_def, betree_node_lookup_back_def, betree_internal_lo
       od))
   /\
   
-  (** [betree_main::betree::Internal::{4}::lookup_in_children] *)
+  (** [betree_main::betree::Internal::{4}::lookup_in_children]: forward function *)
   (betree_internal_lookup_in_children_fwd
      (self : betree_internal_t) (key : u64) (st : state) :
      (state # u64 option) result
@@ -544,7 +545,7 @@ val [betree_node_lookup_fwd_def, betree_node_lookup_back_def, betree_internal_lo
     else betree_node_lookup_fwd self.betree_internal_right key st)
   /\
   
-  (** [betree_main::betree::Internal::{4}::lookup_in_children] *)
+  (** [betree_main::betree::Internal::{4}::lookup_in_children]: backward function 0 *)
   betree_internal_lookup_in_children_back
     (self : betree_internal_t) (key : u64) (st : state) :
     betree_internal_t result
@@ -563,7 +564,7 @@ val [betree_node_lookup_fwd_def, betree_node_lookup_back_def, betree_internal_lo
 ’
 
 val [betree_node_lookup_mut_in_bindings_fwd_def] = DefineDiv ‘
-  (** [betree_main::betree::Node::{5}::lookup_mut_in_bindings] *)
+  (** [betree_main::betree::Node::{5}::lookup_mut_in_bindings]: forward function *)
   betree_node_lookup_mut_in_bindings_fwd
     (key : u64) (bindings : (u64 # u64) betree_list_t) :
     (u64 # u64) betree_list_t result
@@ -578,7 +579,7 @@ val [betree_node_lookup_mut_in_bindings_fwd_def] = DefineDiv ‘
 ’
 
 val [betree_node_lookup_mut_in_bindings_back_def] = DefineDiv ‘
-  (** [betree_main::betree::Node::{5}::lookup_mut_in_bindings] *)
+  (** [betree_main::betree::Node::{5}::lookup_mut_in_bindings]: backward function 0 *)
   betree_node_lookup_mut_in_bindings_back
     (key : u64) (bindings : (u64 # u64) betree_list_t)
     (ret : (u64 # u64) betree_list_t) :
@@ -598,7 +599,8 @@ val [betree_node_lookup_mut_in_bindings_back_def] = DefineDiv ‘
 ’
 
 val betree_node_apply_to_leaf_fwd_back_def = Define ‘
-  (** [betree_main::betree::Node::{5}::apply_to_leaf] *)
+  (** [betree_main::betree::Node::{5}::apply_to_leaf]: merged forward/backward function
+      (there is a single backward function, and the forward function returns ()) *)
   betree_node_apply_to_leaf_fwd_back
     (bindings : (u64 # u64) betree_list_t) (key : u64)
     (new_msg : betree_message_t) :
@@ -651,7 +653,8 @@ val betree_node_apply_to_leaf_fwd_back_def = Define ‘
 ’
 
 val [betree_node_apply_messages_to_leaf_fwd_back_def] = DefineDiv ‘
-  (** [betree_main::betree::Node::{5}::apply_messages_to_leaf] *)
+  (** [betree_main::betree::Node::{5}::apply_messages_to_leaf]: merged forward/backward function
+      (there is a single backward function, and the forward function returns ()) *)
   betree_node_apply_messages_to_leaf_fwd_back
     (bindings : (u64 # u64) betree_list_t)
     (new_msgs : (u64 # betree_message_t) betree_list_t) :
@@ -668,7 +671,8 @@ val [betree_node_apply_messages_to_leaf_fwd_back_def] = DefineDiv ‘
 ’
 
 val [betree_node_filter_messages_for_key_fwd_back_def] = DefineDiv ‘
-  (** [betree_main::betree::Node::{5}::filter_messages_for_key] *)
+  (** [betree_main::betree::Node::{5}::filter_messages_for_key]: merged forward/backward function
+      (there is a single backward function, and the forward function returns ()) *)
   betree_node_filter_messages_for_key_fwd_back
     (key : u64) (msgs : (u64 # betree_message_t) betree_list_t) :
     (u64 # betree_message_t) betree_list_t result
@@ -687,7 +691,7 @@ val [betree_node_filter_messages_for_key_fwd_back_def] = DefineDiv ‘
 ’
 
 val [betree_node_lookup_first_message_after_key_fwd_def] = DefineDiv ‘
-  (** [betree_main::betree::Node::{5}::lookup_first_message_after_key] *)
+  (** [betree_main::betree::Node::{5}::lookup_first_message_after_key]: forward function *)
   betree_node_lookup_first_message_after_key_fwd
     (key : u64) (msgs : (u64 # betree_message_t) betree_list_t) :
     (u64 # betree_message_t) betree_list_t result
@@ -702,7 +706,7 @@ val [betree_node_lookup_first_message_after_key_fwd_def] = DefineDiv ‘
 ’
 
 val [betree_node_lookup_first_message_after_key_back_def] = DefineDiv ‘
-  (** [betree_main::betree::Node::{5}::lookup_first_message_after_key] *)
+  (** [betree_main::betree::Node::{5}::lookup_first_message_after_key]: backward function 0 *)
   betree_node_lookup_first_message_after_key_back
     (key : u64) (msgs : (u64 # betree_message_t) betree_list_t)
     (ret : (u64 # betree_message_t) betree_list_t) :
@@ -723,7 +727,8 @@ val [betree_node_lookup_first_message_after_key_back_def] = DefineDiv ‘
 ’
 
 val betree_node_apply_to_internal_fwd_back_def = Define ‘
-  (** [betree_main::betree::Node::{5}::apply_to_internal] *)
+  (** [betree_main::betree::Node::{5}::apply_to_internal]: merged forward/backward function
+      (there is a single backward function, and the forward function returns ()) *)
   betree_node_apply_to_internal_fwd_back
     (msgs : (u64 # betree_message_t) betree_list_t) (key : u64)
     (new_msg : betree_message_t) :
@@ -789,7 +794,8 @@ val betree_node_apply_to_internal_fwd_back_def = Define ‘
 ’
 
 val [betree_node_apply_messages_to_internal_fwd_back_def] = DefineDiv ‘
-  (** [betree_main::betree::Node::{5}::apply_messages_to_internal] *)
+  (** [betree_main::betree::Node::{5}::apply_messages_to_internal]: merged forward/backward function
+      (there is a single backward function, and the forward function returns ()) *)
   betree_node_apply_messages_to_internal_fwd_back
     (msgs : (u64 # betree_message_t) betree_list_t)
     (new_msgs : (u64 # betree_message_t) betree_list_t) :
@@ -806,7 +812,7 @@ val [betree_node_apply_messages_to_internal_fwd_back_def] = DefineDiv ‘
 ’
 
 val [betree_node_apply_messages_fwd_def, betree_node_apply_messages_back_def, betree_internal_flush_fwd_def, betree_internal_flush_back_def] = DefineDiv ‘
-  (** [betree_main::betree::Node::{5}::apply_messages] *)
+  (** [betree_main::betree::Node::{5}::apply_messages]: forward function *)
   (betree_node_apply_messages_fwd
      (self : betree_node_t) (params : betree_params_t)
      (node_id_cnt : betree_node_id_counter_t)
@@ -861,7 +867,7 @@ val [betree_node_apply_messages_fwd_def, betree_node_apply_messages_back_def, be
       od))
   /\
   
-  (** [betree_main::betree::Node::{5}::apply_messages] *)
+  (** [betree_main::betree::Node::{5}::apply_messages]: backward function 0 *)
   (betree_node_apply_messages_back
      (self : betree_node_t) (params : betree_params_t)
      (node_id_cnt : betree_node_id_counter_t)
@@ -918,7 +924,7 @@ val [betree_node_apply_messages_fwd_def, betree_node_apply_messages_back_def, be
       od))
   /\
   
-  (** [betree_main::betree::Internal::{4}::flush] *)
+  (** [betree_main::betree::Internal::{4}::flush]: forward function *)
   (betree_internal_flush_fwd
      (self : betree_internal_t) (params : betree_params_t)
      (node_id_cnt : betree_node_id_counter_t)
@@ -967,7 +973,7 @@ val [betree_node_apply_messages_fwd_def, betree_node_apply_messages_back_def, be
     od)
   /\
   
-  (** [betree_main::betree::Internal::{4}::flush] *)
+  (** [betree_main::betree::Internal::{4}::flush]: backward function 0 *)
   betree_internal_flush_back
     (self : betree_internal_t) (params : betree_params_t)
     (node_id_cnt : betree_node_id_counter_t)
@@ -1016,7 +1022,7 @@ val [betree_node_apply_messages_fwd_def, betree_node_apply_messages_back_def, be
 ’
 
 val betree_node_apply_fwd_def = Define ‘
-  (** [betree_main::betree::Node::{5}::apply] *)
+  (** [betree_main::betree::Node::{5}::apply]: forward function *)
   betree_node_apply_fwd
     (self : betree_node_t) (params : betree_params_t)
     (node_id_cnt : betree_node_id_counter_t) (key : u64)
@@ -1036,7 +1042,7 @@ val betree_node_apply_fwd_def = Define ‘
 ’
 
 val betree_node_apply_back_def = Define ‘
-  (** [betree_main::betree::Node::{5}::apply] *)
+  (** [betree_main::betree::Node::{5}::apply]: backward function 0 *)
   betree_node_apply_back
     (self : betree_node_t) (params : betree_params_t)
     (node_id_cnt : betree_node_id_counter_t) (key : u64)
@@ -1049,7 +1055,7 @@ val betree_node_apply_back_def = Define ‘
 ’
 
 val betree_be_tree_new_fwd_def = Define ‘
-  (** [betree_main::betree::BeTree::{6}::new] *)
+  (** [betree_main::betree::BeTree::{6}::new]: forward function *)
   betree_be_tree_new_fwd
     (min_flush_size : u64) (split_size : u64) (st : state) :
     (state # betree_be_tree_t) result
@@ -1075,7 +1081,7 @@ val betree_be_tree_new_fwd_def = Define ‘
 ’
 
 val betree_be_tree_apply_fwd_def = Define ‘
-  (** [betree_main::betree::BeTree::{6}::apply] *)
+  (** [betree_main::betree::BeTree::{6}::apply]: forward function *)
   betree_be_tree_apply_fwd
     (self : betree_be_tree_t) (key : u64) (msg : betree_message_t) (st : state)
     :
@@ -1093,7 +1099,7 @@ val betree_be_tree_apply_fwd_def = Define ‘
 ’
 
 val betree_be_tree_apply_back_def = Define ‘
-  (** [betree_main::betree::BeTree::{6}::apply] *)
+  (** [betree_main::betree::BeTree::{6}::apply]: backward function 0 *)
   betree_be_tree_apply_back
     (self : betree_be_tree_t) (key : u64) (msg : betree_message_t) (st : state)
     :
@@ -1113,7 +1119,7 @@ val betree_be_tree_apply_back_def = Define ‘
 ’
 
 val betree_be_tree_insert_fwd_def = Define ‘
-  (** [betree_main::betree::BeTree::{6}::insert] *)
+  (** [betree_main::betree::BeTree::{6}::insert]: forward function *)
   betree_be_tree_insert_fwd
     (self : betree_be_tree_t) (key : u64) (value : u64) (st : state) :
     (state # unit) result
@@ -1127,7 +1133,7 @@ val betree_be_tree_insert_fwd_def = Define ‘
 ’
 
 val betree_be_tree_insert_back_def = Define ‘
-  (** [betree_main::betree::BeTree::{6}::insert] *)
+  (** [betree_main::betree::BeTree::{6}::insert]: backward function 0 *)
   betree_be_tree_insert_back
     (self : betree_be_tree_t) (key : u64) (value : u64) (st : state) :
     betree_be_tree_t result
@@ -1136,7 +1142,7 @@ val betree_be_tree_insert_back_def = Define ‘
 ’
 
 val betree_be_tree_delete_fwd_def = Define ‘
-  (** [betree_main::betree::BeTree::{6}::delete] *)
+  (** [betree_main::betree::BeTree::{6}::delete]: forward function *)
   betree_be_tree_delete_fwd
     (self : betree_be_tree_t) (key : u64) (st : state) :
     (state # unit) result
@@ -1149,7 +1155,7 @@ val betree_be_tree_delete_fwd_def = Define ‘
 ’
 
 val betree_be_tree_delete_back_def = Define ‘
-  (** [betree_main::betree::BeTree::{6}::delete] *)
+  (** [betree_main::betree::BeTree::{6}::delete]: backward function 0 *)
   betree_be_tree_delete_back
     (self : betree_be_tree_t) (key : u64) (st : state) :
     betree_be_tree_t result
@@ -1158,7 +1164,7 @@ val betree_be_tree_delete_back_def = Define ‘
 ’
 
 val betree_be_tree_upsert_fwd_def = Define ‘
-  (** [betree_main::betree::BeTree::{6}::upsert] *)
+  (** [betree_main::betree::BeTree::{6}::upsert]: forward function *)
   betree_be_tree_upsert_fwd
     (self : betree_be_tree_t) (key : u64) (upd : betree_upsert_fun_state_t)
     (st : state) :
@@ -1172,7 +1178,7 @@ val betree_be_tree_upsert_fwd_def = Define ‘
 ’
 
 val betree_be_tree_upsert_back_def = Define ‘
-  (** [betree_main::betree::BeTree::{6}::upsert] *)
+  (** [betree_main::betree::BeTree::{6}::upsert]: backward function 0 *)
   betree_be_tree_upsert_back
     (self : betree_be_tree_t) (key : u64) (upd : betree_upsert_fun_state_t)
     (st : state) :
@@ -1182,7 +1188,7 @@ val betree_be_tree_upsert_back_def = Define ‘
 ’
 
 val betree_be_tree_lookup_fwd_def = Define ‘
-  (** [betree_main::betree::BeTree::{6}::lookup] *)
+  (** [betree_main::betree::BeTree::{6}::lookup]: forward function *)
   betree_be_tree_lookup_fwd
     (self : betree_be_tree_t) (key : u64) (st : state) :
     (state # u64 option) result
@@ -1191,7 +1197,7 @@ val betree_be_tree_lookup_fwd_def = Define ‘
 ’
 
 val betree_be_tree_lookup_back_def = Define ‘
-  (** [betree_main::betree::BeTree::{6}::lookup] *)
+  (** [betree_main::betree::BeTree::{6}::lookup]: backward function 0 *)
   betree_be_tree_lookup_back
     (self : betree_be_tree_t) (key : u64) (st : state) :
     betree_be_tree_t result
@@ -1203,7 +1209,7 @@ val betree_be_tree_lookup_back_def = Define ‘
 ’
 
 val main_fwd_def = Define ‘
-  (** [betree_main::main] *)
+  (** [betree_main::main]: forward function *)
   main_fwd : unit result =
     Return ()
 ’
diff --git a/tests/hol4/betree/betreeMain_OpaqueScript.sml b/tests/hol4/betree/betreeMain_OpaqueScript.sml
index a6f0cf15..1d16db4c 100644
--- a/tests/hol4/betree/betreeMain_OpaqueScript.sml
+++ b/tests/hol4/betree/betreeMain_OpaqueScript.sml
@@ -1,26 +1,26 @@
 (** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
-(** [betree_main]: opaque function definitions *)
+(** [betree_main]: external function declarations *)
 open primitivesLib divDefLib
 open betreeMain_TypesTheory
 
 val _ = new_theory "betreeMain_Opaque"
 
 
-val _ = new_constant ("betree_utils_load_internal_node_fwd",
+(** [betree_main::betree_utils::load_internal_node]: forward function *)val _ = new_constant ("betree_utils_load_internal_node_fwd",
   “:u64 -> state -> (state # (u64 # betree_message_t) betree_list_t)
   result”)
 
-val _ = new_constant ("betree_utils_store_internal_node_fwd",
+(** [betree_main::betree_utils::store_internal_node]: forward function *)val _ = new_constant ("betree_utils_store_internal_node_fwd",
   “:u64 -> (u64 # betree_message_t) betree_list_t -> state -> (state # unit)
   result”)
 
-val _ = new_constant ("betree_utils_load_leaf_node_fwd",
+(** [betree_main::betree_utils::load_leaf_node]: forward function *)val _ = new_constant ("betree_utils_load_leaf_node_fwd",
   “:u64 -> state -> (state # (u64 # u64) betree_list_t) result”)
 
-val _ = new_constant ("betree_utils_store_leaf_node_fwd",
+(** [betree_main::betree_utils::store_leaf_node]: forward function *)val _ = new_constant ("betree_utils_store_leaf_node_fwd",
   “:u64 -> (u64 # u64) betree_list_t -> state -> (state # unit) result”)
 
-val _ = new_constant ("core_option_option_unwrap_fwd",
+(** [core::option::Option::{0}::unwrap]: forward function *)val _ = new_constant ("core_option_option_unwrap_fwd",
   “:'t option -> state -> (state # 't) result”)
 
 val _ = export_theory ()
diff --git a/tests/hol4/hashmap/hashmap_FunsScript.sml b/tests/hol4/hashmap/hashmap_FunsScript.sml
index 9ad497f5..1ed57080 100644
--- a/tests/hol4/hashmap/hashmap_FunsScript.sml
+++ b/tests/hol4/hashmap/hashmap_FunsScript.sml
@@ -7,13 +7,13 @@ val _ = new_theory "hashmap_Funs"
 
 
 val hash_key_fwd_def = Define ‘
-  (** [hashmap::hash_key] *)
+  (** [hashmap::hash_key]: forward function *)
   hash_key_fwd (k : usize) : usize result =
     Return k
 ’
 
 val [hash_map_allocate_slots_loop_fwd_def] = DefineDiv ‘
-  (** [hashmap::HashMap::{0}::allocate_slots] *)
+  (** [hashmap::HashMap::{0}::allocate_slots]: loop 0: forward function *)
   hash_map_allocate_slots_loop_fwd
     (slots : 't list_t vec) (n : usize) : 't list_t vec result =
     if usize_gt n (int_to_usize 0)
@@ -27,14 +27,14 @@ val [hash_map_allocate_slots_loop_fwd_def] = DefineDiv ‘
 ’
 
 val hash_map_allocate_slots_fwd_def = Define ‘
-  (** [hashmap::HashMap::{0}::allocate_slots] *)
+  (** [hashmap::HashMap::{0}::allocate_slots]: forward function *)
   hash_map_allocate_slots_fwd
     (slots : 't list_t vec) (n : usize) : 't list_t vec result =
     hash_map_allocate_slots_loop_fwd slots n
 ’
 
 val hash_map_new_with_capacity_fwd_def = Define ‘
-  (** [hashmap::HashMap::{0}::new_with_capacity] *)
+  (** [hashmap::HashMap::{0}::new_with_capacity]: forward function *)
   hash_map_new_with_capacity_fwd
     (capacity : usize) (max_load_dividend : usize) (max_load_divisor : usize) :
     't hash_map_t result
@@ -55,14 +55,15 @@ val hash_map_new_with_capacity_fwd_def = Define ‘
 ’
 
 val hash_map_new_fwd_def = Define ‘
-  (** [hashmap::HashMap::{0}::new] *)
+  (** [hashmap::HashMap::{0}::new]: forward function *)
   hash_map_new_fwd : 't hash_map_t result =
     hash_map_new_with_capacity_fwd (int_to_usize 32) (int_to_usize 4)
       (int_to_usize 5)
 ’
 
 val [hash_map_clear_loop_fwd_back_def] = DefineDiv ‘
-  (** [hashmap::HashMap::{0}::clear] *)
+  (** [hashmap::HashMap::{0}::clear]: loop 0: merged forward/backward function
+      (there is a single backward function, and the forward function returns ()) *)
   hash_map_clear_loop_fwd_back
     (slots : 't list_t vec) (i : usize) : 't list_t vec result =
     let i0 = vec_len slots in
@@ -77,7 +78,8 @@ val [hash_map_clear_loop_fwd_back_def] = DefineDiv ‘
 ’
 
 val hash_map_clear_fwd_back_def = Define ‘
-  (** [hashmap::HashMap::{0}::clear] *)
+  (** [hashmap::HashMap::{0}::clear]: merged forward/backward function
+      (there is a single backward function, and the forward function returns ()) *)
   hash_map_clear_fwd_back (self : 't hash_map_t) : 't hash_map_t result =
     do
     v <- hash_map_clear_loop_fwd_back self.hash_map_slots (int_to_usize 0);
@@ -91,13 +93,13 @@ val hash_map_clear_fwd_back_def = Define ‘
 ’
 
 val hash_map_len_fwd_def = Define ‘
-  (** [hashmap::HashMap::{0}::len] *)
+  (** [hashmap::HashMap::{0}::len]: forward function *)
   hash_map_len_fwd (self : 't hash_map_t) : usize result =
     Return self.hash_map_num_entries
 ’
 
 val [hash_map_insert_in_list_loop_fwd_def] = DefineDiv ‘
-  (** [hashmap::HashMap::{0}::insert_in_list] *)
+  (** [hashmap::HashMap::{0}::insert_in_list]: loop 0: forward function *)
   hash_map_insert_in_list_loop_fwd
     (key : usize) (value : 't) (ls : 't list_t) : bool result =
     (case ls of
@@ -109,14 +111,14 @@ val [hash_map_insert_in_list_loop_fwd_def] = DefineDiv ‘
 ’
 
 val hash_map_insert_in_list_fwd_def = Define ‘
-  (** [hashmap::HashMap::{0}::insert_in_list] *)
+  (** [hashmap::HashMap::{0}::insert_in_list]: forward function *)
   hash_map_insert_in_list_fwd
     (key : usize) (value : 't) (ls : 't list_t) : bool result =
     hash_map_insert_in_list_loop_fwd key value ls
 ’
 
 val [hash_map_insert_in_list_loop_back_def] = DefineDiv ‘
-  (** [hashmap::HashMap::{0}::insert_in_list] *)
+  (** [hashmap::HashMap::{0}::insert_in_list]: loop 0: backward function 0 *)
   hash_map_insert_in_list_loop_back
     (key : usize) (value : 't) (ls : 't list_t) : 't list_t result =
     (case ls of
@@ -132,14 +134,15 @@ val [hash_map_insert_in_list_loop_back_def] = DefineDiv ‘
 ’
 
 val hash_map_insert_in_list_back_def = Define ‘
-  (** [hashmap::HashMap::{0}::insert_in_list] *)
+  (** [hashmap::HashMap::{0}::insert_in_list]: backward function 0 *)
   hash_map_insert_in_list_back
     (key : usize) (value : 't) (ls : 't list_t) : 't list_t result =
     hash_map_insert_in_list_loop_back key value ls
 ’
 
 val hash_map_insert_no_resize_fwd_back_def = Define ‘
-  (** [hashmap::HashMap::{0}::insert_no_resize] *)
+  (** [hashmap::HashMap::{0}::insert_no_resize]: merged forward/backward function
+      (there is a single backward function, and the forward function returns ()) *)
   hash_map_insert_no_resize_fwd_back
     (self : 't hash_map_t) (key : usize) (value : 't) : 't hash_map_t result =
     do
@@ -176,7 +179,8 @@ Definition core_num_u32_max_c_def:
 End
 
 val [hash_map_move_elements_from_list_loop_fwd_back_def] = DefineDiv ‘
-  (** [hashmap::HashMap::{0}::move_elements_from_list] *)
+  (** [hashmap::HashMap::{0}::move_elements_from_list]: loop 0: merged forward/backward function
+      (there is a single backward function, and the forward function returns ()) *)
   hash_map_move_elements_from_list_loop_fwd_back
     (ntable : 't hash_map_t) (ls : 't list_t) : 't hash_map_t result =
     (case ls of
@@ -189,14 +193,16 @@ val [hash_map_move_elements_from_list_loop_fwd_back_def] = DefineDiv ‘
 ’
 
 val hash_map_move_elements_from_list_fwd_back_def = Define ‘
-  (** [hashmap::HashMap::{0}::move_elements_from_list] *)
+  (** [hashmap::HashMap::{0}::move_elements_from_list]: merged forward/backward function
+      (there is a single backward function, and the forward function returns ()) *)
   hash_map_move_elements_from_list_fwd_back
     (ntable : 't hash_map_t) (ls : 't list_t) : 't hash_map_t result =
     hash_map_move_elements_from_list_loop_fwd_back ntable ls
 ’
 
 val [hash_map_move_elements_loop_fwd_back_def] = DefineDiv ‘
-  (** [hashmap::HashMap::{0}::move_elements] *)
+  (** [hashmap::HashMap::{0}::move_elements]: loop 0: merged forward/backward function
+      (there is a single backward function, and the forward function returns ()) *)
   hash_map_move_elements_loop_fwd_back
     (ntable : 't hash_map_t) (slots : 't list_t vec) (i : usize) :
     ('t hash_map_t # 't list_t vec) result
@@ -221,7 +227,8 @@ val [hash_map_move_elements_loop_fwd_back_def] = DefineDiv ‘
 ’
 
 val hash_map_move_elements_fwd_back_def = Define ‘
-  (** [hashmap::HashMap::{0}::move_elements] *)
+  (** [hashmap::HashMap::{0}::move_elements]: merged forward/backward function
+      (there is a single backward function, and the forward function returns ()) *)
   hash_map_move_elements_fwd_back
     (ntable : 't hash_map_t) (slots : 't list_t vec) (i : usize) :
     ('t hash_map_t # 't list_t vec) result
@@ -230,7 +237,8 @@ val hash_map_move_elements_fwd_back_def = Define ‘
 ’
 
 val hash_map_try_resize_fwd_back_def = Define ‘
-  (** [hashmap::HashMap::{0}::try_resize] *)
+  (** [hashmap::HashMap::{0}::try_resize]: merged forward/backward function
+      (there is a single backward function, and the forward function returns ()) *)
   hash_map_try_resize_fwd_back (self : 't hash_map_t) : 't hash_map_t result =
     do
     max_usize <- mk_usize (u32_to_int core_num_u32_max_c);
@@ -263,7 +271,8 @@ val hash_map_try_resize_fwd_back_def = Define ‘
 ’
 
 val hash_map_insert_fwd_back_def = Define ‘
-  (** [hashmap::HashMap::{0}::insert] *)
+  (** [hashmap::HashMap::{0}::insert]: merged forward/backward function
+      (there is a single backward function, and the forward function returns ()) *)
   hash_map_insert_fwd_back
     (self : 't hash_map_t) (key : usize) (value : 't) : 't hash_map_t result =
     do
@@ -276,7 +285,7 @@ val hash_map_insert_fwd_back_def = Define ‘
 ’
 
 val [hash_map_contains_key_in_list_loop_fwd_def] = DefineDiv ‘
-  (** [hashmap::HashMap::{0}::contains_key_in_list] *)
+  (** [hashmap::HashMap::{0}::contains_key_in_list]: loop 0: forward function *)
   hash_map_contains_key_in_list_loop_fwd
     (key : usize) (ls : 't list_t) : bool result =
     (case ls of
@@ -288,14 +297,14 @@ val [hash_map_contains_key_in_list_loop_fwd_def] = DefineDiv ‘
 ’
 
 val hash_map_contains_key_in_list_fwd_def = Define ‘
-  (** [hashmap::HashMap::{0}::contains_key_in_list] *)
+  (** [hashmap::HashMap::{0}::contains_key_in_list]: forward function *)
   hash_map_contains_key_in_list_fwd
     (key : usize) (ls : 't list_t) : bool result =
     hash_map_contains_key_in_list_loop_fwd key ls
 ’
 
 val hash_map_contains_key_fwd_def = Define ‘
-  (** [hashmap::HashMap::{0}::contains_key] *)
+  (** [hashmap::HashMap::{0}::contains_key]: forward function *)
   hash_map_contains_key_fwd
     (self : 't hash_map_t) (key : usize) : bool result =
     do
@@ -310,7 +319,7 @@ val hash_map_contains_key_fwd_def = Define ‘
 ’
 
 val [hash_map_get_in_list_loop_fwd_def] = DefineDiv ‘
-  (** [hashmap::HashMap::{0}::get_in_list] *)
+  (** [hashmap::HashMap::{0}::get_in_list]: loop 0: forward function *)
   hash_map_get_in_list_loop_fwd (key : usize) (ls : 't list_t) : 't result =
     (case ls of
     | ListCons ckey cvalue tl =>
@@ -321,13 +330,13 @@ val [hash_map_get_in_list_loop_fwd_def] = DefineDiv ‘
 ’
 
 val hash_map_get_in_list_fwd_def = Define ‘
-  (** [hashmap::HashMap::{0}::get_in_list] *)
+  (** [hashmap::HashMap::{0}::get_in_list]: forward function *)
   hash_map_get_in_list_fwd (key : usize) (ls : 't list_t) : 't result =
     hash_map_get_in_list_loop_fwd key ls
 ’
 
 val hash_map_get_fwd_def = Define ‘
-  (** [hashmap::HashMap::{0}::get] *)
+  (** [hashmap::HashMap::{0}::get]: forward function *)
   hash_map_get_fwd (self : 't hash_map_t) (key : usize) : 't result =
     do
     hash <- hash_key_fwd key;
@@ -341,7 +350,7 @@ val hash_map_get_fwd_def = Define ‘
 ’
 
 val [hash_map_get_mut_in_list_loop_fwd_def] = DefineDiv ‘
-  (** [hashmap::HashMap::{0}::get_mut_in_list] *)
+  (** [hashmap::HashMap::{0}::get_mut_in_list]: loop 0: forward function *)
   hash_map_get_mut_in_list_loop_fwd
     (ls : 't list_t) (key : usize) : 't result =
     (case ls of
@@ -353,13 +362,13 @@ val [hash_map_get_mut_in_list_loop_fwd_def] = DefineDiv ‘
 ’
 
 val hash_map_get_mut_in_list_fwd_def = Define ‘
-  (** [hashmap::HashMap::{0}::get_mut_in_list] *)
+  (** [hashmap::HashMap::{0}::get_mut_in_list]: forward function *)
   hash_map_get_mut_in_list_fwd (ls : 't list_t) (key : usize) : 't result =
     hash_map_get_mut_in_list_loop_fwd ls key
 ’
 
 val [hash_map_get_mut_in_list_loop_back_def] = DefineDiv ‘
-  (** [hashmap::HashMap::{0}::get_mut_in_list] *)
+  (** [hashmap::HashMap::{0}::get_mut_in_list]: loop 0: backward function 0 *)
   hash_map_get_mut_in_list_loop_back
     (ls : 't list_t) (key : usize) (ret : 't) : 't list_t result =
     (case ls of
@@ -375,14 +384,14 @@ val [hash_map_get_mut_in_list_loop_back_def] = DefineDiv ‘
 ’
 
 val hash_map_get_mut_in_list_back_def = Define ‘
-  (** [hashmap::HashMap::{0}::get_mut_in_list] *)
+  (** [hashmap::HashMap::{0}::get_mut_in_list]: backward function 0 *)
   hash_map_get_mut_in_list_back
     (ls : 't list_t) (key : usize) (ret : 't) : 't list_t result =
     hash_map_get_mut_in_list_loop_back ls key ret
 ’
 
 val hash_map_get_mut_fwd_def = Define ‘
-  (** [hashmap::HashMap::{0}::get_mut] *)
+  (** [hashmap::HashMap::{0}::get_mut]: forward function *)
   hash_map_get_mut_fwd (self : 't hash_map_t) (key : usize) : 't result =
     do
     hash <- hash_key_fwd key;
@@ -396,7 +405,7 @@ val hash_map_get_mut_fwd_def = Define ‘
 ’
 
 val hash_map_get_mut_back_def = Define ‘
-  (** [hashmap::HashMap::{0}::get_mut] *)
+  (** [hashmap::HashMap::{0}::get_mut]: backward function 0 *)
   hash_map_get_mut_back
     (self : 't hash_map_t) (key : usize) (ret : 't) : 't hash_map_t result =
     do
@@ -413,7 +422,7 @@ val hash_map_get_mut_back_def = Define ‘
 ’
 
 val [hash_map_remove_from_list_loop_fwd_def] = DefineDiv ‘
-  (** [hashmap::HashMap::{0}::remove_from_list] *)
+  (** [hashmap::HashMap::{0}::remove_from_list]: loop 0: forward function *)
   hash_map_remove_from_list_loop_fwd
     (key : usize) (ls : 't list_t) : 't option result =
     (case ls of
@@ -429,14 +438,14 @@ val [hash_map_remove_from_list_loop_fwd_def] = DefineDiv ‘
 ’
 
 val hash_map_remove_from_list_fwd_def = Define ‘
-  (** [hashmap::HashMap::{0}::remove_from_list] *)
+  (** [hashmap::HashMap::{0}::remove_from_list]: forward function *)
   hash_map_remove_from_list_fwd
     (key : usize) (ls : 't list_t) : 't option result =
     hash_map_remove_from_list_loop_fwd key ls
 ’
 
 val [hash_map_remove_from_list_loop_back_def] = DefineDiv ‘
-  (** [hashmap::HashMap::{0}::remove_from_list] *)
+  (** [hashmap::HashMap::{0}::remove_from_list]: loop 0: backward function 1 *)
   hash_map_remove_from_list_loop_back
     (key : usize) (ls : 't list_t) : 't list_t result =
     (case ls of
@@ -456,14 +465,14 @@ val [hash_map_remove_from_list_loop_back_def] = DefineDiv ‘
 ’
 
 val hash_map_remove_from_list_back_def = Define ‘
-  (** [hashmap::HashMap::{0}::remove_from_list] *)
+  (** [hashmap::HashMap::{0}::remove_from_list]: backward function 1 *)
   hash_map_remove_from_list_back
     (key : usize) (ls : 't list_t) : 't list_t result =
     hash_map_remove_from_list_loop_back key ls
 ’
 
 val hash_map_remove_fwd_def = Define ‘
-  (** [hashmap::HashMap::{0}::remove] *)
+  (** [hashmap::HashMap::{0}::remove]: forward function *)
   hash_map_remove_fwd (self : 't hash_map_t) (key : usize) : 't option result =
     do
     hash <- hash_key_fwd key;
@@ -484,7 +493,7 @@ val hash_map_remove_fwd_def = Define ‘
 ’
 
 val hash_map_remove_back_def = Define ‘
-  (** [hashmap::HashMap::{0}::remove] *)
+  (** [hashmap::HashMap::{0}::remove]: backward function 0 *)
   hash_map_remove_back
     (self : 't hash_map_t) (key : usize) : 't hash_map_t result =
     do
@@ -513,7 +522,7 @@ val hash_map_remove_back_def = Define ‘
 ’
 
 val test1_fwd_def = Define ‘
-  (** [hashmap::test1] *)
+  (** [hashmap::test1]: forward function *)
   test1_fwd : unit result =
     do
     hm <- hash_map_new_fwd;
diff --git a/tests/hol4/hashmap_on_disk/hashmapMain_FunsScript.sml b/tests/hol4/hashmap_on_disk/hashmapMain_FunsScript.sml
index 5a8f7ff8..6ec6223d 100644
--- a/tests/hol4/hashmap_on_disk/hashmapMain_FunsScript.sml
+++ b/tests/hol4/hashmap_on_disk/hashmapMain_FunsScript.sml
@@ -7,13 +7,13 @@ val _ = new_theory "hashmapMain_Funs"
 
 
 val hashmap_hash_key_fwd_def = Define ‘
-  (** [hashmap_main::hashmap::hash_key] *)
+  (** [hashmap_main::hashmap::hash_key]: forward function *)
   hashmap_hash_key_fwd (k : usize) : usize result =
     Return k
 ’
 
 val [hashmap_hash_map_allocate_slots_loop_fwd_def] = DefineDiv ‘
-  (** [hashmap_main::hashmap::HashMap::{0}::allocate_slots] *)
+  (** [hashmap_main::hashmap::HashMap::{0}::allocate_slots]: loop 0: forward function *)
   hashmap_hash_map_allocate_slots_loop_fwd
     (slots : 't hashmap_list_t vec) (n : usize) :
     't hashmap_list_t vec result
@@ -29,7 +29,7 @@ val [hashmap_hash_map_allocate_slots_loop_fwd_def] = DefineDiv ‘
 ’
 
 val hashmap_hash_map_allocate_slots_fwd_def = Define ‘
-  (** [hashmap_main::hashmap::HashMap::{0}::allocate_slots] *)
+  (** [hashmap_main::hashmap::HashMap::{0}::allocate_slots]: forward function *)
   hashmap_hash_map_allocate_slots_fwd
     (slots : 't hashmap_list_t vec) (n : usize) :
     't hashmap_list_t vec result
@@ -38,7 +38,7 @@ val hashmap_hash_map_allocate_slots_fwd_def = Define ‘
 ’
 
 val hashmap_hash_map_new_with_capacity_fwd_def = Define ‘
-  (** [hashmap_main::hashmap::HashMap::{0}::new_with_capacity] *)
+  (** [hashmap_main::hashmap::HashMap::{0}::new_with_capacity]: forward function *)
   hashmap_hash_map_new_with_capacity_fwd
     (capacity : usize) (max_load_dividend : usize) (max_load_divisor : usize) :
     't hashmap_hash_map_t result
@@ -60,14 +60,15 @@ val hashmap_hash_map_new_with_capacity_fwd_def = Define ‘
 ’
 
 val hashmap_hash_map_new_fwd_def = Define ‘
-  (** [hashmap_main::hashmap::HashMap::{0}::new] *)
+  (** [hashmap_main::hashmap::HashMap::{0}::new]: forward function *)
   hashmap_hash_map_new_fwd : 't hashmap_hash_map_t result =
     hashmap_hash_map_new_with_capacity_fwd (int_to_usize 32) (int_to_usize 4)
       (int_to_usize 5)
 ’
 
 val [hashmap_hash_map_clear_loop_fwd_back_def] = DefineDiv ‘
-  (** [hashmap_main::hashmap::HashMap::{0}::clear] *)
+  (** [hashmap_main::hashmap::HashMap::{0}::clear]: loop 0: merged forward/backward function
+      (there is a single backward function, and the forward function returns ()) *)
   hashmap_hash_map_clear_loop_fwd_back
     (slots : 't hashmap_list_t vec) (i : usize) :
     't hashmap_list_t vec result
@@ -84,7 +85,8 @@ val [hashmap_hash_map_clear_loop_fwd_back_def] = DefineDiv ‘
 ’
 
 val hashmap_hash_map_clear_fwd_back_def = Define ‘
-  (** [hashmap_main::hashmap::HashMap::{0}::clear] *)
+  (** [hashmap_main::hashmap::HashMap::{0}::clear]: merged forward/backward function
+      (there is a single backward function, and the forward function returns ()) *)
   hashmap_hash_map_clear_fwd_back
     (self : 't hashmap_hash_map_t) : 't hashmap_hash_map_t result =
     do
@@ -102,13 +104,13 @@ val hashmap_hash_map_clear_fwd_back_def = Define ‘
 ’
 
 val hashmap_hash_map_len_fwd_def = Define ‘
-  (** [hashmap_main::hashmap::HashMap::{0}::len] *)
+  (** [hashmap_main::hashmap::HashMap::{0}::len]: forward function *)
   hashmap_hash_map_len_fwd (self : 't hashmap_hash_map_t) : usize result =
     Return self.hashmap_hash_map_num_entries
 ’
 
 val [hashmap_hash_map_insert_in_list_loop_fwd_def] = DefineDiv ‘
-  (** [hashmap_main::hashmap::HashMap::{0}::insert_in_list] *)
+  (** [hashmap_main::hashmap::HashMap::{0}::insert_in_list]: loop 0: forward function *)
   hashmap_hash_map_insert_in_list_loop_fwd
     (key : usize) (value : 't) (ls : 't hashmap_list_t) : bool result =
     (case ls of
@@ -120,14 +122,14 @@ val [hashmap_hash_map_insert_in_list_loop_fwd_def] = DefineDiv ‘
 ’
 
 val hashmap_hash_map_insert_in_list_fwd_def = Define ‘
-  (** [hashmap_main::hashmap::HashMap::{0}::insert_in_list] *)
+  (** [hashmap_main::hashmap::HashMap::{0}::insert_in_list]: forward function *)
   hashmap_hash_map_insert_in_list_fwd
     (key : usize) (value : 't) (ls : 't hashmap_list_t) : bool result =
     hashmap_hash_map_insert_in_list_loop_fwd key value ls
 ’
 
 val [hashmap_hash_map_insert_in_list_loop_back_def] = DefineDiv ‘
-  (** [hashmap_main::hashmap::HashMap::{0}::insert_in_list] *)
+  (** [hashmap_main::hashmap::HashMap::{0}::insert_in_list]: loop 0: backward function 0 *)
   hashmap_hash_map_insert_in_list_loop_back
     (key : usize) (value : 't) (ls : 't hashmap_list_t) :
     't hashmap_list_t result
@@ -146,7 +148,7 @@ val [hashmap_hash_map_insert_in_list_loop_back_def] = DefineDiv ‘
 ’
 
 val hashmap_hash_map_insert_in_list_back_def = Define ‘
-  (** [hashmap_main::hashmap::HashMap::{0}::insert_in_list] *)
+  (** [hashmap_main::hashmap::HashMap::{0}::insert_in_list]: backward function 0 *)
   hashmap_hash_map_insert_in_list_back
     (key : usize) (value : 't) (ls : 't hashmap_list_t) :
     't hashmap_list_t result
@@ -155,7 +157,8 @@ val hashmap_hash_map_insert_in_list_back_def = Define ‘
 ’
 
 val hashmap_hash_map_insert_no_resize_fwd_back_def = Define ‘
-  (** [hashmap_main::hashmap::HashMap::{0}::insert_no_resize] *)
+  (** [hashmap_main::hashmap::HashMap::{0}::insert_no_resize]: merged forward/backward function
+      (there is a single backward function, and the forward function returns ()) *)
   hashmap_hash_map_insert_no_resize_fwd_back
     (self : 't hashmap_hash_map_t) (key : usize) (value : 't) :
     't hashmap_hash_map_t result
@@ -199,7 +202,8 @@ Definition core_num_u32_max_c_def:
 End
 
 val [hashmap_hash_map_move_elements_from_list_loop_fwd_back_def] = DefineDiv ‘
-  (** [hashmap_main::hashmap::HashMap::{0}::move_elements_from_list] *)
+  (** [hashmap_main::hashmap::HashMap::{0}::move_elements_from_list]: loop 0: merged forward/backward function
+      (there is a single backward function, and the forward function returns ()) *)
   hashmap_hash_map_move_elements_from_list_loop_fwd_back
     (ntable : 't hashmap_hash_map_t) (ls : 't hashmap_list_t) :
     't hashmap_hash_map_t result
@@ -214,7 +218,8 @@ val [hashmap_hash_map_move_elements_from_list_loop_fwd_back_def] = DefineDiv ‘
 ’
 
 val hashmap_hash_map_move_elements_from_list_fwd_back_def = Define ‘
-  (** [hashmap_main::hashmap::HashMap::{0}::move_elements_from_list] *)
+  (** [hashmap_main::hashmap::HashMap::{0}::move_elements_from_list]: merged forward/backward function
+      (there is a single backward function, and the forward function returns ()) *)
   hashmap_hash_map_move_elements_from_list_fwd_back
     (ntable : 't hashmap_hash_map_t) (ls : 't hashmap_list_t) :
     't hashmap_hash_map_t result
@@ -223,7 +228,8 @@ val hashmap_hash_map_move_elements_from_list_fwd_back_def = Define ‘
 ’
 
 val [hashmap_hash_map_move_elements_loop_fwd_back_def] = DefineDiv ‘
-  (** [hashmap_main::hashmap::HashMap::{0}::move_elements] *)
+  (** [hashmap_main::hashmap::HashMap::{0}::move_elements]: loop 0: merged forward/backward function
+      (there is a single backward function, and the forward function returns ()) *)
   hashmap_hash_map_move_elements_loop_fwd_back
     (ntable : 't hashmap_hash_map_t) (slots : 't hashmap_list_t vec)
     (i : usize) :
@@ -249,7 +255,8 @@ val [hashmap_hash_map_move_elements_loop_fwd_back_def] = DefineDiv ‘
 ’
 
 val hashmap_hash_map_move_elements_fwd_back_def = Define ‘
-  (** [hashmap_main::hashmap::HashMap::{0}::move_elements] *)
+  (** [hashmap_main::hashmap::HashMap::{0}::move_elements]: merged forward/backward function
+      (there is a single backward function, and the forward function returns ()) *)
   hashmap_hash_map_move_elements_fwd_back
     (ntable : 't hashmap_hash_map_t) (slots : 't hashmap_list_t vec)
     (i : usize) :
@@ -259,7 +266,8 @@ val hashmap_hash_map_move_elements_fwd_back_def = Define ‘
 ’
 
 val hashmap_hash_map_try_resize_fwd_back_def = Define ‘
-  (** [hashmap_main::hashmap::HashMap::{0}::try_resize] *)
+  (** [hashmap_main::hashmap::HashMap::{0}::try_resize]: merged forward/backward function
+      (there is a single backward function, and the forward function returns ()) *)
   hashmap_hash_map_try_resize_fwd_back
     (self : 't hashmap_hash_map_t) : 't hashmap_hash_map_t result =
     do
@@ -293,7 +301,8 @@ val hashmap_hash_map_try_resize_fwd_back_def = Define ‘
 ’
 
 val hashmap_hash_map_insert_fwd_back_def = Define ‘
-  (** [hashmap_main::hashmap::HashMap::{0}::insert] *)
+  (** [hashmap_main::hashmap::HashMap::{0}::insert]: merged forward/backward function
+      (there is a single backward function, and the forward function returns ()) *)
   hashmap_hash_map_insert_fwd_back
     (self : 't hashmap_hash_map_t) (key : usize) (value : 't) :
     't hashmap_hash_map_t result
@@ -308,7 +317,7 @@ val hashmap_hash_map_insert_fwd_back_def = Define ‘
 ’
 
 val [hashmap_hash_map_contains_key_in_list_loop_fwd_def] = DefineDiv ‘
-  (** [hashmap_main::hashmap::HashMap::{0}::contains_key_in_list] *)
+  (** [hashmap_main::hashmap::HashMap::{0}::contains_key_in_list]: loop 0: forward function *)
   hashmap_hash_map_contains_key_in_list_loop_fwd
     (key : usize) (ls : 't hashmap_list_t) : bool result =
     (case ls of
@@ -320,14 +329,14 @@ val [hashmap_hash_map_contains_key_in_list_loop_fwd_def] = DefineDiv ‘
 ’
 
 val hashmap_hash_map_contains_key_in_list_fwd_def = Define ‘
-  (** [hashmap_main::hashmap::HashMap::{0}::contains_key_in_list] *)
+  (** [hashmap_main::hashmap::HashMap::{0}::contains_key_in_list]: forward function *)
   hashmap_hash_map_contains_key_in_list_fwd
     (key : usize) (ls : 't hashmap_list_t) : bool result =
     hashmap_hash_map_contains_key_in_list_loop_fwd key ls
 ’
 
 val hashmap_hash_map_contains_key_fwd_def = Define ‘
-  (** [hashmap_main::hashmap::HashMap::{0}::contains_key] *)
+  (** [hashmap_main::hashmap::HashMap::{0}::contains_key]: forward function *)
   hashmap_hash_map_contains_key_fwd
     (self : 't hashmap_hash_map_t) (key : usize) : bool result =
     do
@@ -342,7 +351,7 @@ val hashmap_hash_map_contains_key_fwd_def = Define ‘
 ’
 
 val [hashmap_hash_map_get_in_list_loop_fwd_def] = DefineDiv ‘
-  (** [hashmap_main::hashmap::HashMap::{0}::get_in_list] *)
+  (** [hashmap_main::hashmap::HashMap::{0}::get_in_list]: loop 0: forward function *)
   hashmap_hash_map_get_in_list_loop_fwd
     (key : usize) (ls : 't hashmap_list_t) : 't result =
     (case ls of
@@ -354,14 +363,14 @@ val [hashmap_hash_map_get_in_list_loop_fwd_def] = DefineDiv ‘
 ’
 
 val hashmap_hash_map_get_in_list_fwd_def = Define ‘
-  (** [hashmap_main::hashmap::HashMap::{0}::get_in_list] *)
+  (** [hashmap_main::hashmap::HashMap::{0}::get_in_list]: forward function *)
   hashmap_hash_map_get_in_list_fwd
     (key : usize) (ls : 't hashmap_list_t) : 't result =
     hashmap_hash_map_get_in_list_loop_fwd key ls
 ’
 
 val hashmap_hash_map_get_fwd_def = Define ‘
-  (** [hashmap_main::hashmap::HashMap::{0}::get] *)
+  (** [hashmap_main::hashmap::HashMap::{0}::get]: forward function *)
   hashmap_hash_map_get_fwd
     (self : 't hashmap_hash_map_t) (key : usize) : 't result =
     do
@@ -376,7 +385,7 @@ val hashmap_hash_map_get_fwd_def = Define ‘
 ’
 
 val [hashmap_hash_map_get_mut_in_list_loop_fwd_def] = DefineDiv ‘
-  (** [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list] *)
+  (** [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list]: loop 0: forward function *)
   hashmap_hash_map_get_mut_in_list_loop_fwd
     (ls : 't hashmap_list_t) (key : usize) : 't result =
     (case ls of
@@ -388,14 +397,14 @@ val [hashmap_hash_map_get_mut_in_list_loop_fwd_def] = DefineDiv ‘
 ’
 
 val hashmap_hash_map_get_mut_in_list_fwd_def = Define ‘
-  (** [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list] *)
+  (** [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list]: forward function *)
   hashmap_hash_map_get_mut_in_list_fwd
     (ls : 't hashmap_list_t) (key : usize) : 't result =
     hashmap_hash_map_get_mut_in_list_loop_fwd ls key
 ’
 
 val [hashmap_hash_map_get_mut_in_list_loop_back_def] = DefineDiv ‘
-  (** [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list] *)
+  (** [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list]: loop 0: backward function 0 *)
   hashmap_hash_map_get_mut_in_list_loop_back
     (ls : 't hashmap_list_t) (key : usize) (ret : 't) :
     't hashmap_list_t result
@@ -413,7 +422,7 @@ val [hashmap_hash_map_get_mut_in_list_loop_back_def] = DefineDiv ‘
 ’
 
 val hashmap_hash_map_get_mut_in_list_back_def = Define ‘
-  (** [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list] *)
+  (** [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list]: backward function 0 *)
   hashmap_hash_map_get_mut_in_list_back
     (ls : 't hashmap_list_t) (key : usize) (ret : 't) :
     't hashmap_list_t result
@@ -422,7 +431,7 @@ val hashmap_hash_map_get_mut_in_list_back_def = Define ‘
 ’
 
 val hashmap_hash_map_get_mut_fwd_def = Define ‘
-  (** [hashmap_main::hashmap::HashMap::{0}::get_mut] *)
+  (** [hashmap_main::hashmap::HashMap::{0}::get_mut]: forward function *)
   hashmap_hash_map_get_mut_fwd
     (self : 't hashmap_hash_map_t) (key : usize) : 't result =
     do
@@ -437,7 +446,7 @@ val hashmap_hash_map_get_mut_fwd_def = Define ‘
 ’
 
 val hashmap_hash_map_get_mut_back_def = Define ‘
-  (** [hashmap_main::hashmap::HashMap::{0}::get_mut] *)
+  (** [hashmap_main::hashmap::HashMap::{0}::get_mut]: backward function 0 *)
   hashmap_hash_map_get_mut_back
     (self : 't hashmap_hash_map_t) (key : usize) (ret : 't) :
     't hashmap_hash_map_t result
@@ -456,7 +465,7 @@ val hashmap_hash_map_get_mut_back_def = Define ‘
 ’
 
 val [hashmap_hash_map_remove_from_list_loop_fwd_def] = DefineDiv ‘
-  (** [hashmap_main::hashmap::HashMap::{0}::remove_from_list] *)
+  (** [hashmap_main::hashmap::HashMap::{0}::remove_from_list]: loop 0: forward function *)
   hashmap_hash_map_remove_from_list_loop_fwd
     (key : usize) (ls : 't hashmap_list_t) : 't option result =
     (case ls of
@@ -473,14 +482,14 @@ val [hashmap_hash_map_remove_from_list_loop_fwd_def] = DefineDiv ‘
 ’
 
 val hashmap_hash_map_remove_from_list_fwd_def = Define ‘
-  (** [hashmap_main::hashmap::HashMap::{0}::remove_from_list] *)
+  (** [hashmap_main::hashmap::HashMap::{0}::remove_from_list]: forward function *)
   hashmap_hash_map_remove_from_list_fwd
     (key : usize) (ls : 't hashmap_list_t) : 't option result =
     hashmap_hash_map_remove_from_list_loop_fwd key ls
 ’
 
 val [hashmap_hash_map_remove_from_list_loop_back_def] = DefineDiv ‘
-  (** [hashmap_main::hashmap::HashMap::{0}::remove_from_list] *)
+  (** [hashmap_main::hashmap::HashMap::{0}::remove_from_list]: loop 0: backward function 1 *)
   hashmap_hash_map_remove_from_list_loop_back
     (key : usize) (ls : 't hashmap_list_t) : 't hashmap_list_t result =
     (case ls of
@@ -501,14 +510,14 @@ val [hashmap_hash_map_remove_from_list_loop_back_def] = DefineDiv ‘
 ’
 
 val hashmap_hash_map_remove_from_list_back_def = Define ‘
-  (** [hashmap_main::hashmap::HashMap::{0}::remove_from_list] *)
+  (** [hashmap_main::hashmap::HashMap::{0}::remove_from_list]: backward function 1 *)
   hashmap_hash_map_remove_from_list_back
     (key : usize) (ls : 't hashmap_list_t) : 't hashmap_list_t result =
     hashmap_hash_map_remove_from_list_loop_back key ls
 ’
 
 val hashmap_hash_map_remove_fwd_def = Define ‘
-  (** [hashmap_main::hashmap::HashMap::{0}::remove] *)
+  (** [hashmap_main::hashmap::HashMap::{0}::remove]: forward function *)
   hashmap_hash_map_remove_fwd
     (self : 't hashmap_hash_map_t) (key : usize) : 't option result =
     do
@@ -530,7 +539,7 @@ val hashmap_hash_map_remove_fwd_def = Define ‘
 ’
 
 val hashmap_hash_map_remove_back_def = Define ‘
-  (** [hashmap_main::hashmap::HashMap::{0}::remove] *)
+  (** [hashmap_main::hashmap::HashMap::{0}::remove]: backward function 0 *)
   hashmap_hash_map_remove_back
     (self : 't hashmap_hash_map_t) (key : usize) :
     't hashmap_hash_map_t result
@@ -566,7 +575,7 @@ val hashmap_hash_map_remove_back_def = Define ‘
 ’
 
 val hashmap_test1_fwd_def = Define ‘
-  (** [hashmap_main::hashmap::test1] *)
+  (** [hashmap_main::hashmap::test1]: forward function *)
   hashmap_test1_fwd : unit result =
     do
     hm <- hashmap_hash_map_new_fwd;
@@ -623,7 +632,7 @@ val hashmap_test1_fwd_def = Define ‘
 val _ = assert_return (“hashmap_test1_fwd”)
 
 val insert_on_disk_fwd_def = Define ‘
-  (** [hashmap_main::insert_on_disk] *)
+  (** [hashmap_main::insert_on_disk]: forward function *)
   insert_on_disk_fwd
     (key : usize) (value : u64) (st : state) : (state # unit) result =
     do
@@ -635,7 +644,7 @@ val insert_on_disk_fwd_def = Define ‘
 ’
 
 val main_fwd_def = Define ‘
-  (** [hashmap_main::main] *)
+  (** [hashmap_main::main]: forward function *)
   main_fwd : unit result =
     Return ()
 ’
diff --git a/tests/hol4/hashmap_on_disk/hashmapMain_OpaqueScript.sml b/tests/hol4/hashmap_on_disk/hashmapMain_OpaqueScript.sml
index 5f6bcbb4..f7221d92 100644
--- a/tests/hol4/hashmap_on_disk/hashmapMain_OpaqueScript.sml
+++ b/tests/hol4/hashmap_on_disk/hashmapMain_OpaqueScript.sml
@@ -1,15 +1,15 @@
 (** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
-(** [hashmap_main]: opaque function definitions *)
+(** [hashmap_main]: external function declarations *)
 open primitivesLib divDefLib
 open hashmapMain_TypesTheory
 
 val _ = new_theory "hashmapMain_Opaque"
 
 
-val _ = new_constant ("hashmap_utils_deserialize_fwd",
+(** [hashmap_main::hashmap_utils::deserialize]: forward function *)val _ = new_constant ("hashmap_utils_deserialize_fwd",
   “:state -> (state # u64 hashmap_hash_map_t) result”)
 
-val _ = new_constant ("hashmap_utils_serialize_fwd",
+(** [hashmap_main::hashmap_utils::serialize]: forward function *)val _ = new_constant ("hashmap_utils_serialize_fwd",
   “:u64 hashmap_hash_map_t -> state -> (state # unit) result”)
 
 val _ = export_theory ()
diff --git a/tests/hol4/misc-constants/constantsScript.sml b/tests/hol4/misc-constants/constantsScript.sml
index 324d553d..145c3e0f 100644
--- a/tests/hol4/misc-constants/constantsScript.sml
+++ b/tests/hol4/misc-constants/constantsScript.sml
@@ -38,7 +38,7 @@ Definition x2_c_def:
 End
 
 val incr_fwd_def = Define ‘
-  (** [constants::incr] *)
+  (** [constants::incr]: forward function *)
   incr_fwd (n : u32) : u32 result =
     u32_add n (int_to_u32 1)
 ’
@@ -52,7 +52,7 @@ Definition x3_c_def:
 End
 
 val mk_pair0_fwd_def = Define ‘
-  (** [constants::mk_pair0] *)
+  (** [constants::mk_pair0]: forward function *)
   mk_pair0_fwd (x : u32) (y : u32) : (u32 # u32) result =
     Return (x, y)
 ’
@@ -63,7 +63,7 @@ Datatype:
 End
 
 val mk_pair1_fwd_def = Define ‘
-  (** [constants::mk_pair1] *)
+  (** [constants::mk_pair1]: forward function *)
   mk_pair1_fwd (x : u32) (y : u32) : (u32, u32) pair_t result =
     Return (<| pair_x := x; pair_y := y |>)
 ’
@@ -108,7 +108,7 @@ Datatype:
 End
 
 val wrap_new_fwd_def = Define ‘
-  (** [constants::Wrap::{0}::new] *)
+  (** [constants::Wrap::{0}::new]: forward function *)
   wrap_new_fwd (val : 't) : 't wrap_t result =
     Return (<| wrap_val := val |>)
 ’
@@ -122,7 +122,7 @@ Definition y_c_def:
 End
 
 val unwrap_y_fwd_def = Define ‘
-  (** [constants::unwrap_y] *)
+  (** [constants::unwrap_y]: forward function *)
   unwrap_y_fwd : i32 result =
     Return y_c.wrap_val
 ’
@@ -144,13 +144,13 @@ Definition get_z1_z1_c_def:
 End
 
 val get_z1_fwd_def = Define ‘
-  (** [constants::get_z1] *)
+  (** [constants::get_z1]: forward function *)
   get_z1_fwd : i32 result =
     Return get_z1_z1_c
 ’
 
 val add_fwd_def = Define ‘
-  (** [constants::add] *)
+  (** [constants::add]: forward function *)
   add_fwd (a : i32) (b : i32) : i32 result =
     i32_add a b
 ’
@@ -180,7 +180,7 @@ Definition q3_c_def:
 End
 
 val get_z2_fwd_def = Define ‘
-  (** [constants::get_z2] *)
+  (** [constants::get_z2]: forward function *)
   get_z2_fwd : i32 result =
     do
     i <- get_z1_fwd;
diff --git a/tests/hol4/misc-external/external_FunsScript.sml b/tests/hol4/misc-external/external_FunsScript.sml
index 8172bc1c..f3692ee2 100644
--- a/tests/hol4/misc-external/external_FunsScript.sml
+++ b/tests/hol4/misc-external/external_FunsScript.sml
@@ -7,7 +7,7 @@ val _ = new_theory "external_Funs"
 
 
 val swap_fwd_def = Define ‘
-  (** [external::swap] *)
+  (** [external::swap]: forward function *)
   swap_fwd (x : 't) (y : 't) (st : state) : (state # unit) result =
     do
     (st0, _) <- core_mem_swap_fwd x y st;
@@ -18,7 +18,7 @@ val swap_fwd_def = Define ‘
 ’
 
 val swap_back_def = Define ‘
-  (** [external::swap] *)
+  (** [external::swap]: backward function 0 *)
   swap_back
     (x : 't) (y : 't) (st : state) (st0 : state) : (state # ('t # 't)) result =
     do
@@ -30,7 +30,7 @@ val swap_back_def = Define ‘
 ’
 
 val test_new_non_zero_u32_fwd_def = Define ‘
-  (** [external::test_new_non_zero_u32] *)
+  (** [external::test_new_non_zero_u32]: forward function *)
   test_new_non_zero_u32_fwd
     (x : u32) (st : state) : (state # core_num_nonzero_non_zero_u32_t) result =
     do
@@ -40,7 +40,7 @@ val test_new_non_zero_u32_fwd_def = Define ‘
 ’
 
 val test_vec_fwd_def = Define ‘
-  (** [external::test_vec] *)
+  (** [external::test_vec]: forward function *)
   test_vec_fwd : unit result =
     let v = vec_new in do
                        _ <- vec_push_back v (int_to_u32 0);
@@ -52,7 +52,7 @@ val test_vec_fwd_def = Define ‘
 val _ = assert_return (“test_vec_fwd”)
 
 val custom_swap_fwd_def = Define ‘
-  (** [external::custom_swap] *)
+  (** [external::custom_swap]: forward function *)
   custom_swap_fwd (x : 't) (y : 't) (st : state) : (state # 't) result =
     do
     (st0, _) <- core_mem_swap_fwd x y st;
@@ -63,7 +63,7 @@ val custom_swap_fwd_def = Define ‘
 ’
 
 val custom_swap_back_def = Define ‘
-  (** [external::custom_swap] *)
+  (** [external::custom_swap]: backward function 0 *)
   custom_swap_back
     (x : 't) (y : 't) (st : state) (ret : 't) (st0 : state) :
     (state # ('t # 't)) result
@@ -77,7 +77,7 @@ val custom_swap_back_def = Define ‘
 ’
 
 val test_custom_swap_fwd_def = Define ‘
-  (** [external::test_custom_swap] *)
+  (** [external::test_custom_swap]: forward function *)
   test_custom_swap_fwd
     (x : u32) (y : u32) (st : state) : (state # unit) result =
     do
@@ -87,7 +87,7 @@ val test_custom_swap_fwd_def = Define ‘
 ’
 
 val test_custom_swap_back_def = Define ‘
-  (** [external::test_custom_swap] *)
+  (** [external::test_custom_swap]: backward function 0 *)
   test_custom_swap_back
     (x : u32) (y : u32) (st : state) (st0 : state) :
     (state # (u32 # u32)) result
@@ -96,7 +96,7 @@ val test_custom_swap_back_def = Define ‘
 ’
 
 val test_swap_non_zero_fwd_def = Define ‘
-  (** [external::test_swap_non_zero] *)
+  (** [external::test_swap_non_zero]: forward function *)
   test_swap_non_zero_fwd (x : u32) (st : state) : (state # u32) result =
     do
     (st0, _) <- swap_fwd x (int_to_u32 0) st;
diff --git a/tests/hol4/misc-external/external_OpaqueScript.sml b/tests/hol4/misc-external/external_OpaqueScript.sml
index e2fd281d..b5a6d91d 100644
--- a/tests/hol4/misc-external/external_OpaqueScript.sml
+++ b/tests/hol4/misc-external/external_OpaqueScript.sml
@@ -1,25 +1,25 @@
 (** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
-(** [external]: opaque function definitions *)
+(** [external]: external function declarations *)
 open primitivesLib divDefLib
 open external_TypesTheory
 
 val _ = new_theory "external_Opaque"
 
 
-val _ = new_constant ("core_mem_swap_fwd",
+(** [core::mem::swap]: forward function *)val _ = new_constant ("core_mem_swap_fwd",
   “:'t -> 't -> state -> (state # unit) result”)
 
-val _ = new_constant ("core_mem_swap_back0",
+(** [core::mem::swap]: backward function 0 *)val _ = new_constant ("core_mem_swap_back0",
   “:'t -> 't -> state -> state -> (state # 't) result”)
 
-val _ = new_constant ("core_mem_swap_back1",
+(** [core::mem::swap]: backward function 1 *)val _ = new_constant ("core_mem_swap_back1",
   “:'t -> 't -> state -> state -> (state # 't) result”)
 
-val _ = new_constant ("core_num_nonzero_non_zero_u32_new_fwd",
+(** [core::num::nonzero::NonZeroU32::{14}::new]: forward function *)val _ = new_constant ("core_num_nonzero_non_zero_u32_new_fwd",
   “:u32 -> state -> (state # core_num_nonzero_non_zero_u32_t option)
   result”)
 
-val _ = new_constant ("core_option_option_unwrap_fwd",
+(** [core::option::Option::{0}::unwrap]: forward function *)val _ = new_constant ("core_option_option_unwrap_fwd",
   “:'t option -> state -> (state # 't) result”)
 
 val _ = export_theory ()
diff --git a/tests/hol4/misc-loops/loops_FunsScript.sml b/tests/hol4/misc-loops/loops_FunsScript.sml
index f0ef036b..65cf77d4 100644
--- a/tests/hol4/misc-loops/loops_FunsScript.sml
+++ b/tests/hol4/misc-loops/loops_FunsScript.sml
@@ -7,7 +7,7 @@ val _ = new_theory "loops_Funs"
 
 
 val [sum_loop_fwd_def] = DefineDiv ‘
-  (** [loops::sum] *)
+  (** [loops::sum]: loop 0: forward function *)
   sum_loop_fwd (max : u32) (i : u32) (s : u32) : u32 result =
     if u32_lt i max
     then (
@@ -20,13 +20,13 @@ val [sum_loop_fwd_def] = DefineDiv ‘
 ’
 
 val sum_fwd_def = Define ‘
-  (** [loops::sum] *)
+  (** [loops::sum]: forward function *)
   sum_fwd (max : u32) : u32 result =
     sum_loop_fwd max (int_to_u32 0) (int_to_u32 0)
 ’
 
 val [sum_with_mut_borrows_loop_fwd_def] = DefineDiv ‘
-  (** [loops::sum_with_mut_borrows] *)
+  (** [loops::sum_with_mut_borrows]: loop 0: forward function *)
   sum_with_mut_borrows_loop_fwd
     (max : u32) (mi : u32) (ms : u32) : u32 result =
     if u32_lt mi max
@@ -40,13 +40,13 @@ val [sum_with_mut_borrows_loop_fwd_def] = DefineDiv ‘
 ’
 
 val sum_with_mut_borrows_fwd_def = Define ‘
-  (** [loops::sum_with_mut_borrows] *)
+  (** [loops::sum_with_mut_borrows]: forward function *)
   sum_with_mut_borrows_fwd (max : u32) : u32 result =
     sum_with_mut_borrows_loop_fwd max (int_to_u32 0) (int_to_u32 0)
 ’
 
 val [sum_with_shared_borrows_loop_fwd_def] = DefineDiv ‘
-  (** [loops::sum_with_shared_borrows] *)
+  (** [loops::sum_with_shared_borrows]: loop 0: forward function *)
   sum_with_shared_borrows_loop_fwd
     (max : u32) (i : u32) (s : u32) : u32 result =
     if u32_lt i max
@@ -60,13 +60,14 @@ val [sum_with_shared_borrows_loop_fwd_def] = DefineDiv ‘
 ’
 
 val sum_with_shared_borrows_fwd_def = Define ‘
-  (** [loops::sum_with_shared_borrows] *)
+  (** [loops::sum_with_shared_borrows]: forward function *)
   sum_with_shared_borrows_fwd (max : u32) : u32 result =
     sum_with_shared_borrows_loop_fwd max (int_to_u32 0) (int_to_u32 0)
 ’
 
 val [clear_loop_fwd_back_def] = DefineDiv ‘
-  (** [loops::clear] *)
+  (** [loops::clear]: loop 0: merged forward/backward function
+      (there is a single backward function, and the forward function returns ()) *)
   clear_loop_fwd_back (v : u32 vec) (i : usize) : u32 vec result =
     let i0 = vec_len v in
     if usize_lt i i0
@@ -80,13 +81,14 @@ val [clear_loop_fwd_back_def] = DefineDiv ‘
 ’
 
 val clear_fwd_back_def = Define ‘
-  (** [loops::clear] *)
+  (** [loops::clear]: merged forward/backward function
+      (there is a single backward function, and the forward function returns ()) *)
   clear_fwd_back (v : u32 vec) : u32 vec result =
     clear_loop_fwd_back v (int_to_usize 0)
 ’
 
 val [list_mem_loop_fwd_def] = DefineDiv ‘
-  (** [loops::list_mem] *)
+  (** [loops::list_mem]: loop 0: forward function *)
   list_mem_loop_fwd (x : u32) (ls : u32 list_t) : bool result =
     (case ls of
     | ListCons y tl => if y = x then Return T else list_mem_loop_fwd x tl
@@ -94,13 +96,13 @@ val [list_mem_loop_fwd_def] = DefineDiv ‘
 ’
 
 val list_mem_fwd_def = Define ‘
-  (** [loops::list_mem] *)
+  (** [loops::list_mem]: forward function *)
   list_mem_fwd (x : u32) (ls : u32 list_t) : bool result =
     list_mem_loop_fwd x ls
 ’
 
 val [list_nth_mut_loop_loop_fwd_def] = DefineDiv ‘
-  (** [loops::list_nth_mut_loop] *)
+  (** [loops::list_nth_mut_loop]: loop 0: forward function *)
   list_nth_mut_loop_loop_fwd (ls : 't list_t) (i : u32) : 't result =
     (case ls of
     | ListCons x tl =>
@@ -115,13 +117,13 @@ val [list_nth_mut_loop_loop_fwd_def] = DefineDiv ‘
 ’
 
 val list_nth_mut_loop_fwd_def = Define ‘
-  (** [loops::list_nth_mut_loop] *)
+  (** [loops::list_nth_mut_loop]: forward function *)
   list_nth_mut_loop_fwd (ls : 't list_t) (i : u32) : 't result =
     list_nth_mut_loop_loop_fwd ls i
 ’
 
 val [list_nth_mut_loop_loop_back_def] = DefineDiv ‘
-  (** [loops::list_nth_mut_loop] *)
+  (** [loops::list_nth_mut_loop]: loop 0: backward function 0 *)
   list_nth_mut_loop_loop_back
     (ls : 't list_t) (i : u32) (ret : 't) : 't list_t result =
     (case ls of
@@ -138,14 +140,14 @@ val [list_nth_mut_loop_loop_back_def] = DefineDiv ‘
 ’
 
 val list_nth_mut_loop_back_def = Define ‘
-  (** [loops::list_nth_mut_loop] *)
+  (** [loops::list_nth_mut_loop]: backward function 0 *)
   list_nth_mut_loop_back
     (ls : 't list_t) (i : u32) (ret : 't) : 't list_t result =
     list_nth_mut_loop_loop_back ls i ret
 ’
 
 val [list_nth_shared_loop_loop_fwd_def] = DefineDiv ‘
-  (** [loops::list_nth_shared_loop] *)
+  (** [loops::list_nth_shared_loop]: loop 0: forward function *)
   list_nth_shared_loop_loop_fwd (ls : 't list_t) (i : u32) : 't result =
     (case ls of
     | ListCons x tl =>
@@ -160,13 +162,13 @@ val [list_nth_shared_loop_loop_fwd_def] = DefineDiv ‘
 ’
 
 val list_nth_shared_loop_fwd_def = Define ‘
-  (** [loops::list_nth_shared_loop] *)
+  (** [loops::list_nth_shared_loop]: forward function *)
   list_nth_shared_loop_fwd (ls : 't list_t) (i : u32) : 't result =
     list_nth_shared_loop_loop_fwd ls i
 ’
 
 val [get_elem_mut_loop_fwd_def] = DefineDiv ‘
-  (** [loops::get_elem_mut] *)
+  (** [loops::get_elem_mut]: loop 0: forward function *)
   get_elem_mut_loop_fwd (x : usize) (ls : usize list_t) : usize result =
     (case ls of
     | ListCons y tl => if y = x then Return y else get_elem_mut_loop_fwd x tl
@@ -174,7 +176,7 @@ val [get_elem_mut_loop_fwd_def] = DefineDiv ‘
 ’
 
 val get_elem_mut_fwd_def = Define ‘
-  (** [loops::get_elem_mut] *)
+  (** [loops::get_elem_mut]: forward function *)
   get_elem_mut_fwd (slots : usize list_t vec) (x : usize) : usize result =
     do
     l <- vec_index_mut_fwd slots (int_to_usize 0);
@@ -183,7 +185,7 @@ val get_elem_mut_fwd_def = Define ‘
 ’
 
 val [get_elem_mut_loop_back_def] = DefineDiv ‘
-  (** [loops::get_elem_mut] *)
+  (** [loops::get_elem_mut]: loop 0: backward function 0 *)
   get_elem_mut_loop_back
     (x : usize) (ls : usize list_t) (ret : usize) : usize list_t result =
     (case ls of
@@ -199,7 +201,7 @@ val [get_elem_mut_loop_back_def] = DefineDiv ‘
 ’
 
 val get_elem_mut_back_def = Define ‘
-  (** [loops::get_elem_mut] *)
+  (** [loops::get_elem_mut]: backward function 0 *)
   get_elem_mut_back
     (slots : usize list_t vec) (x : usize) (ret : usize) :
     usize list_t vec result
@@ -212,7 +214,7 @@ val get_elem_mut_back_def = Define ‘
 ’
 
 val [get_elem_shared_loop_fwd_def] = DefineDiv ‘
-  (** [loops::get_elem_shared] *)
+  (** [loops::get_elem_shared]: loop 0: forward function *)
   get_elem_shared_loop_fwd (x : usize) (ls : usize list_t) : usize result =
     (case ls of
     | ListCons y tl =>
@@ -221,7 +223,7 @@ val [get_elem_shared_loop_fwd_def] = DefineDiv ‘
 ’
 
 val get_elem_shared_fwd_def = Define ‘
-  (** [loops::get_elem_shared] *)
+  (** [loops::get_elem_shared]: forward function *)
   get_elem_shared_fwd (slots : usize list_t vec) (x : usize) : usize result =
     do
     l <- vec_index_fwd slots (int_to_usize 0);
@@ -230,25 +232,25 @@ val get_elem_shared_fwd_def = Define ‘
 ’
 
 val id_mut_fwd_def = Define ‘
-  (** [loops::id_mut] *)
+  (** [loops::id_mut]: forward function *)
   id_mut_fwd (ls : 't list_t) : 't list_t result =
     Return ls
 ’
 
 val id_mut_back_def = Define ‘
-  (** [loops::id_mut] *)
+  (** [loops::id_mut]: backward function 0 *)
   id_mut_back (ls : 't list_t) (ret : 't list_t) : 't list_t result =
     Return ret
 ’
 
 val id_shared_fwd_def = Define ‘
-  (** [loops::id_shared] *)
+  (** [loops::id_shared]: forward function *)
   id_shared_fwd (ls : 't list_t) : 't list_t result =
     Return ls
 ’
 
 val [list_nth_mut_loop_with_id_loop_fwd_def] = DefineDiv ‘
-  (** [loops::list_nth_mut_loop_with_id] *)
+  (** [loops::list_nth_mut_loop_with_id]: loop 0: forward function *)
   list_nth_mut_loop_with_id_loop_fwd (i : u32) (ls : 't list_t) : 't result =
     (case ls of
     | ListCons x tl =>
@@ -263,7 +265,7 @@ val [list_nth_mut_loop_with_id_loop_fwd_def] = DefineDiv ‘
 ’
 
 val list_nth_mut_loop_with_id_fwd_def = Define ‘
-  (** [loops::list_nth_mut_loop_with_id] *)
+  (** [loops::list_nth_mut_loop_with_id]: forward function *)
   list_nth_mut_loop_with_id_fwd (ls : 't list_t) (i : u32) : 't result =
     do
     ls0 <- id_mut_fwd ls;
@@ -272,7 +274,7 @@ val list_nth_mut_loop_with_id_fwd_def = Define ‘
 ’
 
 val [list_nth_mut_loop_with_id_loop_back_def] = DefineDiv ‘
-  (** [loops::list_nth_mut_loop_with_id] *)
+  (** [loops::list_nth_mut_loop_with_id]: loop 0: backward function 0 *)
   list_nth_mut_loop_with_id_loop_back
     (i : u32) (ls : 't list_t) (ret : 't) : 't list_t result =
     (case ls of
@@ -289,7 +291,7 @@ val [list_nth_mut_loop_with_id_loop_back_def] = DefineDiv ‘
 ’
 
 val list_nth_mut_loop_with_id_back_def = Define ‘
-  (** [loops::list_nth_mut_loop_with_id] *)
+  (** [loops::list_nth_mut_loop_with_id]: backward function 0 *)
   list_nth_mut_loop_with_id_back
     (ls : 't list_t) (i : u32) (ret : 't) : 't list_t result =
     do
@@ -300,7 +302,7 @@ val list_nth_mut_loop_with_id_back_def = Define ‘
 ’
 
 val [list_nth_shared_loop_with_id_loop_fwd_def] = DefineDiv ‘
-  (** [loops::list_nth_shared_loop_with_id] *)
+  (** [loops::list_nth_shared_loop_with_id]: loop 0: forward function *)
   list_nth_shared_loop_with_id_loop_fwd
     (i : u32) (ls : 't list_t) : 't result =
     (case ls of
@@ -316,7 +318,7 @@ val [list_nth_shared_loop_with_id_loop_fwd_def] = DefineDiv ‘
 ’
 
 val list_nth_shared_loop_with_id_fwd_def = Define ‘
-  (** [loops::list_nth_shared_loop_with_id] *)
+  (** [loops::list_nth_shared_loop_with_id]: forward function *)
   list_nth_shared_loop_with_id_fwd (ls : 't list_t) (i : u32) : 't result =
     do
     ls0 <- id_shared_fwd ls;
@@ -325,7 +327,7 @@ val list_nth_shared_loop_with_id_fwd_def = Define ‘
 ’
 
 val [list_nth_mut_loop_pair_loop_fwd_def] = DefineDiv ‘
-  (** [loops::list_nth_mut_loop_pair] *)
+  (** [loops::list_nth_mut_loop_pair]: loop 0: forward function *)
   list_nth_mut_loop_pair_loop_fwd
     (ls0 : 't list_t) (ls1 : 't list_t) (i : u32) : ('t # 't) result =
     (case ls0 of
@@ -344,14 +346,14 @@ val [list_nth_mut_loop_pair_loop_fwd_def] = DefineDiv ‘
 ’
 
 val list_nth_mut_loop_pair_fwd_def = Define ‘
-  (** [loops::list_nth_mut_loop_pair] *)
+  (** [loops::list_nth_mut_loop_pair]: forward function *)
   list_nth_mut_loop_pair_fwd
     (ls0 : 't list_t) (ls1 : 't list_t) (i : u32) : ('t # 't) result =
     list_nth_mut_loop_pair_loop_fwd ls0 ls1 i
 ’
 
 val [list_nth_mut_loop_pair_loop_back'a_def] = DefineDiv ‘
-  (** [loops::list_nth_mut_loop_pair] *)
+  (** [loops::list_nth_mut_loop_pair]: loop 0: backward function 0 *)
   list_nth_mut_loop_pair_loop_back'a
     (ls0 : 't list_t) (ls1 : 't list_t) (i : u32) (ret : 't) :
     't list_t result
@@ -373,7 +375,7 @@ val [list_nth_mut_loop_pair_loop_back'a_def] = DefineDiv ‘
 ’
 
 val list_nth_mut_loop_pair_back'a_def = Define ‘
-  (** [loops::list_nth_mut_loop_pair] *)
+  (** [loops::list_nth_mut_loop_pair]: backward function 0 *)
   list_nth_mut_loop_pair_back'a
     (ls0 : 't list_t) (ls1 : 't list_t) (i : u32) (ret : 't) :
     't list_t result
@@ -382,7 +384,7 @@ val list_nth_mut_loop_pair_back'a_def = Define ‘
 ’
 
 val [list_nth_mut_loop_pair_loop_back'b_def] = DefineDiv ‘
-  (** [loops::list_nth_mut_loop_pair] *)
+  (** [loops::list_nth_mut_loop_pair]: loop 0: backward function 1 *)
   list_nth_mut_loop_pair_loop_back'b
     (ls0 : 't list_t) (ls1 : 't list_t) (i : u32) (ret : 't) :
     't list_t result
@@ -404,7 +406,7 @@ val [list_nth_mut_loop_pair_loop_back'b_def] = DefineDiv ‘
 ’
 
 val list_nth_mut_loop_pair_back'b_def = Define ‘
-  (** [loops::list_nth_mut_loop_pair] *)
+  (** [loops::list_nth_mut_loop_pair]: backward function 1 *)
   list_nth_mut_loop_pair_back'b
     (ls0 : 't list_t) (ls1 : 't list_t) (i : u32) (ret : 't) :
     't list_t result
@@ -413,7 +415,7 @@ val list_nth_mut_loop_pair_back'b_def = Define ‘
 ’
 
 val [list_nth_shared_loop_pair_loop_fwd_def] = DefineDiv ‘
-  (** [loops::list_nth_shared_loop_pair] *)
+  (** [loops::list_nth_shared_loop_pair]: loop 0: forward function *)
   list_nth_shared_loop_pair_loop_fwd
     (ls0 : 't list_t) (ls1 : 't list_t) (i : u32) : ('t # 't) result =
     (case ls0 of
@@ -432,14 +434,14 @@ val [list_nth_shared_loop_pair_loop_fwd_def] = DefineDiv ‘
 ’
 
 val list_nth_shared_loop_pair_fwd_def = Define ‘
-  (** [loops::list_nth_shared_loop_pair] *)
+  (** [loops::list_nth_shared_loop_pair]: forward function *)
   list_nth_shared_loop_pair_fwd
     (ls0 : 't list_t) (ls1 : 't list_t) (i : u32) : ('t # 't) result =
     list_nth_shared_loop_pair_loop_fwd ls0 ls1 i
 ’
 
 val [list_nth_mut_loop_pair_merge_loop_fwd_def] = DefineDiv ‘
-  (** [loops::list_nth_mut_loop_pair_merge] *)
+  (** [loops::list_nth_mut_loop_pair_merge]: loop 0: forward function *)
   list_nth_mut_loop_pair_merge_loop_fwd
     (ls0 : 't list_t) (ls1 : 't list_t) (i : u32) : ('t # 't) result =
     (case ls0 of
@@ -458,14 +460,14 @@ val [list_nth_mut_loop_pair_merge_loop_fwd_def] = DefineDiv ‘
 ’
 
 val list_nth_mut_loop_pair_merge_fwd_def = Define ‘
-  (** [loops::list_nth_mut_loop_pair_merge] *)
+  (** [loops::list_nth_mut_loop_pair_merge]: forward function *)
   list_nth_mut_loop_pair_merge_fwd
     (ls0 : 't list_t) (ls1 : 't list_t) (i : u32) : ('t # 't) result =
     list_nth_mut_loop_pair_merge_loop_fwd ls0 ls1 i
 ’
 
 val [list_nth_mut_loop_pair_merge_loop_back_def] = DefineDiv ‘
-  (** [loops::list_nth_mut_loop_pair_merge] *)
+  (** [loops::list_nth_mut_loop_pair_merge]: loop 0: backward function 0 *)
   list_nth_mut_loop_pair_merge_loop_back
     (ls0 : 't list_t) (ls1 : 't list_t) (i : u32) (ret : ('t # 't)) :
     ('t list_t # 't list_t) result
@@ -488,7 +490,7 @@ val [list_nth_mut_loop_pair_merge_loop_back_def] = DefineDiv ‘
 ’
 
 val list_nth_mut_loop_pair_merge_back_def = Define ‘
-  (** [loops::list_nth_mut_loop_pair_merge] *)
+  (** [loops::list_nth_mut_loop_pair_merge]: backward function 0 *)
   list_nth_mut_loop_pair_merge_back
     (ls0 : 't list_t) (ls1 : 't list_t) (i : u32) (ret : ('t # 't)) :
     ('t list_t # 't list_t) result
@@ -497,7 +499,7 @@ val list_nth_mut_loop_pair_merge_back_def = Define ‘
 ’
 
 val [list_nth_shared_loop_pair_merge_loop_fwd_def] = DefineDiv ‘
-  (** [loops::list_nth_shared_loop_pair_merge] *)
+  (** [loops::list_nth_shared_loop_pair_merge]: loop 0: forward function *)
   list_nth_shared_loop_pair_merge_loop_fwd
     (ls0 : 't list_t) (ls1 : 't list_t) (i : u32) : ('t # 't) result =
     (case ls0 of
@@ -516,14 +518,14 @@ val [list_nth_shared_loop_pair_merge_loop_fwd_def] = DefineDiv ‘
 ’
 
 val list_nth_shared_loop_pair_merge_fwd_def = Define ‘
-  (** [loops::list_nth_shared_loop_pair_merge] *)
+  (** [loops::list_nth_shared_loop_pair_merge]: forward function *)
   list_nth_shared_loop_pair_merge_fwd
     (ls0 : 't list_t) (ls1 : 't list_t) (i : u32) : ('t # 't) result =
     list_nth_shared_loop_pair_merge_loop_fwd ls0 ls1 i
 ’
 
 val [list_nth_mut_shared_loop_pair_loop_fwd_def] = DefineDiv ‘
-  (** [loops::list_nth_mut_shared_loop_pair] *)
+  (** [loops::list_nth_mut_shared_loop_pair]: loop 0: forward function *)
   list_nth_mut_shared_loop_pair_loop_fwd
     (ls0 : 't list_t) (ls1 : 't list_t) (i : u32) : ('t # 't) result =
     (case ls0 of
@@ -542,14 +544,14 @@ val [list_nth_mut_shared_loop_pair_loop_fwd_def] = DefineDiv ‘
 ’
 
 val list_nth_mut_shared_loop_pair_fwd_def = Define ‘
-  (** [loops::list_nth_mut_shared_loop_pair] *)
+  (** [loops::list_nth_mut_shared_loop_pair]: forward function *)
   list_nth_mut_shared_loop_pair_fwd
     (ls0 : 't list_t) (ls1 : 't list_t) (i : u32) : ('t # 't) result =
     list_nth_mut_shared_loop_pair_loop_fwd ls0 ls1 i
 ’
 
 val [list_nth_mut_shared_loop_pair_loop_back_def] = DefineDiv ‘
-  (** [loops::list_nth_mut_shared_loop_pair] *)
+  (** [loops::list_nth_mut_shared_loop_pair]: loop 0: backward function 0 *)
   list_nth_mut_shared_loop_pair_loop_back
     (ls0 : 't list_t) (ls1 : 't list_t) (i : u32) (ret : 't) :
     't list_t result
@@ -571,7 +573,7 @@ val [list_nth_mut_shared_loop_pair_loop_back_def] = DefineDiv ‘
 ’
 
 val list_nth_mut_shared_loop_pair_back_def = Define ‘
-  (** [loops::list_nth_mut_shared_loop_pair] *)
+  (** [loops::list_nth_mut_shared_loop_pair]: backward function 0 *)
   list_nth_mut_shared_loop_pair_back
     (ls0 : 't list_t) (ls1 : 't list_t) (i : u32) (ret : 't) :
     't list_t result
@@ -580,7 +582,7 @@ val list_nth_mut_shared_loop_pair_back_def = Define ‘
 ’
 
 val [list_nth_mut_shared_loop_pair_merge_loop_fwd_def] = DefineDiv ‘
-  (** [loops::list_nth_mut_shared_loop_pair_merge] *)
+  (** [loops::list_nth_mut_shared_loop_pair_merge]: loop 0: forward function *)
   list_nth_mut_shared_loop_pair_merge_loop_fwd
     (ls0 : 't list_t) (ls1 : 't list_t) (i : u32) : ('t # 't) result =
     (case ls0 of
@@ -599,14 +601,14 @@ val [list_nth_mut_shared_loop_pair_merge_loop_fwd_def] = DefineDiv ‘
 ’
 
 val list_nth_mut_shared_loop_pair_merge_fwd_def = Define ‘
-  (** [loops::list_nth_mut_shared_loop_pair_merge] *)
+  (** [loops::list_nth_mut_shared_loop_pair_merge]: forward function *)
   list_nth_mut_shared_loop_pair_merge_fwd
     (ls0 : 't list_t) (ls1 : 't list_t) (i : u32) : ('t # 't) result =
     list_nth_mut_shared_loop_pair_merge_loop_fwd ls0 ls1 i
 ’
 
 val [list_nth_mut_shared_loop_pair_merge_loop_back_def] = DefineDiv ‘
-  (** [loops::list_nth_mut_shared_loop_pair_merge] *)
+  (** [loops::list_nth_mut_shared_loop_pair_merge]: loop 0: backward function 0 *)
   list_nth_mut_shared_loop_pair_merge_loop_back
     (ls0 : 't list_t) (ls1 : 't list_t) (i : u32) (ret : 't) :
     't list_t result
@@ -628,7 +630,7 @@ val [list_nth_mut_shared_loop_pair_merge_loop_back_def] = DefineDiv ‘
 ’
 
 val list_nth_mut_shared_loop_pair_merge_back_def = Define ‘
-  (** [loops::list_nth_mut_shared_loop_pair_merge] *)
+  (** [loops::list_nth_mut_shared_loop_pair_merge]: backward function 0 *)
   list_nth_mut_shared_loop_pair_merge_back
     (ls0 : 't list_t) (ls1 : 't list_t) (i : u32) (ret : 't) :
     't list_t result
@@ -637,7 +639,7 @@ val list_nth_mut_shared_loop_pair_merge_back_def = Define ‘
 ’
 
 val [list_nth_shared_mut_loop_pair_loop_fwd_def] = DefineDiv ‘
-  (** [loops::list_nth_shared_mut_loop_pair] *)
+  (** [loops::list_nth_shared_mut_loop_pair]: loop 0: forward function *)
   list_nth_shared_mut_loop_pair_loop_fwd
     (ls0 : 't list_t) (ls1 : 't list_t) (i : u32) : ('t # 't) result =
     (case ls0 of
@@ -656,14 +658,14 @@ val [list_nth_shared_mut_loop_pair_loop_fwd_def] = DefineDiv ‘
 ’
 
 val list_nth_shared_mut_loop_pair_fwd_def = Define ‘
-  (** [loops::list_nth_shared_mut_loop_pair] *)
+  (** [loops::list_nth_shared_mut_loop_pair]: forward function *)
   list_nth_shared_mut_loop_pair_fwd
     (ls0 : 't list_t) (ls1 : 't list_t) (i : u32) : ('t # 't) result =
     list_nth_shared_mut_loop_pair_loop_fwd ls0 ls1 i
 ’
 
 val [list_nth_shared_mut_loop_pair_loop_back_def] = DefineDiv ‘
-  (** [loops::list_nth_shared_mut_loop_pair] *)
+  (** [loops::list_nth_shared_mut_loop_pair]: loop 0: backward function 1 *)
   list_nth_shared_mut_loop_pair_loop_back
     (ls0 : 't list_t) (ls1 : 't list_t) (i : u32) (ret : 't) :
     't list_t result
@@ -685,7 +687,7 @@ val [list_nth_shared_mut_loop_pair_loop_back_def] = DefineDiv ‘
 ’
 
 val list_nth_shared_mut_loop_pair_back_def = Define ‘
-  (** [loops::list_nth_shared_mut_loop_pair] *)
+  (** [loops::list_nth_shared_mut_loop_pair]: backward function 1 *)
   list_nth_shared_mut_loop_pair_back
     (ls0 : 't list_t) (ls1 : 't list_t) (i : u32) (ret : 't) :
     't list_t result
@@ -694,7 +696,7 @@ val list_nth_shared_mut_loop_pair_back_def = Define ‘
 ’
 
 val [list_nth_shared_mut_loop_pair_merge_loop_fwd_def] = DefineDiv ‘
-  (** [loops::list_nth_shared_mut_loop_pair_merge] *)
+  (** [loops::list_nth_shared_mut_loop_pair_merge]: loop 0: forward function *)
   list_nth_shared_mut_loop_pair_merge_loop_fwd
     (ls0 : 't list_t) (ls1 : 't list_t) (i : u32) : ('t # 't) result =
     (case ls0 of
@@ -713,14 +715,14 @@ val [list_nth_shared_mut_loop_pair_merge_loop_fwd_def] = DefineDiv ‘
 ’
 
 val list_nth_shared_mut_loop_pair_merge_fwd_def = Define ‘
-  (** [loops::list_nth_shared_mut_loop_pair_merge] *)
+  (** [loops::list_nth_shared_mut_loop_pair_merge]: forward function *)
   list_nth_shared_mut_loop_pair_merge_fwd
     (ls0 : 't list_t) (ls1 : 't list_t) (i : u32) : ('t # 't) result =
     list_nth_shared_mut_loop_pair_merge_loop_fwd ls0 ls1 i
 ’
 
 val [list_nth_shared_mut_loop_pair_merge_loop_back_def] = DefineDiv ‘
-  (** [loops::list_nth_shared_mut_loop_pair_merge] *)
+  (** [loops::list_nth_shared_mut_loop_pair_merge]: loop 0: backward function 0 *)
   list_nth_shared_mut_loop_pair_merge_loop_back
     (ls0 : 't list_t) (ls1 : 't list_t) (i : u32) (ret : 't) :
     't list_t result
@@ -742,7 +744,7 @@ val [list_nth_shared_mut_loop_pair_merge_loop_back_def] = DefineDiv ‘
 ’
 
 val list_nth_shared_mut_loop_pair_merge_back_def = Define ‘
-  (** [loops::list_nth_shared_mut_loop_pair_merge] *)
+  (** [loops::list_nth_shared_mut_loop_pair_merge]: backward function 0 *)
   list_nth_shared_mut_loop_pair_merge_back
     (ls0 : 't list_t) (ls1 : 't list_t) (i : u32) (ret : 't) :
     't list_t result
diff --git a/tests/hol4/misc-no_nested_borrows/noNestedBorrowsScript.sml b/tests/hol4/misc-no_nested_borrows/noNestedBorrowsScript.sml
index c8b106cd..66614c3f 100644
--- a/tests/hol4/misc-no_nested_borrows/noNestedBorrowsScript.sml
+++ b/tests/hol4/misc-no_nested_borrows/noNestedBorrowsScript.sml
@@ -38,49 +38,49 @@ Datatype:
 End
 
 val neg_test_fwd_def = Define ‘
-  (** [no_nested_borrows::neg_test] *)
+  (** [no_nested_borrows::neg_test]: forward function *)
   neg_test_fwd (x : i32) : i32 result =
     i32_neg x
 ’
 
 val add_test_fwd_def = Define ‘
-  (** [no_nested_borrows::add_test] *)
+  (** [no_nested_borrows::add_test]: forward function *)
   add_test_fwd (x : u32) (y : u32) : u32 result =
     u32_add x y
 ’
 
 val subs_test_fwd_def = Define ‘
-  (** [no_nested_borrows::subs_test] *)
+  (** [no_nested_borrows::subs_test]: forward function *)
   subs_test_fwd (x : u32) (y : u32) : u32 result =
     u32_sub x y
 ’
 
 val div_test_fwd_def = Define ‘
-  (** [no_nested_borrows::div_test] *)
+  (** [no_nested_borrows::div_test]: forward function *)
   div_test_fwd (x : u32) (y : u32) : u32 result =
     u32_div x y
 ’
 
 val div_test1_fwd_def = Define ‘
-  (** [no_nested_borrows::div_test1] *)
+  (** [no_nested_borrows::div_test1]: forward function *)
   div_test1_fwd (x : u32) : u32 result =
     u32_div x (int_to_u32 2)
 ’
 
 val rem_test_fwd_def = Define ‘
-  (** [no_nested_borrows::rem_test] *)
+  (** [no_nested_borrows::rem_test]: forward function *)
   rem_test_fwd (x : u32) (y : u32) : u32 result =
     u32_rem x y
 ’
 
 val cast_test_fwd_def = Define ‘
-  (** [no_nested_borrows::cast_test] *)
+  (** [no_nested_borrows::cast_test]: forward function *)
   cast_test_fwd (x : u32) : i32 result =
     mk_i32 (u32_to_int x)
 ’
 
 val test2_fwd_def = Define ‘
-  (** [no_nested_borrows::test2] *)
+  (** [no_nested_borrows::test2]: forward function *)
   test2_fwd : unit result =
     do
     _ <- u32_add (int_to_u32 23) (int_to_u32 44);
@@ -92,13 +92,13 @@ val test2_fwd_def = Define ‘
 val _ = assert_return (“test2_fwd”)
 
 val get_max_fwd_def = Define ‘
-  (** [no_nested_borrows::get_max] *)
+  (** [no_nested_borrows::get_max]: forward function *)
   get_max_fwd (x : u32) (y : u32) : u32 result =
     if u32_ge x y then Return x else Return y
 ’
 
 val test3_fwd_def = Define ‘
-  (** [no_nested_borrows::test3] *)
+  (** [no_nested_borrows::test3]: forward function *)
   test3_fwd : unit result =
     do
     x <- get_max_fwd (int_to_u32 4) (int_to_u32 3);
@@ -112,7 +112,7 @@ val test3_fwd_def = Define ‘
 val _ = assert_return (“test3_fwd”)
 
 val test_neg1_fwd_def = Define ‘
-  (** [no_nested_borrows::test_neg1] *)
+  (** [no_nested_borrows::test_neg1]: forward function *)
   test_neg1_fwd : unit result =
     do
     y <- i32_neg (int_to_i32 3);
@@ -124,7 +124,7 @@ val test_neg1_fwd_def = Define ‘
 val _ = assert_return (“test_neg1_fwd”)
 
 val refs_test1_fwd_def = Define ‘
-  (** [no_nested_borrows::refs_test1] *)
+  (** [no_nested_borrows::refs_test1]: forward function *)
   refs_test1_fwd : unit result =
     if ~ (int_to_i32 1 = int_to_i32 1) then Fail Failure else Return ()
 ’
@@ -133,7 +133,7 @@ val refs_test1_fwd_def = Define ‘
 val _ = assert_return (“refs_test1_fwd”)
 
 val refs_test2_fwd_def = Define ‘
-  (** [no_nested_borrows::refs_test2] *)
+  (** [no_nested_borrows::refs_test2]: forward function *)
   refs_test2_fwd : unit result =
     if ~ (int_to_i32 2 = int_to_i32 2)
     then Fail Failure
@@ -151,7 +151,7 @@ val refs_test2_fwd_def = Define ‘
 val _ = assert_return (“refs_test2_fwd”)
 
 val test_list1_fwd_def = Define ‘
-  (** [no_nested_borrows::test_list1] *)
+  (** [no_nested_borrows::test_list1]: forward function *)
   test_list1_fwd : unit result =
     Return ()
 ’
@@ -160,7 +160,7 @@ val test_list1_fwd_def = Define ‘
 val _ = assert_return (“test_list1_fwd”)
 
 val test_box1_fwd_def = Define ‘
-  (** [no_nested_borrows::test_box1] *)
+  (** [no_nested_borrows::test_box1]: forward function *)
   test_box1_fwd : unit result =
     let b = int_to_i32 1 in
     let x = b in
@@ -171,25 +171,25 @@ val test_box1_fwd_def = Define ‘
 val _ = assert_return (“test_box1_fwd”)
 
 val copy_int_fwd_def = Define ‘
-  (** [no_nested_borrows::copy_int] *)
+  (** [no_nested_borrows::copy_int]: forward function *)
   copy_int_fwd (x : i32) : i32 result =
     Return x
 ’
 
 val test_unreachable_fwd_def = Define ‘
-  (** [no_nested_borrows::test_unreachable] *)
+  (** [no_nested_borrows::test_unreachable]: forward function *)
   test_unreachable_fwd (b : bool) : unit result =
     if b then Fail Failure else Return ()
 ’
 
 val test_panic_fwd_def = Define ‘
-  (** [no_nested_borrows::test_panic] *)
+  (** [no_nested_borrows::test_panic]: forward function *)
   test_panic_fwd (b : bool) : unit result =
     if b then Fail Failure else Return ()
 ’
 
 val test_copy_int_fwd_def = Define ‘
-  (** [no_nested_borrows::test_copy_int] *)
+  (** [no_nested_borrows::test_copy_int]: forward function *)
   test_copy_int_fwd : unit result =
     do
     y <- copy_int_fwd (int_to_i32 0);
@@ -201,13 +201,13 @@ val test_copy_int_fwd_def = Define ‘
 val _ = assert_return (“test_copy_int_fwd”)
 
 val is_cons_fwd_def = Define ‘
-  (** [no_nested_borrows::is_cons] *)
+  (** [no_nested_borrows::is_cons]: forward function *)
   is_cons_fwd (l : 't list_t) : bool result =
     (case l of | ListCons t l0 => Return T | ListNil => Return F)
 ’
 
 val test_is_cons_fwd_def = Define ‘
-  (** [no_nested_borrows::test_is_cons] *)
+  (** [no_nested_borrows::test_is_cons]: forward function *)
   test_is_cons_fwd : unit result =
     let l = ListNil in
     do
@@ -220,13 +220,13 @@ val test_is_cons_fwd_def = Define ‘
 val _ = assert_return (“test_is_cons_fwd”)
 
 val split_list_fwd_def = Define ‘
-  (** [no_nested_borrows::split_list] *)
+  (** [no_nested_borrows::split_list]: forward function *)
   split_list_fwd (l : 't list_t) : ('t # 't list_t) result =
     (case l of | ListCons hd tl => Return (hd, tl) | ListNil => Fail Failure)
 ’
 
 val test_split_list_fwd_def = Define ‘
-  (** [no_nested_borrows::test_split_list] *)
+  (** [no_nested_borrows::test_split_list]: forward function *)
   test_split_list_fwd : unit result =
     let l = ListNil in
     do
@@ -240,19 +240,19 @@ val test_split_list_fwd_def = Define ‘
 val _ = assert_return (“test_split_list_fwd”)
 
 val choose_fwd_def = Define ‘
-  (** [no_nested_borrows::choose] *)
+  (** [no_nested_borrows::choose]: forward function *)
   choose_fwd (b : bool) (x : 't) (y : 't) : 't result =
     if b then Return x else Return y
 ’
 
 val choose_back_def = Define ‘
-  (** [no_nested_borrows::choose] *)
+  (** [no_nested_borrows::choose]: backward function 0 *)
   choose_back (b : bool) (x : 't) (y : 't) (ret : 't) : ('t # 't) result =
     if b then Return (ret, y) else Return (x, ret)
 ’
 
 val choose_test_fwd_def = Define ‘
-  (** [no_nested_borrows::choose_test] *)
+  (** [no_nested_borrows::choose_test]: forward function *)
   choose_test_fwd : unit result =
     do
     z <- choose_fwd T (int_to_i32 0) (int_to_i32 0);
@@ -273,7 +273,7 @@ val choose_test_fwd_def = Define ‘
 val _ = assert_return (“choose_test_fwd”)
 
 val test_char_fwd_def = Define ‘
-  (** [no_nested_borrows::test_char] *)
+  (** [no_nested_borrows::test_char]: forward function *)
   test_char_fwd : char result =
     Return #"a"
 ’
@@ -287,7 +287,7 @@ Datatype:
 End
 
 val [list_length_fwd_def] = DefineDiv ‘
-  (** [no_nested_borrows::list_length] *)
+  (** [no_nested_borrows::list_length]: forward function *)
   list_length_fwd (l : 't list_t) : u32 result =
     (case l of
     | ListCons t l1 => do
@@ -298,7 +298,7 @@ val [list_length_fwd_def] = DefineDiv ‘
 ’
 
 val [list_nth_shared_fwd_def] = DefineDiv ‘
-  (** [no_nested_borrows::list_nth_shared] *)
+  (** [no_nested_borrows::list_nth_shared]: forward function *)
   list_nth_shared_fwd (l : 't list_t) (i : u32) : 't result =
     (case l of
     | ListCons x tl =>
@@ -312,7 +312,7 @@ val [list_nth_shared_fwd_def] = DefineDiv ‘
 ’
 
 val [list_nth_mut_fwd_def] = DefineDiv ‘
-  (** [no_nested_borrows::list_nth_mut] *)
+  (** [no_nested_borrows::list_nth_mut]: forward function *)
   list_nth_mut_fwd (l : 't list_t) (i : u32) : 't result =
     (case l of
     | ListCons x tl =>
@@ -326,7 +326,7 @@ val [list_nth_mut_fwd_def] = DefineDiv ‘
 ’
 
 val [list_nth_mut_back_def] = DefineDiv ‘
-  (** [no_nested_borrows::list_nth_mut] *)
+  (** [no_nested_borrows::list_nth_mut]: backward function 0 *)
   list_nth_mut_back (l : 't list_t) (i : u32) (ret : 't) : 't list_t result =
     (case l of
     | ListCons x tl =>
@@ -342,7 +342,7 @@ val [list_nth_mut_back_def] = DefineDiv ‘
 ’
 
 val [list_rev_aux_fwd_def] = DefineDiv ‘
-  (** [no_nested_borrows::list_rev_aux] *)
+  (** [no_nested_borrows::list_rev_aux]: forward function *)
   list_rev_aux_fwd (li : 't list_t) (lo : 't list_t) : 't list_t result =
     (case li of
     | ListCons hd tl => list_rev_aux_fwd tl (ListCons hd lo)
@@ -350,13 +350,14 @@ val [list_rev_aux_fwd_def] = DefineDiv ‘
 ’
 
 val list_rev_fwd_back_def = Define ‘
-  (** [no_nested_borrows::list_rev] *)
+  (** [no_nested_borrows::list_rev]: merged forward/backward function
+      (there is a single backward function, and the forward function returns ()) *)
   list_rev_fwd_back (l : 't list_t) : 't list_t result =
     let li = mem_replace_fwd l ListNil in list_rev_aux_fwd li ListNil
 ’
 
 val test_list_functions_fwd_def = Define ‘
-  (** [no_nested_borrows::test_list_functions] *)
+  (** [no_nested_borrows::test_list_functions]: forward function *)
   test_list_functions_fwd : unit result =
     let l = ListNil in
     let l0 = ListCons (int_to_i32 2) l in
@@ -411,63 +412,63 @@ val test_list_functions_fwd_def = Define ‘
 val _ = assert_return (“test_list_functions_fwd”)
 
 val id_mut_pair1_fwd_def = Define ‘
-  (** [no_nested_borrows::id_mut_pair1] *)
+  (** [no_nested_borrows::id_mut_pair1]: forward function *)
   id_mut_pair1_fwd (x : 't1) (y : 't2) : ('t1 # 't2) result =
     Return (x, y)
 ’
 
 val id_mut_pair1_back_def = Define ‘
-  (** [no_nested_borrows::id_mut_pair1] *)
+  (** [no_nested_borrows::id_mut_pair1]: backward function 0 *)
   id_mut_pair1_back
     (x : 't1) (y : 't2) (ret : ('t1 # 't2)) : ('t1 # 't2) result =
     let (t, t0) = ret in Return (t, t0)
 ’
 
 val id_mut_pair2_fwd_def = Define ‘
-  (** [no_nested_borrows::id_mut_pair2] *)
+  (** [no_nested_borrows::id_mut_pair2]: forward function *)
   id_mut_pair2_fwd (p : ('t1 # 't2)) : ('t1 # 't2) result =
     let (t, t0) = p in Return (t, t0)
 ’
 
 val id_mut_pair2_back_def = Define ‘
-  (** [no_nested_borrows::id_mut_pair2] *)
+  (** [no_nested_borrows::id_mut_pair2]: backward function 0 *)
   id_mut_pair2_back
     (p : ('t1 # 't2)) (ret : ('t1 # 't2)) : ('t1 # 't2) result =
     let (t, t0) = ret in Return (t, t0)
 ’
 
 val id_mut_pair3_fwd_def = Define ‘
-  (** [no_nested_borrows::id_mut_pair3] *)
+  (** [no_nested_borrows::id_mut_pair3]: forward function *)
   id_mut_pair3_fwd (x : 't1) (y : 't2) : ('t1 # 't2) result =
     Return (x, y)
 ’
 
 val id_mut_pair3_back'a_def = Define ‘
-  (** [no_nested_borrows::id_mut_pair3] *)
+  (** [no_nested_borrows::id_mut_pair3]: backward function 0 *)
   id_mut_pair3_back'a (x : 't1) (y : 't2) (ret : 't1) : 't1 result =
     Return ret
 ’
 
 val id_mut_pair3_back'b_def = Define ‘
-  (** [no_nested_borrows::id_mut_pair3] *)
+  (** [no_nested_borrows::id_mut_pair3]: backward function 1 *)
   id_mut_pair3_back'b (x : 't1) (y : 't2) (ret : 't2) : 't2 result =
     Return ret
 ’
 
 val id_mut_pair4_fwd_def = Define ‘
-  (** [no_nested_borrows::id_mut_pair4] *)
+  (** [no_nested_borrows::id_mut_pair4]: forward function *)
   id_mut_pair4_fwd (p : ('t1 # 't2)) : ('t1 # 't2) result =
     let (t, t0) = p in Return (t, t0)
 ’
 
 val id_mut_pair4_back'a_def = Define ‘
-  (** [no_nested_borrows::id_mut_pair4] *)
+  (** [no_nested_borrows::id_mut_pair4]: backward function 0 *)
   id_mut_pair4_back'a (p : ('t1 # 't2)) (ret : 't1) : 't1 result =
     Return ret
 ’
 
 val id_mut_pair4_back'b_def = Define ‘
-  (** [no_nested_borrows::id_mut_pair4] *)
+  (** [no_nested_borrows::id_mut_pair4]: backward function 1 *)
   id_mut_pair4_back'b (p : ('t1 # 't2)) (ret : 't2) : 't2 result =
     Return ret
 ’
@@ -478,19 +479,19 @@ Datatype:
 End
 
 val new_tuple1_fwd_def = Define ‘
-  (** [no_nested_borrows::new_tuple1] *)
+  (** [no_nested_borrows::new_tuple1]: forward function *)
   new_tuple1_fwd : (u32, u32) struct_with_tuple_t result =
     Return (<| struct_with_tuple_p := (int_to_u32 1, int_to_u32 2) |>)
 ’
 
 val new_tuple2_fwd_def = Define ‘
-  (** [no_nested_borrows::new_tuple2] *)
+  (** [no_nested_borrows::new_tuple2]: forward function *)
   new_tuple2_fwd : (i16, i16) struct_with_tuple_t result =
     Return (<| struct_with_tuple_p := (int_to_i16 1, int_to_i16 2) |>)
 ’
 
 val new_tuple3_fwd_def = Define ‘
-  (** [no_nested_borrows::new_tuple3] *)
+  (** [no_nested_borrows::new_tuple3]: forward function *)
   new_tuple3_fwd : (u64, i64) struct_with_tuple_t result =
     Return (<| struct_with_tuple_p := (int_to_u64 1, int_to_i64 2) |>)
 ’
@@ -501,7 +502,7 @@ Datatype:
 End
 
 val new_pair1_fwd_def = Define ‘
-  (** [no_nested_borrows::new_pair1] *)
+  (** [no_nested_borrows::new_pair1]: forward function *)
   new_pair1_fwd : (u32, u32) struct_with_pair_t result =
     Return
     (<|
@@ -511,7 +512,7 @@ val new_pair1_fwd_def = Define ‘
 ’
 
 val test_constants_fwd_def = Define ‘
-  (** [no_nested_borrows::test_constants] *)
+  (** [no_nested_borrows::test_constants]: forward function *)
   test_constants_fwd : unit result =
     do
     swt <- new_tuple1_fwd;
@@ -546,7 +547,7 @@ val test_constants_fwd_def = Define ‘
 val _ = assert_return (“test_constants_fwd”)
 
 val test_weird_borrows1_fwd_def = Define ‘
-  (** [no_nested_borrows::test_weird_borrows1] *)
+  (** [no_nested_borrows::test_weird_borrows1]: forward function *)
   test_weird_borrows1_fwd : unit result =
     Return ()
 ’
@@ -555,26 +556,27 @@ val test_weird_borrows1_fwd_def = Define ‘
 val _ = assert_return (“test_weird_borrows1_fwd”)
 
 val test_mem_replace_fwd_back_def = Define ‘
-  (** [no_nested_borrows::test_mem_replace] *)
+  (** [no_nested_borrows::test_mem_replace]: merged forward/backward function
+      (there is a single backward function, and the forward function returns ()) *)
   test_mem_replace_fwd_back (px : u32) : u32 result =
     let y = mem_replace_fwd px (int_to_u32 1) in
     if ~ (y = int_to_u32 0) then Fail Failure else Return (int_to_u32 2)
 ’
 
 val test_shared_borrow_bool1_fwd_def = Define ‘
-  (** [no_nested_borrows::test_shared_borrow_bool1] *)
+  (** [no_nested_borrows::test_shared_borrow_bool1]: forward function *)
   test_shared_borrow_bool1_fwd (b : bool) : u32 result =
     if b then Return (int_to_u32 0) else Return (int_to_u32 1)
 ’
 
 val test_shared_borrow_bool2_fwd_def = Define ‘
-  (** [no_nested_borrows::test_shared_borrow_bool2] *)
+  (** [no_nested_borrows::test_shared_borrow_bool2]: forward function *)
   test_shared_borrow_bool2_fwd : u32 result =
     Return (int_to_u32 0)
 ’
 
 val test_shared_borrow_enum1_fwd_def = Define ‘
-  (** [no_nested_borrows::test_shared_borrow_enum1] *)
+  (** [no_nested_borrows::test_shared_borrow_enum1]: forward function *)
   test_shared_borrow_enum1_fwd (l : u32 list_t) : u32 result =
     (case l of
     | ListCons i l0 => Return (int_to_u32 1)
@@ -582,7 +584,7 @@ val test_shared_borrow_enum1_fwd_def = Define ‘
 ’
 
 val test_shared_borrow_enum2_fwd_def = Define ‘
-  (** [no_nested_borrows::test_shared_borrow_enum2] *)
+  (** [no_nested_borrows::test_shared_borrow_enum2]: forward function *)
   test_shared_borrow_enum2_fwd : u32 result =
     Return (int_to_u32 0)
 ’
diff --git a/tests/hol4/misc-paper/paperScript.sml b/tests/hol4/misc-paper/paperScript.sml
index 4d6e99ba..3ac5b6ca 100644
--- a/tests/hol4/misc-paper/paperScript.sml
+++ b/tests/hol4/misc-paper/paperScript.sml
@@ -6,13 +6,14 @@ val _ = new_theory "paper"
 
 
 val ref_incr_fwd_back_def = Define ‘
-  (** [paper::ref_incr] *)
+  (** [paper::ref_incr]: merged forward/backward function
+      (there is a single backward function, and the forward function returns ()) *)
   ref_incr_fwd_back (x : i32) : i32 result =
     i32_add x (int_to_i32 1)
 ’
 
 val test_incr_fwd_def = Define ‘
-  (** [paper::test_incr] *)
+  (** [paper::test_incr]: forward function *)
   test_incr_fwd : unit result =
     do
     x <- ref_incr_fwd_back (int_to_i32 0);
@@ -24,19 +25,19 @@ val test_incr_fwd_def = Define ‘
 val _ = assert_return (“test_incr_fwd”)
 
 val choose_fwd_def = Define ‘
-  (** [paper::choose] *)
+  (** [paper::choose]: forward function *)
   choose_fwd (b : bool) (x : 't) (y : 't) : 't result =
     if b then Return x else Return y
 ’
 
 val choose_back_def = Define ‘
-  (** [paper::choose] *)
+  (** [paper::choose]: backward function 0 *)
   choose_back (b : bool) (x : 't) (y : 't) (ret : 't) : ('t # 't) result =
     if b then Return (ret, y) else Return (x, ret)
 ’
 
 val test_choose_fwd_def = Define ‘
-  (** [paper::test_choose] *)
+  (** [paper::test_choose]: forward function *)
   test_choose_fwd : unit result =
     do
     z <- choose_fwd T (int_to_i32 0) (int_to_i32 0);
@@ -62,7 +63,7 @@ Datatype:
 End
 
 val [list_nth_mut_fwd_def] = DefineDiv ‘
-  (** [paper::list_nth_mut] *)
+  (** [paper::list_nth_mut]: forward function *)
   list_nth_mut_fwd (l : 't list_t) (i : u32) : 't result =
     (case l of
     | ListCons x tl =>
@@ -76,7 +77,7 @@ val [list_nth_mut_fwd_def] = DefineDiv ‘
 ’
 
 val [list_nth_mut_back_def] = DefineDiv ‘
-  (** [paper::list_nth_mut] *)
+  (** [paper::list_nth_mut]: backward function 0 *)
   list_nth_mut_back (l : 't list_t) (i : u32) (ret : 't) : 't list_t result =
     (case l of
     | ListCons x tl =>
@@ -92,7 +93,7 @@ val [list_nth_mut_back_def] = DefineDiv ‘
 ’
 
 val [sum_fwd_def] = DefineDiv ‘
-  (** [paper::sum] *)
+  (** [paper::sum]: forward function *)
   sum_fwd (l : i32 list_t) : i32 result =
     (case l of
     | ListCons x tl => do
@@ -103,7 +104,7 @@ val [sum_fwd_def] = DefineDiv ‘
 ’
 
 val test_nth_fwd_def = Define ‘
-  (** [paper::test_nth] *)
+  (** [paper::test_nth]: forward function *)
   test_nth_fwd : unit result =
     let l = ListNil in
     let l0 = ListCons (int_to_i32 3) l in
@@ -121,7 +122,7 @@ val test_nth_fwd_def = Define ‘
 val _ = assert_return (“test_nth_fwd”)
 
 val call_choose_fwd_def = Define ‘
-  (** [paper::call_choose] *)
+  (** [paper::call_choose]: forward function *)
   call_choose_fwd (p : (u32 # u32)) : u32 result =
     let (px, py) = p in
     do
diff --git a/tests/hol4/misc-polonius_list/poloniusListScript.sml b/tests/hol4/misc-polonius_list/poloniusListScript.sml
index dd631169..06876ed4 100644
--- a/tests/hol4/misc-polonius_list/poloniusListScript.sml
+++ b/tests/hol4/misc-polonius_list/poloniusListScript.sml
@@ -11,7 +11,7 @@ Datatype:
 End
 
 val [get_list_at_x_fwd_def] = DefineDiv ‘
-  (** [polonius_list::get_list_at_x] *)
+  (** [polonius_list::get_list_at_x]: forward function *)
   get_list_at_x_fwd (ls : u32 list_t) (x : u32) : u32 list_t result =
     (case ls of
     | ListCons hd tl =>
@@ -20,7 +20,7 @@ val [get_list_at_x_fwd_def] = DefineDiv ‘
 ’
 
 val [get_list_at_x_back_def] = DefineDiv ‘
-  (** [polonius_list::get_list_at_x] *)
+  (** [polonius_list::get_list_at_x]: backward function 0 *)
   get_list_at_x_back
     (ls : u32 list_t) (x : u32) (ret : u32 list_t) : u32 list_t result =
     (case ls of
diff --git a/tests/lean/.gitignore b/tests/lean/.gitignore
index e74f9899..4d1c5853 100644
--- a/tests/lean/.gitignore
+++ b/tests/lean/.gitignore
@@ -1,2 +1,2 @@
-*/lake-packages/
-*/build/
\ No newline at end of file
+lake-packages
+build
\ No newline at end of file
diff --git a/tests/lean/BetreeMain.lean b/tests/lean/BetreeMain.lean
new file mode 100644
index 00000000..5f307877
--- /dev/null
+++ b/tests/lean/BetreeMain.lean
@@ -0,0 +1 @@
+import BetreeMain.Funs
diff --git a/tests/lean/BetreeMain/Funs.lean b/tests/lean/BetreeMain/Funs.lean
new file mode 100644
index 00000000..142adf08
--- /dev/null
+++ b/tests/lean/BetreeMain/Funs.lean
@@ -0,0 +1,1023 @@
+-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
+-- [betree_main]: function definitions
+import Base
+import BetreeMain.Types
+import BetreeMain.FunsExternal
+open Primitives
+namespace betree_main
+
+/- [betree_main::betree::load_internal_node]: forward function -/
+def betree.load_internal_node
+  (id : U64) (st : State) :
+  Result (State × (betree.List (U64 × betree.Message)))
+  :=
+  betree_utils.load_internal_node id st
+
+/- [betree_main::betree::store_internal_node]: forward function -/
+def betree.store_internal_node
+  (id : U64) (content : betree.List (U64 × betree.Message)) (st : State) :
+  Result (State × Unit)
+  :=
+  do
+    let (st0, _) ← betree_utils.store_internal_node id content st
+    Result.ret (st0, ())
+
+/- [betree_main::betree::load_leaf_node]: forward function -/
+def betree.load_leaf_node
+  (id : U64) (st : State) : Result (State × (betree.List (U64 × U64))) :=
+  betree_utils.load_leaf_node id st
+
+/- [betree_main::betree::store_leaf_node]: forward function -/
+def betree.store_leaf_node
+  (id : U64) (content : betree.List (U64 × U64)) (st : State) :
+  Result (State × Unit)
+  :=
+  do
+    let (st0, _) ← betree_utils.store_leaf_node id content st
+    Result.ret (st0, ())
+
+/- [betree_main::betree::fresh_node_id]: forward function -/
+def betree.fresh_node_id (counter : U64) : Result U64 :=
+  do
+    let _ ← counter + (U64.ofInt 1)
+    Result.ret counter
+
+/- [betree_main::betree::fresh_node_id]: backward function 0 -/
+def betree.fresh_node_id_back (counter : U64) : Result U64 :=
+  counter + (U64.ofInt 1)
+
+/- [betree_main::betree::NodeIdCounter::{0}::new]: forward function -/
+def betree.NodeIdCounter.new : Result betree.NodeIdCounter :=
+  Result.ret { next_node_id := (U64.ofInt 0) }
+
+/- [betree_main::betree::NodeIdCounter::{0}::fresh_id]: forward function -/
+def betree.NodeIdCounter.fresh_id (self : betree.NodeIdCounter) : Result U64 :=
+  do
+    let _ ← self.next_node_id + (U64.ofInt 1)
+    Result.ret self.next_node_id
+
+/- [betree_main::betree::NodeIdCounter::{0}::fresh_id]: backward function 0 -/
+def betree.NodeIdCounter.fresh_id_back
+  (self : betree.NodeIdCounter) : Result betree.NodeIdCounter :=
+  do
+    let i ← self.next_node_id + (U64.ofInt 1)
+    Result.ret { next_node_id := i }
+
+/- [core::num::u64::{10}::MAX] -/
+def core_num_u64_max_body : Result U64 :=
+  Result.ret (U64.ofInt 18446744073709551615)
+def core_num_u64_max_c : U64 := eval_global core_num_u64_max_body (by simp)
+
+/- [betree_main::betree::upsert_update]: forward function -/
+def betree.upsert_update
+  (prev : Option U64) (st : betree.UpsertFunState) : Result U64 :=
+  match prev with
+  | Option.none =>
+    match st with
+    | betree.UpsertFunState.Add v => Result.ret v
+    | betree.UpsertFunState.Sub i => Result.ret (U64.ofInt 0)
+  | Option.some prev0 =>
+    match st with
+    | betree.UpsertFunState.Add v =>
+      do
+        let margin ← core_num_u64_max_c - prev0
+        if margin >= v
+        then prev0 + v
+        else Result.ret core_num_u64_max_c
+    | betree.UpsertFunState.Sub v =>
+      if prev0 >= v
+      then prev0 - v
+      else Result.ret (U64.ofInt 0)
+
+/- [betree_main::betree::List::{1}::len]: forward function -/
+divergent def betree.List.len (T : Type) (self : betree.List T) : Result U64 :=
+  match self with
+  | betree.List.Cons t tl =>
+    do
+      let i ← betree.List.len T tl
+      (U64.ofInt 1) + i
+  | betree.List.Nil => Result.ret (U64.ofInt 0)
+
+/- [betree_main::betree::List::{1}::split_at]: forward function -/
+divergent def betree.List.split_at
+  (T : Type) (self : betree.List T) (n : U64) :
+  Result ((betree.List T) × (betree.List T))
+  :=
+  if n = (U64.ofInt 0)
+  then Result.ret (betree.List.Nil, self)
+  else
+    match self with
+    | betree.List.Cons hd tl =>
+      do
+        let i ← n - (U64.ofInt 1)
+        let p ← betree.List.split_at T tl i
+        let (ls0, ls1) := p
+        let l := ls0
+        Result.ret (betree.List.Cons hd l, ls1)
+    | betree.List.Nil => Result.fail Error.panic
+
+/- [betree_main::betree::List::{1}::push_front]: merged forward/backward function
+   (there is a single backward function, and the forward function returns ()) -/
+def betree.List.push_front
+  (T : Type) (self : betree.List T) (x : T) : Result (betree.List T) :=
+  let tl := mem.replace (betree.List T) self betree.List.Nil
+  let l := tl
+  Result.ret (betree.List.Cons x l)
+
+/- [betree_main::betree::List::{1}::pop_front]: forward function -/
+def betree.List.pop_front (T : Type) (self : betree.List T) : Result T :=
+  let ls := mem.replace (betree.List T) self betree.List.Nil
+  match ls with
+  | betree.List.Cons x tl => Result.ret x
+  | betree.List.Nil => Result.fail Error.panic
+
+/- [betree_main::betree::List::{1}::pop_front]: backward function 0 -/
+def betree.List.pop_front_back
+  (T : Type) (self : betree.List T) : Result (betree.List T) :=
+  let ls := mem.replace (betree.List T) self betree.List.Nil
+  match ls with
+  | betree.List.Cons x tl => Result.ret tl
+  | betree.List.Nil => Result.fail Error.panic
+
+/- [betree_main::betree::List::{1}::hd]: forward function -/
+def betree.List.hd (T : Type) (self : betree.List T) : Result T :=
+  match self with
+  | betree.List.Cons hd l => Result.ret hd
+  | betree.List.Nil => Result.fail Error.panic
+
+/- [betree_main::betree::List::{2}::head_has_key]: forward function -/
+def betree.List.head_has_key
+  (T : Type) (self : betree.List (U64 × T)) (key : U64) : Result Bool :=
+  match self with
+  | betree.List.Cons hd l => let (i, _) := hd
+                             Result.ret (i = key)
+  | betree.List.Nil => Result.ret false
+
+/- [betree_main::betree::List::{2}::partition_at_pivot]: forward function -/
+divergent def betree.List.partition_at_pivot
+  (T : Type) (self : betree.List (U64 × T)) (pivot : U64) :
+  Result ((betree.List (U64 × T)) × (betree.List (U64 × T)))
+  :=
+  match self with
+  | betree.List.Cons hd tl =>
+    let (i, t) := hd
+    if i >= pivot
+    then Result.ret (betree.List.Nil, betree.List.Cons (i, t) tl)
+    else
+      do
+        let p ← betree.List.partition_at_pivot T tl pivot
+        let (ls0, ls1) := p
+        let l := ls0
+        Result.ret (betree.List.Cons (i, t) l, ls1)
+  | betree.List.Nil => Result.ret (betree.List.Nil, betree.List.Nil)
+
+/- [betree_main::betree::Leaf::{3}::split]: forward function -/
+def betree.Leaf.split
+  (self : betree.Leaf) (content : betree.List (U64 × U64))
+  (params : betree.Params) (node_id_cnt : betree.NodeIdCounter) (st : State) :
+  Result (State × betree.Internal)
+  :=
+  do
+    let p ← betree.List.split_at (U64 × U64) content params.split_size
+    let (content0, content1) := p
+    let p0 ← betree.List.hd (U64 × U64) content1
+    let (pivot, _) := p0
+    let id0 ← betree.NodeIdCounter.fresh_id node_id_cnt
+    let node_id_cnt0 ← betree.NodeIdCounter.fresh_id_back node_id_cnt
+    let id1 ← betree.NodeIdCounter.fresh_id node_id_cnt0
+    let (st0, _) ← betree.store_leaf_node id0 content0 st
+    let (st1, _) ← betree.store_leaf_node id1 content1 st0
+    let n := betree.Node.Leaf { id := id0, size := params.split_size }
+    let n0 := betree.Node.Leaf { id := id1, size := params.split_size }
+    Result.ret (st1, betree.Internal.mk self.id pivot n n0)
+
+/- [betree_main::betree::Leaf::{3}::split]: backward function 2 -/
+def betree.Leaf.split_back
+  (self : betree.Leaf) (content : betree.List (U64 × U64))
+  (params : betree.Params) (node_id_cnt : betree.NodeIdCounter) (st : State) :
+  Result betree.NodeIdCounter
+  :=
+  do
+    let p ← betree.List.split_at (U64 × U64) content params.split_size
+    let (content0, content1) := p
+    let _ ← betree.List.hd (U64 × U64) content1
+    let id0 ← betree.NodeIdCounter.fresh_id node_id_cnt
+    let node_id_cnt0 ← betree.NodeIdCounter.fresh_id_back node_id_cnt
+    let id1 ← betree.NodeIdCounter.fresh_id node_id_cnt0
+    let (st0, _) ← betree.store_leaf_node id0 content0 st
+    let _ ← betree.store_leaf_node id1 content1 st0
+    betree.NodeIdCounter.fresh_id_back node_id_cnt0
+
+/- [betree_main::betree::Node::{5}::lookup_in_bindings]: forward function -/
+divergent def betree.Node.lookup_in_bindings
+  (key : U64) (bindings : betree.List (U64 × U64)) : Result (Option U64) :=
+  match bindings with
+  | betree.List.Cons hd tl =>
+    let (i, i0) := hd
+    if i = key
+    then Result.ret (Option.some i0)
+    else
+      if i > key
+      then Result.ret Option.none
+      else betree.Node.lookup_in_bindings key tl
+  | betree.List.Nil => Result.ret Option.none
+
+/- [betree_main::betree::Node::{5}::lookup_first_message_for_key]: forward function -/
+divergent def betree.Node.lookup_first_message_for_key
+  (key : U64) (msgs : betree.List (U64 × betree.Message)) :
+  Result (betree.List (U64 × betree.Message))
+  :=
+  match msgs with
+  | betree.List.Cons x next_msgs =>
+    let (i, m) := x
+    if i >= key
+    then Result.ret (betree.List.Cons (i, m) next_msgs)
+    else betree.Node.lookup_first_message_for_key key next_msgs
+  | betree.List.Nil => Result.ret betree.List.Nil
+
+/- [betree_main::betree::Node::{5}::lookup_first_message_for_key]: backward function 0 -/
+divergent def betree.Node.lookup_first_message_for_key_back
+  (key : U64) (msgs : betree.List (U64 × betree.Message))
+  (ret0 : betree.List (U64 × betree.Message)) :
+  Result (betree.List (U64 × betree.Message))
+  :=
+  match msgs with
+  | betree.List.Cons x next_msgs =>
+    let (i, m) := x
+    if i >= key
+    then Result.ret ret0
+    else
+      do
+        let next_msgs0 ←
+          betree.Node.lookup_first_message_for_key_back key next_msgs ret0
+        Result.ret (betree.List.Cons (i, m) next_msgs0)
+  | betree.List.Nil => Result.ret ret0
+
+/- [betree_main::betree::Node::{5}::apply_upserts]: forward function -/
+divergent def betree.Node.apply_upserts
+  (msgs : betree.List (U64 × betree.Message)) (prev : Option U64) (key : U64)
+  (st : State) :
+  Result (State × U64)
+  :=
+  do
+    let b ← betree.List.head_has_key betree.Message msgs key
+    if b
+    then
+      do
+        let msg ← betree.List.pop_front (U64 × betree.Message) msgs
+        let (_, m) := msg
+        match m with
+        | betree.Message.Insert i => Result.fail Error.panic
+        | betree.Message.Delete => Result.fail Error.panic
+        | betree.Message.Upsert s =>
+          do
+            let v ← betree.upsert_update prev s
+            let msgs0 ←
+              betree.List.pop_front_back (U64 × betree.Message) msgs
+            betree.Node.apply_upserts msgs0 (Option.some v) key st
+    else
+      do
+        let (st0, v) ← core.option.Option.unwrap U64 prev st
+        let _ ←
+          betree.List.push_front (U64 × betree.Message) msgs (key,
+            betree.Message.Insert v)
+        Result.ret (st0, v)
+
+/- [betree_main::betree::Node::{5}::apply_upserts]: backward function 0 -/
+divergent def betree.Node.apply_upserts_back
+  (msgs : betree.List (U64 × betree.Message)) (prev : Option U64) (key : U64)
+  (st : State) :
+  Result (betree.List (U64 × betree.Message))
+  :=
+  do
+    let b ← betree.List.head_has_key betree.Message msgs key
+    if b
+    then
+      do
+        let msg ← betree.List.pop_front (U64 × betree.Message) msgs
+        let (_, m) := msg
+        match m with
+        | betree.Message.Insert i => Result.fail Error.panic
+        | betree.Message.Delete => Result.fail Error.panic
+        | betree.Message.Upsert s =>
+          do
+            let v ← betree.upsert_update prev s
+            let msgs0 ←
+              betree.List.pop_front_back (U64 × betree.Message) msgs
+            betree.Node.apply_upserts_back msgs0 (Option.some v) key st
+    else
+      do
+        let (_, v) ← core.option.Option.unwrap U64 prev st
+        betree.List.push_front (U64 × betree.Message) msgs (key,
+          betree.Message.Insert v)
+
+/- [betree_main::betree::Node::{5}::lookup]: forward function -/
+mutual divergent def betree.Node.lookup
+  (self : betree.Node) (key : U64) (st : State) :
+  Result (State × (Option U64))
+  :=
+  match self with
+  | betree.Node.Internal node =>
+    do
+      let ⟨ i, i0, n, n0 ⟩ := node
+      let (st0, msgs) ← betree.load_internal_node i st
+      let pending ← betree.Node.lookup_first_message_for_key key msgs
+      match pending with
+      | betree.List.Cons p l =>
+        let (k, msg) := p
+        if k != key
+        then
+          do
+            let (st1, opt) ←
+              betree.Internal.lookup_in_children (betree.Internal.mk i i0 n n0)
+                key st0
+            let _ ←
+              betree.Node.lookup_first_message_for_key_back key msgs
+                (betree.List.Cons (k, msg) l)
+            Result.ret (st1, opt)
+        else
+          match msg with
+          | betree.Message.Insert v =>
+            do
+              let _ ←
+                betree.Node.lookup_first_message_for_key_back key msgs
+                  (betree.List.Cons (k, betree.Message.Insert v) l)
+              Result.ret (st0, Option.some v)
+          | betree.Message.Delete =>
+            do
+              let _ ←
+                betree.Node.lookup_first_message_for_key_back key msgs
+                  (betree.List.Cons (k, betree.Message.Delete) l)
+              Result.ret (st0, Option.none)
+          | betree.Message.Upsert ufs =>
+            do
+              let (st1, v) ←
+                betree.Internal.lookup_in_children (betree.Internal.mk i i0 n
+                  n0) key st0
+              let (st2, v0) ←
+                betree.Node.apply_upserts (betree.List.Cons (k,
+                  betree.Message.Upsert ufs) l) v key st1
+              let node0 ←
+                betree.Internal.lookup_in_children_back (betree.Internal.mk i
+                  i0 n n0) key st0
+              let ⟨ i1, _, _, _ ⟩ := node0
+              let pending0 ←
+                betree.Node.apply_upserts_back (betree.List.Cons (k,
+                  betree.Message.Upsert ufs) l) v key st1
+              let msgs0 ←
+                betree.Node.lookup_first_message_for_key_back key msgs pending0
+              let (st3, _) ← betree.store_internal_node i1 msgs0 st2
+              Result.ret (st3, Option.some v0)
+      | betree.List.Nil =>
+        do
+          let (st1, opt) ←
+            betree.Internal.lookup_in_children (betree.Internal.mk i i0 n n0)
+              key st0
+          let _ ←
+            betree.Node.lookup_first_message_for_key_back key msgs
+              betree.List.Nil
+          Result.ret (st1, opt)
+  | betree.Node.Leaf node =>
+    do
+      let (st0, bindings) ← betree.load_leaf_node node.id st
+      let opt ← betree.Node.lookup_in_bindings key bindings
+      Result.ret (st0, opt)
+
+/- [betree_main::betree::Node::{5}::lookup]: backward function 0 -/
+divergent def betree.Node.lookup_back
+  (self : betree.Node) (key : U64) (st : State) : Result betree.Node :=
+  match self with
+  | betree.Node.Internal node =>
+    do
+      let ⟨ i, i0, n, n0 ⟩ := node
+      let (st0, msgs) ← betree.load_internal_node i st
+      let pending ← betree.Node.lookup_first_message_for_key key msgs
+      match pending with
+      | betree.List.Cons p l =>
+        let (k, msg) := p
+        if k != key
+        then
+          do
+            let _ ←
+              betree.Node.lookup_first_message_for_key_back key msgs
+                (betree.List.Cons (k, msg) l)
+            let node0 ←
+              betree.Internal.lookup_in_children_back (betree.Internal.mk i i0
+                n n0) key st0
+            Result.ret (betree.Node.Internal node0)
+        else
+          match msg with
+          | betree.Message.Insert v =>
+            do
+              let _ ←
+                betree.Node.lookup_first_message_for_key_back key msgs
+                  (betree.List.Cons (k, betree.Message.Insert v) l)
+              Result.ret (betree.Node.Internal (betree.Internal.mk i i0 n n0))
+          | betree.Message.Delete =>
+            do
+              let _ ←
+                betree.Node.lookup_first_message_for_key_back key msgs
+                  (betree.List.Cons (k, betree.Message.Delete) l)
+              Result.ret (betree.Node.Internal (betree.Internal.mk i i0 n n0))
+          | betree.Message.Upsert ufs =>
+            do
+              let (st1, v) ←
+                betree.Internal.lookup_in_children (betree.Internal.mk i i0 n
+                  n0) key st0
+              let (st2, _) ←
+                betree.Node.apply_upserts (betree.List.Cons (k,
+                  betree.Message.Upsert ufs) l) v key st1
+              let node0 ←
+                betree.Internal.lookup_in_children_back (betree.Internal.mk i
+                  i0 n n0) key st0
+              let ⟨ i1, i2, n1, n2 ⟩ := node0
+              let pending0 ←
+                betree.Node.apply_upserts_back (betree.List.Cons (k,
+                  betree.Message.Upsert ufs) l) v key st1
+              let msgs0 ←
+                betree.Node.lookup_first_message_for_key_back key msgs pending0
+              let _ ← betree.store_internal_node i1 msgs0 st2
+              Result.ret (betree.Node.Internal (betree.Internal.mk i1 i2 n1
+                n2))
+      | betree.List.Nil =>
+        do
+          let _ ←
+            betree.Node.lookup_first_message_for_key_back key msgs
+              betree.List.Nil
+          let node0 ←
+            betree.Internal.lookup_in_children_back (betree.Internal.mk i i0 n
+              n0) key st0
+          Result.ret (betree.Node.Internal node0)
+  | betree.Node.Leaf node =>
+    do
+      let (_, bindings) ← betree.load_leaf_node node.id st
+      let _ ← betree.Node.lookup_in_bindings key bindings
+      Result.ret (betree.Node.Leaf node)
+
+/- [betree_main::betree::Internal::{4}::lookup_in_children]: forward function -/
+divergent def betree.Internal.lookup_in_children
+  (self : betree.Internal) (key : U64) (st : State) :
+  Result (State × (Option U64))
+  :=
+  let ⟨ _, i, n, n0 ⟩ := self
+  if key < i
+  then betree.Node.lookup n key st
+  else betree.Node.lookup n0 key st
+
+/- [betree_main::betree::Internal::{4}::lookup_in_children]: backward function 0 -/
+divergent def betree.Internal.lookup_in_children_back
+  (self : betree.Internal) (key : U64) (st : State) : Result betree.Internal :=
+  let ⟨ i, i0, n, n0 ⟩ := self
+  if key < i0
+  then
+    do
+      let n1 ← betree.Node.lookup_back n key st
+      Result.ret (betree.Internal.mk i i0 n1 n0)
+  else
+    do
+      let n1 ← betree.Node.lookup_back n0 key st
+      Result.ret (betree.Internal.mk i i0 n n1)
+
+end
+
+/- [betree_main::betree::Node::{5}::lookup_mut_in_bindings]: forward function -/
+divergent def betree.Node.lookup_mut_in_bindings
+  (key : U64) (bindings : betree.List (U64 × U64)) :
+  Result (betree.List (U64 × U64))
+  :=
+  match bindings with
+  | betree.List.Cons hd tl =>
+    let (i, i0) := hd
+    if i >= key
+    then Result.ret (betree.List.Cons (i, i0) tl)
+    else betree.Node.lookup_mut_in_bindings key tl
+  | betree.List.Nil => Result.ret betree.List.Nil
+
+/- [betree_main::betree::Node::{5}::lookup_mut_in_bindings]: backward function 0 -/
+divergent def betree.Node.lookup_mut_in_bindings_back
+  (key : U64) (bindings : betree.List (U64 × U64))
+  (ret0 : betree.List (U64 × U64)) :
+  Result (betree.List (U64 × U64))
+  :=
+  match bindings with
+  | betree.List.Cons hd tl =>
+    let (i, i0) := hd
+    if i >= key
+    then Result.ret ret0
+    else
+      do
+        let tl0 ← betree.Node.lookup_mut_in_bindings_back key tl ret0
+        Result.ret (betree.List.Cons (i, i0) tl0)
+  | betree.List.Nil => Result.ret ret0
+
+/- [betree_main::betree::Node::{5}::apply_to_leaf]: merged forward/backward function
+   (there is a single backward function, and the forward function returns ()) -/
+def betree.Node.apply_to_leaf
+  (bindings : betree.List (U64 × U64)) (key : U64) (new_msg : betree.Message)
+  :
+  Result (betree.List (U64 × U64))
+  :=
+  do
+    let bindings0 ← betree.Node.lookup_mut_in_bindings key bindings
+    let b ← betree.List.head_has_key U64 bindings0 key
+    if b
+    then
+      do
+        let hd ← betree.List.pop_front (U64 × U64) bindings0
+        match new_msg with
+        | betree.Message.Insert v =>
+          do
+            let bindings1 ← betree.List.pop_front_back (U64 × U64) bindings0
+            let bindings2 ←
+              betree.List.push_front (U64 × U64) bindings1 (key, v)
+            betree.Node.lookup_mut_in_bindings_back key bindings bindings2
+        | betree.Message.Delete =>
+          do
+            let bindings1 ← betree.List.pop_front_back (U64 × U64) bindings0
+            betree.Node.lookup_mut_in_bindings_back key bindings bindings1
+        | betree.Message.Upsert s =>
+          do
+            let (_, i) := hd
+            let v ← betree.upsert_update (Option.some i) s
+            let bindings1 ← betree.List.pop_front_back (U64 × U64) bindings0
+            let bindings2 ←
+              betree.List.push_front (U64 × U64) bindings1 (key, v)
+            betree.Node.lookup_mut_in_bindings_back key bindings bindings2
+    else
+      match new_msg with
+      | betree.Message.Insert v =>
+        do
+          let bindings1 ←
+            betree.List.push_front (U64 × U64) bindings0 (key, v)
+          betree.Node.lookup_mut_in_bindings_back key bindings bindings1
+      | betree.Message.Delete =>
+        betree.Node.lookup_mut_in_bindings_back key bindings bindings0
+      | betree.Message.Upsert s =>
+        do
+          let v ← betree.upsert_update Option.none s
+          let bindings1 ←
+            betree.List.push_front (U64 × U64) bindings0 (key, v)
+          betree.Node.lookup_mut_in_bindings_back key bindings bindings1
+
+/- [betree_main::betree::Node::{5}::apply_messages_to_leaf]: merged forward/backward function
+   (there is a single backward function, and the forward function returns ()) -/
+divergent def betree.Node.apply_messages_to_leaf
+  (bindings : betree.List (U64 × U64))
+  (new_msgs : betree.List (U64 × betree.Message)) :
+  Result (betree.List (U64 × U64))
+  :=
+  match new_msgs with
+  | betree.List.Cons new_msg new_msgs_tl =>
+    do
+      let (i, m) := new_msg
+      let bindings0 ← betree.Node.apply_to_leaf bindings i m
+      betree.Node.apply_messages_to_leaf bindings0 new_msgs_tl
+  | betree.List.Nil => Result.ret bindings
+
+/- [betree_main::betree::Node::{5}::filter_messages_for_key]: merged forward/backward function
+   (there is a single backward function, and the forward function returns ()) -/
+divergent def betree.Node.filter_messages_for_key
+  (key : U64) (msgs : betree.List (U64 × betree.Message)) :
+  Result (betree.List (U64 × betree.Message))
+  :=
+  match msgs with
+  | betree.List.Cons p l =>
+    let (k, m) := p
+    if k = key
+    then
+      do
+        let msgs0 ←
+          betree.List.pop_front_back (U64 × betree.Message) (betree.List.Cons
+            (k, m) l)
+        betree.Node.filter_messages_for_key key msgs0
+    else Result.ret (betree.List.Cons (k, m) l)
+  | betree.List.Nil => Result.ret betree.List.Nil
+
+/- [betree_main::betree::Node::{5}::lookup_first_message_after_key]: forward function -/
+divergent def betree.Node.lookup_first_message_after_key
+  (key : U64) (msgs : betree.List (U64 × betree.Message)) :
+  Result (betree.List (U64 × betree.Message))
+  :=
+  match msgs with
+  | betree.List.Cons p next_msgs =>
+    let (k, m) := p
+    if k = key
+    then betree.Node.lookup_first_message_after_key key next_msgs
+    else Result.ret (betree.List.Cons (k, m) next_msgs)
+  | betree.List.Nil => Result.ret betree.List.Nil
+
+/- [betree_main::betree::Node::{5}::lookup_first_message_after_key]: backward function 0 -/
+divergent def betree.Node.lookup_first_message_after_key_back
+  (key : U64) (msgs : betree.List (U64 × betree.Message))
+  (ret0 : betree.List (U64 × betree.Message)) :
+  Result (betree.List (U64 × betree.Message))
+  :=
+  match msgs with
+  | betree.List.Cons p next_msgs =>
+    let (k, m) := p
+    if k = key
+    then
+      do
+        let next_msgs0 ←
+          betree.Node.lookup_first_message_after_key_back key next_msgs ret0
+        Result.ret (betree.List.Cons (k, m) next_msgs0)
+    else Result.ret ret0
+  | betree.List.Nil => Result.ret ret0
+
+/- [betree_main::betree::Node::{5}::apply_to_internal]: merged forward/backward function
+   (there is a single backward function, and the forward function returns ()) -/
+def betree.Node.apply_to_internal
+  (msgs : betree.List (U64 × betree.Message)) (key : U64)
+  (new_msg : betree.Message) :
+  Result (betree.List (U64 × betree.Message))
+  :=
+  do
+    let msgs0 ← betree.Node.lookup_first_message_for_key key msgs
+    let b ← betree.List.head_has_key betree.Message msgs0 key
+    if b
+    then
+      match new_msg with
+      | betree.Message.Insert i =>
+        do
+          let msgs1 ← betree.Node.filter_messages_for_key key msgs0
+          let msgs2 ←
+            betree.List.push_front (U64 × betree.Message) msgs1 (key,
+              betree.Message.Insert i)
+          betree.Node.lookup_first_message_for_key_back key msgs msgs2
+      | betree.Message.Delete =>
+        do
+          let msgs1 ← betree.Node.filter_messages_for_key key msgs0
+          let msgs2 ←
+            betree.List.push_front (U64 × betree.Message) msgs1 (key,
+              betree.Message.Delete)
+          betree.Node.lookup_first_message_for_key_back key msgs msgs2
+      | betree.Message.Upsert s =>
+        do
+          let p ← betree.List.hd (U64 × betree.Message) msgs0
+          let (_, m) := p
+          match m with
+          | betree.Message.Insert prev =>
+            do
+              let v ← betree.upsert_update (Option.some prev) s
+              let msgs1 ←
+                betree.List.pop_front_back (U64 × betree.Message) msgs0
+              let msgs2 ←
+                betree.List.push_front (U64 × betree.Message) msgs1 (key,
+                  betree.Message.Insert v)
+              betree.Node.lookup_first_message_for_key_back key msgs msgs2
+          | betree.Message.Delete =>
+            do
+              let v ← betree.upsert_update Option.none s
+              let msgs1 ←
+                betree.List.pop_front_back (U64 × betree.Message) msgs0
+              let msgs2 ←
+                betree.List.push_front (U64 × betree.Message) msgs1 (key,
+                  betree.Message.Insert v)
+              betree.Node.lookup_first_message_for_key_back key msgs msgs2
+          | betree.Message.Upsert ufs =>
+            do
+              let msgs1 ←
+                betree.Node.lookup_first_message_after_key key msgs0
+              let msgs2 ←
+                betree.List.push_front (U64 × betree.Message) msgs1 (key,
+                  betree.Message.Upsert s)
+              let msgs3 ←
+                betree.Node.lookup_first_message_after_key_back key msgs0 msgs2
+              betree.Node.lookup_first_message_for_key_back key msgs msgs3
+    else
+      do
+        let msgs1 ←
+          betree.List.push_front (U64 × betree.Message) msgs0 (key, new_msg)
+        betree.Node.lookup_first_message_for_key_back key msgs msgs1
+
+/- [betree_main::betree::Node::{5}::apply_messages_to_internal]: merged forward/backward function
+   (there is a single backward function, and the forward function returns ()) -/
+divergent def betree.Node.apply_messages_to_internal
+  (msgs : betree.List (U64 × betree.Message))
+  (new_msgs : betree.List (U64 × betree.Message)) :
+  Result (betree.List (U64 × betree.Message))
+  :=
+  match new_msgs with
+  | betree.List.Cons new_msg new_msgs_tl =>
+    do
+      let (i, m) := new_msg
+      let msgs0 ← betree.Node.apply_to_internal msgs i m
+      betree.Node.apply_messages_to_internal msgs0 new_msgs_tl
+  | betree.List.Nil => Result.ret msgs
+
+/- [betree_main::betree::Node::{5}::apply_messages]: forward function -/
+mutual divergent def betree.Node.apply_messages
+  (self : betree.Node) (params : betree.Params)
+  (node_id_cnt : betree.NodeIdCounter)
+  (msgs : betree.List (U64 × betree.Message)) (st : State) :
+  Result (State × Unit)
+  :=
+  match self with
+  | betree.Node.Internal node =>
+    do
+      let ⟨ i, i0, n, n0 ⟩ := node
+      let (st0, content) ← betree.load_internal_node i st
+      let content0 ← betree.Node.apply_messages_to_internal content msgs
+      let num_msgs ← betree.List.len (U64 × betree.Message) content0
+      if num_msgs >= params.min_flush_size
+      then
+        do
+          let (st1, content1) ←
+            betree.Internal.flush (betree.Internal.mk i i0 n n0) params
+              node_id_cnt content0 st0
+          let (node0, _) ←
+            betree.Internal.flush_back (betree.Internal.mk i i0 n n0) params
+              node_id_cnt content0 st0
+          let ⟨ i1, _, _, _ ⟩ := node0
+          let (st2, _) ← betree.store_internal_node i1 content1 st1
+          Result.ret (st2, ())
+      else
+        do
+          let (st1, _) ← betree.store_internal_node i content0 st0
+          Result.ret (st1, ())
+  | betree.Node.Leaf node =>
+    do
+      let (st0, content) ← betree.load_leaf_node node.id st
+      let content0 ← betree.Node.apply_messages_to_leaf content msgs
+      let len ← betree.List.len (U64 × U64) content0
+      let i ← (U64.ofInt 2) * params.split_size
+      if len >= i
+      then
+        do
+          let (st1, _) ←
+            betree.Leaf.split node content0 params node_id_cnt st0
+          let (st2, _) ← betree.store_leaf_node node.id betree.List.Nil st1
+          Result.ret (st2, ())
+      else
+        do
+          let (st1, _) ← betree.store_leaf_node node.id content0 st0
+          Result.ret (st1, ())
+
+/- [betree_main::betree::Node::{5}::apply_messages]: backward function 0 -/
+divergent def betree.Node.apply_messages_back
+  (self : betree.Node) (params : betree.Params)
+  (node_id_cnt : betree.NodeIdCounter)
+  (msgs : betree.List (U64 × betree.Message)) (st : State) :
+  Result (betree.Node × betree.NodeIdCounter)
+  :=
+  match self with
+  | betree.Node.Internal node =>
+    do
+      let ⟨ i, i0, n, n0 ⟩ := node
+      let (st0, content) ← betree.load_internal_node i st
+      let content0 ← betree.Node.apply_messages_to_internal content msgs
+      let num_msgs ← betree.List.len (U64 × betree.Message) content0
+      if num_msgs >= params.min_flush_size
+      then
+        do
+          let (st1, content1) ←
+            betree.Internal.flush (betree.Internal.mk i i0 n n0) params
+              node_id_cnt content0 st0
+          let (node0, node_id_cnt0) ←
+            betree.Internal.flush_back (betree.Internal.mk i i0 n n0) params
+              node_id_cnt content0 st0
+          let ⟨ i1, i2, n1, n2 ⟩ := node0
+          let _ ← betree.store_internal_node i1 content1 st1
+          Result.ret (betree.Node.Internal (betree.Internal.mk i1 i2 n1 n2),
+            node_id_cnt0)
+      else
+        do
+          let _ ← betree.store_internal_node i content0 st0
+          Result.ret (betree.Node.Internal (betree.Internal.mk i i0 n n0),
+            node_id_cnt)
+  | betree.Node.Leaf node =>
+    do
+      let (st0, content) ← betree.load_leaf_node node.id st
+      let content0 ← betree.Node.apply_messages_to_leaf content msgs
+      let len ← betree.List.len (U64 × U64) content0
+      let i ← (U64.ofInt 2) * params.split_size
+      if len >= i
+      then
+        do
+          let (st1, new_node) ←
+            betree.Leaf.split node content0 params node_id_cnt st0
+          let _ ← betree.store_leaf_node node.id betree.List.Nil st1
+          let node_id_cnt0 ←
+            betree.Leaf.split_back node content0 params node_id_cnt st0
+          Result.ret (betree.Node.Internal new_node, node_id_cnt0)
+      else
+        do
+          let _ ← betree.store_leaf_node node.id content0 st0
+          Result.ret (betree.Node.Leaf { node with size := len }, node_id_cnt)
+
+/- [betree_main::betree::Internal::{4}::flush]: forward function -/
+divergent def betree.Internal.flush
+  (self : betree.Internal) (params : betree.Params)
+  (node_id_cnt : betree.NodeIdCounter)
+  (content : betree.List (U64 × betree.Message)) (st : State) :
+  Result (State × (betree.List (U64 × betree.Message)))
+  :=
+  do
+    let ⟨ _, i, n, n0 ⟩ := self
+    let p ← betree.List.partition_at_pivot betree.Message content i
+    let (msgs_left, msgs_right) := p
+    let len_left ← betree.List.len (U64 × betree.Message) msgs_left
+    if len_left >= params.min_flush_size
+    then
+      do
+        let (st0, _) ←
+          betree.Node.apply_messages n params node_id_cnt msgs_left st
+        let (_, node_id_cnt0) ←
+          betree.Node.apply_messages_back n params node_id_cnt msgs_left st
+        let len_right ← betree.List.len (U64 × betree.Message) msgs_right
+        if len_right >= params.min_flush_size
+        then
+          do
+            let (st1, _) ←
+              betree.Node.apply_messages n0 params node_id_cnt0 msgs_right st0
+            let _ ←
+              betree.Node.apply_messages_back n0 params node_id_cnt0 msgs_right
+                st0
+            Result.ret (st1, betree.List.Nil)
+        else Result.ret (st0, msgs_right)
+    else
+      do
+        let (st0, _) ←
+          betree.Node.apply_messages n0 params node_id_cnt msgs_right st
+        let _ ←
+          betree.Node.apply_messages_back n0 params node_id_cnt msgs_right st
+        Result.ret (st0, msgs_left)
+
+/- [betree_main::betree::Internal::{4}::flush]: backward function 0 -/
+divergent def betree.Internal.flush_back
+  (self : betree.Internal) (params : betree.Params)
+  (node_id_cnt : betree.NodeIdCounter)
+  (content : betree.List (U64 × betree.Message)) (st : State) :
+  Result (betree.Internal × betree.NodeIdCounter)
+  :=
+  do
+    let ⟨ i, i0, n, n0 ⟩ := self
+    let p ← betree.List.partition_at_pivot betree.Message content i0
+    let (msgs_left, msgs_right) := p
+    let len_left ← betree.List.len (U64 × betree.Message) msgs_left
+    if len_left >= params.min_flush_size
+    then
+      do
+        let (st0, _) ←
+          betree.Node.apply_messages n params node_id_cnt msgs_left st
+        let (n1, node_id_cnt0) ←
+          betree.Node.apply_messages_back n params node_id_cnt msgs_left st
+        let len_right ← betree.List.len (U64 × betree.Message) msgs_right
+        if len_right >= params.min_flush_size
+        then
+          do
+            let (n2, node_id_cnt1) ←
+              betree.Node.apply_messages_back n0 params node_id_cnt0 msgs_right
+                st0
+            Result.ret (betree.Internal.mk i i0 n1 n2, node_id_cnt1)
+        else Result.ret (betree.Internal.mk i i0 n1 n0, node_id_cnt0)
+    else
+      do
+        let (n1, node_id_cnt0) ←
+          betree.Node.apply_messages_back n0 params node_id_cnt msgs_right st
+        Result.ret (betree.Internal.mk i i0 n n1, node_id_cnt0)
+
+end
+
+/- [betree_main::betree::Node::{5}::apply]: forward function -/
+def betree.Node.apply
+  (self : betree.Node) (params : betree.Params)
+  (node_id_cnt : betree.NodeIdCounter) (key : U64) (new_msg : betree.Message)
+  (st : State) :
+  Result (State × Unit)
+  :=
+  do
+    let l := betree.List.Nil
+    let (st0, _) ←
+      betree.Node.apply_messages self params node_id_cnt (betree.List.Cons
+        (key, new_msg) l) st
+    let _ ←
+      betree.Node.apply_messages_back self params node_id_cnt (betree.List.Cons
+        (key, new_msg) l) st
+    Result.ret (st0, ())
+
+/- [betree_main::betree::Node::{5}::apply]: backward function 0 -/
+def betree.Node.apply_back
+  (self : betree.Node) (params : betree.Params)
+  (node_id_cnt : betree.NodeIdCounter) (key : U64) (new_msg : betree.Message)
+  (st : State) :
+  Result (betree.Node × betree.NodeIdCounter)
+  :=
+  let l := betree.List.Nil
+  betree.Node.apply_messages_back self params node_id_cnt (betree.List.Cons
+    (key, new_msg) l) st
+
+/- [betree_main::betree::BeTree::{6}::new]: forward function -/
+def betree.BeTree.new
+  (min_flush_size : U64) (split_size : U64) (st : State) :
+  Result (State × betree.BeTree)
+  :=
+  do
+    let node_id_cnt ← betree.NodeIdCounter.new
+    let id ← betree.NodeIdCounter.fresh_id node_id_cnt
+    let (st0, _) ← betree.store_leaf_node id betree.List.Nil st
+    let node_id_cnt0 ← betree.NodeIdCounter.fresh_id_back node_id_cnt
+    Result.ret (st0,
+      {
+        params :=
+          { min_flush_size := min_flush_size, split_size := split_size },
+        node_id_cnt := node_id_cnt0,
+        root := (betree.Node.Leaf { id := id, size := (U64.ofInt 0) })
+      })
+
+/- [betree_main::betree::BeTree::{6}::apply]: forward function -/
+def betree.BeTree.apply
+  (self : betree.BeTree) (key : U64) (msg : betree.Message) (st : State) :
+  Result (State × Unit)
+  :=
+  do
+    let (st0, _) ←
+      betree.Node.apply self.root self.params self.node_id_cnt key msg st
+    let _ ←
+      betree.Node.apply_back self.root self.params self.node_id_cnt key msg st
+    Result.ret (st0, ())
+
+/- [betree_main::betree::BeTree::{6}::apply]: backward function 0 -/
+def betree.BeTree.apply_back
+  (self : betree.BeTree) (key : U64) (msg : betree.Message) (st : State) :
+  Result betree.BeTree
+  :=
+  do
+    let (n, nic) ←
+      betree.Node.apply_back self.root self.params self.node_id_cnt key msg st
+    Result.ret { self with node_id_cnt := nic, root := n }
+
+/- [betree_main::betree::BeTree::{6}::insert]: forward function -/
+def betree.BeTree.insert
+  (self : betree.BeTree) (key : U64) (value : U64) (st : State) :
+  Result (State × Unit)
+  :=
+  do
+    let (st0, _) ←
+      betree.BeTree.apply self key (betree.Message.Insert value) st
+    let _ ←
+      betree.BeTree.apply_back self key (betree.Message.Insert value) st
+    Result.ret (st0, ())
+
+/- [betree_main::betree::BeTree::{6}::insert]: backward function 0 -/
+def betree.BeTree.insert_back
+  (self : betree.BeTree) (key : U64) (value : U64) (st : State) :
+  Result betree.BeTree
+  :=
+  betree.BeTree.apply_back self key (betree.Message.Insert value) st
+
+/- [betree_main::betree::BeTree::{6}::delete]: forward function -/
+def betree.BeTree.delete
+  (self : betree.BeTree) (key : U64) (st : State) : Result (State × Unit) :=
+  do
+    let (st0, _) ← betree.BeTree.apply self key betree.Message.Delete st
+    let _ ← betree.BeTree.apply_back self key betree.Message.Delete st
+    Result.ret (st0, ())
+
+/- [betree_main::betree::BeTree::{6}::delete]: backward function 0 -/
+def betree.BeTree.delete_back
+  (self : betree.BeTree) (key : U64) (st : State) : Result betree.BeTree :=
+  betree.BeTree.apply_back self key betree.Message.Delete st
+
+/- [betree_main::betree::BeTree::{6}::upsert]: forward function -/
+def betree.BeTree.upsert
+  (self : betree.BeTree) (key : U64) (upd : betree.UpsertFunState) (st : State)
+  :
+  Result (State × Unit)
+  :=
+  do
+    let (st0, _) ←
+      betree.BeTree.apply self key (betree.Message.Upsert upd) st
+    let _ ← betree.BeTree.apply_back self key (betree.Message.Upsert upd) st
+    Result.ret (st0, ())
+
+/- [betree_main::betree::BeTree::{6}::upsert]: backward function 0 -/
+def betree.BeTree.upsert_back
+  (self : betree.BeTree) (key : U64) (upd : betree.UpsertFunState) (st : State)
+  :
+  Result betree.BeTree
+  :=
+  betree.BeTree.apply_back self key (betree.Message.Upsert upd) st
+
+/- [betree_main::betree::BeTree::{6}::lookup]: forward function -/
+def betree.BeTree.lookup
+  (self : betree.BeTree) (key : U64) (st : State) :
+  Result (State × (Option U64))
+  :=
+  betree.Node.lookup self.root key st
+
+/- [betree_main::betree::BeTree::{6}::lookup]: backward function 0 -/
+def betree.BeTree.lookup_back
+  (self : betree.BeTree) (key : U64) (st : State) : Result betree.BeTree :=
+  do
+    let n ← betree.Node.lookup_back self.root key st
+    Result.ret { self with root := n }
+
+/- [betree_main::main]: forward function -/
+def main : Result Unit :=
+  Result.ret ()
+
+/- Unit test for [betree_main::main] -/
+#assert (main == .ret ())
+
+end betree_main
diff --git a/tests/lean/BetreeMain/FunsExternal.lean b/tests/lean/BetreeMain/FunsExternal.lean
new file mode 100644
index 00000000..71d26da4
--- /dev/null
+++ b/tests/lean/BetreeMain/FunsExternal.lean
@@ -0,0 +1,35 @@
+-- [betree_main]: external functions.
+import Base
+import BetreeMain.Types
+open Primitives
+open betree_main
+
+-- TODO: fill those bodies
+
+/- [betree_main::betree_utils::load_internal_node] -/
+def betree_utils.load_internal_node
+  :
+  U64 → State → Result (State × (betree.List (U64 × betree.Message))) :=
+  fun _ _ => .fail .panic
+
+/- [betree_main::betree_utils::store_internal_node] -/
+def betree_utils.store_internal_node
+  :
+  U64 → betree.List (U64 × betree.Message) → State → Result (State
+    × Unit) :=
+  fun _ _ _ => .fail .panic
+
+/- [betree_main::betree_utils::load_leaf_node] -/
+def betree_utils.load_leaf_node
+  : U64 → State → Result (State × (betree.List (U64 × U64))) :=
+  fun _ _ => .fail .panic
+
+/- [betree_main::betree_utils::store_leaf_node] -/
+def betree_utils.store_leaf_node
+  : U64 → betree.List (U64 × U64) → State → Result (State × Unit) :=
+  fun _ _ _ => .fail .panic
+
+/- [core::option::Option::{0}::unwrap] -/
+def core.option.Option.unwrap
+  (T : Type) : Option T → State → Result (State × T) :=
+  fun _ _ => .fail .panic
diff --git a/tests/lean/BetreeMain/FunsExternal_Template.lean b/tests/lean/BetreeMain/FunsExternal_Template.lean
new file mode 100644
index 00000000..430d2dda
--- /dev/null
+++ b/tests/lean/BetreeMain/FunsExternal_Template.lean
@@ -0,0 +1,30 @@
+-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
+-- [betree_main]: external functions.
+-- This is a template file: rename it to "FunsExternal.lean" and fill the holes.
+import Base
+import BetreeMain.Types
+open Primitives
+open betree_main
+
+/- [betree_main::betree_utils::load_internal_node]: forward function -/
+axiom betree_utils.load_internal_node
+  : U64 → State → Result (State × (betree.List (U64 × betree.Message)))
+
+/- [betree_main::betree_utils::store_internal_node]: forward function -/
+axiom betree_utils.store_internal_node
+  :
+  U64 → betree.List (U64 × betree.Message) → State → Result (State ×
+    Unit)
+
+/- [betree_main::betree_utils::load_leaf_node]: forward function -/
+axiom betree_utils.load_leaf_node
+  : U64 → State → Result (State × (betree.List (U64 × U64)))
+
+/- [betree_main::betree_utils::store_leaf_node]: forward function -/
+axiom betree_utils.store_leaf_node
+  : U64 → betree.List (U64 × U64) → State → Result (State × Unit)
+
+/- [core::option::Option::{0}::unwrap]: forward function -/
+axiom core.option.Option.unwrap
+  (T : Type) : Option T → State → Result (State × T)
+
diff --git a/tests/lean/BetreeMain/Types.lean b/tests/lean/BetreeMain/Types.lean
new file mode 100644
index 00000000..783ade64
--- /dev/null
+++ b/tests/lean/BetreeMain/Types.lean
@@ -0,0 +1,59 @@
+-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
+-- [betree_main]: type definitions
+import Base
+open Primitives
+namespace betree_main
+
+/- [betree_main::betree::List] -/
+inductive betree.List (T : Type) :=
+| Cons : T → betree.List T → betree.List T
+| Nil : betree.List T
+
+/- [betree_main::betree::UpsertFunState] -/
+inductive betree.UpsertFunState :=
+| Add : U64 → betree.UpsertFunState
+| Sub : U64 → betree.UpsertFunState
+
+/- [betree_main::betree::Message] -/
+inductive betree.Message :=
+| Insert : U64 → betree.Message
+| Delete : betree.Message
+| Upsert : betree.UpsertFunState → betree.Message
+
+/- [betree_main::betree::Leaf] -/
+structure betree.Leaf where
+  id : U64
+  size : U64
+
+mutual
+
+/- [betree_main::betree::Node] -/
+inductive betree.Node :=
+| Internal : betree.Internal → betree.Node
+| Leaf : betree.Leaf → betree.Node
+
+/- [betree_main::betree::Internal] -/
+inductive betree.Internal :=
+| mk : U64 → U64 → betree.Node → betree.Node → betree.Internal
+
+end
+
+/- [betree_main::betree::Params] -/
+structure betree.Params where
+  min_flush_size : U64
+  split_size : U64
+
+/- [betree_main::betree::NodeIdCounter] -/
+structure betree.NodeIdCounter where
+  next_node_id : U64
+
+/- [betree_main::betree::BeTree] -/
+structure betree.BeTree where
+  params : betree.Params
+  node_id_cnt : betree.NodeIdCounter
+  root : betree.Node
+
+/- The state type used in the state-error monad -/
+axiom State : Type
+
+end betree_main
diff --git a/tests/lean/Constants.lean b/tests/lean/Constants.lean
new file mode 100644
index 00000000..4a5a7b8f
--- /dev/null
+++ b/tests/lean/Constants.lean
@@ -0,0 +1,128 @@
+-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
+-- [constants]
+import Base
+open Primitives
+namespace constants
+
+/- [constants::X0] -/
+def x0_body : Result U32 := Result.ret (U32.ofInt 0)
+def x0_c : U32 := eval_global x0_body (by simp)
+
+/- [core::num::u32::{9}::MAX] -/
+def core_num_u32_max_body : Result U32 := Result.ret (U32.ofInt 4294967295)
+def core_num_u32_max_c : U32 := eval_global core_num_u32_max_body (by simp)
+
+/- [constants::X1] -/
+def x1_body : Result U32 := Result.ret core_num_u32_max_c
+def x1_c : U32 := eval_global x1_body (by simp)
+
+/- [constants::X2] -/
+def x2_body : Result U32 := Result.ret (U32.ofInt 3)
+def x2_c : U32 := eval_global x2_body (by simp)
+
+/- [constants::incr]: forward function -/
+def incr (n : U32) : Result U32 :=
+  n + (U32.ofInt 1)
+
+/- [constants::X3] -/
+def x3_body : Result U32 := incr (U32.ofInt 32)
+def x3_c : U32 := eval_global x3_body (by simp)
+
+/- [constants::mk_pair0]: forward function -/
+def mk_pair0 (x : U32) (y : U32) : Result (U32 × U32) :=
+  Result.ret (x, y)
+
+/- [constants::Pair] -/
+structure Pair (T1 T2 : Type) where
+  x : T1
+  y : T2
+
+/- [constants::mk_pair1]: forward function -/
+def mk_pair1 (x : U32) (y : U32) : Result (Pair U32 U32) :=
+  Result.ret { x := x, y := y }
+
+/- [constants::P0] -/
+def p0_body : Result (U32 × U32) := mk_pair0 (U32.ofInt 0) (U32.ofInt 1)
+def p0_c : (U32 × U32) := eval_global p0_body (by simp)
+
+/- [constants::P1] -/
+def p1_body : Result (Pair U32 U32) := mk_pair1 (U32.ofInt 0) (U32.ofInt 1)
+def p1_c : Pair U32 U32 := eval_global p1_body (by simp)
+
+/- [constants::P2] -/
+def p2_body : Result (U32 × U32) := Result.ret ((U32.ofInt 0), (U32.ofInt 1))
+def p2_c : (U32 × U32) := eval_global p2_body (by simp)
+
+/- [constants::P3] -/
+def p3_body : Result (Pair U32 U32) :=
+  Result.ret { x := (U32.ofInt 0), y := (U32.ofInt 1) }
+def p3_c : Pair U32 U32 := eval_global p3_body (by simp)
+
+/- [constants::Wrap] -/
+structure Wrap (T : Type) where
+  val : T
+
+/- [constants::Wrap::{0}::new]: forward function -/
+def Wrap.new (T : Type) (val : T) : Result (Wrap T) :=
+  Result.ret { val := val }
+
+/- [constants::Y] -/
+def y_body : Result (Wrap I32) := Wrap.new I32 (I32.ofInt 2)
+def y_c : Wrap I32 := eval_global y_body (by simp)
+
+/- [constants::unwrap_y]: forward function -/
+def unwrap_y : Result I32 :=
+  Result.ret y_c.val
+
+/- [constants::YVAL] -/
+def yval_body : Result I32 := unwrap_y
+def yval_c : I32 := eval_global yval_body (by simp)
+
+/- [constants::get_z1::Z1] -/
+def get_z1_z1_body : Result I32 := Result.ret (I32.ofInt 3)
+def get_z1_z1_c : I32 := eval_global get_z1_z1_body (by simp)
+
+/- [constants::get_z1]: forward function -/
+def get_z1 : Result I32 :=
+  Result.ret get_z1_z1_c
+
+/- [constants::add]: forward function -/
+def add (a : I32) (b : I32) : Result I32 :=
+  a + b
+
+/- [constants::Q1] -/
+def q1_body : Result I32 := Result.ret (I32.ofInt 5)
+def q1_c : I32 := eval_global q1_body (by simp)
+
+/- [constants::Q2] -/
+def q2_body : Result I32 := Result.ret q1_c
+def q2_c : I32 := eval_global q2_body (by simp)
+
+/- [constants::Q3] -/
+def q3_body : Result I32 := add q2_c (I32.ofInt 3)
+def q3_c : I32 := eval_global q3_body (by simp)
+
+/- [constants::get_z2]: forward function -/
+def get_z2 : Result I32 :=
+  do
+    let i ← get_z1
+    let i0 ← add i q3_c
+    add q1_c i0
+
+/- [constants::S1] -/
+def s1_body : Result U32 := Result.ret (U32.ofInt 6)
+def s1_c : U32 := eval_global s1_body (by simp)
+
+/- [constants::S2] -/
+def s2_body : Result U32 := incr s1_c
+def s2_c : U32 := eval_global s2_body (by simp)
+
+/- [constants::S3] -/
+def s3_body : Result (Pair U32 U32) := Result.ret p3_c
+def s3_c : Pair U32 U32 := eval_global s3_body (by simp)
+
+/- [constants::S4] -/
+def s4_body : Result (Pair U32 U32) := mk_pair1 (U32.ofInt 7) (U32.ofInt 8)
+def s4_c : Pair U32 U32 := eval_global s4_body (by simp)
+
+end constants
diff --git a/tests/lean/misc-external/External.lean b/tests/lean/External.lean
index b95db309..b95db309 100644
--- a/tests/lean/misc-external/External.lean
+++ b/tests/lean/External.lean
diff --git a/tests/lean/External/Funs.lean b/tests/lean/External/Funs.lean
new file mode 100644
index 00000000..674aaebd
--- /dev/null
+++ b/tests/lean/External/Funs.lean
@@ -0,0 +1,88 @@
+-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
+-- [external]: function definitions
+import Base
+import External.Types
+import External.FunsExternal
+open Primitives
+namespace external
+
+/- [external::swap]: forward function -/
+def swap (T : Type) (x : T) (y : T) (st : State) : Result (State × Unit) :=
+  do
+    let (st0, _) ← core.mem.swap T x y st
+    let (st1, _) ← core.mem.swap_back0 T x y st st0
+    let (st2, _) ← core.mem.swap_back1 T x y st st1
+    Result.ret (st2, ())
+
+/- [external::swap]: backward function 0 -/
+def swap_back
+  (T : Type) (x : T) (y : T) (st : State) (st0 : State) :
+  Result (State × (T × T))
+  :=
+  do
+    let (st1, _) ← core.mem.swap T x y st
+    let (st2, x0) ← core.mem.swap_back0 T x y st st1
+    let (_, y0) ← core.mem.swap_back1 T x y st st2
+    Result.ret (st0, (x0, y0))
+
+/- [external::test_new_non_zero_u32]: forward function -/
+def test_new_non_zero_u32
+  (x : U32) (st : State) : Result (State × core.num.nonzero.NonZeroU32) :=
+  do
+    let (st0, opt) ← core.num.nonzero.NonZeroU32.new x st
+    core.option.Option.unwrap core.num.nonzero.NonZeroU32 opt st0
+
+/- [external::test_vec]: forward function -/
+def test_vec : Result Unit :=
+  do
+    let v := Vec.new U32
+    let _ ← Vec.push U32 v (U32.ofInt 0)
+    Result.ret ()
+
+/- Unit test for [external::test_vec] -/
+#assert (test_vec == .ret ())
+
+/- [external::custom_swap]: forward function -/
+def custom_swap
+  (T : Type) (x : T) (y : T) (st : State) : Result (State × T) :=
+  do
+    let (st0, _) ← core.mem.swap T x y st
+    let (st1, x0) ← core.mem.swap_back0 T x y st st0
+    let (st2, _) ← core.mem.swap_back1 T x y st st1
+    Result.ret (st2, x0)
+
+/- [external::custom_swap]: backward function 0 -/
+def custom_swap_back
+  (T : Type) (x : T) (y : T) (st : State) (ret0 : T) (st0 : State) :
+  Result (State × (T × T))
+  :=
+  do
+    let (st1, _) ← core.mem.swap T x y st
+    let (st2, _) ← core.mem.swap_back0 T x y st st1
+    let (_, y0) ← core.mem.swap_back1 T x y st st2
+    Result.ret (st0, (ret0, y0))
+
+/- [external::test_custom_swap]: forward function -/
+def test_custom_swap
+  (x : U32) (y : U32) (st : State) : Result (State × Unit) :=
+  do
+    let (st0, _) ← custom_swap U32 x y st
+    Result.ret (st0, ())
+
+/- [external::test_custom_swap]: backward function 0 -/
+def test_custom_swap_back
+  (x : U32) (y : U32) (st : State) (st0 : State) :
+  Result (State × (U32 × U32))
+  :=
+  custom_swap_back U32 x y st (U32.ofInt 1) st0
+
+/- [external::test_swap_non_zero]: forward function -/
+def test_swap_non_zero (x : U32) (st : State) : Result (State × U32) :=
+  do
+    let (st0, _) ← swap U32 x (U32.ofInt 0) st
+    let (st1, (x0, _)) ← swap_back U32 x (U32.ofInt 0) st st0
+    if x0 = (U32.ofInt 0)
+    then Result.fail Error.panic
+    else Result.ret (st1, x0)
+
+end external
diff --git a/tests/lean/External/FunsExternal.lean b/tests/lean/External/FunsExternal.lean
new file mode 100644
index 00000000..aae11ba1
--- /dev/null
+++ b/tests/lean/External/FunsExternal.lean
@@ -0,0 +1,33 @@
+-- [external]: templates for the external functions.
+import Base
+import External.Types
+open Primitives
+open external
+
+-- TODO: fill those bodies
+
+/- [core::mem::swap] -/
+def core.mem.swap
+  (T : Type) : T → T → State → Result (State × Unit) :=
+  fun _x _y s => .ret (s, ())
+
+/- [core::mem::swap] -/
+def core.mem.swap_back0
+  (T : Type) : T → T → State → State → Result (State × T) :=
+  fun _x y _s0 s1 => .ret (s1, y)
+
+/- [core::mem::swap] -/
+def core.mem.swap_back1
+  (T : Type) : T → T → State → State → Result (State × T) :=
+  fun x _y _s0 s1 => .ret (s1, x)
+
+/- [core::num::nonzero::NonZeroU32::{14}::new] -/
+def core.num.nonzero.NonZeroU32.new
+  :
+  U32 → State → Result (State × (Option core_num_nonzero_non_zero_u32_t)) :=
+  fun _ _ => .fail .panic
+
+/- [core::option::Option::{0}::unwrap] -/
+def core.option.Option.unwrap
+  (T : Type) : Option T → State → Result (State × T) :=
+  fun _ _ => .fail .panic
diff --git a/tests/lean/External/FunsExternal_Template.lean b/tests/lean/External/FunsExternal_Template.lean
new file mode 100644
index 00000000..c8bc397f
--- /dev/null
+++ b/tests/lean/External/FunsExternal_Template.lean
@@ -0,0 +1,27 @@
+-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
+-- [external]: external functions.
+-- This is a template file: rename it to "FunsExternal.lean" and fill the holes.
+import Base
+import External.Types
+open Primitives
+open external
+
+/- [core::mem::swap]: forward function -/
+axiom core.mem.swap (T : Type) : T → T → State → Result (State × Unit)
+
+/- [core::mem::swap]: backward function 0 -/
+axiom core.mem.swap_back0
+  (T : Type) : T → T → State → State → Result (State × T)
+
+/- [core::mem::swap]: backward function 1 -/
+axiom core.mem.swap_back1
+  (T : Type) : T → T → State → State → Result (State × T)
+
+/- [core::num::nonzero::NonZeroU32::{14}::new]: forward function -/
+axiom core.num.nonzero.NonZeroU32.new
+  : U32 → State → Result (State × (Option core.num.nonzero.NonZeroU32))
+
+/- [core::option::Option::{0}::unwrap]: forward function -/
+axiom core.option.Option.unwrap
+  (T : Type) : Option T → State → Result (State × T)
+
diff --git a/tests/lean/External/Opaque.lean b/tests/lean/External/Opaque.lean
new file mode 100644
index 00000000..d0297523
--- /dev/null
+++ b/tests/lean/External/Opaque.lean
@@ -0,0 +1,32 @@
+-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
+-- [external]: opaque function definitions
+import Base
+import External.Types
+open Primitives
+
+namespace external
+
+structure OpaqueDefs where
+  
+  /- [core::mem::swap] -/
+  core.mem.swap_fwd (T : Type) : T → T → State → Result (State × Unit)
+  
+  /- [core::mem::swap] -/
+  core.mem.swap_back0
+    (T : Type) : T → T → State → State → Result (State × T)
+  
+  /- [core::mem::swap] -/
+  core.mem.swap_back1
+    (T : Type) : T → T → State → State → Result (State × T)
+  
+  /- [core::num::nonzero::NonZeroU32::{14}::new] -/
+  core.num.nonzero.NonZeroU32.new_fwd
+    :
+    U32 → State → Result (State × (Option
+      core_num_nonzero_non_zero_u32_t))
+  
+  /- [core::option::Option::{0}::unwrap] -/
+  core.option.Option.unwrap_fwd
+    (T : Type) : Option T → State → Result (State × T)
+  
+end external
diff --git a/tests/lean/misc-external/External/Types.lean b/tests/lean/External/Types.lean
index ed1842be..ba984e2a 100644
--- a/tests/lean/misc-external/External/Types.lean
+++ b/tests/lean/External/Types.lean
@@ -1,10 +1,13 @@
 -- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
 -- [external]: type definitions
-import Base.Primitives
+import Base
+open Primitives
+namespace external
 
 /- [core::num::nonzero::NonZeroU32] -/
-axiom core_num_nonzero_non_zero_u32_t : Type
+axiom core.num.nonzero.NonZeroU32 : Type
 
 /- The state type used in the state-error monad -/
 axiom State : Type
 
+end external
diff --git a/tests/lean/Hashmap.lean b/tests/lean/Hashmap.lean
new file mode 100644
index 00000000..35034754
--- /dev/null
+++ b/tests/lean/Hashmap.lean
@@ -0,0 +1,2 @@
+import Hashmap.Funs
+import Hashmap.Properties
diff --git a/tests/lean/Hashmap/Funs.lean b/tests/lean/Hashmap/Funs.lean
new file mode 100644
index 00000000..870693b5
--- /dev/null
+++ b/tests/lean/Hashmap/Funs.lean
@@ -0,0 +1,449 @@
+-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
+-- [hashmap]: function definitions
+import Base
+import Hashmap.Types
+open Primitives
+namespace hashmap
+
+/- [hashmap::hash_key]: forward function -/
+def hash_key (k : Usize) : Result Usize :=
+  Result.ret k
+
+/- [hashmap::HashMap::{0}::allocate_slots]: loop 0: forward function -/
+divergent def HashMap.allocate_slots_loop
+  (T : Type) (slots : Vec (List T)) (n : Usize) : Result (Vec (List T)) :=
+  if n > (Usize.ofInt 0)
+  then
+    do
+      let slots0 ← Vec.push (List T) slots List.Nil
+      let n0 ← n - (Usize.ofInt 1)
+      HashMap.allocate_slots_loop T slots0 n0
+  else Result.ret slots
+
+/- [hashmap::HashMap::{0}::allocate_slots]: forward function -/
+def HashMap.allocate_slots
+  (T : Type) (slots : Vec (List T)) (n : Usize) : Result (Vec (List T)) :=
+  HashMap.allocate_slots_loop T slots n
+
+/- [hashmap::HashMap::{0}::new_with_capacity]: forward function -/
+def HashMap.new_with_capacity
+  (T : Type) (capacity : Usize) (max_load_dividend : Usize)
+  (max_load_divisor : Usize) :
+  Result (HashMap T)
+  :=
+  do
+    let v := Vec.new (List T)
+    let slots ← HashMap.allocate_slots T v capacity
+    let i ← capacity * max_load_dividend
+    let i0 ← i / max_load_divisor
+    Result.ret
+      {
+        num_entries := (Usize.ofInt 0),
+        max_load_factor := (max_load_dividend, max_load_divisor),
+        max_load := i0,
+        slots := slots
+      }
+
+/- [hashmap::HashMap::{0}::new]: forward function -/
+def HashMap.new (T : Type) : Result (HashMap T) :=
+  HashMap.new_with_capacity T (Usize.ofInt 32) (Usize.ofInt 4) (Usize.ofInt 5)
+
+/- [hashmap::HashMap::{0}::clear]: loop 0: merged forward/backward function
+   (there is a single backward function, and the forward function returns ()) -/
+divergent def HashMap.clear_loop
+  (T : Type) (slots : Vec (List T)) (i : Usize) : Result (Vec (List T)) :=
+  let i0 := Vec.len (List T) slots
+  if i < i0
+  then
+    do
+      let i1 ← i + (Usize.ofInt 1)
+      let slots0 ← Vec.index_mut_back (List T) slots i List.Nil
+      HashMap.clear_loop T slots0 i1
+  else Result.ret slots
+
+/- [hashmap::HashMap::{0}::clear]: merged forward/backward function
+   (there is a single backward function, and the forward function returns ()) -/
+def HashMap.clear (T : Type) (self : HashMap T) : Result (HashMap T) :=
+  do
+    let v ← HashMap.clear_loop T self.slots (Usize.ofInt 0)
+    Result.ret { self with num_entries := (Usize.ofInt 0), slots := v }
+
+/- [hashmap::HashMap::{0}::len]: forward function -/
+def HashMap.len (T : Type) (self : HashMap T) : Result Usize :=
+  Result.ret self.num_entries
+
+/- [hashmap::HashMap::{0}::insert_in_list]: loop 0: forward function -/
+divergent def HashMap.insert_in_list_loop
+  (T : Type) (key : Usize) (value : T) (ls : List T) : Result Bool :=
+  match ls with
+  | List.Cons ckey cvalue tl =>
+    if ckey = key
+    then Result.ret false
+    else HashMap.insert_in_list_loop T key value tl
+  | List.Nil => Result.ret true
+
+/- [hashmap::HashMap::{0}::insert_in_list]: forward function -/
+def HashMap.insert_in_list
+  (T : Type) (key : Usize) (value : T) (ls : List T) : Result Bool :=
+  HashMap.insert_in_list_loop T key value ls
+
+/- [hashmap::HashMap::{0}::insert_in_list]: loop 0: backward function 0 -/
+divergent def HashMap.insert_in_list_loop_back
+  (T : Type) (key : Usize) (value : T) (ls : List T) : Result (List T) :=
+  match ls with
+  | List.Cons ckey cvalue tl =>
+    if ckey = key
+    then Result.ret (List.Cons ckey value tl)
+    else
+      do
+        let tl0 ← HashMap.insert_in_list_loop_back T key value tl
+        Result.ret (List.Cons ckey cvalue tl0)
+  | List.Nil => let l := List.Nil
+                Result.ret (List.Cons key value l)
+
+/- [hashmap::HashMap::{0}::insert_in_list]: backward function 0 -/
+def HashMap.insert_in_list_back
+  (T : Type) (key : Usize) (value : T) (ls : List T) : Result (List T) :=
+  HashMap.insert_in_list_loop_back T key value ls
+
+/- [hashmap::HashMap::{0}::insert_no_resize]: merged forward/backward function
+   (there is a single backward function, and the forward function returns ()) -/
+def HashMap.insert_no_resize
+  (T : Type) (self : HashMap T) (key : Usize) (value : T) :
+  Result (HashMap T)
+  :=
+  do
+    let hash ← hash_key key
+    let i := Vec.len (List T) self.slots
+    let hash_mod ← hash % i
+    let l ← Vec.index_mut (List T) self.slots hash_mod
+    let inserted ← HashMap.insert_in_list T key value l
+    if inserted
+    then
+      do
+        let i0 ← self.num_entries + (Usize.ofInt 1)
+        let l0 ← HashMap.insert_in_list_back T key value l
+        let v ← Vec.index_mut_back (List T) self.slots hash_mod l0
+        Result.ret { self with num_entries := i0, slots := v }
+    else
+      do
+        let l0 ← HashMap.insert_in_list_back T key value l
+        let v ← Vec.index_mut_back (List T) self.slots hash_mod l0
+        Result.ret { self with slots := v }
+
+/- [core::num::u32::{9}::MAX] -/
+def core_num_u32_max_body : Result U32 := Result.ret (U32.ofInt 4294967295)
+def core_num_u32_max_c : U32 := eval_global core_num_u32_max_body (by simp)
+
+/- [hashmap::HashMap::{0}::move_elements_from_list]: loop 0: merged forward/backward function
+   (there is a single backward function, and the forward function returns ()) -/
+divergent def HashMap.move_elements_from_list_loop
+  (T : Type) (ntable : HashMap T) (ls : List T) : Result (HashMap T) :=
+  match ls with
+  | List.Cons k v tl =>
+    do
+      let ntable0 ← HashMap.insert_no_resize T ntable k v
+      HashMap.move_elements_from_list_loop T ntable0 tl
+  | List.Nil => Result.ret ntable
+
+/- [hashmap::HashMap::{0}::move_elements_from_list]: merged forward/backward function
+   (there is a single backward function, and the forward function returns ()) -/
+def HashMap.move_elements_from_list
+  (T : Type) (ntable : HashMap T) (ls : List T) : Result (HashMap T) :=
+  HashMap.move_elements_from_list_loop T ntable ls
+
+/- [hashmap::HashMap::{0}::move_elements]: loop 0: merged forward/backward function
+   (there is a single backward function, and the forward function returns ()) -/
+divergent def HashMap.move_elements_loop
+  (T : Type) (ntable : HashMap T) (slots : Vec (List T)) (i : Usize) :
+  Result ((HashMap T) × (Vec (List T)))
+  :=
+  let i0 := Vec.len (List T) slots
+  if i < i0
+  then
+    do
+      let l ← Vec.index_mut (List T) slots i
+      let ls := mem.replace (List T) l List.Nil
+      let ntable0 ← HashMap.move_elements_from_list T ntable ls
+      let i1 ← i + (Usize.ofInt 1)
+      let l0 := mem.replace_back (List T) l List.Nil
+      let slots0 ← Vec.index_mut_back (List T) slots i l0
+      HashMap.move_elements_loop T ntable0 slots0 i1
+  else Result.ret (ntable, slots)
+
+/- [hashmap::HashMap::{0}::move_elements]: merged forward/backward function
+   (there is a single backward function, and the forward function returns ()) -/
+def HashMap.move_elements
+  (T : Type) (ntable : HashMap T) (slots : Vec (List T)) (i : Usize) :
+  Result ((HashMap T) × (Vec (List T)))
+  :=
+  HashMap.move_elements_loop T ntable slots i
+
+/- [hashmap::HashMap::{0}::try_resize]: merged forward/backward function
+   (there is a single backward function, and the forward function returns ()) -/
+def HashMap.try_resize (T : Type) (self : HashMap T) : Result (HashMap T) :=
+  do
+    let max_usize ← Scalar.cast .Usize core_num_u32_max_c
+    let capacity := Vec.len (List T) self.slots
+    let n1 ← max_usize / (Usize.ofInt 2)
+    let (i, i0) := self.max_load_factor
+    let i1 ← n1 / i
+    if capacity <= i1
+    then
+      do
+        let i2 ← capacity * (Usize.ofInt 2)
+        let ntable ← HashMap.new_with_capacity T i2 i i0
+        let (ntable0, _) ←
+          HashMap.move_elements T ntable self.slots (Usize.ofInt 0)
+        Result.ret
+          {
+            ntable0
+              with
+              num_entries := self.num_entries, max_load_factor := (i, i0)
+          }
+    else Result.ret { self with max_load_factor := (i, i0) }
+
+/- [hashmap::HashMap::{0}::insert]: merged forward/backward function
+   (there is a single backward function, and the forward function returns ()) -/
+def HashMap.insert
+  (T : Type) (self : HashMap T) (key : Usize) (value : T) :
+  Result (HashMap T)
+  :=
+  do
+    let self0 ← HashMap.insert_no_resize T self key value
+    let i ← HashMap.len T self0
+    if i > self0.max_load
+    then HashMap.try_resize T self0
+    else Result.ret self0
+
+/- [hashmap::HashMap::{0}::contains_key_in_list]: loop 0: forward function -/
+divergent def HashMap.contains_key_in_list_loop
+  (T : Type) (key : Usize) (ls : List T) : Result Bool :=
+  match ls with
+  | List.Cons ckey t tl =>
+    if ckey = key
+    then Result.ret true
+    else HashMap.contains_key_in_list_loop T key tl
+  | List.Nil => Result.ret false
+
+/- [hashmap::HashMap::{0}::contains_key_in_list]: forward function -/
+def HashMap.contains_key_in_list
+  (T : Type) (key : Usize) (ls : List T) : Result Bool :=
+  HashMap.contains_key_in_list_loop T key ls
+
+/- [hashmap::HashMap::{0}::contains_key]: forward function -/
+def HashMap.contains_key
+  (T : Type) (self : HashMap T) (key : Usize) : Result Bool :=
+  do
+    let hash ← hash_key key
+    let i := Vec.len (List T) self.slots
+    let hash_mod ← hash % i
+    let l ← Vec.index (List T) self.slots hash_mod
+    HashMap.contains_key_in_list T key l
+
+/- [hashmap::HashMap::{0}::get_in_list]: loop 0: forward function -/
+divergent def HashMap.get_in_list_loop
+  (T : Type) (key : Usize) (ls : List T) : Result T :=
+  match ls with
+  | List.Cons ckey cvalue tl =>
+    if ckey = key
+    then Result.ret cvalue
+    else HashMap.get_in_list_loop T key tl
+  | List.Nil => Result.fail Error.panic
+
+/- [hashmap::HashMap::{0}::get_in_list]: forward function -/
+def HashMap.get_in_list (T : Type) (key : Usize) (ls : List T) : Result T :=
+  HashMap.get_in_list_loop T key ls
+
+/- [hashmap::HashMap::{0}::get]: forward function -/
+def HashMap.get (T : Type) (self : HashMap T) (key : Usize) : Result T :=
+  do
+    let hash ← hash_key key
+    let i := Vec.len (List T) self.slots
+    let hash_mod ← hash % i
+    let l ← Vec.index (List T) self.slots hash_mod
+    HashMap.get_in_list T key l
+
+/- [hashmap::HashMap::{0}::get_mut_in_list]: loop 0: forward function -/
+divergent def HashMap.get_mut_in_list_loop
+  (T : Type) (ls : List T) (key : Usize) : Result T :=
+  match ls with
+  | List.Cons ckey cvalue tl =>
+    if ckey = key
+    then Result.ret cvalue
+    else HashMap.get_mut_in_list_loop T tl key
+  | List.Nil => Result.fail Error.panic
+
+/- [hashmap::HashMap::{0}::get_mut_in_list]: forward function -/
+def HashMap.get_mut_in_list
+  (T : Type) (ls : List T) (key : Usize) : Result T :=
+  HashMap.get_mut_in_list_loop T ls key
+
+/- [hashmap::HashMap::{0}::get_mut_in_list]: loop 0: backward function 0 -/
+divergent def HashMap.get_mut_in_list_loop_back
+  (T : Type) (ls : List T) (key : Usize) (ret0 : T) : Result (List T) :=
+  match ls with
+  | List.Cons ckey cvalue tl =>
+    if ckey = key
+    then Result.ret (List.Cons ckey ret0 tl)
+    else
+      do
+        let tl0 ← HashMap.get_mut_in_list_loop_back T tl key ret0
+        Result.ret (List.Cons ckey cvalue tl0)
+  | List.Nil => Result.fail Error.panic
+
+/- [hashmap::HashMap::{0}::get_mut_in_list]: backward function 0 -/
+def HashMap.get_mut_in_list_back
+  (T : Type) (ls : List T) (key : Usize) (ret0 : T) : Result (List T) :=
+  HashMap.get_mut_in_list_loop_back T ls key ret0
+
+/- [hashmap::HashMap::{0}::get_mut]: forward function -/
+def HashMap.get_mut (T : Type) (self : HashMap T) (key : Usize) : Result T :=
+  do
+    let hash ← hash_key key
+    let i := Vec.len (List T) self.slots
+    let hash_mod ← hash % i
+    let l ← Vec.index_mut (List T) self.slots hash_mod
+    HashMap.get_mut_in_list T l key
+
+/- [hashmap::HashMap::{0}::get_mut]: backward function 0 -/
+def HashMap.get_mut_back
+  (T : Type) (self : HashMap T) (key : Usize) (ret0 : T) :
+  Result (HashMap T)
+  :=
+  do
+    let hash ← hash_key key
+    let i := Vec.len (List T) self.slots
+    let hash_mod ← hash % i
+    let l ← Vec.index_mut (List T) self.slots hash_mod
+    let l0 ← HashMap.get_mut_in_list_back T l key ret0
+    let v ← Vec.index_mut_back (List T) self.slots hash_mod l0
+    Result.ret { self with slots := v }
+
+/- [hashmap::HashMap::{0}::remove_from_list]: loop 0: forward function -/
+divergent def HashMap.remove_from_list_loop
+  (T : Type) (key : Usize) (ls : List T) : Result (Option T) :=
+  match ls with
+  | List.Cons ckey t tl =>
+    if ckey = key
+    then
+      let mv_ls := mem.replace (List T) (List.Cons ckey t tl) List.Nil
+      match mv_ls with
+      | List.Cons i cvalue tl0 => Result.ret (Option.some cvalue)
+      | List.Nil => Result.fail Error.panic
+    else HashMap.remove_from_list_loop T key tl
+  | List.Nil => Result.ret Option.none
+
+/- [hashmap::HashMap::{0}::remove_from_list]: forward function -/
+def HashMap.remove_from_list
+  (T : Type) (key : Usize) (ls : List T) : Result (Option T) :=
+  HashMap.remove_from_list_loop T key ls
+
+/- [hashmap::HashMap::{0}::remove_from_list]: loop 0: backward function 1 -/
+divergent def HashMap.remove_from_list_loop_back
+  (T : Type) (key : Usize) (ls : List T) : Result (List T) :=
+  match ls with
+  | List.Cons ckey t tl =>
+    if ckey = key
+    then
+      let mv_ls := mem.replace (List T) (List.Cons ckey t tl) List.Nil
+      match mv_ls with
+      | List.Cons i cvalue tl0 => Result.ret tl0
+      | List.Nil => Result.fail Error.panic
+    else
+      do
+        let tl0 ← HashMap.remove_from_list_loop_back T key tl
+        Result.ret (List.Cons ckey t tl0)
+  | List.Nil => Result.ret List.Nil
+
+/- [hashmap::HashMap::{0}::remove_from_list]: backward function 1 -/
+def HashMap.remove_from_list_back
+  (T : Type) (key : Usize) (ls : List T) : Result (List T) :=
+  HashMap.remove_from_list_loop_back T key ls
+
+/- [hashmap::HashMap::{0}::remove]: forward function -/
+def HashMap.remove
+  (T : Type) (self : HashMap T) (key : Usize) : Result (Option T) :=
+  do
+    let hash ← hash_key key
+    let i := Vec.len (List T) self.slots
+    let hash_mod ← hash % i
+    let l ← Vec.index_mut (List T) self.slots hash_mod
+    let x ← HashMap.remove_from_list T key l
+    match x with
+    | Option.none => Result.ret Option.none
+    | Option.some x0 =>
+      do
+        let _ ← self.num_entries - (Usize.ofInt 1)
+        Result.ret (Option.some x0)
+
+/- [hashmap::HashMap::{0}::remove]: backward function 0 -/
+def HashMap.remove_back
+  (T : Type) (self : HashMap T) (key : Usize) : Result (HashMap T) :=
+  do
+    let hash ← hash_key key
+    let i := Vec.len (List T) self.slots
+    let hash_mod ← hash % i
+    let l ← Vec.index_mut (List T) self.slots hash_mod
+    let x ← HashMap.remove_from_list T key l
+    match x with
+    | Option.none =>
+      do
+        let l0 ← HashMap.remove_from_list_back T key l
+        let v ← Vec.index_mut_back (List T) self.slots hash_mod l0
+        Result.ret { self with slots := v }
+    | Option.some x0 =>
+      do
+        let i0 ← self.num_entries - (Usize.ofInt 1)
+        let l0 ← HashMap.remove_from_list_back T key l
+        let v ← Vec.index_mut_back (List T) self.slots hash_mod l0
+        Result.ret { self with num_entries := i0, slots := v }
+
+/- [hashmap::test1]: forward function -/
+def test1 : Result Unit :=
+  do
+    let hm ← HashMap.new U64
+    let hm0 ← HashMap.insert U64 hm (Usize.ofInt 0) (U64.ofInt 42)
+    let hm1 ← HashMap.insert U64 hm0 (Usize.ofInt 128) (U64.ofInt 18)
+    let hm2 ← HashMap.insert U64 hm1 (Usize.ofInt 1024) (U64.ofInt 138)
+    let hm3 ← HashMap.insert U64 hm2 (Usize.ofInt 1056) (U64.ofInt 256)
+    let i ← HashMap.get U64 hm3 (Usize.ofInt 128)
+    if not (i = (U64.ofInt 18))
+    then Result.fail Error.panic
+    else
+      do
+        let hm4 ←
+          HashMap.get_mut_back U64 hm3 (Usize.ofInt 1024) (U64.ofInt 56)
+        let i0 ← HashMap.get U64 hm4 (Usize.ofInt 1024)
+        if not (i0 = (U64.ofInt 56))
+        then Result.fail Error.panic
+        else
+          do
+            let x ← HashMap.remove U64 hm4 (Usize.ofInt 1024)
+            match x with
+            | Option.none => Result.fail Error.panic
+            | Option.some x0 =>
+              if not (x0 = (U64.ofInt 56))
+              then Result.fail Error.panic
+              else
+                do
+                  let hm5 ← HashMap.remove_back U64 hm4 (Usize.ofInt 1024)
+                  let i1 ← HashMap.get U64 hm5 (Usize.ofInt 0)
+                  if not (i1 = (U64.ofInt 42))
+                  then Result.fail Error.panic
+                  else
+                    do
+                      let i2 ← HashMap.get U64 hm5 (Usize.ofInt 128)
+                      if not (i2 = (U64.ofInt 18))
+                      then Result.fail Error.panic
+                      else
+                        do
+                          let i3 ← HashMap.get U64 hm5 (Usize.ofInt 1056)
+                          if not (i3 = (U64.ofInt 256))
+                          then Result.fail Error.panic
+                          else Result.ret ()
+
+/- Unit test for [hashmap::test1] -/
+#assert (test1 == .ret ())
+
+end hashmap
diff --git a/tests/lean/Hashmap/Properties.lean b/tests/lean/Hashmap/Properties.lean
new file mode 100644
index 00000000..3652f608
--- /dev/null
+++ b/tests/lean/Hashmap/Properties.lean
@@ -0,0 +1,439 @@
+import Hashmap.Funs
+
+open Primitives
+open Result
+
+namespace List
+
+-- TODO: we don't want to use the original List.lookup because it uses BEq
+-- TODO: rewrite rule: match x == y with ... -> if x = y then ... else ... ? (actually doesn't work because of sugar)
+-- TODO: move?
+@[simp]
+def lookup' {α : Type} (ls: _root_.List (Usize × α)) (key: Usize) : Option α :=
+  match ls with
+  | [] => none
+  | (k, x) :: tl => if k = key then some x else lookup' tl key
+
+end List
+
+namespace hashmap
+
+namespace List
+
+def v {α : Type} (ls: List α) : _root_.List (Usize × α) :=
+  match ls with
+  | Nil => []
+  | Cons k x tl => (k, x) :: v tl
+
+@[simp] theorem v_nil (α : Type) : (Nil : List α).v = [] := by rfl
+@[simp] theorem v_cons {α : Type} k x (tl: List α) : (Cons k x tl).v = (k, x) :: v tl := by rfl
+
+@[simp]
+abbrev lookup {α : Type} (ls: List α) (key: Usize) : Option α :=
+  ls.v.lookup' key
+
+@[simp]
+abbrev len {α : Type} (ls : List α) : Int := ls.v.len
+
+end List
+
+namespace HashMap
+
+abbrev Core.List := _root_.List
+
+namespace List
+
+end List
+
+-- TODO: move
+@[simp] theorem neq_imp_nbeq [BEq α] [LawfulBEq α] (x y : α) (heq : ¬ x = y) : ¬ x == y := by simp [*]
+@[simp] theorem neq_imp_nbeq_rev [BEq α] [LawfulBEq α] (x y : α) (heq : ¬ x = y) : ¬ y == x := by simp [*]
+
+-- TODO: move
+-- TODO: this doesn't work because of sugar
+theorem match_lawful_beq [BEq α] [LawfulBEq α] [DecidableEq α] (x y : α) :
+  (x == y) = (if x = y then true else false) := by
+  split <;> simp_all
+
+@[pspec]
+theorem insert_in_list_spec0 {α : Type} (key: Usize) (value: α) (ls: List α) :
+  ∃ b,
+    insert_in_list α key value ls = ret b ∧
+    (b ↔ ls.lookup key = none)
+  := match ls with
+  | .Nil => by simp [insert_in_list, insert_in_list_loop]
+  | .Cons k v tl =>
+    if h: k = key then -- TODO: The order of k/key matters
+      by
+        simp [insert_in_list]
+        rw [insert_in_list_loop]
+        simp [h]
+    else
+      have ⟨ b, hi ⟩ := insert_in_list_spec0 key value tl
+      by
+        exists b
+        simp [insert_in_list]
+        rw [insert_in_list_loop] -- TODO: Using simp leads to infinite recursion
+        simp only [insert_in_list] at hi
+        simp [*]
+
+-- Variation: use progress
+theorem insert_in_list_spec1 {α : Type} (key: Usize) (value: α) (ls: List α) :
+  ∃ b,
+    insert_in_list α key value ls = ret b ∧
+    (b ↔ ls.lookup key = none)
+  := match ls with
+  | .Nil => by simp [insert_in_list, insert_in_list_loop]
+  | .Cons k v tl =>
+    if h: k = key then -- TODO: The order of k/key matters
+      by
+        simp [insert_in_list]
+        rw [insert_in_list_loop]
+        simp [h]
+    else
+      by
+        simp only [insert_in_list]
+        rw [insert_in_list_loop]
+        conv => rhs; ext; simp [*]
+        progress keep heq as ⟨ b, hi ⟩
+        simp only [insert_in_list] at heq
+        exists b
+
+-- Variation: use tactics from the beginning
+theorem insert_in_list_spec2 {α : Type} (key: Usize) (value: α) (ls: List α) :
+  ∃ b,
+    insert_in_list α key value ls = ret b ∧
+    (b ↔ (ls.lookup key = none))
+  := by
+  induction ls
+  case Nil => simp [insert_in_list, insert_in_list_loop]
+  case Cons k v tl ih =>
+    simp only [insert_in_list]
+    rw [insert_in_list_loop]
+    simp only
+    if h: k = key then
+     simp [h]
+    else
+     conv => rhs; ext; left; simp [h] -- TODO: Simplify
+     simp only [insert_in_list] at ih;
+     -- TODO: give the possibility of using underscores
+     progress as ⟨ b, h ⟩
+     simp [*]
+
+def distinct_keys (ls : Core.List (Usize × α)) := ls.pairwise_rel (λ x y => x.fst ≠ y.fst)
+
+def hash_mod_key (k : Usize) (l : Int) : Int :=
+  match hash_key k with
+  | .ret k => k.val % l
+  | _ => 0
+
+@[simp]
+theorem hash_mod_key_eq : hash_mod_key k l = k.val % l := by
+  simp [hash_mod_key, hash_key]
+
+def slot_s_inv_hash (l i : Int) (ls : Core.List (Usize × α)) : Prop :=
+  ls.allP (λ (k, _) => hash_mod_key k l = i)
+
+@[simp]
+def slot_s_inv (l i : Int) (ls : Core.List (Usize × α)) : Prop :=
+  distinct_keys ls ∧
+  slot_s_inv_hash l i ls
+
+def slot_t_inv (l i : Int) (s : List α) : Prop := slot_s_inv l i s.v
+
+-- Interpret the hashmap as a list of lists
+def v (hm : HashMap α) : Core.List (Core.List (Usize × α)) :=
+  hm.slots.val.map List.v
+
+-- Interpret the hashmap as an associative list
+def al_v (hm : HashMap α) : Core.List (Usize × α) :=
+  hm.v.flatten
+
+-- TODO: automatic derivation
+instance : Inhabited (List α) where
+  default := .Nil
+
+@[simp]
+def slots_s_inv (s : Core.List (List α)) : Prop :=
+  ∀ (i : Int), 0 ≤ i → i < s.len → slot_t_inv s.len i (s.index i)
+
+def slots_t_inv (s : Vec (List α)) : Prop :=
+  slots_s_inv s.v
+
+@[simp]
+def base_inv (hm : HashMap α) : Prop :=
+  -- [num_entries] correctly tracks the number of entries
+  hm.num_entries.val = hm.al_v.len ∧
+  -- Slots invariant
+  slots_t_inv hm.slots ∧
+  -- The capacity must be > 0 (otherwise we can't resize)
+  0 < hm.slots.length
+  -- TODO: load computation
+
+def inv (hm : HashMap α) : Prop :=
+  -- Base invariant
+  base_inv hm
+  -- TODO: either the hashmap is not overloaded, or we can't resize it
+
+theorem insert_in_list_back_spec_aux {α : Type} (l : Int) (key: Usize) (value: α) (l0: List α)
+  (hinv : slot_s_inv_hash l (hash_mod_key key l) l0.v)
+  (hdk : distinct_keys l0.v) :
+  ∃ l1,
+    insert_in_list_back α key value l0 = ret l1 ∧
+    -- We update the binding
+    l1.lookup key = value ∧
+    (∀ k, k ≠ key → l1.lookup k = l0.lookup k) ∧
+    -- We preserve part of the key invariant
+    slot_s_inv_hash l (hash_mod_key key l) l1.v ∧
+    -- Reasoning about the length
+    (match l0.lookup key with
+     | none => l1.len = l0.len + 1
+     | some _ => l1.len = l0.len) ∧
+    -- The keys are distinct
+    distinct_keys l1.v ∧
+    -- We need this auxiliary property to prove that the keys distinct properties is preserved
+    (∀ k, k ≠ key → l0.v.allP (λ (k1, _) => k ≠ k1) → l1.v.allP (λ (k1, _) => k ≠ k1))
+  := match l0 with
+  | .Nil => by checkpoint
+    simp (config := {contextual := true})
+      [insert_in_list_back, insert_in_list_loop_back,
+       List.v, slot_s_inv_hash, distinct_keys, List.pairwise_rel]
+  | .Cons k v tl0 =>
+     if h: k = key then by checkpoint
+       simp [insert_in_list_back]
+       rw [insert_in_list_loop_back]
+       simp [h]
+       split_conjs
+       . intros; simp [*]
+       . simp [List.v, slot_s_inv_hash] at *
+         simp [*]
+       . simp [*, distinct_keys] at *
+         apply hdk
+       . tauto
+     else by checkpoint
+       simp [insert_in_list_back]
+       rw [insert_in_list_loop_back]
+       simp [h]
+       have : slot_s_inv_hash l (hash_mod_key key l) (List.v tl0) := by checkpoint
+         simp_all [List.v, slot_s_inv_hash]
+       have : distinct_keys (List.v tl0) := by checkpoint
+         simp [distinct_keys] at hdk
+         simp [hdk, distinct_keys]
+       progress keep heq as ⟨ tl1 .. ⟩
+       simp only [insert_in_list_back] at heq
+       have : slot_s_inv_hash l (hash_mod_key key l) (List.v (List.Cons k v tl1)) := by checkpoint
+         simp [List.v, slot_s_inv_hash] at *
+         simp [*]
+       have : distinct_keys ((k, v) :: List.v tl1) := by checkpoint
+         simp [distinct_keys] at *
+         simp [*]
+       -- TODO: canonize addition by default?
+       simp_all [Int.add_assoc, Int.add_comm, Int.add_left_comm]
+
+@[pspec]
+theorem insert_in_list_back_spec {α : Type} (l : Int) (key: Usize) (value: α) (l0: List α)
+  (hinv : slot_s_inv_hash l (hash_mod_key key l) l0.v)
+  (hdk : distinct_keys l0.v) :
+  ∃ l1,
+    insert_in_list_back α key value l0 = ret l1 ∧
+    -- We update the binding
+    l1.lookup key = value ∧
+    (∀ k, k ≠ key → l1.lookup k = l0.lookup k) ∧
+    -- We preserve part of the key invariant
+    slot_s_inv_hash l (hash_mod_key key l) l1.v ∧
+    -- Reasoning about the length
+    (match l0.lookup key with
+     | none => l1.len = l0.len + 1
+     | some _ => l1.len = l0.len) ∧
+    -- The keys are distinct
+    distinct_keys l1.v
+  := by
+  progress with insert_in_list_back_spec_aux as ⟨ l1 .. ⟩
+  exists l1
+
+@[simp]
+def slots_t_lookup (s : Core.List (List α)) (k : Usize) : Option α :=
+  let i := hash_mod_key k s.len
+  let slot := s.index i
+  slot.lookup k
+
+def lookup (hm : HashMap α) (k : Usize) : Option α :=
+  slots_t_lookup hm.slots.val k
+
+@[simp]
+abbrev len_s (hm : HashMap α) : Int := hm.al_v.len
+
+-- Remark: α and β must live in the same universe, otherwise the
+-- bind doesn't work
+theorem if_update_eq
+  {α β : Type u} (b : Bool) (y : α) (e : Result α) (f : α → Result β) :
+  (if b then Bind.bind e f else f y) = Bind.bind (if b then e else pure y) f
+  := by
+  split <;> simp [Pure.pure]
+
+-- Small helper
+-- TODO: move, and introduce a better solution with nice syntax
+def mk_opaque {α : Sort u} (x : α) : { y : α // y = x}  :=
+  ⟨ x, by simp ⟩
+
+--set_option profiler true
+--set_option profiler.threshold 10
+--set_option trace.profiler true
+
+-- For pretty printing (useful when copy-pasting goals)
+attribute [pp_dot] List.length -- use the dot notation when printing
+set_option pp.coercions false -- do not print coercions with ↑ (this doesn't parse)
+
+theorem insert_no_resize_spec {α : Type} (hm : HashMap α) (key : Usize) (value : α)
+  (hinv : hm.inv) (hnsat : hm.lookup key = none → hm.len_s < Usize.max) :
+  ∃ nhm, hm.insert_no_resize α key value = ret nhm  ∧
+  -- We preserve the invariant
+  nhm.inv ∧
+  -- We updated the binding for key
+  nhm.lookup key = some value ∧
+  -- We left the other bindings unchanged
+  (∀ k, ¬ k = key → nhm.lookup k = hm.lookup k) ∧
+  -- Reasoning about the length
+  (match hm.lookup key with
+   | none => nhm.len_s = hm.len_s + 1
+   | some _ => nhm.len_s = hm.len_s) := by
+  rw [insert_no_resize]
+  simp only [hash_key, bind_tc_ret] -- TODO: annoying
+  have _ : (Vec.len (List α) hm.slots).val ≠ 0 := by checkpoint
+   intro
+   simp_all [inv]
+  progress keep _ as ⟨ hash_mod, hhm ⟩
+  have _ : 0 ≤ hash_mod.val := by checkpoint scalar_tac
+  have _ : hash_mod.val < Vec.length hm.slots := by
+    have : 0 < hm.slots.val.len := by
+      simp [inv] at hinv
+      simp [hinv]
+    -- TODO: we want to automate that
+    simp [*, Int.emod_lt_of_pos]
+  -- TODO: change the spec of Vec.index_mut to introduce a let-binding.
+  -- or: make progress introduce the let-binding by itself (this is clearer)
+  progress as ⟨ l, h_leq ⟩
+  -- TODO: make progress use the names written in the goal
+  progress as ⟨ inserted ⟩
+  rw [if_update_eq] -- TODO: necessary because we don't have a join
+  -- TODO: progress to ...
+  have hipost :
+    ∃ i0, (if inserted = true then hm.num_entries + Usize.ofInt 1 else pure hm.num_entries) = ret i0 ∧
+    i0.val = if inserted then hm.num_entries.val + 1 else hm.num_entries.val
+    := by
+    if inserted then
+      simp [*]
+      have hbounds : hm.num_entries.val + (Usize.ofInt 1).val ≤ Usize.max := by
+        simp [lookup] at hnsat
+        simp_all
+        simp [inv] at hinv
+        int_tac
+      -- TODO: progress fails in command line mode with "index out of bounds"
+      -- and I have no idea how to fix this. The error happens after progress
+      -- introduced the new goals. It must be when we exit the "withApp", etc.
+      -- helpers.
+      -- progress as ⟨ z, hp ⟩
+      have ⟨ z, hp ⟩ := Usize.add_spec hbounds
+      simp [hp]
+    else
+      simp [*, Pure.pure]
+  progress as ⟨ i0 ⟩
+  have h_slot : slot_s_inv_hash hm.slots.length (hash_mod_key key hm.slots.length) l.v
+    := by
+    simp [inv] at hinv
+    have h := (hinv.right.left hash_mod.val (by assumption) (by assumption)).right
+    simp [slot_t_inv, hhm] at h
+    simp [h, hhm, h_leq]
+  have hd : distinct_keys l.v := by checkpoint
+    simp [inv, slots_t_inv, slot_t_inv] at hinv
+    have h := hinv.right.left hash_mod.val (by assumption) (by assumption)
+    simp [h, h_leq]
+  -- TODO: hide the variables and only keep the props
+  -- TODO: allow providing terms to progress to instantiate the meta variables
+  -- which are not propositions
+  progress as ⟨ l0, _, _, _, hlen .. ⟩
+  progress keep hv as ⟨ v, h_veq ⟩
+  -- TODO: update progress to automate that
+  -- TODO: later I don't want to inline nhm - we need to control simp: deactivate
+  -- zeta reduction? For now I have to do this peculiar manipulation
+  have ⟨ nhm, nhm_eq ⟩ := @mk_opaque (HashMap α) { num_entries := i0, max_load_factor := hm.max_load_factor, max_load := hm.max_load, slots := v }
+  exists nhm
+  have hupdt : lookup nhm key = some value := by checkpoint
+    simp [lookup, List.lookup] at *
+    simp_all
+  have hlkp : ∀ k, ¬ k = key → nhm.lookup k = hm.lookup k := by
+    simp [lookup, List.lookup] at *
+    intro k hk
+    -- We have to make a case disjunction: either the hashes are different,
+    -- in which case we don't even lookup the same slots, or the hashes
+    -- are the same, in which case we have to reason about what happens
+    -- in one slot
+    let k_hash_mod := k.val % v.val.len
+    have : 0 < hm.slots.val.len := by simp_all [inv]
+    have hvpos : 0 < v.val.len := by simp_all
+    have hvnz: v.val.len ≠ 0 := by
+      simp_all
+    have _ : 0 ≤ k_hash_mod := by
+      -- TODO: we want to automate this
+      simp
+      apply Int.emod_nonneg k.val hvnz
+    have _ : k_hash_mod < Vec.length hm.slots := by
+      -- TODO: we want to automate this
+      simp
+      have h := Int.emod_lt_of_pos k.val hvpos
+      simp_all
+    if h_hm : k_hash_mod = hash_mod.val then
+      simp_all
+    else
+      simp_all
+  have _ :
+    match hm.lookup key with
+    | none => nhm.len_s = hm.len_s + 1
+    | some _ => nhm.len_s = hm.len_s := by checkpoint
+    simp only [lookup, List.lookup, len_s, al_v, HashMap.v, slots_t_lookup] at *
+    -- We have to do a case disjunction
+    simp_all
+    simp [_root_.List.update_map_eq]
+    -- TODO: dependent rewrites
+    have _ : key.val % hm.slots.val.len < (List.map List.v hm.slots.val).len := by
+      simp [*]
+    simp [_root_.List.len_flatten_update_eq, *]
+    split <;>
+    rename_i heq <;>
+    simp [heq] at hlen <;>
+    -- TODO: canonize addition by default? We need a tactic to simplify arithmetic equalities
+    -- with addition and substractions ((ℤ, +) is a group or something - there should exist a tactic
+    -- somewhere in mathlib?)
+    simp [Int.add_assoc, Int.add_comm, Int.add_left_comm] <;>
+    int_tac
+  have hinv : inv nhm := by
+    simp [inv] at *
+    split_conjs
+    . match h: lookup hm key with
+      | none =>
+        simp [h, lookup] at *
+        simp_all
+      | some _ =>
+        simp_all [lookup]
+    . simp [slots_t_inv, slot_t_inv] at *
+      intro i hipos _
+      have _ := hinv.right.left i hipos (by simp_all)
+      simp [hhm, h_veq, nhm_eq] at * -- TODO: annoying, we do that because simp_all fails below
+      -- We need a case disjunction
+      if h_ieq : i = key.val % _root_.List.len hm.slots.val then
+        -- TODO: simp_all fails: "(deterministic) timeout at 'whnf'"
+        -- Also, it is annoying to do this kind
+        -- of rewritings by hand. We could have a different simp
+        -- which safely substitutes variables when we have an
+        -- equality `x = ...` and `x` doesn't appear in the rhs
+        simp [h_ieq] at *
+        simp [*]
+      else
+        simp [*]
+    . -- TODO: simp[*] fails: "(deterministic) timeout at 'whnf'"
+      simp [hinv, h_veq, nhm_eq]
+  simp_all
+
+end HashMap
+
+end hashmap
diff --git a/tests/lean/Hashmap/Types.lean b/tests/lean/Hashmap/Types.lean
new file mode 100644
index 00000000..6606cf9e
--- /dev/null
+++ b/tests/lean/Hashmap/Types.lean
@@ -0,0 +1,19 @@
+-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
+-- [hashmap]: type definitions
+import Base
+open Primitives
+namespace hashmap
+
+/- [hashmap::List] -/
+inductive List (T : Type) :=
+| Cons : Usize → T → List T → List T
+| Nil : List T
+
+/- [hashmap::HashMap] -/
+structure HashMap (T : Type) where
+  num_entries : Usize
+  max_load_factor : (Usize × Usize)
+  max_load : Usize
+  slots : Vec (List T)
+
+end hashmap
diff --git a/tests/lean/hashmap_on_disk/HashmapMain.lean b/tests/lean/HashmapMain.lean
index 1a4e7f82..1a4e7f82 100644
--- a/tests/lean/hashmap_on_disk/HashmapMain.lean
+++ b/tests/lean/HashmapMain.lean
diff --git a/tests/lean/HashmapMain/Funs.lean b/tests/lean/HashmapMain/Funs.lean
new file mode 100644
index 00000000..610bae46
--- /dev/null
+++ b/tests/lean/HashmapMain/Funs.lean
@@ -0,0 +1,505 @@
+-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
+-- [hashmap_main]: function definitions
+import Base
+import HashmapMain.Types
+import HashmapMain.FunsExternal
+open Primitives
+namespace hashmap_main
+
+/- [hashmap_main::hashmap::hash_key]: forward function -/
+def hashmap.hash_key (k : Usize) : Result Usize :=
+  Result.ret k
+
+/- [hashmap_main::hashmap::HashMap::{0}::allocate_slots]: loop 0: forward function -/
+divergent def hashmap.HashMap.allocate_slots_loop
+  (T : Type) (slots : Vec (hashmap.List T)) (n : Usize) :
+  Result (Vec (hashmap.List T))
+  :=
+  if n > (Usize.ofInt 0)
+  then
+    do
+      let slots0 ← Vec.push (hashmap.List T) slots hashmap.List.Nil
+      let n0 ← n - (Usize.ofInt 1)
+      hashmap.HashMap.allocate_slots_loop T slots0 n0
+  else Result.ret slots
+
+/- [hashmap_main::hashmap::HashMap::{0}::allocate_slots]: forward function -/
+def hashmap.HashMap.allocate_slots
+  (T : Type) (slots : Vec (hashmap.List T)) (n : Usize) :
+  Result (Vec (hashmap.List T))
+  :=
+  hashmap.HashMap.allocate_slots_loop T slots n
+
+/- [hashmap_main::hashmap::HashMap::{0}::new_with_capacity]: forward function -/
+def hashmap.HashMap.new_with_capacity
+  (T : Type) (capacity : Usize) (max_load_dividend : Usize)
+  (max_load_divisor : Usize) :
+  Result (hashmap.HashMap T)
+  :=
+  do
+    let v := Vec.new (hashmap.List T)
+    let slots ← hashmap.HashMap.allocate_slots T v capacity
+    let i ← capacity * max_load_dividend
+    let i0 ← i / max_load_divisor
+    Result.ret
+      {
+        num_entries := (Usize.ofInt 0),
+        max_load_factor := (max_load_dividend, max_load_divisor),
+        max_load := i0,
+        slots := slots
+      }
+
+/- [hashmap_main::hashmap::HashMap::{0}::new]: forward function -/
+def hashmap.HashMap.new (T : Type) : Result (hashmap.HashMap T) :=
+  hashmap.HashMap.new_with_capacity T (Usize.ofInt 32) (Usize.ofInt 4)
+    (Usize.ofInt 5)
+
+/- [hashmap_main::hashmap::HashMap::{0}::clear]: loop 0: merged forward/backward function
+   (there is a single backward function, and the forward function returns ()) -/
+divergent def hashmap.HashMap.clear_loop
+  (T : Type) (slots : Vec (hashmap.List T)) (i : Usize) :
+  Result (Vec (hashmap.List T))
+  :=
+  let i0 := Vec.len (hashmap.List T) slots
+  if i < i0
+  then
+    do
+      let i1 ← i + (Usize.ofInt 1)
+      let slots0 ←
+        Vec.index_mut_back (hashmap.List T) slots i hashmap.List.Nil
+      hashmap.HashMap.clear_loop T slots0 i1
+  else Result.ret slots
+
+/- [hashmap_main::hashmap::HashMap::{0}::clear]: merged forward/backward function
+   (there is a single backward function, and the forward function returns ()) -/
+def hashmap.HashMap.clear
+  (T : Type) (self : hashmap.HashMap T) : Result (hashmap.HashMap T) :=
+  do
+    let v ← hashmap.HashMap.clear_loop T self.slots (Usize.ofInt 0)
+    Result.ret { self with num_entries := (Usize.ofInt 0), slots := v }
+
+/- [hashmap_main::hashmap::HashMap::{0}::len]: forward function -/
+def hashmap.HashMap.len (T : Type) (self : hashmap.HashMap T) : Result Usize :=
+  Result.ret self.num_entries
+
+/- [hashmap_main::hashmap::HashMap::{0}::insert_in_list]: loop 0: forward function -/
+divergent def hashmap.HashMap.insert_in_list_loop
+  (T : Type) (key : Usize) (value : T) (ls : hashmap.List T) : Result Bool :=
+  match ls with
+  | hashmap.List.Cons ckey cvalue tl =>
+    if ckey = key
+    then Result.ret false
+    else hashmap.HashMap.insert_in_list_loop T key value tl
+  | hashmap.List.Nil => Result.ret true
+
+/- [hashmap_main::hashmap::HashMap::{0}::insert_in_list]: forward function -/
+def hashmap.HashMap.insert_in_list
+  (T : Type) (key : Usize) (value : T) (ls : hashmap.List T) : Result Bool :=
+  hashmap.HashMap.insert_in_list_loop T key value ls
+
+/- [hashmap_main::hashmap::HashMap::{0}::insert_in_list]: loop 0: backward function 0 -/
+divergent def hashmap.HashMap.insert_in_list_loop_back
+  (T : Type) (key : Usize) (value : T) (ls : hashmap.List T) :
+  Result (hashmap.List T)
+  :=
+  match ls with
+  | hashmap.List.Cons ckey cvalue tl =>
+    if ckey = key
+    then Result.ret (hashmap.List.Cons ckey value tl)
+    else
+      do
+        let tl0 ← hashmap.HashMap.insert_in_list_loop_back T key value tl
+        Result.ret (hashmap.List.Cons ckey cvalue tl0)
+  | hashmap.List.Nil =>
+    let l := hashmap.List.Nil
+    Result.ret (hashmap.List.Cons key value l)
+
+/- [hashmap_main::hashmap::HashMap::{0}::insert_in_list]: backward function 0 -/
+def hashmap.HashMap.insert_in_list_back
+  (T : Type) (key : Usize) (value : T) (ls : hashmap.List T) :
+  Result (hashmap.List T)
+  :=
+  hashmap.HashMap.insert_in_list_loop_back T key value ls
+
+/- [hashmap_main::hashmap::HashMap::{0}::insert_no_resize]: merged forward/backward function
+   (there is a single backward function, and the forward function returns ()) -/
+def hashmap.HashMap.insert_no_resize
+  (T : Type) (self : hashmap.HashMap T) (key : Usize) (value : T) :
+  Result (hashmap.HashMap T)
+  :=
+  do
+    let hash ← hashmap.hash_key key
+    let i := Vec.len (hashmap.List T) self.slots
+    let hash_mod ← hash % i
+    let l ← Vec.index_mut (hashmap.List T) self.slots hash_mod
+    let inserted ← hashmap.HashMap.insert_in_list T key value l
+    if inserted
+    then
+      do
+        let i0 ← self.num_entries + (Usize.ofInt 1)
+        let l0 ← hashmap.HashMap.insert_in_list_back T key value l
+        let v ← Vec.index_mut_back (hashmap.List T) self.slots hash_mod l0
+        Result.ret { self with num_entries := i0, slots := v }
+    else
+      do
+        let l0 ← hashmap.HashMap.insert_in_list_back T key value l
+        let v ← Vec.index_mut_back (hashmap.List T) self.slots hash_mod l0
+        Result.ret { self with slots := v }
+
+/- [core::num::u32::{9}::MAX] -/
+def core_num_u32_max_body : Result U32 := Result.ret (U32.ofInt 4294967295)
+def core_num_u32_max_c : U32 := eval_global core_num_u32_max_body (by simp)
+
+/- [hashmap_main::hashmap::HashMap::{0}::move_elements_from_list]: loop 0: merged forward/backward function
+   (there is a single backward function, and the forward function returns ()) -/
+divergent def hashmap.HashMap.move_elements_from_list_loop
+  (T : Type) (ntable : hashmap.HashMap T) (ls : hashmap.List T) :
+  Result (hashmap.HashMap T)
+  :=
+  match ls with
+  | hashmap.List.Cons k v tl =>
+    do
+      let ntable0 ← hashmap.HashMap.insert_no_resize T ntable k v
+      hashmap.HashMap.move_elements_from_list_loop T ntable0 tl
+  | hashmap.List.Nil => Result.ret ntable
+
+/- [hashmap_main::hashmap::HashMap::{0}::move_elements_from_list]: merged forward/backward function
+   (there is a single backward function, and the forward function returns ()) -/
+def hashmap.HashMap.move_elements_from_list
+  (T : Type) (ntable : hashmap.HashMap T) (ls : hashmap.List T) :
+  Result (hashmap.HashMap T)
+  :=
+  hashmap.HashMap.move_elements_from_list_loop T ntable ls
+
+/- [hashmap_main::hashmap::HashMap::{0}::move_elements]: loop 0: merged forward/backward function
+   (there is a single backward function, and the forward function returns ()) -/
+divergent def hashmap.HashMap.move_elements_loop
+  (T : Type) (ntable : hashmap.HashMap T) (slots : Vec (hashmap.List T))
+  (i : Usize) :
+  Result ((hashmap.HashMap T) × (Vec (hashmap.List T)))
+  :=
+  let i0 := Vec.len (hashmap.List T) slots
+  if i < i0
+  then
+    do
+      let l ← Vec.index_mut (hashmap.List T) slots i
+      let ls := mem.replace (hashmap.List T) l hashmap.List.Nil
+      let ntable0 ← hashmap.HashMap.move_elements_from_list T ntable ls
+      let i1 ← i + (Usize.ofInt 1)
+      let l0 := mem.replace_back (hashmap.List T) l hashmap.List.Nil
+      let slots0 ← Vec.index_mut_back (hashmap.List T) slots i l0
+      hashmap.HashMap.move_elements_loop T ntable0 slots0 i1
+  else Result.ret (ntable, slots)
+
+/- [hashmap_main::hashmap::HashMap::{0}::move_elements]: merged forward/backward function
+   (there is a single backward function, and the forward function returns ()) -/
+def hashmap.HashMap.move_elements
+  (T : Type) (ntable : hashmap.HashMap T) (slots : Vec (hashmap.List T))
+  (i : Usize) :
+  Result ((hashmap.HashMap T) × (Vec (hashmap.List T)))
+  :=
+  hashmap.HashMap.move_elements_loop T ntable slots i
+
+/- [hashmap_main::hashmap::HashMap::{0}::try_resize]: merged forward/backward function
+   (there is a single backward function, and the forward function returns ()) -/
+def hashmap.HashMap.try_resize
+  (T : Type) (self : hashmap.HashMap T) : Result (hashmap.HashMap T) :=
+  do
+    let max_usize ← Scalar.cast .Usize core_num_u32_max_c
+    let capacity := Vec.len (hashmap.List T) self.slots
+    let n1 ← max_usize / (Usize.ofInt 2)
+    let (i, i0) := self.max_load_factor
+    let i1 ← n1 / i
+    if capacity <= i1
+    then
+      do
+        let i2 ← capacity * (Usize.ofInt 2)
+        let ntable ← hashmap.HashMap.new_with_capacity T i2 i i0
+        let (ntable0, _) ←
+          hashmap.HashMap.move_elements T ntable self.slots (Usize.ofInt 0)
+        Result.ret
+          {
+            ntable0
+              with
+              num_entries := self.num_entries, max_load_factor := (i, i0)
+          }
+    else Result.ret { self with max_load_factor := (i, i0) }
+
+/- [hashmap_main::hashmap::HashMap::{0}::insert]: merged forward/backward function
+   (there is a single backward function, and the forward function returns ()) -/
+def hashmap.HashMap.insert
+  (T : Type) (self : hashmap.HashMap T) (key : Usize) (value : T) :
+  Result (hashmap.HashMap T)
+  :=
+  do
+    let self0 ← hashmap.HashMap.insert_no_resize T self key value
+    let i ← hashmap.HashMap.len T self0
+    if i > self0.max_load
+    then hashmap.HashMap.try_resize T self0
+    else Result.ret self0
+
+/- [hashmap_main::hashmap::HashMap::{0}::contains_key_in_list]: loop 0: forward function -/
+divergent def hashmap.HashMap.contains_key_in_list_loop
+  (T : Type) (key : Usize) (ls : hashmap.List T) : Result Bool :=
+  match ls with
+  | hashmap.List.Cons ckey t tl =>
+    if ckey = key
+    then Result.ret true
+    else hashmap.HashMap.contains_key_in_list_loop T key tl
+  | hashmap.List.Nil => Result.ret false
+
+/- [hashmap_main::hashmap::HashMap::{0}::contains_key_in_list]: forward function -/
+def hashmap.HashMap.contains_key_in_list
+  (T : Type) (key : Usize) (ls : hashmap.List T) : Result Bool :=
+  hashmap.HashMap.contains_key_in_list_loop T key ls
+
+/- [hashmap_main::hashmap::HashMap::{0}::contains_key]: forward function -/
+def hashmap.HashMap.contains_key
+  (T : Type) (self : hashmap.HashMap T) (key : Usize) : Result Bool :=
+  do
+    let hash ← hashmap.hash_key key
+    let i := Vec.len (hashmap.List T) self.slots
+    let hash_mod ← hash % i
+    let l ← Vec.index (hashmap.List T) self.slots hash_mod
+    hashmap.HashMap.contains_key_in_list T key l
+
+/- [hashmap_main::hashmap::HashMap::{0}::get_in_list]: loop 0: forward function -/
+divergent def hashmap.HashMap.get_in_list_loop
+  (T : Type) (key : Usize) (ls : hashmap.List T) : Result T :=
+  match ls with
+  | hashmap.List.Cons ckey cvalue tl =>
+    if ckey = key
+    then Result.ret cvalue
+    else hashmap.HashMap.get_in_list_loop T key tl
+  | hashmap.List.Nil => Result.fail Error.panic
+
+/- [hashmap_main::hashmap::HashMap::{0}::get_in_list]: forward function -/
+def hashmap.HashMap.get_in_list
+  (T : Type) (key : Usize) (ls : hashmap.List T) : Result T :=
+  hashmap.HashMap.get_in_list_loop T key ls
+
+/- [hashmap_main::hashmap::HashMap::{0}::get]: forward function -/
+def hashmap.HashMap.get
+  (T : Type) (self : hashmap.HashMap T) (key : Usize) : Result T :=
+  do
+    let hash ← hashmap.hash_key key
+    let i := Vec.len (hashmap.List T) self.slots
+    let hash_mod ← hash % i
+    let l ← Vec.index (hashmap.List T) self.slots hash_mod
+    hashmap.HashMap.get_in_list T key l
+
+/- [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list]: loop 0: forward function -/
+divergent def hashmap.HashMap.get_mut_in_list_loop
+  (T : Type) (ls : hashmap.List T) (key : Usize) : Result T :=
+  match ls with
+  | hashmap.List.Cons ckey cvalue tl =>
+    if ckey = key
+    then Result.ret cvalue
+    else hashmap.HashMap.get_mut_in_list_loop T tl key
+  | hashmap.List.Nil => Result.fail Error.panic
+
+/- [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list]: forward function -/
+def hashmap.HashMap.get_mut_in_list
+  (T : Type) (ls : hashmap.List T) (key : Usize) : Result T :=
+  hashmap.HashMap.get_mut_in_list_loop T ls key
+
+/- [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list]: loop 0: backward function 0 -/
+divergent def hashmap.HashMap.get_mut_in_list_loop_back
+  (T : Type) (ls : hashmap.List T) (key : Usize) (ret0 : T) :
+  Result (hashmap.List T)
+  :=
+  match ls with
+  | hashmap.List.Cons ckey cvalue tl =>
+    if ckey = key
+    then Result.ret (hashmap.List.Cons ckey ret0 tl)
+    else
+      do
+        let tl0 ← hashmap.HashMap.get_mut_in_list_loop_back T tl key ret0
+        Result.ret (hashmap.List.Cons ckey cvalue tl0)
+  | hashmap.List.Nil => Result.fail Error.panic
+
+/- [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list]: backward function 0 -/
+def hashmap.HashMap.get_mut_in_list_back
+  (T : Type) (ls : hashmap.List T) (key : Usize) (ret0 : T) :
+  Result (hashmap.List T)
+  :=
+  hashmap.HashMap.get_mut_in_list_loop_back T ls key ret0
+
+/- [hashmap_main::hashmap::HashMap::{0}::get_mut]: forward function -/
+def hashmap.HashMap.get_mut
+  (T : Type) (self : hashmap.HashMap T) (key : Usize) : Result T :=
+  do
+    let hash ← hashmap.hash_key key
+    let i := Vec.len (hashmap.List T) self.slots
+    let hash_mod ← hash % i
+    let l ← Vec.index_mut (hashmap.List T) self.slots hash_mod
+    hashmap.HashMap.get_mut_in_list T l key
+
+/- [hashmap_main::hashmap::HashMap::{0}::get_mut]: backward function 0 -/
+def hashmap.HashMap.get_mut_back
+  (T : Type) (self : hashmap.HashMap T) (key : Usize) (ret0 : T) :
+  Result (hashmap.HashMap T)
+  :=
+  do
+    let hash ← hashmap.hash_key key
+    let i := Vec.len (hashmap.List T) self.slots
+    let hash_mod ← hash % i
+    let l ← Vec.index_mut (hashmap.List T) self.slots hash_mod
+    let l0 ← hashmap.HashMap.get_mut_in_list_back T l key ret0
+    let v ← Vec.index_mut_back (hashmap.List T) self.slots hash_mod l0
+    Result.ret { self with slots := v }
+
+/- [hashmap_main::hashmap::HashMap::{0}::remove_from_list]: loop 0: forward function -/
+divergent def hashmap.HashMap.remove_from_list_loop
+  (T : Type) (key : Usize) (ls : hashmap.List T) : Result (Option T) :=
+  match ls with
+  | hashmap.List.Cons ckey t tl =>
+    if ckey = key
+    then
+      let mv_ls :=
+        mem.replace (hashmap.List T) (hashmap.List.Cons ckey t tl)
+          hashmap.List.Nil
+      match mv_ls with
+      | hashmap.List.Cons i cvalue tl0 => Result.ret (Option.some cvalue)
+      | hashmap.List.Nil => Result.fail Error.panic
+    else hashmap.HashMap.remove_from_list_loop T key tl
+  | hashmap.List.Nil => Result.ret Option.none
+
+/- [hashmap_main::hashmap::HashMap::{0}::remove_from_list]: forward function -/
+def hashmap.HashMap.remove_from_list
+  (T : Type) (key : Usize) (ls : hashmap.List T) : Result (Option T) :=
+  hashmap.HashMap.remove_from_list_loop T key ls
+
+/- [hashmap_main::hashmap::HashMap::{0}::remove_from_list]: loop 0: backward function 1 -/
+divergent def hashmap.HashMap.remove_from_list_loop_back
+  (T : Type) (key : Usize) (ls : hashmap.List T) : Result (hashmap.List T) :=
+  match ls with
+  | hashmap.List.Cons ckey t tl =>
+    if ckey = key
+    then
+      let mv_ls :=
+        mem.replace (hashmap.List T) (hashmap.List.Cons ckey t tl)
+          hashmap.List.Nil
+      match mv_ls with
+      | hashmap.List.Cons i cvalue tl0 => Result.ret tl0
+      | hashmap.List.Nil => Result.fail Error.panic
+    else
+      do
+        let tl0 ← hashmap.HashMap.remove_from_list_loop_back T key tl
+        Result.ret (hashmap.List.Cons ckey t tl0)
+  | hashmap.List.Nil => Result.ret hashmap.List.Nil
+
+/- [hashmap_main::hashmap::HashMap::{0}::remove_from_list]: backward function 1 -/
+def hashmap.HashMap.remove_from_list_back
+  (T : Type) (key : Usize) (ls : hashmap.List T) : Result (hashmap.List T) :=
+  hashmap.HashMap.remove_from_list_loop_back T key ls
+
+/- [hashmap_main::hashmap::HashMap::{0}::remove]: forward function -/
+def hashmap.HashMap.remove
+  (T : Type) (self : hashmap.HashMap T) (key : Usize) : Result (Option T) :=
+  do
+    let hash ← hashmap.hash_key key
+    let i := Vec.len (hashmap.List T) self.slots
+    let hash_mod ← hash % i
+    let l ← Vec.index_mut (hashmap.List T) self.slots hash_mod
+    let x ← hashmap.HashMap.remove_from_list T key l
+    match x with
+    | Option.none => Result.ret Option.none
+    | Option.some x0 =>
+      do
+        let _ ← self.num_entries - (Usize.ofInt 1)
+        Result.ret (Option.some x0)
+
+/- [hashmap_main::hashmap::HashMap::{0}::remove]: backward function 0 -/
+def hashmap.HashMap.remove_back
+  (T : Type) (self : hashmap.HashMap T) (key : Usize) :
+  Result (hashmap.HashMap T)
+  :=
+  do
+    let hash ← hashmap.hash_key key
+    let i := Vec.len (hashmap.List T) self.slots
+    let hash_mod ← hash % i
+    let l ← Vec.index_mut (hashmap.List T) self.slots hash_mod
+    let x ← hashmap.HashMap.remove_from_list T key l
+    match x with
+    | Option.none =>
+      do
+        let l0 ← hashmap.HashMap.remove_from_list_back T key l
+        let v ← Vec.index_mut_back (hashmap.List T) self.slots hash_mod l0
+        Result.ret { self with slots := v }
+    | Option.some x0 =>
+      do
+        let i0 ← self.num_entries - (Usize.ofInt 1)
+        let l0 ← hashmap.HashMap.remove_from_list_back T key l
+        let v ← Vec.index_mut_back (hashmap.List T) self.slots hash_mod l0
+        Result.ret { self with num_entries := i0, slots := v }
+
+/- [hashmap_main::hashmap::test1]: forward function -/
+def hashmap.test1 : Result Unit :=
+  do
+    let hm ← hashmap.HashMap.new U64
+    let hm0 ← hashmap.HashMap.insert U64 hm (Usize.ofInt 0) (U64.ofInt 42)
+    let hm1 ← hashmap.HashMap.insert U64 hm0 (Usize.ofInt 128) (U64.ofInt 18)
+    let hm2 ←
+      hashmap.HashMap.insert U64 hm1 (Usize.ofInt 1024) (U64.ofInt 138)
+    let hm3 ←
+      hashmap.HashMap.insert U64 hm2 (Usize.ofInt 1056) (U64.ofInt 256)
+    let i ← hashmap.HashMap.get U64 hm3 (Usize.ofInt 128)
+    if not (i = (U64.ofInt 18))
+    then Result.fail Error.panic
+    else
+      do
+        let hm4 ←
+          hashmap.HashMap.get_mut_back U64 hm3 (Usize.ofInt 1024)
+            (U64.ofInt 56)
+        let i0 ← hashmap.HashMap.get U64 hm4 (Usize.ofInt 1024)
+        if not (i0 = (U64.ofInt 56))
+        then Result.fail Error.panic
+        else
+          do
+            let x ← hashmap.HashMap.remove U64 hm4 (Usize.ofInt 1024)
+            match x with
+            | Option.none => Result.fail Error.panic
+            | Option.some x0 =>
+              if not (x0 = (U64.ofInt 56))
+              then Result.fail Error.panic
+              else
+                do
+                  let hm5 ←
+                    hashmap.HashMap.remove_back U64 hm4 (Usize.ofInt 1024)
+                  let i1 ← hashmap.HashMap.get U64 hm5 (Usize.ofInt 0)
+                  if not (i1 = (U64.ofInt 42))
+                  then Result.fail Error.panic
+                  else
+                    do
+                      let i2 ← hashmap.HashMap.get U64 hm5 (Usize.ofInt 128)
+                      if not (i2 = (U64.ofInt 18))
+                      then Result.fail Error.panic
+                      else
+                        do
+                          let i3 ←
+                            hashmap.HashMap.get U64 hm5 (Usize.ofInt 1056)
+                          if not (i3 = (U64.ofInt 256))
+                          then Result.fail Error.panic
+                          else Result.ret ()
+
+/- Unit test for [hashmap_main::hashmap::test1] -/
+#assert (hashmap.test1 == .ret ())
+
+/- [hashmap_main::insert_on_disk]: forward function -/
+def insert_on_disk
+  (key : Usize) (value : U64) (st : State) : Result (State × Unit) :=
+  do
+    let (st0, hm) ← hashmap_utils.deserialize st
+    let hm0 ← hashmap.HashMap.insert U64 hm key value
+    let (st1, _) ← hashmap_utils.serialize hm0 st0
+    Result.ret (st1, ())
+
+/- [hashmap_main::main]: forward function -/
+def main : Result Unit :=
+  Result.ret ()
+
+/- Unit test for [hashmap_main::main] -/
+#assert (main == .ret ())
+
+end hashmap_main
diff --git a/tests/lean/HashmapMain/FunsExternal.lean b/tests/lean/HashmapMain/FunsExternal.lean
new file mode 100644
index 00000000..b394b32b
--- /dev/null
+++ b/tests/lean/HashmapMain/FunsExternal.lean
@@ -0,0 +1,17 @@
+-- [hashmap_main]: templates for the external functions.
+import Base
+import HashmapMain.Types
+open Primitives
+open hashmap_main
+
+-- TODO: fill those bodies
+
+/- [hashmap_main::hashmap_utils::deserialize] -/
+def hashmap_utils.deserialize
+  : State → Result (State × (hashmap.HashMap U64)) :=
+  fun _ => .fail .panic
+
+/- [hashmap_main::hashmap_utils::serialize] -/
+def hashmap_utils.serialize
+  : hashmap.HashMap U64 → State → Result (State × Unit) :=
+  fun _ _ => .fail .panic
diff --git a/tests/lean/HashmapMain/FunsExternal_Template.lean b/tests/lean/HashmapMain/FunsExternal_Template.lean
new file mode 100644
index 00000000..f537fc8f
--- /dev/null
+++ b/tests/lean/HashmapMain/FunsExternal_Template.lean
@@ -0,0 +1,16 @@
+-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
+-- [hashmap_main]: external functions.
+-- This is a template file: rename it to "FunsExternal.lean" and fill the holes.
+import Base
+import HashmapMain.Types
+open Primitives
+open hashmap_main
+
+/- [hashmap_main::hashmap_utils::deserialize]: forward function -/
+axiom hashmap_utils.deserialize
+  : State → Result (State × (hashmap.HashMap U64))
+
+/- [hashmap_main::hashmap_utils::serialize]: forward function -/
+axiom hashmap_utils.serialize
+  : hashmap.HashMap U64 → State → Result (State × Unit)
+
diff --git a/tests/lean/hashmap_on_disk/HashmapMain/Opaque.lean b/tests/lean/HashmapMain/Opaque.lean
index d98f431a..abf04c94 100644
--- a/tests/lean/hashmap_on_disk/HashmapMain/Opaque.lean
+++ b/tests/lean/HashmapMain/Opaque.lean
@@ -1,15 +1,19 @@
 -- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
 -- [hashmap_main]: opaque function definitions
-import Base.Primitives
+import Base
 import HashmapMain.Types
+open Primitives
+
+namespace hashmap_main
 
 structure OpaqueDefs where
   
   /- [hashmap_main::hashmap_utils::deserialize] -/
-  hashmap_utils_deserialize_fwd
-    : State -> Result (State × (hashmap_hash_map_t U64))
+  hashmap_utils.deserialize_fwd
+    : State → Result (State × (hashmap_hash_map_t U64))
   
   /- [hashmap_main::hashmap_utils::serialize] -/
-  hashmap_utils_serialize_fwd
-    : hashmap_hash_map_t U64 -> State -> Result (State × Unit)
+  hashmap_utils.serialize_fwd
+    : hashmap_hash_map_t U64 → State → Result (State × Unit)
   
+end hashmap_main
diff --git a/tests/lean/HashmapMain/Types.lean b/tests/lean/HashmapMain/Types.lean
new file mode 100644
index 00000000..3b3d0d7c
--- /dev/null
+++ b/tests/lean/HashmapMain/Types.lean
@@ -0,0 +1,22 @@
+-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
+-- [hashmap_main]: type definitions
+import Base
+open Primitives
+namespace hashmap_main
+
+/- [hashmap_main::hashmap::List] -/
+inductive hashmap.List (T : Type) :=
+| Cons : Usize → T → hashmap.List T → hashmap.List T
+| Nil : hashmap.List T
+
+/- [hashmap_main::hashmap::HashMap] -/
+structure hashmap.HashMap (T : Type) where
+  num_entries : Usize
+  max_load_factor : (Usize × Usize)
+  max_load : Usize
+  slots : Vec (hashmap.List T)
+
+/- The state type used in the state-error monad -/
+axiom State : Type
+
+end hashmap_main
diff --git a/tests/lean/misc-loops/Loops.lean b/tests/lean/Loops.lean
index 60c73776..60c73776 100644
--- a/tests/lean/misc-loops/Loops.lean
+++ b/tests/lean/Loops.lean
diff --git a/tests/lean/Loops/Funs.lean b/tests/lean/Loops/Funs.lean
new file mode 100644
index 00000000..f7e6603d
--- /dev/null
+++ b/tests/lean/Loops/Funs.lean
@@ -0,0 +1,611 @@
+-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
+-- [loops]: function definitions
+import Base
+import Loops.Types
+open Primitives
+namespace loops
+
+/- [loops::sum]: loop 0: forward function -/
+divergent def sum_loop (max : U32) (i : U32) (s : U32) : Result U32 :=
+  if i < max
+  then do
+         let s0 ← s + i
+         let i0 ← i + (U32.ofInt 1)
+         sum_loop max i0 s0
+  else s * (U32.ofInt 2)
+
+/- [loops::sum]: forward function -/
+def sum (max : U32) : Result U32 :=
+  sum_loop max (U32.ofInt 0) (U32.ofInt 0)
+
+/- [loops::sum_with_mut_borrows]: loop 0: forward function -/
+divergent def sum_with_mut_borrows_loop
+  (max : U32) (mi : U32) (ms : U32) : Result U32 :=
+  if mi < max
+  then
+    do
+      let ms0 ← ms + mi
+      let mi0 ← mi + (U32.ofInt 1)
+      sum_with_mut_borrows_loop max mi0 ms0
+  else ms * (U32.ofInt 2)
+
+/- [loops::sum_with_mut_borrows]: forward function -/
+def sum_with_mut_borrows (max : U32) : Result U32 :=
+  sum_with_mut_borrows_loop max (U32.ofInt 0) (U32.ofInt 0)
+
+/- [loops::sum_with_shared_borrows]: loop 0: forward function -/
+divergent def sum_with_shared_borrows_loop
+  (max : U32) (i : U32) (s : U32) : Result U32 :=
+  if i < max
+  then
+    do
+      let i0 ← i + (U32.ofInt 1)
+      let s0 ← s + i0
+      sum_with_shared_borrows_loop max i0 s0
+  else s * (U32.ofInt 2)
+
+/- [loops::sum_with_shared_borrows]: forward function -/
+def sum_with_shared_borrows (max : U32) : Result U32 :=
+  sum_with_shared_borrows_loop max (U32.ofInt 0) (U32.ofInt 0)
+
+/- [loops::clear]: loop 0: merged forward/backward function
+   (there is a single backward function, and the forward function returns ()) -/
+divergent def clear_loop (v : Vec U32) (i : Usize) : Result (Vec U32) :=
+  let i0 := Vec.len U32 v
+  if i < i0
+  then
+    do
+      let i1 ← i + (Usize.ofInt 1)
+      let v0 ← Vec.index_mut_back U32 v i (U32.ofInt 0)
+      clear_loop v0 i1
+  else Result.ret v
+
+/- [loops::clear]: merged forward/backward function
+   (there is a single backward function, and the forward function returns ()) -/
+def clear (v : Vec U32) : Result (Vec U32) :=
+  clear_loop v (Usize.ofInt 0)
+
+/- [loops::list_mem]: loop 0: forward function -/
+divergent def list_mem_loop (x : U32) (ls : List U32) : Result Bool :=
+  match ls with
+  | List.Cons y tl => if y = x
+                      then Result.ret true
+                      else list_mem_loop x tl
+  | List.Nil => Result.ret false
+
+/- [loops::list_mem]: forward function -/
+def list_mem (x : U32) (ls : List U32) : Result Bool :=
+  list_mem_loop x ls
+
+/- [loops::list_nth_mut_loop]: loop 0: forward function -/
+divergent def list_nth_mut_loop_loop
+  (T : Type) (ls : List T) (i : U32) : Result T :=
+  match ls with
+  | List.Cons x tl =>
+    if i = (U32.ofInt 0)
+    then Result.ret x
+    else do
+           let i0 ← i - (U32.ofInt 1)
+           list_nth_mut_loop_loop T tl i0
+  | List.Nil => Result.fail Error.panic
+
+/- [loops::list_nth_mut_loop]: forward function -/
+def list_nth_mut_loop (T : Type) (ls : List T) (i : U32) : Result T :=
+  list_nth_mut_loop_loop T ls i
+
+/- [loops::list_nth_mut_loop]: loop 0: backward function 0 -/
+divergent def list_nth_mut_loop_loop_back
+  (T : Type) (ls : List T) (i : U32) (ret0 : T) : Result (List T) :=
+  match ls with
+  | List.Cons x tl =>
+    if i = (U32.ofInt 0)
+    then Result.ret (List.Cons ret0 tl)
+    else
+      do
+        let i0 ← i - (U32.ofInt 1)
+        let tl0 ← list_nth_mut_loop_loop_back T tl i0 ret0
+        Result.ret (List.Cons x tl0)
+  | List.Nil => Result.fail Error.panic
+
+/- [loops::list_nth_mut_loop]: backward function 0 -/
+def list_nth_mut_loop_back
+  (T : Type) (ls : List T) (i : U32) (ret0 : T) : Result (List T) :=
+  list_nth_mut_loop_loop_back T ls i ret0
+
+/- [loops::list_nth_shared_loop]: loop 0: forward function -/
+divergent def list_nth_shared_loop_loop
+  (T : Type) (ls : List T) (i : U32) : Result T :=
+  match ls with
+  | List.Cons x tl =>
+    if i = (U32.ofInt 0)
+    then Result.ret x
+    else do
+           let i0 ← i - (U32.ofInt 1)
+           list_nth_shared_loop_loop T tl i0
+  | List.Nil => Result.fail Error.panic
+
+/- [loops::list_nth_shared_loop]: forward function -/
+def list_nth_shared_loop (T : Type) (ls : List T) (i : U32) : Result T :=
+  list_nth_shared_loop_loop T ls i
+
+/- [loops::get_elem_mut]: loop 0: forward function -/
+divergent def get_elem_mut_loop (x : Usize) (ls : List Usize) : Result Usize :=
+  match ls with
+  | List.Cons y tl => if y = x
+                      then Result.ret y
+                      else get_elem_mut_loop x tl
+  | List.Nil => Result.fail Error.panic
+
+/- [loops::get_elem_mut]: forward function -/
+def get_elem_mut (slots : Vec (List Usize)) (x : Usize) : Result Usize :=
+  do
+    let l ← Vec.index_mut (List Usize) slots (Usize.ofInt 0)
+    get_elem_mut_loop x l
+
+/- [loops::get_elem_mut]: loop 0: backward function 0 -/
+divergent def get_elem_mut_loop_back
+  (x : Usize) (ls : List Usize) (ret0 : Usize) : Result (List Usize) :=
+  match ls with
+  | List.Cons y tl =>
+    if y = x
+    then Result.ret (List.Cons ret0 tl)
+    else
+      do
+        let tl0 ← get_elem_mut_loop_back x tl ret0
+        Result.ret (List.Cons y tl0)
+  | List.Nil => Result.fail Error.panic
+
+/- [loops::get_elem_mut]: backward function 0 -/
+def get_elem_mut_back
+  (slots : Vec (List Usize)) (x : Usize) (ret0 : Usize) :
+  Result (Vec (List Usize))
+  :=
+  do
+    let l ← Vec.index_mut (List Usize) slots (Usize.ofInt 0)
+    let l0 ← get_elem_mut_loop_back x l ret0
+    Vec.index_mut_back (List Usize) slots (Usize.ofInt 0) l0
+
+/- [loops::get_elem_shared]: loop 0: forward function -/
+divergent def get_elem_shared_loop
+  (x : Usize) (ls : List Usize) : Result Usize :=
+  match ls with
+  | List.Cons y tl => if y = x
+                      then Result.ret y
+                      else get_elem_shared_loop x tl
+  | List.Nil => Result.fail Error.panic
+
+/- [loops::get_elem_shared]: forward function -/
+def get_elem_shared (slots : Vec (List Usize)) (x : Usize) : Result Usize :=
+  do
+    let l ← Vec.index (List Usize) slots (Usize.ofInt 0)
+    get_elem_shared_loop x l
+
+/- [loops::id_mut]: forward function -/
+def id_mut (T : Type) (ls : List T) : Result (List T) :=
+  Result.ret ls
+
+/- [loops::id_mut]: backward function 0 -/
+def id_mut_back (T : Type) (ls : List T) (ret0 : List T) : Result (List T) :=
+  Result.ret ret0
+
+/- [loops::id_shared]: forward function -/
+def id_shared (T : Type) (ls : List T) : Result (List T) :=
+  Result.ret ls
+
+/- [loops::list_nth_mut_loop_with_id]: loop 0: forward function -/
+divergent def list_nth_mut_loop_with_id_loop
+  (T : Type) (i : U32) (ls : List T) : Result T :=
+  match ls with
+  | List.Cons x tl =>
+    if i = (U32.ofInt 0)
+    then Result.ret x
+    else do
+           let i0 ← i - (U32.ofInt 1)
+           list_nth_mut_loop_with_id_loop T i0 tl
+  | List.Nil => Result.fail Error.panic
+
+/- [loops::list_nth_mut_loop_with_id]: forward function -/
+def list_nth_mut_loop_with_id (T : Type) (ls : List T) (i : U32) : Result T :=
+  do
+    let ls0 ← id_mut T ls
+    list_nth_mut_loop_with_id_loop T i ls0
+
+/- [loops::list_nth_mut_loop_with_id]: loop 0: backward function 0 -/
+divergent def list_nth_mut_loop_with_id_loop_back
+  (T : Type) (i : U32) (ls : List T) (ret0 : T) : Result (List T) :=
+  match ls with
+  | List.Cons x tl =>
+    if i = (U32.ofInt 0)
+    then Result.ret (List.Cons ret0 tl)
+    else
+      do
+        let i0 ← i - (U32.ofInt 1)
+        let tl0 ← list_nth_mut_loop_with_id_loop_back T i0 tl ret0
+        Result.ret (List.Cons x tl0)
+  | List.Nil => Result.fail Error.panic
+
+/- [loops::list_nth_mut_loop_with_id]: backward function 0 -/
+def list_nth_mut_loop_with_id_back
+  (T : Type) (ls : List T) (i : U32) (ret0 : T) : Result (List T) :=
+  do
+    let ls0 ← id_mut T ls
+    let l ← list_nth_mut_loop_with_id_loop_back T i ls0 ret0
+    id_mut_back T ls l
+
+/- [loops::list_nth_shared_loop_with_id]: loop 0: forward function -/
+divergent def list_nth_shared_loop_with_id_loop
+  (T : Type) (i : U32) (ls : List T) : Result T :=
+  match ls with
+  | List.Cons x tl =>
+    if i = (U32.ofInt 0)
+    then Result.ret x
+    else
+      do
+        let i0 ← i - (U32.ofInt 1)
+        list_nth_shared_loop_with_id_loop T i0 tl
+  | List.Nil => Result.fail Error.panic
+
+/- [loops::list_nth_shared_loop_with_id]: forward function -/
+def list_nth_shared_loop_with_id
+  (T : Type) (ls : List T) (i : U32) : Result T :=
+  do
+    let ls0 ← id_shared T ls
+    list_nth_shared_loop_with_id_loop T i ls0
+
+/- [loops::list_nth_mut_loop_pair]: loop 0: forward function -/
+divergent def list_nth_mut_loop_pair_loop
+  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
+  match ls0 with
+  | List.Cons x0 tl0 =>
+    match ls1 with
+    | List.Cons x1 tl1 =>
+      if i = (U32.ofInt 0)
+      then Result.ret (x0, x1)
+      else
+        do
+          let i0 ← i - (U32.ofInt 1)
+          list_nth_mut_loop_pair_loop T tl0 tl1 i0
+    | List.Nil => Result.fail Error.panic
+  | List.Nil => Result.fail Error.panic
+
+/- [loops::list_nth_mut_loop_pair]: forward function -/
+def list_nth_mut_loop_pair
+  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
+  list_nth_mut_loop_pair_loop T ls0 ls1 i
+
+/- [loops::list_nth_mut_loop_pair]: loop 0: backward function 0 -/
+divergent def list_nth_mut_loop_pair_loop_back'a
+  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret0 : T) :
+  Result (List T)
+  :=
+  match ls0 with
+  | List.Cons x0 tl0 =>
+    match ls1 with
+    | List.Cons x1 tl1 =>
+      if i = (U32.ofInt 0)
+      then Result.ret (List.Cons ret0 tl0)
+      else
+        do
+          let i0 ← i - (U32.ofInt 1)
+          let tl00 ← list_nth_mut_loop_pair_loop_back'a T tl0 tl1 i0 ret0
+          Result.ret (List.Cons x0 tl00)
+    | List.Nil => Result.fail Error.panic
+  | List.Nil => Result.fail Error.panic
+
+/- [loops::list_nth_mut_loop_pair]: backward function 0 -/
+def list_nth_mut_loop_pair_back'a
+  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret0 : T) :
+  Result (List T)
+  :=
+  list_nth_mut_loop_pair_loop_back'a T ls0 ls1 i ret0
+
+/- [loops::list_nth_mut_loop_pair]: loop 0: backward function 1 -/
+divergent def list_nth_mut_loop_pair_loop_back'b
+  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret0 : T) :
+  Result (List T)
+  :=
+  match ls0 with
+  | List.Cons x0 tl0 =>
+    match ls1 with
+    | List.Cons x1 tl1 =>
+      if i = (U32.ofInt 0)
+      then Result.ret (List.Cons ret0 tl1)
+      else
+        do
+          let i0 ← i - (U32.ofInt 1)
+          let tl10 ← list_nth_mut_loop_pair_loop_back'b T tl0 tl1 i0 ret0
+          Result.ret (List.Cons x1 tl10)
+    | List.Nil => Result.fail Error.panic
+  | List.Nil => Result.fail Error.panic
+
+/- [loops::list_nth_mut_loop_pair]: backward function 1 -/
+def list_nth_mut_loop_pair_back'b
+  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret0 : T) :
+  Result (List T)
+  :=
+  list_nth_mut_loop_pair_loop_back'b T ls0 ls1 i ret0
+
+/- [loops::list_nth_shared_loop_pair]: loop 0: forward function -/
+divergent def list_nth_shared_loop_pair_loop
+  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
+  match ls0 with
+  | List.Cons x0 tl0 =>
+    match ls1 with
+    | List.Cons x1 tl1 =>
+      if i = (U32.ofInt 0)
+      then Result.ret (x0, x1)
+      else
+        do
+          let i0 ← i - (U32.ofInt 1)
+          list_nth_shared_loop_pair_loop T tl0 tl1 i0
+    | List.Nil => Result.fail Error.panic
+  | List.Nil => Result.fail Error.panic
+
+/- [loops::list_nth_shared_loop_pair]: forward function -/
+def list_nth_shared_loop_pair
+  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
+  list_nth_shared_loop_pair_loop T ls0 ls1 i
+
+/- [loops::list_nth_mut_loop_pair_merge]: loop 0: forward function -/
+divergent def list_nth_mut_loop_pair_merge_loop
+  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
+  match ls0 with
+  | List.Cons x0 tl0 =>
+    match ls1 with
+    | List.Cons x1 tl1 =>
+      if i = (U32.ofInt 0)
+      then Result.ret (x0, x1)
+      else
+        do
+          let i0 ← i - (U32.ofInt 1)
+          list_nth_mut_loop_pair_merge_loop T tl0 tl1 i0
+    | List.Nil => Result.fail Error.panic
+  | List.Nil => Result.fail Error.panic
+
+/- [loops::list_nth_mut_loop_pair_merge]: forward function -/
+def list_nth_mut_loop_pair_merge
+  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
+  list_nth_mut_loop_pair_merge_loop T ls0 ls1 i
+
+/- [loops::list_nth_mut_loop_pair_merge]: loop 0: backward function 0 -/
+divergent def list_nth_mut_loop_pair_merge_loop_back
+  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret0 : (T × T)) :
+  Result ((List T) × (List T))
+  :=
+  match ls0 with
+  | List.Cons x0 tl0 =>
+    match ls1 with
+    | List.Cons x1 tl1 =>
+      if i = (U32.ofInt 0)
+      then let (t, t0) := ret0
+           Result.ret (List.Cons t tl0, List.Cons t0 tl1)
+      else
+        do
+          let i0 ← i - (U32.ofInt 1)
+          let (tl00, tl10) ←
+            list_nth_mut_loop_pair_merge_loop_back T tl0 tl1 i0 ret0
+          Result.ret (List.Cons x0 tl00, List.Cons x1 tl10)
+    | List.Nil => Result.fail Error.panic
+  | List.Nil => Result.fail Error.panic
+
+/- [loops::list_nth_mut_loop_pair_merge]: backward function 0 -/
+def list_nth_mut_loop_pair_merge_back
+  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret0 : (T × T)) :
+  Result ((List T) × (List T))
+  :=
+  list_nth_mut_loop_pair_merge_loop_back T ls0 ls1 i ret0
+
+/- [loops::list_nth_shared_loop_pair_merge]: loop 0: forward function -/
+divergent def list_nth_shared_loop_pair_merge_loop
+  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
+  match ls0 with
+  | List.Cons x0 tl0 =>
+    match ls1 with
+    | List.Cons x1 tl1 =>
+      if i = (U32.ofInt 0)
+      then Result.ret (x0, x1)
+      else
+        do
+          let i0 ← i - (U32.ofInt 1)
+          list_nth_shared_loop_pair_merge_loop T tl0 tl1 i0
+    | List.Nil => Result.fail Error.panic
+  | List.Nil => Result.fail Error.panic
+
+/- [loops::list_nth_shared_loop_pair_merge]: forward function -/
+def list_nth_shared_loop_pair_merge
+  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
+  list_nth_shared_loop_pair_merge_loop T ls0 ls1 i
+
+/- [loops::list_nth_mut_shared_loop_pair]: loop 0: forward function -/
+divergent def list_nth_mut_shared_loop_pair_loop
+  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
+  match ls0 with
+  | List.Cons x0 tl0 =>
+    match ls1 with
+    | List.Cons x1 tl1 =>
+      if i = (U32.ofInt 0)
+      then Result.ret (x0, x1)
+      else
+        do
+          let i0 ← i - (U32.ofInt 1)
+          list_nth_mut_shared_loop_pair_loop T tl0 tl1 i0
+    | List.Nil => Result.fail Error.panic
+  | List.Nil => Result.fail Error.panic
+
+/- [loops::list_nth_mut_shared_loop_pair]: forward function -/
+def list_nth_mut_shared_loop_pair
+  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
+  list_nth_mut_shared_loop_pair_loop T ls0 ls1 i
+
+/- [loops::list_nth_mut_shared_loop_pair]: loop 0: backward function 0 -/
+divergent def list_nth_mut_shared_loop_pair_loop_back
+  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret0 : T) :
+  Result (List T)
+  :=
+  match ls0 with
+  | List.Cons x0 tl0 =>
+    match ls1 with
+    | List.Cons x1 tl1 =>
+      if i = (U32.ofInt 0)
+      then Result.ret (List.Cons ret0 tl0)
+      else
+        do
+          let i0 ← i - (U32.ofInt 1)
+          let tl00 ←
+            list_nth_mut_shared_loop_pair_loop_back T tl0 tl1 i0 ret0
+          Result.ret (List.Cons x0 tl00)
+    | List.Nil => Result.fail Error.panic
+  | List.Nil => Result.fail Error.panic
+
+/- [loops::list_nth_mut_shared_loop_pair]: backward function 0 -/
+def list_nth_mut_shared_loop_pair_back
+  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret0 : T) :
+  Result (List T)
+  :=
+  list_nth_mut_shared_loop_pair_loop_back T ls0 ls1 i ret0
+
+/- [loops::list_nth_mut_shared_loop_pair_merge]: loop 0: forward function -/
+divergent def list_nth_mut_shared_loop_pair_merge_loop
+  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
+  match ls0 with
+  | List.Cons x0 tl0 =>
+    match ls1 with
+    | List.Cons x1 tl1 =>
+      if i = (U32.ofInt 0)
+      then Result.ret (x0, x1)
+      else
+        do
+          let i0 ← i - (U32.ofInt 1)
+          list_nth_mut_shared_loop_pair_merge_loop T tl0 tl1 i0
+    | List.Nil => Result.fail Error.panic
+  | List.Nil => Result.fail Error.panic
+
+/- [loops::list_nth_mut_shared_loop_pair_merge]: forward function -/
+def list_nth_mut_shared_loop_pair_merge
+  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
+  list_nth_mut_shared_loop_pair_merge_loop T ls0 ls1 i
+
+/- [loops::list_nth_mut_shared_loop_pair_merge]: loop 0: backward function 0 -/
+divergent def list_nth_mut_shared_loop_pair_merge_loop_back
+  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret0 : T) :
+  Result (List T)
+  :=
+  match ls0 with
+  | List.Cons x0 tl0 =>
+    match ls1 with
+    | List.Cons x1 tl1 =>
+      if i = (U32.ofInt 0)
+      then Result.ret (List.Cons ret0 tl0)
+      else
+        do
+          let i0 ← i - (U32.ofInt 1)
+          let tl00 ←
+            list_nth_mut_shared_loop_pair_merge_loop_back T tl0 tl1 i0 ret0
+          Result.ret (List.Cons x0 tl00)
+    | List.Nil => Result.fail Error.panic
+  | List.Nil => Result.fail Error.panic
+
+/- [loops::list_nth_mut_shared_loop_pair_merge]: backward function 0 -/
+def list_nth_mut_shared_loop_pair_merge_back
+  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret0 : T) :
+  Result (List T)
+  :=
+  list_nth_mut_shared_loop_pair_merge_loop_back T ls0 ls1 i ret0
+
+/- [loops::list_nth_shared_mut_loop_pair]: loop 0: forward function -/
+divergent def list_nth_shared_mut_loop_pair_loop
+  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
+  match ls0 with
+  | List.Cons x0 tl0 =>
+    match ls1 with
+    | List.Cons x1 tl1 =>
+      if i = (U32.ofInt 0)
+      then Result.ret (x0, x1)
+      else
+        do
+          let i0 ← i - (U32.ofInt 1)
+          list_nth_shared_mut_loop_pair_loop T tl0 tl1 i0
+    | List.Nil => Result.fail Error.panic
+  | List.Nil => Result.fail Error.panic
+
+/- [loops::list_nth_shared_mut_loop_pair]: forward function -/
+def list_nth_shared_mut_loop_pair
+  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
+  list_nth_shared_mut_loop_pair_loop T ls0 ls1 i
+
+/- [loops::list_nth_shared_mut_loop_pair]: loop 0: backward function 1 -/
+divergent def list_nth_shared_mut_loop_pair_loop_back
+  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret0 : T) :
+  Result (List T)
+  :=
+  match ls0 with
+  | List.Cons x0 tl0 =>
+    match ls1 with
+    | List.Cons x1 tl1 =>
+      if i = (U32.ofInt 0)
+      then Result.ret (List.Cons ret0 tl1)
+      else
+        do
+          let i0 ← i - (U32.ofInt 1)
+          let tl10 ←
+            list_nth_shared_mut_loop_pair_loop_back T tl0 tl1 i0 ret0
+          Result.ret (List.Cons x1 tl10)
+    | List.Nil => Result.fail Error.panic
+  | List.Nil => Result.fail Error.panic
+
+/- [loops::list_nth_shared_mut_loop_pair]: backward function 1 -/
+def list_nth_shared_mut_loop_pair_back
+  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret0 : T) :
+  Result (List T)
+  :=
+  list_nth_shared_mut_loop_pair_loop_back T ls0 ls1 i ret0
+
+/- [loops::list_nth_shared_mut_loop_pair_merge]: loop 0: forward function -/
+divergent def list_nth_shared_mut_loop_pair_merge_loop
+  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
+  match ls0 with
+  | List.Cons x0 tl0 =>
+    match ls1 with
+    | List.Cons x1 tl1 =>
+      if i = (U32.ofInt 0)
+      then Result.ret (x0, x1)
+      else
+        do
+          let i0 ← i - (U32.ofInt 1)
+          list_nth_shared_mut_loop_pair_merge_loop T tl0 tl1 i0
+    | List.Nil => Result.fail Error.panic
+  | List.Nil => Result.fail Error.panic
+
+/- [loops::list_nth_shared_mut_loop_pair_merge]: forward function -/
+def list_nth_shared_mut_loop_pair_merge
+  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
+  list_nth_shared_mut_loop_pair_merge_loop T ls0 ls1 i
+
+/- [loops::list_nth_shared_mut_loop_pair_merge]: loop 0: backward function 0 -/
+divergent def list_nth_shared_mut_loop_pair_merge_loop_back
+  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret0 : T) :
+  Result (List T)
+  :=
+  match ls0 with
+  | List.Cons x0 tl0 =>
+    match ls1 with
+    | List.Cons x1 tl1 =>
+      if i = (U32.ofInt 0)
+      then Result.ret (List.Cons ret0 tl1)
+      else
+        do
+          let i0 ← i - (U32.ofInt 1)
+          let tl10 ←
+            list_nth_shared_mut_loop_pair_merge_loop_back T tl0 tl1 i0 ret0
+          Result.ret (List.Cons x1 tl10)
+    | List.Nil => Result.fail Error.panic
+  | List.Nil => Result.fail Error.panic
+
+/- [loops::list_nth_shared_mut_loop_pair_merge]: backward function 0 -/
+def list_nth_shared_mut_loop_pair_merge_back
+  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret0 : T) :
+  Result (List T)
+  :=
+  list_nth_shared_mut_loop_pair_merge_loop_back T ls0 ls1 i ret0
+
+end loops
diff --git a/tests/lean/Loops/Types.lean b/tests/lean/Loops/Types.lean
new file mode 100644
index 00000000..f8bc193b
--- /dev/null
+++ b/tests/lean/Loops/Types.lean
@@ -0,0 +1,12 @@
+-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
+-- [loops]: type definitions
+import Base
+open Primitives
+namespace loops
+
+/- [loops::List] -/
+inductive List (T : Type) :=
+| Cons : T → List T → List T
+| Nil : List T
+
+end loops
diff --git a/tests/lean/Makefile b/tests/lean/Makefile
index ed3b3e3b..3ccfbec2 100644
--- a/tests/lean/Makefile
+++ b/tests/lean/Makefile
@@ -1,40 +1,35 @@
 ALL_DIRS ?= $(filter-out %~ lean-toolchain% Makefile%, $(wildcard *))
 
+# TODO: remove
 UPDATE_DIRS = $(addprefix update-,$(ALL_DIRS))
 
+# TODO: remove
 VERIFY_DIRS = $(addprefix verif-,$(ALL_DIRS))
 
+# TODO: remove
 CLEAN_DIRS = $(addprefix clean-,$(ALL_DIRS))
 
+# TODO: remove
 COPY_LEAN_TOOLCHAIN = $(addprefix copy-lean-toolchain-,$(ALL_DIRS))
 
 .PHONY: all
 all: prepare-projects verify
 
 .PHONY: prepare-projects
-prepare-projects: $(COPY_LEAN_TOOLCHAIN)
+prepare-projects: copy-lean-toolchain
 
 .PHONY: prepare-projects
-copy-lean-toolchain-%:
-	cp lean-toolchain $*
+copy-lean-toolchain:
+	cp ../../backends/lean/lean-toolchain .
 
 .PHONY: update
-update: $(UPDATE_DIRS)
-
-.PHONY: update-%
-update-%:
-	cd $* && lake update
+update:
+	lake update
 
 .PHONY: verify
-verify: $(VERIFY_DIRS)
-
-.PHONY: verif-%
-verif-%:
-	cd $* && lake build
+verify:
+	lake build
 
 .PHONY: clean
-clean: $(CLEAN_DIRS)
-
-.PHONY: clean-%
-clean-%:
-	cd $* && lake clean
+clean:
+	lake clean
diff --git a/tests/lean/NoNestedBorrows.lean b/tests/lean/NoNestedBorrows.lean
new file mode 100644
index 00000000..bc707fd9
--- /dev/null
+++ b/tests/lean/NoNestedBorrows.lean
@@ -0,0 +1,511 @@
+-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
+-- [no_nested_borrows]
+import Base
+open Primitives
+namespace no_nested_borrows
+
+/- [no_nested_borrows::Pair] -/
+structure Pair (T1 T2 : Type) where
+  x : T1
+  y : T2
+
+/- [no_nested_borrows::List] -/
+inductive List (T : Type) :=
+| Cons : T → List T → List T
+| Nil : List T
+
+/- [no_nested_borrows::One] -/
+inductive One (T1 : Type) :=
+| One : T1 → One T1
+
+/- [no_nested_borrows::EmptyEnum] -/
+inductive EmptyEnum :=
+| Empty : EmptyEnum
+
+/- [no_nested_borrows::Enum] -/
+inductive Enum :=
+| Variant1 : Enum
+| Variant2 : Enum
+
+/- [no_nested_borrows::EmptyStruct] -/
+structure EmptyStruct where
+
+/- [no_nested_borrows::Sum] -/
+inductive Sum (T1 T2 : Type) :=
+| Left : T1 → Sum T1 T2
+| Right : T2 → Sum T1 T2
+
+/- [no_nested_borrows::neg_test]: forward function -/
+def neg_test (x : I32) : Result I32 :=
+  - x
+
+/- [no_nested_borrows::add_test]: forward function -/
+def add_test (x : U32) (y : U32) : Result U32 :=
+  x + y
+
+/- [no_nested_borrows::subs_test]: forward function -/
+def subs_test (x : U32) (y : U32) : Result U32 :=
+  x - y
+
+/- [no_nested_borrows::div_test]: forward function -/
+def div_test (x : U32) (y : U32) : Result U32 :=
+  x / y
+
+/- [no_nested_borrows::div_test1]: forward function -/
+def div_test1 (x : U32) : Result U32 :=
+  x / (U32.ofInt 2)
+
+/- [no_nested_borrows::rem_test]: forward function -/
+def rem_test (x : U32) (y : U32) : Result U32 :=
+  x % y
+
+/- [no_nested_borrows::cast_test]: forward function -/
+def cast_test (x : U32) : Result I32 :=
+  Scalar.cast .I32 x
+
+/- [no_nested_borrows::test2]: forward function -/
+def test2 : Result Unit :=
+  do
+    let _ ← (U32.ofInt 23) + (U32.ofInt 44)
+    Result.ret ()
+
+/- Unit test for [no_nested_borrows::test2] -/
+#assert (test2 == .ret ())
+
+/- [no_nested_borrows::get_max]: forward function -/
+def get_max (x : U32) (y : U32) : Result U32 :=
+  if x >= y
+  then Result.ret x
+  else Result.ret y
+
+/- [no_nested_borrows::test3]: forward function -/
+def test3 : Result Unit :=
+  do
+    let x ← get_max (U32.ofInt 4) (U32.ofInt 3)
+    let y ← get_max (U32.ofInt 10) (U32.ofInt 11)
+    let z ← x + y
+    if not (z = (U32.ofInt 15))
+    then Result.fail Error.panic
+    else Result.ret ()
+
+/- Unit test for [no_nested_borrows::test3] -/
+#assert (test3 == .ret ())
+
+/- [no_nested_borrows::test_neg1]: forward function -/
+def test_neg1 : Result Unit :=
+  do
+    let y ← - (I32.ofInt 3)
+    if not (y = (I32.ofInt (-(3:Int))))
+    then Result.fail Error.panic
+    else Result.ret ()
+
+/- Unit test for [no_nested_borrows::test_neg1] -/
+#assert (test_neg1 == .ret ())
+
+/- [no_nested_borrows::refs_test1]: forward function -/
+def refs_test1 : Result Unit :=
+  if not ((I32.ofInt 1) = (I32.ofInt 1))
+  then Result.fail Error.panic
+  else Result.ret ()
+
+/- Unit test for [no_nested_borrows::refs_test1] -/
+#assert (refs_test1 == .ret ())
+
+/- [no_nested_borrows::refs_test2]: forward function -/
+def refs_test2 : Result Unit :=
+  if not ((I32.ofInt 2) = (I32.ofInt 2))
+  then Result.fail Error.panic
+  else
+    if not ((I32.ofInt 0) = (I32.ofInt 0))
+    then Result.fail Error.panic
+    else
+      if not ((I32.ofInt 2) = (I32.ofInt 2))
+      then Result.fail Error.panic
+      else
+        if not ((I32.ofInt 2) = (I32.ofInt 2))
+        then Result.fail Error.panic
+        else Result.ret ()
+
+/- Unit test for [no_nested_borrows::refs_test2] -/
+#assert (refs_test2 == .ret ())
+
+/- [no_nested_borrows::test_list1]: forward function -/
+def test_list1 : Result Unit :=
+  Result.ret ()
+
+/- Unit test for [no_nested_borrows::test_list1] -/
+#assert (test_list1 == .ret ())
+
+/- [no_nested_borrows::test_box1]: forward function -/
+def test_box1 : Result Unit :=
+  let b := (I32.ofInt 1)
+  let x := b
+  if not (x = (I32.ofInt 1))
+  then Result.fail Error.panic
+  else Result.ret ()
+
+/- Unit test for [no_nested_borrows::test_box1] -/
+#assert (test_box1 == .ret ())
+
+/- [no_nested_borrows::copy_int]: forward function -/
+def copy_int (x : I32) : Result I32 :=
+  Result.ret x
+
+/- [no_nested_borrows::test_unreachable]: forward function -/
+def test_unreachable (b : Bool) : Result Unit :=
+  if b
+  then Result.fail Error.panic
+  else Result.ret ()
+
+/- [no_nested_borrows::test_panic]: forward function -/
+def test_panic (b : Bool) : Result Unit :=
+  if b
+  then Result.fail Error.panic
+  else Result.ret ()
+
+/- [no_nested_borrows::test_copy_int]: forward function -/
+def test_copy_int : Result Unit :=
+  do
+    let y ← copy_int (I32.ofInt 0)
+    if not ((I32.ofInt 0) = y)
+    then Result.fail Error.panic
+    else Result.ret ()
+
+/- Unit test for [no_nested_borrows::test_copy_int] -/
+#assert (test_copy_int == .ret ())
+
+/- [no_nested_borrows::is_cons]: forward function -/
+def is_cons (T : Type) (l : List T) : Result Bool :=
+  match l with
+  | List.Cons t l0 => Result.ret true
+  | List.Nil => Result.ret false
+
+/- [no_nested_borrows::test_is_cons]: forward function -/
+def test_is_cons : Result Unit :=
+  do
+    let l := List.Nil
+    let b ← is_cons I32 (List.Cons (I32.ofInt 0) l)
+    if not b
+    then Result.fail Error.panic
+    else Result.ret ()
+
+/- Unit test for [no_nested_borrows::test_is_cons] -/
+#assert (test_is_cons == .ret ())
+
+/- [no_nested_borrows::split_list]: forward function -/
+def split_list (T : Type) (l : List T) : Result (T × (List T)) :=
+  match l with
+  | List.Cons hd tl => Result.ret (hd, tl)
+  | List.Nil => Result.fail Error.panic
+
+/- [no_nested_borrows::test_split_list]: forward function -/
+def test_split_list : Result Unit :=
+  do
+    let l := List.Nil
+    let p ← split_list I32 (List.Cons (I32.ofInt 0) l)
+    let (hd, _) := p
+    if not (hd = (I32.ofInt 0))
+    then Result.fail Error.panic
+    else Result.ret ()
+
+/- Unit test for [no_nested_borrows::test_split_list] -/
+#assert (test_split_list == .ret ())
+
+/- [no_nested_borrows::choose]: forward function -/
+def choose (T : Type) (b : Bool) (x : T) (y : T) : Result T :=
+  if b
+  then Result.ret x
+  else Result.ret y
+
+/- [no_nested_borrows::choose]: backward function 0 -/
+def choose_back
+  (T : Type) (b : Bool) (x : T) (y : T) (ret0 : T) : Result (T × T) :=
+  if b
+  then Result.ret (ret0, y)
+  else Result.ret (x, ret0)
+
+/- [no_nested_borrows::choose_test]: forward function -/
+def choose_test : Result Unit :=
+  do
+    let z ← choose I32 true (I32.ofInt 0) (I32.ofInt 0)
+    let z0 ← z + (I32.ofInt 1)
+    if not (z0 = (I32.ofInt 1))
+    then Result.fail Error.panic
+    else
+      do
+        let (x, y) ← choose_back I32 true (I32.ofInt 0) (I32.ofInt 0) z0
+        if not (x = (I32.ofInt 1))
+        then Result.fail Error.panic
+        else
+          if not (y = (I32.ofInt 0))
+          then Result.fail Error.panic
+          else Result.ret ()
+
+/- Unit test for [no_nested_borrows::choose_test] -/
+#assert (choose_test == .ret ())
+
+/- [no_nested_borrows::test_char]: forward function -/
+def test_char : Result Char :=
+  Result.ret 'a'
+
+mutual
+
+/- [no_nested_borrows::NodeElem] -/
+inductive NodeElem (T : Type) :=
+| Cons : Tree T → NodeElem T → NodeElem T
+| Nil : NodeElem T
+
+/- [no_nested_borrows::Tree] -/
+inductive Tree (T : Type) :=
+| Leaf : T → Tree T
+| Node : T → NodeElem T → Tree T → Tree T
+
+end
+
+/- [no_nested_borrows::list_length]: forward function -/
+divergent def list_length (T : Type) (l : List T) : Result U32 :=
+  match l with
+  | List.Cons t l1 => do
+                        let i ← list_length T l1
+                        (U32.ofInt 1) + i
+  | List.Nil => Result.ret (U32.ofInt 0)
+
+/- [no_nested_borrows::list_nth_shared]: forward function -/
+divergent def list_nth_shared (T : Type) (l : List T) (i : U32) : Result T :=
+  match l with
+  | List.Cons x tl =>
+    if i = (U32.ofInt 0)
+    then Result.ret x
+    else do
+           let i0 ← i - (U32.ofInt 1)
+           list_nth_shared T tl i0
+  | List.Nil => Result.fail Error.panic
+
+/- [no_nested_borrows::list_nth_mut]: forward function -/
+divergent def list_nth_mut (T : Type) (l : List T) (i : U32) : Result T :=
+  match l with
+  | List.Cons x tl =>
+    if i = (U32.ofInt 0)
+    then Result.ret x
+    else do
+           let i0 ← i - (U32.ofInt 1)
+           list_nth_mut T tl i0
+  | List.Nil => Result.fail Error.panic
+
+/- [no_nested_borrows::list_nth_mut]: backward function 0 -/
+divergent def list_nth_mut_back
+  (T : Type) (l : List T) (i : U32) (ret0 : T) : Result (List T) :=
+  match l with
+  | List.Cons x tl =>
+    if i = (U32.ofInt 0)
+    then Result.ret (List.Cons ret0 tl)
+    else
+      do
+        let i0 ← i - (U32.ofInt 1)
+        let tl0 ← list_nth_mut_back T tl i0 ret0
+        Result.ret (List.Cons x tl0)
+  | List.Nil => Result.fail Error.panic
+
+/- [no_nested_borrows::list_rev_aux]: forward function -/
+divergent def list_rev_aux
+  (T : Type) (li : List T) (lo : List T) : Result (List T) :=
+  match li with
+  | List.Cons hd tl => list_rev_aux T tl (List.Cons hd lo)
+  | List.Nil => Result.ret lo
+
+/- [no_nested_borrows::list_rev]: merged forward/backward function
+   (there is a single backward function, and the forward function returns ()) -/
+def list_rev (T : Type) (l : List T) : Result (List T) :=
+  let li := mem.replace (List T) l List.Nil
+  list_rev_aux T li List.Nil
+
+/- [no_nested_borrows::test_list_functions]: forward function -/
+def test_list_functions : Result Unit :=
+  do
+    let l := List.Nil
+    let l0 := List.Cons (I32.ofInt 2) l
+    let l1 := List.Cons (I32.ofInt 1) l0
+    let i ← list_length I32 (List.Cons (I32.ofInt 0) l1)
+    if not (i = (U32.ofInt 3))
+    then Result.fail Error.panic
+    else
+      do
+        let i0 ←
+          list_nth_shared I32 (List.Cons (I32.ofInt 0) l1) (U32.ofInt 0)
+        if not (i0 = (I32.ofInt 0))
+        then Result.fail Error.panic
+        else
+          do
+            let i1 ←
+              list_nth_shared I32 (List.Cons (I32.ofInt 0) l1) (U32.ofInt 1)
+            if not (i1 = (I32.ofInt 1))
+            then Result.fail Error.panic
+            else
+              do
+                let i2 ←
+                  list_nth_shared I32 (List.Cons (I32.ofInt 0) l1)
+                    (U32.ofInt 2)
+                if not (i2 = (I32.ofInt 2))
+                then Result.fail Error.panic
+                else
+                  do
+                    let ls ←
+                      list_nth_mut_back I32 (List.Cons (I32.ofInt 0) l1)
+                        (U32.ofInt 1) (I32.ofInt 3)
+                    let i3 ← list_nth_shared I32 ls (U32.ofInt 0)
+                    if not (i3 = (I32.ofInt 0))
+                    then Result.fail Error.panic
+                    else
+                      do
+                        let i4 ← list_nth_shared I32 ls (U32.ofInt 1)
+                        if not (i4 = (I32.ofInt 3))
+                        then Result.fail Error.panic
+                        else
+                          do
+                            let i5 ← list_nth_shared I32 ls (U32.ofInt 2)
+                            if not (i5 = (I32.ofInt 2))
+                            then Result.fail Error.panic
+                            else Result.ret ()
+
+/- Unit test for [no_nested_borrows::test_list_functions] -/
+#assert (test_list_functions == .ret ())
+
+/- [no_nested_borrows::id_mut_pair1]: forward function -/
+def id_mut_pair1 (T1 T2 : Type) (x : T1) (y : T2) : Result (T1 × T2) :=
+  Result.ret (x, y)
+
+/- [no_nested_borrows::id_mut_pair1]: backward function 0 -/
+def id_mut_pair1_back
+  (T1 T2 : Type) (x : T1) (y : T2) (ret0 : (T1 × T2)) : Result (T1 × T2) :=
+  let (t, t0) := ret0
+  Result.ret (t, t0)
+
+/- [no_nested_borrows::id_mut_pair2]: forward function -/
+def id_mut_pair2 (T1 T2 : Type) (p : (T1 × T2)) : Result (T1 × T2) :=
+  let (t, t0) := p
+  Result.ret (t, t0)
+
+/- [no_nested_borrows::id_mut_pair2]: backward function 0 -/
+def id_mut_pair2_back
+  (T1 T2 : Type) (p : (T1 × T2)) (ret0 : (T1 × T2)) : Result (T1 × T2) :=
+  let (t, t0) := ret0
+  Result.ret (t, t0)
+
+/- [no_nested_borrows::id_mut_pair3]: forward function -/
+def id_mut_pair3 (T1 T2 : Type) (x : T1) (y : T2) : Result (T1 × T2) :=
+  Result.ret (x, y)
+
+/- [no_nested_borrows::id_mut_pair3]: backward function 0 -/
+def id_mut_pair3_back'a
+  (T1 T2 : Type) (x : T1) (y : T2) (ret0 : T1) : Result T1 :=
+  Result.ret ret0
+
+/- [no_nested_borrows::id_mut_pair3]: backward function 1 -/
+def id_mut_pair3_back'b
+  (T1 T2 : Type) (x : T1) (y : T2) (ret0 : T2) : Result T2 :=
+  Result.ret ret0
+
+/- [no_nested_borrows::id_mut_pair4]: forward function -/
+def id_mut_pair4 (T1 T2 : Type) (p : (T1 × T2)) : Result (T1 × T2) :=
+  let (t, t0) := p
+  Result.ret (t, t0)
+
+/- [no_nested_borrows::id_mut_pair4]: backward function 0 -/
+def id_mut_pair4_back'a
+  (T1 T2 : Type) (p : (T1 × T2)) (ret0 : T1) : Result T1 :=
+  Result.ret ret0
+
+/- [no_nested_borrows::id_mut_pair4]: backward function 1 -/
+def id_mut_pair4_back'b
+  (T1 T2 : Type) (p : (T1 × T2)) (ret0 : T2) : Result T2 :=
+  Result.ret ret0
+
+/- [no_nested_borrows::StructWithTuple] -/
+structure StructWithTuple (T1 T2 : Type) where
+  p : (T1 × T2)
+
+/- [no_nested_borrows::new_tuple1]: forward function -/
+def new_tuple1 : Result (StructWithTuple U32 U32) :=
+  Result.ret { p := ((U32.ofInt 1), (U32.ofInt 2)) }
+
+/- [no_nested_borrows::new_tuple2]: forward function -/
+def new_tuple2 : Result (StructWithTuple I16 I16) :=
+  Result.ret { p := ((I16.ofInt 1), (I16.ofInt 2)) }
+
+/- [no_nested_borrows::new_tuple3]: forward function -/
+def new_tuple3 : Result (StructWithTuple U64 I64) :=
+  Result.ret { p := ((U64.ofInt 1), (I64.ofInt 2)) }
+
+/- [no_nested_borrows::StructWithPair] -/
+structure StructWithPair (T1 T2 : Type) where
+  p : Pair T1 T2
+
+/- [no_nested_borrows::new_pair1]: forward function -/
+def new_pair1 : Result (StructWithPair U32 U32) :=
+  Result.ret { p := { x := (U32.ofInt 1), y := (U32.ofInt 2) } }
+
+/- [no_nested_borrows::test_constants]: forward function -/
+def test_constants : Result Unit :=
+  do
+    let swt ← new_tuple1
+    let (i, _) := swt.p
+    if not (i = (U32.ofInt 1))
+    then Result.fail Error.panic
+    else
+      do
+        let swt0 ← new_tuple2
+        let (i0, _) := swt0.p
+        if not (i0 = (I16.ofInt 1))
+        then Result.fail Error.panic
+        else
+          do
+            let swt1 ← new_tuple3
+            let (i1, _) := swt1.p
+            if not (i1 = (U64.ofInt 1))
+            then Result.fail Error.panic
+            else
+              do
+                let swp ← new_pair1
+                if not (swp.p.x = (U32.ofInt 1))
+                then Result.fail Error.panic
+                else Result.ret ()
+
+/- Unit test for [no_nested_borrows::test_constants] -/
+#assert (test_constants == .ret ())
+
+/- [no_nested_borrows::test_weird_borrows1]: forward function -/
+def test_weird_borrows1 : Result Unit :=
+  Result.ret ()
+
+/- Unit test for [no_nested_borrows::test_weird_borrows1] -/
+#assert (test_weird_borrows1 == .ret ())
+
+/- [no_nested_borrows::test_mem_replace]: merged forward/backward function
+   (there is a single backward function, and the forward function returns ()) -/
+def test_mem_replace (px : U32) : Result U32 :=
+  let y := mem.replace U32 px (U32.ofInt 1)
+  if not (y = (U32.ofInt 0))
+  then Result.fail Error.panic
+  else Result.ret (U32.ofInt 2)
+
+/- [no_nested_borrows::test_shared_borrow_bool1]: forward function -/
+def test_shared_borrow_bool1 (b : Bool) : Result U32 :=
+  if b
+  then Result.ret (U32.ofInt 0)
+  else Result.ret (U32.ofInt 1)
+
+/- [no_nested_borrows::test_shared_borrow_bool2]: forward function -/
+def test_shared_borrow_bool2 : Result U32 :=
+  Result.ret (U32.ofInt 0)
+
+/- [no_nested_borrows::test_shared_borrow_enum1]: forward function -/
+def test_shared_borrow_enum1 (l : List U32) : Result U32 :=
+  match l with
+  | List.Cons i l0 => Result.ret (U32.ofInt 1)
+  | List.Nil => Result.ret (U32.ofInt 0)
+
+/- [no_nested_borrows::test_shared_borrow_enum2]: forward function -/
+def test_shared_borrow_enum2 : Result U32 :=
+  Result.ret (U32.ofInt 0)
+
+end no_nested_borrows
diff --git a/tests/lean/Paper.lean b/tests/lean/Paper.lean
new file mode 100644
index 00000000..cee7128a
--- /dev/null
+++ b/tests/lean/Paper.lean
@@ -0,0 +1,121 @@
+-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
+-- [paper]
+import Base
+open Primitives
+namespace paper
+
+/- [paper::ref_incr]: merged forward/backward function
+   (there is a single backward function, and the forward function returns ()) -/
+def ref_incr (x : I32) : Result I32 :=
+  x + (I32.ofInt 1)
+
+/- [paper::test_incr]: forward function -/
+def test_incr : Result Unit :=
+  do
+    let x ← ref_incr (I32.ofInt 0)
+    if not (x = (I32.ofInt 1))
+    then Result.fail Error.panic
+    else Result.ret ()
+
+/- Unit test for [paper::test_incr] -/
+#assert (test_incr == .ret ())
+
+/- [paper::choose]: forward function -/
+def choose (T : Type) (b : Bool) (x : T) (y : T) : Result T :=
+  if b
+  then Result.ret x
+  else Result.ret y
+
+/- [paper::choose]: backward function 0 -/
+def choose_back
+  (T : Type) (b : Bool) (x : T) (y : T) (ret0 : T) : Result (T × T) :=
+  if b
+  then Result.ret (ret0, y)
+  else Result.ret (x, ret0)
+
+/- [paper::test_choose]: forward function -/
+def test_choose : Result Unit :=
+  do
+    let z ← choose I32 true (I32.ofInt 0) (I32.ofInt 0)
+    let z0 ← z + (I32.ofInt 1)
+    if not (z0 = (I32.ofInt 1))
+    then Result.fail Error.panic
+    else
+      do
+        let (x, y) ← choose_back I32 true (I32.ofInt 0) (I32.ofInt 0) z0
+        if not (x = (I32.ofInt 1))
+        then Result.fail Error.panic
+        else
+          if not (y = (I32.ofInt 0))
+          then Result.fail Error.panic
+          else Result.ret ()
+
+/- Unit test for [paper::test_choose] -/
+#assert (test_choose == .ret ())
+
+/- [paper::List] -/
+inductive List (T : Type) :=
+| Cons : T → List T → List T
+| Nil : List T
+
+/- [paper::list_nth_mut]: forward function -/
+divergent def list_nth_mut (T : Type) (l : List T) (i : U32) : Result T :=
+  match l with
+  | List.Cons x tl =>
+    if i = (U32.ofInt 0)
+    then Result.ret x
+    else do
+           let i0 ← i - (U32.ofInt 1)
+           list_nth_mut T tl i0
+  | List.Nil => Result.fail Error.panic
+
+/- [paper::list_nth_mut]: backward function 0 -/
+divergent def list_nth_mut_back
+  (T : Type) (l : List T) (i : U32) (ret0 : T) : Result (List T) :=
+  match l with
+  | List.Cons x tl =>
+    if i = (U32.ofInt 0)
+    then Result.ret (List.Cons ret0 tl)
+    else
+      do
+        let i0 ← i - (U32.ofInt 1)
+        let tl0 ← list_nth_mut_back T tl i0 ret0
+        Result.ret (List.Cons x tl0)
+  | List.Nil => Result.fail Error.panic
+
+/- [paper::sum]: forward function -/
+divergent def sum (l : List I32) : Result I32 :=
+  match l with
+  | List.Cons x tl => do
+                        let i ← sum tl
+                        x + i
+  | List.Nil => Result.ret (I32.ofInt 0)
+
+/- [paper::test_nth]: forward function -/
+def test_nth : Result Unit :=
+  do
+    let l := List.Nil
+    let l0 := List.Cons (I32.ofInt 3) l
+    let l1 := List.Cons (I32.ofInt 2) l0
+    let x ← list_nth_mut I32 (List.Cons (I32.ofInt 1) l1) (U32.ofInt 2)
+    let x0 ← x + (I32.ofInt 1)
+    let l2 ←
+      list_nth_mut_back I32 (List.Cons (I32.ofInt 1) l1) (U32.ofInt 2) x0
+    let i ← sum l2
+    if not (i = (I32.ofInt 7))
+    then Result.fail Error.panic
+    else Result.ret ()
+
+/- Unit test for [paper::test_nth] -/
+#assert (test_nth == .ret ())
+
+/- [paper::call_choose]: forward function -/
+def call_choose (p : (U32 × U32)) : Result U32 :=
+  do
+    let (px, py) := p
+    let pz ← choose U32 true px py
+    let pz0 ← pz + (U32.ofInt 1)
+    let (px0, _) ← choose_back U32 true px py pz0
+    Result.ret px0
+
+end paper
diff --git a/tests/lean/PoloniusList.lean b/tests/lean/PoloniusList.lean
new file mode 100644
index 00000000..1453c275
--- /dev/null
+++ b/tests/lean/PoloniusList.lean
@@ -0,0 +1,34 @@
+-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
+-- [polonius_list]
+import Base
+open Primitives
+namespace polonius_list
+
+/- [polonius_list::List] -/
+inductive List (T : Type) :=
+| Cons : T → List T → List T
+| Nil : List T
+
+/- [polonius_list::get_list_at_x]: forward function -/
+divergent def get_list_at_x (ls : List U32) (x : U32) : Result (List U32) :=
+  match ls with
+  | List.Cons hd tl =>
+    if hd = x
+    then Result.ret (List.Cons hd tl)
+    else get_list_at_x tl x
+  | List.Nil => Result.ret List.Nil
+
+/- [polonius_list::get_list_at_x]: backward function 0 -/
+divergent def get_list_at_x_back
+  (ls : List U32) (x : U32) (ret0 : List U32) : Result (List U32) :=
+  match ls with
+  | List.Cons hd tl =>
+    if hd = x
+    then Result.ret ret0
+    else
+      do
+        let tl0 ← get_list_at_x_back tl x ret0
+        Result.ret (List.Cons hd tl0)
+  | List.Nil => Result.ret ret0
+
+end polonius_list
diff --git a/tests/lean/hashmap/Base/Primitives.lean b/tests/lean/hashmap/Base/Primitives.lean
deleted file mode 100644
index 4a66a453..00000000
--- a/tests/lean/hashmap/Base/Primitives.lean
+++ /dev/null
@@ -1,583 +0,0 @@
-import Lean
-import Lean.Meta.Tactic.Simp
-import Init.Data.List.Basic
-import Mathlib.Tactic.RunCmd
-
---------------------
--- ASSERT COMMAND --
---------------------
-
-open Lean Elab Command Term Meta
-
-syntax (name := assert) "#assert" term: command
-
-@[command_elab assert]
-unsafe
-def assertImpl : CommandElab := fun (_stx: Syntax) => do
-  runTermElabM (fun _ => do
-    let r ← evalTerm Bool (mkConst ``Bool) _stx[1]
-    if not r then
-      logInfo "Assertion failed for: "
-      logInfo _stx[1]
-      logError "Expression reduced to false"
-    pure ())
-
-#eval 2 == 2
-#assert (2 == 2)
-
--------------
--- PRELUDE --
--------------
-
--- Results & monadic combinators
-
-inductive Error where
-   | assertionFailure: Error
-   | integerOverflow: Error
-   | divisionByZero: Error
-   | arrayOutOfBounds: Error
-   | maximumSizeExceeded: Error
-   | panic: Error
-deriving Repr, BEq
-
-open Error
-
-inductive Result (α : Type u) where
-  | ret (v: α): Result α
-  | fail (e: Error): Result α
-deriving Repr, BEq
-
-open Result
-
-instance Result_Inhabited (α : Type u) : Inhabited (Result α) :=
-  Inhabited.mk (fail panic)
-
-/- HELPERS -/
-
-def ret? {α: Type} (r: Result α): Bool :=
-  match r with
-  | Result.ret _ => true
-  | Result.fail _ => false
-
-def massert (b:Bool) : Result Unit :=
-  if b then .ret () else fail assertionFailure
-
-def eval_global {α: Type} (x: Result α) (_: ret? x): α :=
-  match x with
-  | Result.fail _ => by contradiction
-  | Result.ret x => x
-
-/- DO-DSL SUPPORT -/
-
-def bind (x: Result α) (f: α -> Result β) : Result β :=
-  match x with
-  | ret v  => f v 
-  | fail v => fail v
-
--- Allows using Result in do-blocks
-instance : Bind Result where
-  bind := bind
-
--- Allows using return x in do-blocks
-instance : Pure Result where
-  pure := fun x => ret x
-
-/- CUSTOM-DSL SUPPORT -/
-
--- Let-binding the Result of a monadic operation is oftentimes not sufficient,
--- because we may need a hypothesis for equational reasoning in the scope. We
--- rely on subtype, and a custom let-binding operator, in effect recreating our
--- own variant of the do-dsl
-
-def Result.attach {α: Type} (o : Result α): Result { x : α // o = ret x } :=
-  match o with
-  | .ret x => .ret ⟨x, rfl⟩
-  | .fail e => .fail e
-
-macro "let" e:term " ⟵ " f:term : doElem =>
-  `(doElem| let ⟨$e, h⟩ ← Result.attach $f)
-
--- TODO: any way to factorize both definitions?
-macro "let" e:term " <-- " f:term : doElem =>
-  `(doElem| let ⟨$e, h⟩ ← Result.attach $f)
-
--- We call the hypothesis `h`, in effect making it unavailable to the user
--- (because too much shadowing). But in practice, once can use the French single
--- quote notation (input with f< and f>), where `‹ h ›` finds a suitable
--- hypothesis in the context, this is equivalent to `have x: h := by assumption in x`
-#eval do
-  let y <-- .ret (0: Nat)
-  let _: y = 0 := by cases ‹ ret 0 = ret y › ; decide
-  let r: { x: Nat // x = 0 } := ⟨ y, by assumption ⟩
-  .ret r
-
-----------------------
--- MACHINE INTEGERS --
-----------------------
-
--- We redefine our machine integers types.
-
--- For Isize/Usize, we reuse `getNumBits` from `USize`. You cannot reduce `getNumBits`
--- using the simplifier, meaning that proofs do not depend on the compile-time value of
--- USize.size. (Lean assumes 32 or 64-bit platforms, and Rust doesn't really support, at
--- least officially, 16-bit microcontrollers, so this seems like a fine design decision
--- for now.)
-
--- Note from Chris Bailey: "If there's more than one salient property of your
--- definition then the subtyping strategy might get messy, and the property part
--- of a subtype is less discoverable by the simplifier or tactics like
--- library_search." So, we will not add refinements on the return values of the
--- operations defined on Primitives, but will rather rely on custom lemmas to
--- invert on possible return values of the primitive operations.
-
--- Machine integer constants, done via `ofNatCore`, which requires a proof that
--- the `Nat` fits within the desired integer type. We provide a custom tactic.
-
-open System.Platform.getNumBits
-
--- TODO: is there a way of only importing System.Platform.getNumBits?
---
-@[simp] def size_num_bits : Nat := (System.Platform.getNumBits ()).val
-
--- Remark: Lean seems to use < for the comparisons with the upper bounds by convention.
--- We keep the F* convention for now.
-@[simp] def Isize.min : Int := - (HPow.hPow 2 (size_num_bits - 1))
-@[simp] def Isize.max : Int := (HPow.hPow 2 (size_num_bits - 1)) - 1
-@[simp] def I8.min    : Int := - (HPow.hPow 2 7)
-@[simp] def I8.max    : Int := HPow.hPow 2 7 - 1
-@[simp] def I16.min   : Int := - (HPow.hPow 2 15)
-@[simp] def I16.max   : Int := HPow.hPow 2 15 - 1
-@[simp] def I32.min   : Int := -(HPow.hPow 2 31)
-@[simp] def I32.max   : Int := HPow.hPow 2 31 - 1
-@[simp] def I64.min   : Int := -(HPow.hPow 2 63)
-@[simp] def I64.max   : Int := HPow.hPow 2 63 - 1
-@[simp] def I128.min  : Int := -(HPow.hPow 2 127)
-@[simp] def I128.max  : Int := HPow.hPow 2 127 - 1
-@[simp] def Usize.min : Int := 0
-@[simp] def Usize.max : Int := HPow.hPow 2 size_num_bits - 1
-@[simp] def U8.min    : Int := 0
-@[simp] def U8.max    : Int := HPow.hPow 2 8 - 1
-@[simp] def U16.min   : Int := 0
-@[simp] def U16.max   : Int := HPow.hPow 2 16 - 1
-@[simp] def U32.min   : Int := 0
-@[simp] def U32.max   : Int := HPow.hPow 2 32 - 1
-@[simp] def U64.min   : Int := 0
-@[simp] def U64.max   : Int := HPow.hPow 2 64 - 1
-@[simp] def U128.min  : Int := 0
-@[simp] def U128.max  : Int := HPow.hPow 2 128 - 1
-
-#assert (I8.min   == -128)
-#assert (I8.max   == 127)
-#assert (I16.min  == -32768)
-#assert (I16.max  == 32767)
-#assert (I32.min  == -2147483648)
-#assert (I32.max  == 2147483647)
-#assert (I64.min  == -9223372036854775808)
-#assert (I64.max  == 9223372036854775807)
-#assert (I128.min == -170141183460469231731687303715884105728)
-#assert (I128.max == 170141183460469231731687303715884105727)
-#assert (U8.min   == 0)
-#assert (U8.max   == 255)
-#assert (U16.min  == 0)
-#assert (U16.max  == 65535)
-#assert (U32.min  == 0)
-#assert (U32.max  == 4294967295)
-#assert (U64.min  == 0)
-#assert (U64.max  == 18446744073709551615)
-#assert (U128.min == 0)
-#assert (U128.max == 340282366920938463463374607431768211455)
-
-inductive ScalarTy :=
-| Isize
-| I8
-| I16
-| I32
-| I64
-| I128
-| Usize
-| U8
-| U16
-| U32
-| U64
-| U128
-
-def Scalar.min (ty : ScalarTy) : Int :=
-  match ty with
-  | .Isize => Isize.min
-  | .I8    => I8.min
-  | .I16   => I16.min
-  | .I32   => I32.min
-  | .I64   => I64.min
-  | .I128  => I128.min
-  | .Usize => Usize.min
-  | .U8    => U8.min
-  | .U16   => U16.min
-  | .U32   => U32.min
-  | .U64   => U64.min
-  | .U128  => U128.min
-
-def Scalar.max (ty : ScalarTy) : Int :=
-  match ty with
-  | .Isize => Isize.max
-  | .I8    => I8.max
-  | .I16   => I16.max
-  | .I32   => I32.max
-  | .I64   => I64.max
-  | .I128  => I128.max
-  | .Usize => Usize.max
-  | .U8    => U8.max
-  | .U16   => U16.max
-  | .U32   => U32.max
-  | .U64   => U64.max
-  | .U128  => U128.max
-
--- "Conservative" bounds
--- We use those because we can't compare to the isize bounds (which can't
--- reduce at compile-time). Whenever we perform an arithmetic operation like
--- addition we need to check that the result is in bounds: we first compare
--- to the conservative bounds, which reduce, then compare to the real bounds.
--- This is useful for the various #asserts that we want to reduce at
--- type-checking time.
-def Scalar.cMin (ty : ScalarTy) : Int :=
-  match ty with
-  | .Isize => I32.min
-  | _ => Scalar.min ty
-
-def Scalar.cMax (ty : ScalarTy) : Int :=
-  match ty with
-  | .Isize => I32.max
-  | .Usize => U32.max
-  | _ => Scalar.max ty
-
-theorem Scalar.cMin_bound ty : Scalar.min ty <= Scalar.cMin ty := by sorry
-theorem Scalar.cMax_bound ty : Scalar.min ty <= Scalar.cMin ty := by sorry
-
-structure Scalar (ty : ScalarTy) where
-  val : Int
-  hmin : Scalar.min ty <= val
-  hmax : val <= Scalar.max ty
-
-theorem Scalar.bound_suffices (ty : ScalarTy) (x : Int) :
-  Scalar.cMin ty <= x && x <= Scalar.cMax ty ->
-  (decide (Scalar.min ty ≤ x) && decide (x ≤ Scalar.max ty)) = true
-  := by sorry
-
-def Scalar.ofIntCore {ty : ScalarTy} (x : Int)
-  (hmin : Scalar.min ty <= x) (hmax : x <= Scalar.max ty) : Scalar ty :=
-  { val := x, hmin := hmin, hmax := hmax }
-
-def Scalar.ofInt {ty : ScalarTy} (x : Int)
-  (h : Scalar.min ty <= x && x <= Scalar.max ty) : Scalar ty :=
-  let hmin: Scalar.min ty <= x := by sorry
-  let hmax: x <= Scalar.max ty := by sorry
-  Scalar.ofIntCore x hmin hmax
-
--- Further thoughts: look at what has been done here:
--- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/Fin/Basic.lean
--- and
--- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/UInt.lean
--- which both contain a fair amount of reasoning already!
-def Scalar.tryMk (ty : ScalarTy) (x : Int) : Result (Scalar ty) :=
-  -- TODO: write this with only one if then else
-  if hmin_cons: Scalar.cMin ty <= x || Scalar.min ty <= x then
-    if hmax_cons: x <= Scalar.cMax ty || x <= Scalar.max ty then
-      let hmin: Scalar.min ty <= x := by sorry
-      let hmax: x <= Scalar.max ty := by sorry
-      return Scalar.ofIntCore x hmin hmax
-    else fail integerOverflow
-  else fail integerOverflow
-
-def Scalar.neg {ty : ScalarTy} (x : Scalar ty) : Result (Scalar ty) := Scalar.tryMk ty (- x.val)
-
-def Scalar.div {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
-  if y.val != 0 then Scalar.tryMk ty (x.val / y.val) else fail divisionByZero
-
--- Checking that the % operation in Lean computes the same as the remainder operation in Rust
-#assert 1 % 2 = (1:Int)
-#assert (-1) % 2 = -1
-#assert 1 % (-2) = 1
-#assert (-1) % (-2) = -1
-
-def Scalar.rem {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
-  if y.val != 0 then Scalar.tryMk ty (x.val % y.val) else fail divisionByZero
-
-def Scalar.add {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
-  Scalar.tryMk ty (x.val + y.val)
-
-def Scalar.sub {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
-  Scalar.tryMk ty (x.val - y.val)
-
-def Scalar.mul {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
-  Scalar.tryMk ty (x.val * y.val)
-
--- TODO: instances of +, -, * etc. for scalars
-
--- Cast an integer from a [src_ty] to a [tgt_ty]
--- TODO: check the semantics of casts in Rust
-def Scalar.cast {src_ty : ScalarTy} (tgt_ty : ScalarTy) (x : Scalar src_ty) : Result (Scalar tgt_ty) :=
-  Scalar.tryMk tgt_ty x.val
-
--- The scalar types
--- We declare the definitions as reducible so that Lean can unfold them (useful
--- for type class resolution for instance).
-@[reducible] def Isize := Scalar .Isize
-@[reducible] def I8    := Scalar .I8
-@[reducible] def I16   := Scalar .I16
-@[reducible] def I32   := Scalar .I32
-@[reducible] def I64   := Scalar .I64
-@[reducible] def I128  := Scalar .I128
-@[reducible] def Usize := Scalar .Usize
-@[reducible] def U8    := Scalar .U8
-@[reducible] def U16   := Scalar .U16
-@[reducible] def U32   := Scalar .U32
-@[reducible] def U64   := Scalar .U64
-@[reducible] def U128  := Scalar .U128
-
--- TODO: below: not sure this is the best way.
--- Should we rather overload operations like +, -, etc.?
--- Also, it is possible to automate the generation of those definitions
--- with macros (but would it be a good idea? It would be less easy to
--- read the file, which is not supposed to change a lot)
-
--- Negation
-
-/--
-Remark: there is no heterogeneous negation in the Lean prelude: we thus introduce
-one here.
-
-The notation typeclass for heterogeneous addition.
-This enables the notation `- a : β` where `a : α`.
--/
-class HNeg (α : Type u) (β : outParam (Type v)) where
-  /-- `- a` computes the negation of `a`.
-  The meaning of this notation is type-dependent. -/
-  hNeg : α → β
-
-prefix:75  "-"   => HNeg.hNeg
-
-instance : HNeg Isize (Result Isize) where hNeg x := Scalar.neg x
-instance : HNeg I8 (Result I8) where hNeg x := Scalar.neg x
-instance : HNeg I16 (Result I16) where hNeg x := Scalar.neg x
-instance : HNeg I32 (Result I32) where hNeg x := Scalar.neg x
-instance : HNeg I64 (Result I64) where hNeg x := Scalar.neg x
-instance : HNeg I128 (Result I128) where hNeg x := Scalar.neg x
-
--- Addition
-instance {ty} : HAdd (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
-  hAdd x y := Scalar.add x y
-
--- Substraction
-instance {ty} : HSub (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
-  hSub x y := Scalar.sub x y
-
--- Multiplication
-instance {ty} : HMul (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
-  hMul x y := Scalar.mul x y
-
--- Division
-instance {ty} : HDiv (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
-  hDiv x y := Scalar.div x y
-
--- Remainder
-instance {ty} : HMod (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
-  hMod x y := Scalar.rem x y
-
--- ofIntCore
--- TODO: typeclass?
-def Isize.ofIntCore := @Scalar.ofIntCore .Isize
-def I8.ofIntCore    := @Scalar.ofIntCore .I8
-def I16.ofIntCore   := @Scalar.ofIntCore .I16
-def I32.ofIntCore   := @Scalar.ofIntCore .I32
-def I64.ofIntCore   := @Scalar.ofIntCore .I64
-def I128.ofIntCore  := @Scalar.ofIntCore .I128
-def Usize.ofIntCore := @Scalar.ofIntCore .Usize
-def U8.ofIntCore    := @Scalar.ofIntCore .U8
-def U16.ofIntCore   := @Scalar.ofIntCore .U16
-def U32.ofIntCore   := @Scalar.ofIntCore .U32
-def U64.ofIntCore   := @Scalar.ofIntCore .U64
-def U128.ofIntCore  := @Scalar.ofIntCore .U128
-
---  ofInt
--- TODO: typeclass?
-def Isize.ofInt := @Scalar.ofInt .Isize
-def I8.ofInt    := @Scalar.ofInt .I8
-def I16.ofInt   := @Scalar.ofInt .I16
-def I32.ofInt   := @Scalar.ofInt .I32
-def I64.ofInt   := @Scalar.ofInt .I64
-def I128.ofInt  := @Scalar.ofInt .I128
-def Usize.ofInt := @Scalar.ofInt .Usize
-def U8.ofInt    := @Scalar.ofInt .U8
-def U16.ofInt   := @Scalar.ofInt .U16
-def U32.ofInt   := @Scalar.ofInt .U32
-def U64.ofInt   := @Scalar.ofInt .U64
-def U128.ofInt  := @Scalar.ofInt .U128
-
--- Comparisons
-instance {ty} : LT (Scalar ty) where
-  lt a b := LT.lt a.val b.val
-
-instance {ty} : LE (Scalar ty) where le a b := LE.le a.val b.val
-
-instance Scalar.decLt {ty} (a b : Scalar ty) : Decidable (LT.lt a b) := Int.decLt ..
-instance Scalar.decLe {ty} (a b : Scalar ty) : Decidable (LE.le a b) := Int.decLe ..
-
-theorem Scalar.eq_of_val_eq {ty} : ∀ {i j : Scalar ty}, Eq i.val j.val → Eq i j
-  | ⟨_, _, _⟩, ⟨_, _, _⟩, rfl => rfl
-
-theorem Scalar.val_eq_of_eq {ty} {i j : Scalar ty} (h : Eq i j) : Eq i.val j.val :=
-  h ▸ rfl
-
-theorem Scalar.ne_of_val_ne {ty} {i j : Scalar ty} (h : Not (Eq i.val j.val)) : Not (Eq i j) :=
-  fun h' => absurd (val_eq_of_eq h') h
-
-instance (ty : ScalarTy) : DecidableEq (Scalar ty) :=
-  fun i j =>
-    match decEq i.val j.val with
-    | isTrue h  => isTrue (Scalar.eq_of_val_eq h)
-    | isFalse h => isFalse (Scalar.ne_of_val_ne h)
-
-def Scalar.toInt {ty} (n : Scalar ty) : Int := n.val
-
--- Tactic to prove that integers are in bounds
-syntax "intlit" : tactic
-
-macro_rules
-  | `(tactic| intlit) => `(tactic| apply Scalar.bound_suffices ; decide)
-
--- -- We now define a type class that subsumes the various machine integer types, so
--- -- as to write a concise definition for scalar_cast, rather than exhaustively
--- -- enumerating all of the possible pairs. We remark that Rust has sane semantics
--- -- and fails if a cast operation would involve a truncation or modulo.
-
--- class MachineInteger (t: Type) where
---   size: Nat
---   val: t -> Fin size
---   ofNatCore: (n:Nat) -> LT.lt n size -> t
-
--- set_option hygiene false in
--- run_cmd
---   for typeName in [`UInt8, `UInt16, `UInt32, `UInt64, `USize].map Lean.mkIdent do
---   Lean.Elab.Command.elabCommand (← `(
---     namespace $typeName
---     instance: MachineInteger $typeName where
---       size := size
---       val := val
---       ofNatCore := ofNatCore
---     end $typeName
---   ))
-
--- -- Aeneas only instantiates the destination type (`src` is implicit). We rely on
--- -- Lean to infer `src`.
-
--- def scalar_cast { src: Type } (dst: Type) [ MachineInteger src ] [ MachineInteger dst ] (x: src): Result dst :=
---   if h: MachineInteger.val x < MachineInteger.size dst then
---     .ret (MachineInteger.ofNatCore (MachineInteger.val x).val h)
---   else
---     .fail integerOverflow
-
--------------
--- VECTORS --
--------------
-
-def Vec (α : Type u) := { l : List α // List.length l <= Usize.max }
-
-def vec_new (α : Type u): Vec α := ⟨ [], by sorry ⟩
-
-def vec_len (α : Type u) (v : Vec α) : Usize :=
-  let ⟨ v, l ⟩ := v
-  Usize.ofIntCore (List.length v) (by sorry) l
- 
-def vec_push_fwd (α : Type u) (_ : Vec α) (_ : α) : Unit := ()
-
-def vec_push_back (α : Type u) (v : Vec α) (x : α) : Result (Vec α)
-  :=
-  if h : List.length v.val <= U32.max || List.length v.val <= Usize.max then
-    return ⟨ List.concat v.val x, by sorry ⟩
-  else
-    fail maximumSizeExceeded
-
-def vec_insert_fwd (α : Type u) (v: Vec α) (i: Usize) (_: α): Result Unit :=
-  if i.val < List.length v.val then
-    .ret ()
-  else
-    .fail arrayOutOfBounds
-
-def vec_insert_back (α : Type u) (v: Vec α) (i: Usize) (x: α): Result (Vec α) :=
-  if i.val < List.length v.val then
-    -- TODO: maybe we should redefine a list library which uses integers
-    -- (instead of natural numbers)
-    let i : Nat :=
-      match i.val with
-      | .ofNat n => n
-      | .negSucc n => by sorry -- TODO: we can't get here
-    let isLt: i < USize.size := by sorry
-    let i : Fin USize.size := { val := i, isLt := isLt }
-    .ret ⟨ List.set v.val i.val x, by
-      have h: List.length v.val <= Usize.max := v.property
-      rewrite [ List.length_set v.val i.val x ]
-      assumption
-    ⟩
-  else
-    .fail arrayOutOfBounds
-
-def vec_index_fwd (α : Type u) (v: Vec α) (i: Usize): Result α :=
-  if i.val < List.length v.val then
-    let i : Nat :=
-      match i.val with
-      | .ofNat n => n
-      | .negSucc n => by sorry -- TODO: we can't get here
-    let isLt: i < USize.size := by sorry
-    let i : Fin USize.size := { val := i, isLt := isLt }
-    let h: i < List.length v.val := by sorry
-    .ret (List.get v.val ⟨i.val, h⟩)
-  else
-    .fail arrayOutOfBounds
-
-def vec_index_back (α : Type u) (v: Vec α) (i: Usize) (_: α): Result Unit :=
-  if i.val < List.length v.val then
-    .ret ()
-  else
-    .fail arrayOutOfBounds
-
-def vec_index_mut_fwd (α : Type u) (v: Vec α) (i: Usize): Result α :=
-  if i.val < List.length v.val then
-    let i : Nat :=
-      match i.val with
-      | .ofNat n => n
-      | .negSucc n => by sorry -- TODO: we can't get here
-    let isLt: i < USize.size := by sorry
-    let i : Fin USize.size := { val := i, isLt := isLt }
-    let h: i < List.length v.val := by sorry
-    .ret (List.get v.val ⟨i.val, h⟩)
-  else
-    .fail arrayOutOfBounds
-
-def vec_index_mut_back (α : Type u) (v: Vec α) (i: Usize) (x: α): Result (Vec α) :=
-  if i.val < List.length v.val then
-    let i : Nat :=
-      match i.val with
-      | .ofNat n => n
-      | .negSucc n => by sorry -- TODO: we can't get here
-    let isLt: i < USize.size := by sorry
-    let i : Fin USize.size := { val := i, isLt := isLt }
-    .ret ⟨ List.set v.val i.val x, by
-      have h: List.length v.val <= Usize.max := v.property
-      rewrite [ List.length_set v.val i.val x ]
-      assumption
-    ⟩
-  else
-    .fail arrayOutOfBounds
-
-----------
--- MISC --
-----------
-
-def mem_replace_fwd (a : Type) (x : a) (_ : a) : a :=
-  x
-
-def mem_replace_back (a : Type) (_ : a) (y : a) : a :=
-  y
-
-/-- Aeneas-translated function -- useful to reduce non-recursive definitions.
- Use with `simp [ aeneas ]` -/
-register_simp_attr aeneas
diff --git a/tests/lean/hashmap/Hashmap.lean b/tests/lean/hashmap/Hashmap.lean
deleted file mode 100644
index 41630205..00000000
--- a/tests/lean/hashmap/Hashmap.lean
+++ /dev/null
@@ -1 +0,0 @@
-import Hashmap.Funs
diff --git a/tests/lean/hashmap/Hashmap/Clauses/Clauses.lean b/tests/lean/hashmap/Hashmap/Clauses/Clauses.lean
deleted file mode 100644
index 197b0a6a..00000000
--- a/tests/lean/hashmap/Hashmap/Clauses/Clauses.lean
+++ /dev/null
@@ -1,107 +0,0 @@
--- [hashmap]: templates for the decreases clauses
-import Base.Primitives
-import Hashmap.Types
-
-/- [hashmap::HashMap::{0}::allocate_slots]: termination measure -/
-@[simp]
-def hash_map_allocate_slots_loop_terminates (T : Type) (slots : Vec (list_t T))
-  (n : Usize) :=
-  (slots, n)
-
-/- [hashmap::HashMap::{0}::allocate_slots]: decreases_by tactic -/
-syntax "hash_map_allocate_slots_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| hash_map_allocate_slots_loop_decreases $slots $n) =>`(tactic| sorry)
-
-/- [hashmap::HashMap::{0}::clear]: termination measure -/
-@[simp]
-def hash_map_clear_loop_terminates (T : Type) (slots : Vec (list_t T))
-  (i : Usize) :=
-  (slots, i)
-
-/- [hashmap::HashMap::{0}::clear]: decreases_by tactic -/
-syntax "hash_map_clear_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| hash_map_clear_loop_decreases $slots $i) =>`(tactic| sorry)
-
-/- [hashmap::HashMap::{0}::insert_in_list]: termination measure -/
-@[simp]
-def hash_map_insert_in_list_loop_terminates (T : Type) (key : Usize)
-  (value : T) (ls : list_t T) :=
-  (key, value, ls)
-
-/- [hashmap::HashMap::{0}::insert_in_list]: decreases_by tactic -/
-syntax "hash_map_insert_in_list_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| hash_map_insert_in_list_loop_decreases $key $value $ls) =>
-  `(tactic| sorry)
-
-/- [hashmap::HashMap::{0}::move_elements_from_list]: termination measure -/
-@[simp]
-def hash_map_move_elements_from_list_loop_terminates (T : Type)
-  (ntable : hash_map_t T) (ls : list_t T) :=
-  (ntable, ls)
-
-/- [hashmap::HashMap::{0}::move_elements_from_list]: decreases_by tactic -/
-syntax "hash_map_move_elements_from_list_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| hash_map_move_elements_from_list_loop_decreases $ntable $ls) =>
-  `(tactic| sorry)
-
-/- [hashmap::HashMap::{0}::move_elements]: termination measure -/
-@[simp]
-def hash_map_move_elements_loop_terminates (T : Type) (ntable : hash_map_t T)
-  (slots : Vec (list_t T)) (i : Usize) :=
-  (ntable, slots, i)
-
-/- [hashmap::HashMap::{0}::move_elements]: decreases_by tactic -/
-syntax "hash_map_move_elements_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| hash_map_move_elements_loop_decreases $ntable $slots $i) =>
-  `(tactic| sorry)
-
-/- [hashmap::HashMap::{0}::contains_key_in_list]: termination measure -/
-@[simp]
-def hash_map_contains_key_in_list_loop_terminates (T : Type) (key : Usize)
-  (ls : list_t T) :=
-  (key, ls)
-
-/- [hashmap::HashMap::{0}::contains_key_in_list]: decreases_by tactic -/
-syntax "hash_map_contains_key_in_list_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| hash_map_contains_key_in_list_loop_decreases $key $ls) =>
-  `(tactic| sorry)
-
-/- [hashmap::HashMap::{0}::get_in_list]: termination measure -/
-@[simp]
-def hash_map_get_in_list_loop_terminates (T : Type) (key : Usize)
-  (ls : list_t T) :=
-  (key, ls)
-
-/- [hashmap::HashMap::{0}::get_in_list]: decreases_by tactic -/
-syntax "hash_map_get_in_list_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| hash_map_get_in_list_loop_decreases $key $ls) =>`(tactic| sorry)
-
-/- [hashmap::HashMap::{0}::get_mut_in_list]: termination measure -/
-@[simp]
-def hash_map_get_mut_in_list_loop_terminates (T : Type) (ls : list_t T)
-  (key : Usize) :=
-  (ls, key)
-
-/- [hashmap::HashMap::{0}::get_mut_in_list]: decreases_by tactic -/
-syntax "hash_map_get_mut_in_list_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| hash_map_get_mut_in_list_loop_decreases $ls $key) =>`(tactic| sorry)
-
-/- [hashmap::HashMap::{0}::remove_from_list]: termination measure -/
-@[simp]
-def hash_map_remove_from_list_loop_terminates (T : Type) (key : Usize)
-  (ls : list_t T) :=
-  (key, ls)
-
-/- [hashmap::HashMap::{0}::remove_from_list]: decreases_by tactic -/
-syntax "hash_map_remove_from_list_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| hash_map_remove_from_list_loop_decreases $key $ls) =>`(tactic| sorry)
-
diff --git a/tests/lean/hashmap/Hashmap/Clauses/Template.lean b/tests/lean/hashmap/Hashmap/Clauses/Template.lean
deleted file mode 100644
index 560592c8..00000000
--- a/tests/lean/hashmap/Hashmap/Clauses/Template.lean
+++ /dev/null
@@ -1,108 +0,0 @@
--- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
--- [hashmap]: templates for the decreases clauses
-import Base.Primitives
-import Hashmap.Types
-
-/- [hashmap::HashMap::{0}::allocate_slots]: termination measure -/
-@[simp]
-def hash_map_allocate_slots_loop_terminates (T : Type) (slots : Vec (list_t T))
-  (n : Usize) :=
-  (slots, n)
-
-/- [hashmap::HashMap::{0}::allocate_slots]: decreases_by tactic -/
-syntax "hash_map_allocate_slots_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| hash_map_allocate_slots_loop_decreases $slots $n) =>`(tactic| sorry)
-
-/- [hashmap::HashMap::{0}::clear]: termination measure -/
-@[simp]
-def hash_map_clear_loop_terminates (T : Type) (slots : Vec (list_t T))
-  (i : Usize) :=
-  (slots, i)
-
-/- [hashmap::HashMap::{0}::clear]: decreases_by tactic -/
-syntax "hash_map_clear_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| hash_map_clear_loop_decreases $slots $i) =>`(tactic| sorry)
-
-/- [hashmap::HashMap::{0}::insert_in_list]: termination measure -/
-@[simp]
-def hash_map_insert_in_list_loop_terminates (T : Type) (key : Usize)
-  (value : T) (ls : list_t T) :=
-  (key, value, ls)
-
-/- [hashmap::HashMap::{0}::insert_in_list]: decreases_by tactic -/
-syntax "hash_map_insert_in_list_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| hash_map_insert_in_list_loop_decreases $key $value $ls) =>
-  `(tactic| sorry)
-
-/- [hashmap::HashMap::{0}::move_elements_from_list]: termination measure -/
-@[simp]
-def hash_map_move_elements_from_list_loop_terminates (T : Type)
-  (ntable : hash_map_t T) (ls : list_t T) :=
-  (ntable, ls)
-
-/- [hashmap::HashMap::{0}::move_elements_from_list]: decreases_by tactic -/
-syntax "hash_map_move_elements_from_list_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| hash_map_move_elements_from_list_loop_decreases $ntable $ls) =>
-  `(tactic| sorry)
-
-/- [hashmap::HashMap::{0}::move_elements]: termination measure -/
-@[simp]
-def hash_map_move_elements_loop_terminates (T : Type) (ntable : hash_map_t T)
-  (slots : Vec (list_t T)) (i : Usize) :=
-  (ntable, slots, i)
-
-/- [hashmap::HashMap::{0}::move_elements]: decreases_by tactic -/
-syntax "hash_map_move_elements_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| hash_map_move_elements_loop_decreases $ntable $slots $i) =>
-  `(tactic| sorry)
-
-/- [hashmap::HashMap::{0}::contains_key_in_list]: termination measure -/
-@[simp]
-def hash_map_contains_key_in_list_loop_terminates (T : Type) (key : Usize)
-  (ls : list_t T) :=
-  (key, ls)
-
-/- [hashmap::HashMap::{0}::contains_key_in_list]: decreases_by tactic -/
-syntax "hash_map_contains_key_in_list_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| hash_map_contains_key_in_list_loop_decreases $key $ls) =>
-  `(tactic| sorry)
-
-/- [hashmap::HashMap::{0}::get_in_list]: termination measure -/
-@[simp]
-def hash_map_get_in_list_loop_terminates (T : Type) (key : Usize)
-  (ls : list_t T) :=
-  (key, ls)
-
-/- [hashmap::HashMap::{0}::get_in_list]: decreases_by tactic -/
-syntax "hash_map_get_in_list_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| hash_map_get_in_list_loop_decreases $key $ls) =>`(tactic| sorry)
-
-/- [hashmap::HashMap::{0}::get_mut_in_list]: termination measure -/
-@[simp]
-def hash_map_get_mut_in_list_loop_terminates (T : Type) (ls : list_t T)
-  (key : Usize) :=
-  (ls, key)
-
-/- [hashmap::HashMap::{0}::get_mut_in_list]: decreases_by tactic -/
-syntax "hash_map_get_mut_in_list_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| hash_map_get_mut_in_list_loop_decreases $ls $key) =>`(tactic| sorry)
-
-/- [hashmap::HashMap::{0}::remove_from_list]: termination measure -/
-@[simp]
-def hash_map_remove_from_list_loop_terminates (T : Type) (key : Usize)
-  (ls : list_t T) :=
-  (key, ls)
-
-/- [hashmap::HashMap::{0}::remove_from_list]: decreases_by tactic -/
-syntax "hash_map_remove_from_list_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| hash_map_remove_from_list_loop_decreases $key $ls) =>`(tactic| sorry)
-
diff --git a/tests/lean/hashmap/Hashmap/Funs.lean b/tests/lean/hashmap/Hashmap/Funs.lean
deleted file mode 100644
index 77b1a157..00000000
--- a/tests/lean/hashmap/Hashmap/Funs.lean
+++ /dev/null
@@ -1,513 +0,0 @@
--- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
--- [hashmap]: function definitions
-import Base.Primitives
-import Hashmap.Types
-import Hashmap.Clauses.Clauses
-
-/- [hashmap::hash_key] -/
-def hash_key_fwd (k : Usize) : Result Usize :=
-  Result.ret k
-
-/- [hashmap::HashMap::{0}::allocate_slots] -/
-def hash_map_allocate_slots_loop_fwd
-  (T : Type) (slots : Vec (list_t T)) (n : Usize) :
-  (Result (Vec (list_t T)))
-  :=
-  if h: n > (Usize.ofInt 0 (by intlit))
-  then
-    do
-      let slots0 ← vec_push_back (list_t T) slots list_t.Nil
-      let n0 ← n - (Usize.ofInt 1 (by intlit))
-      hash_map_allocate_slots_loop_fwd T slots0 n0
-  else Result.ret slots
-termination_by hash_map_allocate_slots_loop_fwd slots n =>
-  hash_map_allocate_slots_loop_terminates T slots n
-decreasing_by hash_map_allocate_slots_loop_decreases slots n
-
-/- [hashmap::HashMap::{0}::allocate_slots] -/
-def hash_map_allocate_slots_fwd
-  (T : Type) (slots : Vec (list_t T)) (n : Usize) : Result (Vec (list_t T)) :=
-  hash_map_allocate_slots_loop_fwd T slots n
-
-/- [hashmap::HashMap::{0}::new_with_capacity] -/
-def hash_map_new_with_capacity_fwd
-  (T : Type) (capacity : Usize) (max_load_dividend : Usize)
-  (max_load_divisor : Usize) :
-  Result (hash_map_t T)
-  :=
-  do
-    let v := vec_new (list_t T)
-    let slots ← hash_map_allocate_slots_fwd T v capacity
-    let i ← capacity * max_load_dividend
-    let i0 ← i / max_load_divisor
-    Result.ret
-      {
-        hash_map_num_entries := (Usize.ofInt 0 (by intlit)),
-        hash_map_max_load_factor := (max_load_dividend, max_load_divisor),
-        hash_map_max_load := i0,
-        hash_map_slots := slots
-      }
-
-/- [hashmap::HashMap::{0}::new] -/
-def hash_map_new_fwd (T : Type) : Result (hash_map_t T) :=
-  hash_map_new_with_capacity_fwd T (Usize.ofInt 32 (by intlit))
-    (Usize.ofInt 4 (by intlit)) (Usize.ofInt 5 (by intlit))
-
-/- [hashmap::HashMap::{0}::clear] -/
-def hash_map_clear_loop_fwd_back
-  (T : Type) (slots : Vec (list_t T)) (i : Usize) :
-  (Result (Vec (list_t T)))
-  :=
-  let i0 := vec_len (list_t T) slots
-  if h: i < i0
-  then
-    do
-      let i1 ← i + (Usize.ofInt 1 (by intlit))
-      let slots0 ← vec_index_mut_back (list_t T) slots i list_t.Nil
-      hash_map_clear_loop_fwd_back T slots0 i1
-  else Result.ret slots
-termination_by hash_map_clear_loop_fwd_back slots i =>
-  hash_map_clear_loop_terminates T slots i
-decreasing_by hash_map_clear_loop_decreases slots i
-
-/- [hashmap::HashMap::{0}::clear] -/
-def hash_map_clear_fwd_back
-  (T : Type) (self : hash_map_t T) : Result (hash_map_t T) :=
-  do
-    let v ←
-      hash_map_clear_loop_fwd_back T self.hash_map_slots
-        (Usize.ofInt 0 (by intlit))
-    Result.ret
-      {
-        self
-          with
-          hash_map_num_entries := (Usize.ofInt 0 (by intlit)),
-          hash_map_slots := v
-      }
-
-/- [hashmap::HashMap::{0}::len] -/
-def hash_map_len_fwd (T : Type) (self : hash_map_t T) : Result Usize :=
-  Result.ret self.hash_map_num_entries
-
-/- [hashmap::HashMap::{0}::insert_in_list] -/
-def hash_map_insert_in_list_loop_fwd
-  (T : Type) (key : Usize) (value : T) (ls : list_t T) : (Result Bool) :=
-  match h: ls with
-  | list_t.Cons ckey cvalue tl =>
-    if h: ckey = key
-    then Result.ret false
-    else hash_map_insert_in_list_loop_fwd T key value tl
-  | list_t.Nil => Result.ret true
-termination_by hash_map_insert_in_list_loop_fwd key value ls =>
-  hash_map_insert_in_list_loop_terminates T key value ls
-decreasing_by hash_map_insert_in_list_loop_decreases key value ls
-
-/- [hashmap::HashMap::{0}::insert_in_list] -/
-def hash_map_insert_in_list_fwd
-  (T : Type) (key : Usize) (value : T) (ls : list_t T) : Result Bool :=
-  hash_map_insert_in_list_loop_fwd T key value ls
-
-/- [hashmap::HashMap::{0}::insert_in_list] -/
-def hash_map_insert_in_list_loop_back
-  (T : Type) (key : Usize) (value : T) (ls : list_t T) : (Result (list_t T)) :=
-  match h: ls with
-  | list_t.Cons ckey cvalue tl =>
-    if h: ckey = key
-    then Result.ret (list_t.Cons ckey value tl)
-    else
-      do
-        let tl0 ← hash_map_insert_in_list_loop_back T key value tl
-        Result.ret (list_t.Cons ckey cvalue tl0)
-  | list_t.Nil => let l := list_t.Nil
-                  Result.ret (list_t.Cons key value l)
-termination_by hash_map_insert_in_list_loop_back key value ls =>
-  hash_map_insert_in_list_loop_terminates T key value ls
-decreasing_by hash_map_insert_in_list_loop_decreases key value ls
-
-/- [hashmap::HashMap::{0}::insert_in_list] -/
-def hash_map_insert_in_list_back
-  (T : Type) (key : Usize) (value : T) (ls : list_t T) : Result (list_t T) :=
-  hash_map_insert_in_list_loop_back T key value ls
-
-/- [hashmap::HashMap::{0}::insert_no_resize] -/
-def hash_map_insert_no_resize_fwd_back
-  (T : Type) (self : hash_map_t T) (key : Usize) (value : T) :
-  Result (hash_map_t T)
-  :=
-  do
-    let hash ← hash_key_fwd key
-    let i := vec_len (list_t T) self.hash_map_slots
-    let hash_mod ← hash % i
-    let l ← vec_index_mut_fwd (list_t T) self.hash_map_slots hash_mod
-    let inserted ← hash_map_insert_in_list_fwd T key value l
-    if h: inserted
-    then
-      do
-        let i0 ← self.hash_map_num_entries + (Usize.ofInt 1 (by intlit))
-        let l0 ← hash_map_insert_in_list_back T key value l
-        let v ← vec_index_mut_back (list_t T) self.hash_map_slots hash_mod l0
-        Result.ret
-          { self with hash_map_num_entries := i0, hash_map_slots := v }
-    else
-      do
-        let l0 ← hash_map_insert_in_list_back T key value l
-        let v ← vec_index_mut_back (list_t T) self.hash_map_slots hash_mod l0
-        Result.ret { self with hash_map_slots := v }
-
-/- [core::num::u32::{9}::MAX] -/
-def core_num_u32_max_body : Result U32 :=
-  Result.ret (U32.ofInt 4294967295 (by intlit))
-def core_num_u32_max_c : U32 := eval_global core_num_u32_max_body (by simp)
-
-/- [hashmap::HashMap::{0}::move_elements_from_list] -/
-def hash_map_move_elements_from_list_loop_fwd_back
-  (T : Type) (ntable : hash_map_t T) (ls : list_t T) :
-  (Result (hash_map_t T))
-  :=
-  match h: ls with
-  | list_t.Cons k v tl =>
-    do
-      let ntable0 ← hash_map_insert_no_resize_fwd_back T ntable k v
-      hash_map_move_elements_from_list_loop_fwd_back T ntable0 tl
-  | list_t.Nil => Result.ret ntable
-termination_by hash_map_move_elements_from_list_loop_fwd_back ntable ls =>
-  hash_map_move_elements_from_list_loop_terminates T ntable ls
-decreasing_by hash_map_move_elements_from_list_loop_decreases ntable ls
-
-/- [hashmap::HashMap::{0}::move_elements_from_list] -/
-def hash_map_move_elements_from_list_fwd_back
-  (T : Type) (ntable : hash_map_t T) (ls : list_t T) : Result (hash_map_t T) :=
-  hash_map_move_elements_from_list_loop_fwd_back T ntable ls
-
-/- [hashmap::HashMap::{0}::move_elements] -/
-def hash_map_move_elements_loop_fwd_back
-  (T : Type) (ntable : hash_map_t T) (slots : Vec (list_t T)) (i : Usize) :
-  (Result ((hash_map_t T) × (Vec (list_t T))))
-  :=
-  let i0 := vec_len (list_t T) slots
-  if h: i < i0
-  then
-    do
-      let l ← vec_index_mut_fwd (list_t T) slots i
-      let ls := mem_replace_fwd (list_t T) l list_t.Nil
-      let ntable0 ← hash_map_move_elements_from_list_fwd_back T ntable ls
-      let i1 ← i + (Usize.ofInt 1 (by intlit))
-      let l0 := mem_replace_back (list_t T) l list_t.Nil
-      let slots0 ← vec_index_mut_back (list_t T) slots i l0
-      hash_map_move_elements_loop_fwd_back T ntable0 slots0 i1
-  else Result.ret (ntable, slots)
-termination_by hash_map_move_elements_loop_fwd_back ntable slots i =>
-  hash_map_move_elements_loop_terminates T ntable slots i
-decreasing_by hash_map_move_elements_loop_decreases ntable slots i
-
-/- [hashmap::HashMap::{0}::move_elements] -/
-def hash_map_move_elements_fwd_back
-  (T : Type) (ntable : hash_map_t T) (slots : Vec (list_t T)) (i : Usize) :
-  Result ((hash_map_t T) × (Vec (list_t T)))
-  :=
-  hash_map_move_elements_loop_fwd_back T ntable slots i
-
-/- [hashmap::HashMap::{0}::try_resize] -/
-def hash_map_try_resize_fwd_back
-  (T : Type) (self : hash_map_t T) : Result (hash_map_t T) :=
-  do
-    let max_usize ← Scalar.cast .Usize core_num_u32_max_c
-    let capacity := vec_len (list_t T) self.hash_map_slots
-    let n1 ← max_usize / (Usize.ofInt 2 (by intlit))
-    let (i, i0) := self.hash_map_max_load_factor
-    let i1 ← n1 / i
-    if h: capacity <= i1
-    then
-      do
-        let i2 ← capacity * (Usize.ofInt 2 (by intlit))
-        let ntable ← hash_map_new_with_capacity_fwd T i2 i i0
-        let (ntable0, _) ←
-          hash_map_move_elements_fwd_back T ntable self.hash_map_slots
-            (Usize.ofInt 0 (by intlit))
-        Result.ret
-          {
-            ntable0
-              with
-              hash_map_num_entries := self.hash_map_num_entries,
-              hash_map_max_load_factor := (i, i0)
-          }
-    else Result.ret { self with hash_map_max_load_factor := (i, i0) }
-
-/- [hashmap::HashMap::{0}::insert] -/
-def hash_map_insert_fwd_back
-  (T : Type) (self : hash_map_t T) (key : Usize) (value : T) :
-  Result (hash_map_t T)
-  :=
-  do
-    let self0 ← hash_map_insert_no_resize_fwd_back T self key value
-    let i ← hash_map_len_fwd T self0
-    if h: i > self0.hash_map_max_load
-    then hash_map_try_resize_fwd_back T self0
-    else Result.ret self0
-
-/- [hashmap::HashMap::{0}::contains_key_in_list] -/
-def hash_map_contains_key_in_list_loop_fwd
-  (T : Type) (key : Usize) (ls : list_t T) : (Result Bool) :=
-  match h: ls with
-  | list_t.Cons ckey t tl =>
-    if h: ckey = key
-    then Result.ret true
-    else hash_map_contains_key_in_list_loop_fwd T key tl
-  | list_t.Nil => Result.ret false
-termination_by hash_map_contains_key_in_list_loop_fwd key ls =>
-  hash_map_contains_key_in_list_loop_terminates T key ls
-decreasing_by hash_map_contains_key_in_list_loop_decreases key ls
-
-/- [hashmap::HashMap::{0}::contains_key_in_list] -/
-def hash_map_contains_key_in_list_fwd
-  (T : Type) (key : Usize) (ls : list_t T) : Result Bool :=
-  hash_map_contains_key_in_list_loop_fwd T key ls
-
-/- [hashmap::HashMap::{0}::contains_key] -/
-def hash_map_contains_key_fwd
-  (T : Type) (self : hash_map_t T) (key : Usize) : Result Bool :=
-  do
-    let hash ← hash_key_fwd key
-    let i := vec_len (list_t T) self.hash_map_slots
-    let hash_mod ← hash % i
-    let l ← vec_index_fwd (list_t T) self.hash_map_slots hash_mod
-    hash_map_contains_key_in_list_fwd T key l
-
-/- [hashmap::HashMap::{0}::get_in_list] -/
-def hash_map_get_in_list_loop_fwd
-  (T : Type) (key : Usize) (ls : list_t T) : (Result T) :=
-  match h: ls with
-  | list_t.Cons ckey cvalue tl =>
-    if h: ckey = key
-    then Result.ret cvalue
-    else hash_map_get_in_list_loop_fwd T key tl
-  | list_t.Nil => Result.fail Error.panic
-termination_by hash_map_get_in_list_loop_fwd key ls =>
-  hash_map_get_in_list_loop_terminates T key ls
-decreasing_by hash_map_get_in_list_loop_decreases key ls
-
-/- [hashmap::HashMap::{0}::get_in_list] -/
-def hash_map_get_in_list_fwd
-  (T : Type) (key : Usize) (ls : list_t T) : Result T :=
-  hash_map_get_in_list_loop_fwd T key ls
-
-/- [hashmap::HashMap::{0}::get] -/
-def hash_map_get_fwd
-  (T : Type) (self : hash_map_t T) (key : Usize) : Result T :=
-  do
-    let hash ← hash_key_fwd key
-    let i := vec_len (list_t T) self.hash_map_slots
-    let hash_mod ← hash % i
-    let l ← vec_index_fwd (list_t T) self.hash_map_slots hash_mod
-    hash_map_get_in_list_fwd T key l
-
-/- [hashmap::HashMap::{0}::get_mut_in_list] -/
-def hash_map_get_mut_in_list_loop_fwd
-  (T : Type) (ls : list_t T) (key : Usize) : (Result T) :=
-  match h: ls with
-  | list_t.Cons ckey cvalue tl =>
-    if h: ckey = key
-    then Result.ret cvalue
-    else hash_map_get_mut_in_list_loop_fwd T tl key
-  | list_t.Nil => Result.fail Error.panic
-termination_by hash_map_get_mut_in_list_loop_fwd ls key =>
-  hash_map_get_mut_in_list_loop_terminates T ls key
-decreasing_by hash_map_get_mut_in_list_loop_decreases ls key
-
-/- [hashmap::HashMap::{0}::get_mut_in_list] -/
-def hash_map_get_mut_in_list_fwd
-  (T : Type) (ls : list_t T) (key : Usize) : Result T :=
-  hash_map_get_mut_in_list_loop_fwd T ls key
-
-/- [hashmap::HashMap::{0}::get_mut_in_list] -/
-def hash_map_get_mut_in_list_loop_back
-  (T : Type) (ls : list_t T) (key : Usize) (ret0 : T) : (Result (list_t T)) :=
-  match h: ls with
-  | list_t.Cons ckey cvalue tl =>
-    if h: ckey = key
-    then Result.ret (list_t.Cons ckey ret0 tl)
-    else
-      do
-        let tl0 ← hash_map_get_mut_in_list_loop_back T tl key ret0
-        Result.ret (list_t.Cons ckey cvalue tl0)
-  | list_t.Nil => Result.fail Error.panic
-termination_by hash_map_get_mut_in_list_loop_back ls key ret0 =>
-  hash_map_get_mut_in_list_loop_terminates T ls key
-decreasing_by hash_map_get_mut_in_list_loop_decreases ls key
-
-/- [hashmap::HashMap::{0}::get_mut_in_list] -/
-def hash_map_get_mut_in_list_back
-  (T : Type) (ls : list_t T) (key : Usize) (ret0 : T) : Result (list_t T) :=
-  hash_map_get_mut_in_list_loop_back T ls key ret0
-
-/- [hashmap::HashMap::{0}::get_mut] -/
-def hash_map_get_mut_fwd
-  (T : Type) (self : hash_map_t T) (key : Usize) : Result T :=
-  do
-    let hash ← hash_key_fwd key
-    let i := vec_len (list_t T) self.hash_map_slots
-    let hash_mod ← hash % i
-    let l ← vec_index_mut_fwd (list_t T) self.hash_map_slots hash_mod
-    hash_map_get_mut_in_list_fwd T l key
-
-/- [hashmap::HashMap::{0}::get_mut] -/
-def hash_map_get_mut_back
-  (T : Type) (self : hash_map_t T) (key : Usize) (ret0 : T) :
-  Result (hash_map_t T)
-  :=
-  do
-    let hash ← hash_key_fwd key
-    let i := vec_len (list_t T) self.hash_map_slots
-    let hash_mod ← hash % i
-    let l ← vec_index_mut_fwd (list_t T) self.hash_map_slots hash_mod
-    let l0 ← hash_map_get_mut_in_list_back T l key ret0
-    let v ← vec_index_mut_back (list_t T) self.hash_map_slots hash_mod l0
-    Result.ret { self with hash_map_slots := v }
-
-/- [hashmap::HashMap::{0}::remove_from_list] -/
-def hash_map_remove_from_list_loop_fwd
-  (T : Type) (key : Usize) (ls : list_t T) : (Result (Option T)) :=
-  match h: ls with
-  | list_t.Cons ckey t tl =>
-    if h: ckey = key
-    then
-      let mv_ls :=
-        mem_replace_fwd (list_t T) (list_t.Cons ckey t tl) list_t.Nil
-      match h: mv_ls with
-      | list_t.Cons i cvalue tl0 => Result.ret (Option.some cvalue)
-      | list_t.Nil => Result.fail Error.panic
-    else hash_map_remove_from_list_loop_fwd T key tl
-  | list_t.Nil => Result.ret Option.none
-termination_by hash_map_remove_from_list_loop_fwd key ls =>
-  hash_map_remove_from_list_loop_terminates T key ls
-decreasing_by hash_map_remove_from_list_loop_decreases key ls
-
-/- [hashmap::HashMap::{0}::remove_from_list] -/
-def hash_map_remove_from_list_fwd
-  (T : Type) (key : Usize) (ls : list_t T) : Result (Option T) :=
-  hash_map_remove_from_list_loop_fwd T key ls
-
-/- [hashmap::HashMap::{0}::remove_from_list] -/
-def hash_map_remove_from_list_loop_back
-  (T : Type) (key : Usize) (ls : list_t T) : (Result (list_t T)) :=
-  match h: ls with
-  | list_t.Cons ckey t tl =>
-    if h: ckey = key
-    then
-      let mv_ls :=
-        mem_replace_fwd (list_t T) (list_t.Cons ckey t tl) list_t.Nil
-      match h: mv_ls with
-      | list_t.Cons i cvalue tl0 => Result.ret tl0
-      | list_t.Nil => Result.fail Error.panic
-    else
-      do
-        let tl0 ← hash_map_remove_from_list_loop_back T key tl
-        Result.ret (list_t.Cons ckey t tl0)
-  | list_t.Nil => Result.ret list_t.Nil
-termination_by hash_map_remove_from_list_loop_back key ls =>
-  hash_map_remove_from_list_loop_terminates T key ls
-decreasing_by hash_map_remove_from_list_loop_decreases key ls
-
-/- [hashmap::HashMap::{0}::remove_from_list] -/
-def hash_map_remove_from_list_back
-  (T : Type) (key : Usize) (ls : list_t T) : Result (list_t T) :=
-  hash_map_remove_from_list_loop_back T key ls
-
-/- [hashmap::HashMap::{0}::remove] -/
-def hash_map_remove_fwd
-  (T : Type) (self : hash_map_t T) (key : Usize) : Result (Option T) :=
-  do
-    let hash ← hash_key_fwd key
-    let i := vec_len (list_t T) self.hash_map_slots
-    let hash_mod ← hash % i
-    let l ← vec_index_mut_fwd (list_t T) self.hash_map_slots hash_mod
-    let x ← hash_map_remove_from_list_fwd T key l
-    match h: x with
-    | Option.none => Result.ret Option.none
-    | Option.some x0 =>
-      do
-        let _ ← self.hash_map_num_entries - (Usize.ofInt 1 (by intlit))
-        Result.ret (Option.some x0)
-
-/- [hashmap::HashMap::{0}::remove] -/
-def hash_map_remove_back
-  (T : Type) (self : hash_map_t T) (key : Usize) : Result (hash_map_t T) :=
-  do
-    let hash ← hash_key_fwd key
-    let i := vec_len (list_t T) self.hash_map_slots
-    let hash_mod ← hash % i
-    let l ← vec_index_mut_fwd (list_t T) self.hash_map_slots hash_mod
-    let x ← hash_map_remove_from_list_fwd T key l
-    match h: x with
-    | Option.none =>
-      do
-        let l0 ← hash_map_remove_from_list_back T key l
-        let v ← vec_index_mut_back (list_t T) self.hash_map_slots hash_mod l0
-        Result.ret { self with hash_map_slots := v }
-    | Option.some x0 =>
-      do
-        let i0 ← self.hash_map_num_entries - (Usize.ofInt 1 (by intlit))
-        let l0 ← hash_map_remove_from_list_back T key l
-        let v ← vec_index_mut_back (list_t T) self.hash_map_slots hash_mod l0
-        Result.ret
-          { self with hash_map_num_entries := i0, hash_map_slots := v }
-
-/- [hashmap::test1] -/
-def test1_fwd : Result Unit :=
-  do
-    let hm ← hash_map_new_fwd U64
-    let hm0 ←
-      hash_map_insert_fwd_back U64 hm (Usize.ofInt 0 (by intlit))
-        (U64.ofInt 42 (by intlit))
-    let hm1 ←
-      hash_map_insert_fwd_back U64 hm0 (Usize.ofInt 128 (by intlit))
-        (U64.ofInt 18 (by intlit))
-    let hm2 ←
-      hash_map_insert_fwd_back U64 hm1 (Usize.ofInt 1024 (by intlit))
-        (U64.ofInt 138 (by intlit))
-    let hm3 ←
-      hash_map_insert_fwd_back U64 hm2 (Usize.ofInt 1056 (by intlit))
-        (U64.ofInt 256 (by intlit))
-    let i ← hash_map_get_fwd U64 hm3 (Usize.ofInt 128 (by intlit))
-    if h: not (i = (U64.ofInt 18 (by intlit)))
-    then Result.fail Error.panic
-    else
-      do
-        let hm4 ←
-          hash_map_get_mut_back U64 hm3 (Usize.ofInt 1024 (by intlit))
-            (U64.ofInt 56 (by intlit))
-        let i0 ← hash_map_get_fwd U64 hm4 (Usize.ofInt 1024 (by intlit))
-        if h: not (i0 = (U64.ofInt 56 (by intlit)))
-        then Result.fail Error.panic
-        else
-          do
-            let x ←
-              hash_map_remove_fwd U64 hm4 (Usize.ofInt 1024 (by intlit))
-            match h: x with
-            | Option.none => Result.fail Error.panic
-            | Option.some x0 =>
-              if h: not (x0 = (U64.ofInt 56 (by intlit)))
-              then Result.fail Error.panic
-              else
-                do
-                  let hm5 ←
-                    hash_map_remove_back U64 hm4 (Usize.ofInt 1024 (by intlit))
-                  let i1 ←
-                    hash_map_get_fwd U64 hm5 (Usize.ofInt 0 (by intlit))
-                  if h: not (i1 = (U64.ofInt 42 (by intlit)))
-                  then Result.fail Error.panic
-                  else
-                    do
-                      let i2 ←
-                        hash_map_get_fwd U64 hm5 (Usize.ofInt 128 (by intlit))
-                      if h: not (i2 = (U64.ofInt 18 (by intlit)))
-                      then Result.fail Error.panic
-                      else
-                        do
-                          let i3 ←
-                            hash_map_get_fwd U64 hm5
-                              (Usize.ofInt 1056 (by intlit))
-                          if h: not (i3 = (U64.ofInt 256 (by intlit)))
-                          then Result.fail Error.panic
-                          else Result.ret ()
-
diff --git a/tests/lean/hashmap/Hashmap/Types.lean b/tests/lean/hashmap/Hashmap/Types.lean
deleted file mode 100644
index 6eabf7da..00000000
--- a/tests/lean/hashmap/Hashmap/Types.lean
+++ /dev/null
@@ -1,16 +0,0 @@
--- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
--- [hashmap]: type definitions
-import Base.Primitives
-
-/- [hashmap::List] -/
-inductive list_t (T : Type) :=
-| Cons : Usize -> T -> list_t T -> list_t T
-| Nil : list_t T
-
-/- [hashmap::HashMap] -/
-structure hash_map_t (T : Type) where
-  hash_map_num_entries : Usize
-  hash_map_max_load_factor : (Usize × Usize)
-  hash_map_max_load : Usize
-  hash_map_slots : Vec (list_t T)
-
diff --git a/tests/lean/hashmap/lake-manifest.json b/tests/lean/hashmap/lake-manifest.json
deleted file mode 100644
index 88e446e5..00000000
--- a/tests/lean/hashmap/lake-manifest.json
+++ /dev/null
@@ -1,27 +0,0 @@
-{"version": 4,
- "packagesDir": "./lake-packages",
- "packages":
- [{"git":
-   {"url": "https://github.com/leanprover-community/mathlib4.git",
-    "subDir?": null,
-    "rev": "1c5ed7840906e29e1f8ca7dbf088cf155e5397e9",
-    "name": "mathlib",
-    "inputRev?": null}},
-  {"git":
-   {"url": "https://github.com/gebner/quote4",
-    "subDir?": null,
-    "rev": "2412c4fdf4a8b689f4467618e5e7b371ae5014aa",
-    "name": "Qq",
-    "inputRev?": "master"}},
-  {"git":
-   {"url": "https://github.com/JLimperg/aesop",
-    "subDir?": null,
-    "rev": "7fe9ecd9339b0e1796e89d243b776849c305c690",
-    "name": "aesop",
-    "inputRev?": "master"}},
-  {"git":
-   {"url": "https://github.com/leanprover/std4",
-    "subDir?": null,
-    "rev": "24897887905b3a1254b244369f5dd2cf6174b0ee",
-    "name": "std",
-    "inputRev?": "main"}}]}
diff --git a/tests/lean/hashmap/lakefile.lean b/tests/lean/hashmap/lakefile.lean
deleted file mode 100644
index 713785f6..00000000
--- a/tests/lean/hashmap/lakefile.lean
+++ /dev/null
@@ -1,12 +0,0 @@
-import Lake
-open Lake DSL
-
-require mathlib from git
-  "https://github.com/leanprover-community/mathlib4.git"
-
-package «hashmap» {}
-
-lean_lib «Base» {}
-
-@[default_target]
-lean_lib «Hashmap» {}
diff --git a/tests/lean/hashmap/lean-toolchain b/tests/lean/hashmap/lean-toolchain
deleted file mode 100644
index bbf57f10..00000000
--- a/tests/lean/hashmap/lean-toolchain
+++ /dev/null
@@ -1 +0,0 @@
-leanprover/lean4:nightly-2023-01-21
diff --git a/tests/lean/hashmap_on_disk/.gitignore b/tests/lean/hashmap_on_disk/.gitignore
deleted file mode 100644
index a1735e7c..00000000
--- a/tests/lean/hashmap_on_disk/.gitignore
+++ /dev/null
@@ -1,5 +0,0 @@
-/build
-/lean_packages/*
-!/lean_packages/manifest.json
-/build
-/lake-packages/*
diff --git a/tests/lean/hashmap_on_disk/Base/Primitives.lean b/tests/lean/hashmap_on_disk/Base/Primitives.lean
deleted file mode 100644
index 4a66a453..00000000
--- a/tests/lean/hashmap_on_disk/Base/Primitives.lean
+++ /dev/null
@@ -1,583 +0,0 @@
-import Lean
-import Lean.Meta.Tactic.Simp
-import Init.Data.List.Basic
-import Mathlib.Tactic.RunCmd
-
---------------------
--- ASSERT COMMAND --
---------------------
-
-open Lean Elab Command Term Meta
-
-syntax (name := assert) "#assert" term: command
-
-@[command_elab assert]
-unsafe
-def assertImpl : CommandElab := fun (_stx: Syntax) => do
-  runTermElabM (fun _ => do
-    let r ← evalTerm Bool (mkConst ``Bool) _stx[1]
-    if not r then
-      logInfo "Assertion failed for: "
-      logInfo _stx[1]
-      logError "Expression reduced to false"
-    pure ())
-
-#eval 2 == 2
-#assert (2 == 2)
-
--------------
--- PRELUDE --
--------------
-
--- Results & monadic combinators
-
-inductive Error where
-   | assertionFailure: Error
-   | integerOverflow: Error
-   | divisionByZero: Error
-   | arrayOutOfBounds: Error
-   | maximumSizeExceeded: Error
-   | panic: Error
-deriving Repr, BEq
-
-open Error
-
-inductive Result (α : Type u) where
-  | ret (v: α): Result α
-  | fail (e: Error): Result α
-deriving Repr, BEq
-
-open Result
-
-instance Result_Inhabited (α : Type u) : Inhabited (Result α) :=
-  Inhabited.mk (fail panic)
-
-/- HELPERS -/
-
-def ret? {α: Type} (r: Result α): Bool :=
-  match r with
-  | Result.ret _ => true
-  | Result.fail _ => false
-
-def massert (b:Bool) : Result Unit :=
-  if b then .ret () else fail assertionFailure
-
-def eval_global {α: Type} (x: Result α) (_: ret? x): α :=
-  match x with
-  | Result.fail _ => by contradiction
-  | Result.ret x => x
-
-/- DO-DSL SUPPORT -/
-
-def bind (x: Result α) (f: α -> Result β) : Result β :=
-  match x with
-  | ret v  => f v 
-  | fail v => fail v
-
--- Allows using Result in do-blocks
-instance : Bind Result where
-  bind := bind
-
--- Allows using return x in do-blocks
-instance : Pure Result where
-  pure := fun x => ret x
-
-/- CUSTOM-DSL SUPPORT -/
-
--- Let-binding the Result of a monadic operation is oftentimes not sufficient,
--- because we may need a hypothesis for equational reasoning in the scope. We
--- rely on subtype, and a custom let-binding operator, in effect recreating our
--- own variant of the do-dsl
-
-def Result.attach {α: Type} (o : Result α): Result { x : α // o = ret x } :=
-  match o with
-  | .ret x => .ret ⟨x, rfl⟩
-  | .fail e => .fail e
-
-macro "let" e:term " ⟵ " f:term : doElem =>
-  `(doElem| let ⟨$e, h⟩ ← Result.attach $f)
-
--- TODO: any way to factorize both definitions?
-macro "let" e:term " <-- " f:term : doElem =>
-  `(doElem| let ⟨$e, h⟩ ← Result.attach $f)
-
--- We call the hypothesis `h`, in effect making it unavailable to the user
--- (because too much shadowing). But in practice, once can use the French single
--- quote notation (input with f< and f>), where `‹ h ›` finds a suitable
--- hypothesis in the context, this is equivalent to `have x: h := by assumption in x`
-#eval do
-  let y <-- .ret (0: Nat)
-  let _: y = 0 := by cases ‹ ret 0 = ret y › ; decide
-  let r: { x: Nat // x = 0 } := ⟨ y, by assumption ⟩
-  .ret r
-
-----------------------
--- MACHINE INTEGERS --
-----------------------
-
--- We redefine our machine integers types.
-
--- For Isize/Usize, we reuse `getNumBits` from `USize`. You cannot reduce `getNumBits`
--- using the simplifier, meaning that proofs do not depend on the compile-time value of
--- USize.size. (Lean assumes 32 or 64-bit platforms, and Rust doesn't really support, at
--- least officially, 16-bit microcontrollers, so this seems like a fine design decision
--- for now.)
-
--- Note from Chris Bailey: "If there's more than one salient property of your
--- definition then the subtyping strategy might get messy, and the property part
--- of a subtype is less discoverable by the simplifier or tactics like
--- library_search." So, we will not add refinements on the return values of the
--- operations defined on Primitives, but will rather rely on custom lemmas to
--- invert on possible return values of the primitive operations.
-
--- Machine integer constants, done via `ofNatCore`, which requires a proof that
--- the `Nat` fits within the desired integer type. We provide a custom tactic.
-
-open System.Platform.getNumBits
-
--- TODO: is there a way of only importing System.Platform.getNumBits?
---
-@[simp] def size_num_bits : Nat := (System.Platform.getNumBits ()).val
-
--- Remark: Lean seems to use < for the comparisons with the upper bounds by convention.
--- We keep the F* convention for now.
-@[simp] def Isize.min : Int := - (HPow.hPow 2 (size_num_bits - 1))
-@[simp] def Isize.max : Int := (HPow.hPow 2 (size_num_bits - 1)) - 1
-@[simp] def I8.min    : Int := - (HPow.hPow 2 7)
-@[simp] def I8.max    : Int := HPow.hPow 2 7 - 1
-@[simp] def I16.min   : Int := - (HPow.hPow 2 15)
-@[simp] def I16.max   : Int := HPow.hPow 2 15 - 1
-@[simp] def I32.min   : Int := -(HPow.hPow 2 31)
-@[simp] def I32.max   : Int := HPow.hPow 2 31 - 1
-@[simp] def I64.min   : Int := -(HPow.hPow 2 63)
-@[simp] def I64.max   : Int := HPow.hPow 2 63 - 1
-@[simp] def I128.min  : Int := -(HPow.hPow 2 127)
-@[simp] def I128.max  : Int := HPow.hPow 2 127 - 1
-@[simp] def Usize.min : Int := 0
-@[simp] def Usize.max : Int := HPow.hPow 2 size_num_bits - 1
-@[simp] def U8.min    : Int := 0
-@[simp] def U8.max    : Int := HPow.hPow 2 8 - 1
-@[simp] def U16.min   : Int := 0
-@[simp] def U16.max   : Int := HPow.hPow 2 16 - 1
-@[simp] def U32.min   : Int := 0
-@[simp] def U32.max   : Int := HPow.hPow 2 32 - 1
-@[simp] def U64.min   : Int := 0
-@[simp] def U64.max   : Int := HPow.hPow 2 64 - 1
-@[simp] def U128.min  : Int := 0
-@[simp] def U128.max  : Int := HPow.hPow 2 128 - 1
-
-#assert (I8.min   == -128)
-#assert (I8.max   == 127)
-#assert (I16.min  == -32768)
-#assert (I16.max  == 32767)
-#assert (I32.min  == -2147483648)
-#assert (I32.max  == 2147483647)
-#assert (I64.min  == -9223372036854775808)
-#assert (I64.max  == 9223372036854775807)
-#assert (I128.min == -170141183460469231731687303715884105728)
-#assert (I128.max == 170141183460469231731687303715884105727)
-#assert (U8.min   == 0)
-#assert (U8.max   == 255)
-#assert (U16.min  == 0)
-#assert (U16.max  == 65535)
-#assert (U32.min  == 0)
-#assert (U32.max  == 4294967295)
-#assert (U64.min  == 0)
-#assert (U64.max  == 18446744073709551615)
-#assert (U128.min == 0)
-#assert (U128.max == 340282366920938463463374607431768211455)
-
-inductive ScalarTy :=
-| Isize
-| I8
-| I16
-| I32
-| I64
-| I128
-| Usize
-| U8
-| U16
-| U32
-| U64
-| U128
-
-def Scalar.min (ty : ScalarTy) : Int :=
-  match ty with
-  | .Isize => Isize.min
-  | .I8    => I8.min
-  | .I16   => I16.min
-  | .I32   => I32.min
-  | .I64   => I64.min
-  | .I128  => I128.min
-  | .Usize => Usize.min
-  | .U8    => U8.min
-  | .U16   => U16.min
-  | .U32   => U32.min
-  | .U64   => U64.min
-  | .U128  => U128.min
-
-def Scalar.max (ty : ScalarTy) : Int :=
-  match ty with
-  | .Isize => Isize.max
-  | .I8    => I8.max
-  | .I16   => I16.max
-  | .I32   => I32.max
-  | .I64   => I64.max
-  | .I128  => I128.max
-  | .Usize => Usize.max
-  | .U8    => U8.max
-  | .U16   => U16.max
-  | .U32   => U32.max
-  | .U64   => U64.max
-  | .U128  => U128.max
-
--- "Conservative" bounds
--- We use those because we can't compare to the isize bounds (which can't
--- reduce at compile-time). Whenever we perform an arithmetic operation like
--- addition we need to check that the result is in bounds: we first compare
--- to the conservative bounds, which reduce, then compare to the real bounds.
--- This is useful for the various #asserts that we want to reduce at
--- type-checking time.
-def Scalar.cMin (ty : ScalarTy) : Int :=
-  match ty with
-  | .Isize => I32.min
-  | _ => Scalar.min ty
-
-def Scalar.cMax (ty : ScalarTy) : Int :=
-  match ty with
-  | .Isize => I32.max
-  | .Usize => U32.max
-  | _ => Scalar.max ty
-
-theorem Scalar.cMin_bound ty : Scalar.min ty <= Scalar.cMin ty := by sorry
-theorem Scalar.cMax_bound ty : Scalar.min ty <= Scalar.cMin ty := by sorry
-
-structure Scalar (ty : ScalarTy) where
-  val : Int
-  hmin : Scalar.min ty <= val
-  hmax : val <= Scalar.max ty
-
-theorem Scalar.bound_suffices (ty : ScalarTy) (x : Int) :
-  Scalar.cMin ty <= x && x <= Scalar.cMax ty ->
-  (decide (Scalar.min ty ≤ x) && decide (x ≤ Scalar.max ty)) = true
-  := by sorry
-
-def Scalar.ofIntCore {ty : ScalarTy} (x : Int)
-  (hmin : Scalar.min ty <= x) (hmax : x <= Scalar.max ty) : Scalar ty :=
-  { val := x, hmin := hmin, hmax := hmax }
-
-def Scalar.ofInt {ty : ScalarTy} (x : Int)
-  (h : Scalar.min ty <= x && x <= Scalar.max ty) : Scalar ty :=
-  let hmin: Scalar.min ty <= x := by sorry
-  let hmax: x <= Scalar.max ty := by sorry
-  Scalar.ofIntCore x hmin hmax
-
--- Further thoughts: look at what has been done here:
--- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/Fin/Basic.lean
--- and
--- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/UInt.lean
--- which both contain a fair amount of reasoning already!
-def Scalar.tryMk (ty : ScalarTy) (x : Int) : Result (Scalar ty) :=
-  -- TODO: write this with only one if then else
-  if hmin_cons: Scalar.cMin ty <= x || Scalar.min ty <= x then
-    if hmax_cons: x <= Scalar.cMax ty || x <= Scalar.max ty then
-      let hmin: Scalar.min ty <= x := by sorry
-      let hmax: x <= Scalar.max ty := by sorry
-      return Scalar.ofIntCore x hmin hmax
-    else fail integerOverflow
-  else fail integerOverflow
-
-def Scalar.neg {ty : ScalarTy} (x : Scalar ty) : Result (Scalar ty) := Scalar.tryMk ty (- x.val)
-
-def Scalar.div {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
-  if y.val != 0 then Scalar.tryMk ty (x.val / y.val) else fail divisionByZero
-
--- Checking that the % operation in Lean computes the same as the remainder operation in Rust
-#assert 1 % 2 = (1:Int)
-#assert (-1) % 2 = -1
-#assert 1 % (-2) = 1
-#assert (-1) % (-2) = -1
-
-def Scalar.rem {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
-  if y.val != 0 then Scalar.tryMk ty (x.val % y.val) else fail divisionByZero
-
-def Scalar.add {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
-  Scalar.tryMk ty (x.val + y.val)
-
-def Scalar.sub {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
-  Scalar.tryMk ty (x.val - y.val)
-
-def Scalar.mul {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
-  Scalar.tryMk ty (x.val * y.val)
-
--- TODO: instances of +, -, * etc. for scalars
-
--- Cast an integer from a [src_ty] to a [tgt_ty]
--- TODO: check the semantics of casts in Rust
-def Scalar.cast {src_ty : ScalarTy} (tgt_ty : ScalarTy) (x : Scalar src_ty) : Result (Scalar tgt_ty) :=
-  Scalar.tryMk tgt_ty x.val
-
--- The scalar types
--- We declare the definitions as reducible so that Lean can unfold them (useful
--- for type class resolution for instance).
-@[reducible] def Isize := Scalar .Isize
-@[reducible] def I8    := Scalar .I8
-@[reducible] def I16   := Scalar .I16
-@[reducible] def I32   := Scalar .I32
-@[reducible] def I64   := Scalar .I64
-@[reducible] def I128  := Scalar .I128
-@[reducible] def Usize := Scalar .Usize
-@[reducible] def U8    := Scalar .U8
-@[reducible] def U16   := Scalar .U16
-@[reducible] def U32   := Scalar .U32
-@[reducible] def U64   := Scalar .U64
-@[reducible] def U128  := Scalar .U128
-
--- TODO: below: not sure this is the best way.
--- Should we rather overload operations like +, -, etc.?
--- Also, it is possible to automate the generation of those definitions
--- with macros (but would it be a good idea? It would be less easy to
--- read the file, which is not supposed to change a lot)
-
--- Negation
-
-/--
-Remark: there is no heterogeneous negation in the Lean prelude: we thus introduce
-one here.
-
-The notation typeclass for heterogeneous addition.
-This enables the notation `- a : β` where `a : α`.
--/
-class HNeg (α : Type u) (β : outParam (Type v)) where
-  /-- `- a` computes the negation of `a`.
-  The meaning of this notation is type-dependent. -/
-  hNeg : α → β
-
-prefix:75  "-"   => HNeg.hNeg
-
-instance : HNeg Isize (Result Isize) where hNeg x := Scalar.neg x
-instance : HNeg I8 (Result I8) where hNeg x := Scalar.neg x
-instance : HNeg I16 (Result I16) where hNeg x := Scalar.neg x
-instance : HNeg I32 (Result I32) where hNeg x := Scalar.neg x
-instance : HNeg I64 (Result I64) where hNeg x := Scalar.neg x
-instance : HNeg I128 (Result I128) where hNeg x := Scalar.neg x
-
--- Addition
-instance {ty} : HAdd (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
-  hAdd x y := Scalar.add x y
-
--- Substraction
-instance {ty} : HSub (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
-  hSub x y := Scalar.sub x y
-
--- Multiplication
-instance {ty} : HMul (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
-  hMul x y := Scalar.mul x y
-
--- Division
-instance {ty} : HDiv (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
-  hDiv x y := Scalar.div x y
-
--- Remainder
-instance {ty} : HMod (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
-  hMod x y := Scalar.rem x y
-
--- ofIntCore
--- TODO: typeclass?
-def Isize.ofIntCore := @Scalar.ofIntCore .Isize
-def I8.ofIntCore    := @Scalar.ofIntCore .I8
-def I16.ofIntCore   := @Scalar.ofIntCore .I16
-def I32.ofIntCore   := @Scalar.ofIntCore .I32
-def I64.ofIntCore   := @Scalar.ofIntCore .I64
-def I128.ofIntCore  := @Scalar.ofIntCore .I128
-def Usize.ofIntCore := @Scalar.ofIntCore .Usize
-def U8.ofIntCore    := @Scalar.ofIntCore .U8
-def U16.ofIntCore   := @Scalar.ofIntCore .U16
-def U32.ofIntCore   := @Scalar.ofIntCore .U32
-def U64.ofIntCore   := @Scalar.ofIntCore .U64
-def U128.ofIntCore  := @Scalar.ofIntCore .U128
-
---  ofInt
--- TODO: typeclass?
-def Isize.ofInt := @Scalar.ofInt .Isize
-def I8.ofInt    := @Scalar.ofInt .I8
-def I16.ofInt   := @Scalar.ofInt .I16
-def I32.ofInt   := @Scalar.ofInt .I32
-def I64.ofInt   := @Scalar.ofInt .I64
-def I128.ofInt  := @Scalar.ofInt .I128
-def Usize.ofInt := @Scalar.ofInt .Usize
-def U8.ofInt    := @Scalar.ofInt .U8
-def U16.ofInt   := @Scalar.ofInt .U16
-def U32.ofInt   := @Scalar.ofInt .U32
-def U64.ofInt   := @Scalar.ofInt .U64
-def U128.ofInt  := @Scalar.ofInt .U128
-
--- Comparisons
-instance {ty} : LT (Scalar ty) where
-  lt a b := LT.lt a.val b.val
-
-instance {ty} : LE (Scalar ty) where le a b := LE.le a.val b.val
-
-instance Scalar.decLt {ty} (a b : Scalar ty) : Decidable (LT.lt a b) := Int.decLt ..
-instance Scalar.decLe {ty} (a b : Scalar ty) : Decidable (LE.le a b) := Int.decLe ..
-
-theorem Scalar.eq_of_val_eq {ty} : ∀ {i j : Scalar ty}, Eq i.val j.val → Eq i j
-  | ⟨_, _, _⟩, ⟨_, _, _⟩, rfl => rfl
-
-theorem Scalar.val_eq_of_eq {ty} {i j : Scalar ty} (h : Eq i j) : Eq i.val j.val :=
-  h ▸ rfl
-
-theorem Scalar.ne_of_val_ne {ty} {i j : Scalar ty} (h : Not (Eq i.val j.val)) : Not (Eq i j) :=
-  fun h' => absurd (val_eq_of_eq h') h
-
-instance (ty : ScalarTy) : DecidableEq (Scalar ty) :=
-  fun i j =>
-    match decEq i.val j.val with
-    | isTrue h  => isTrue (Scalar.eq_of_val_eq h)
-    | isFalse h => isFalse (Scalar.ne_of_val_ne h)
-
-def Scalar.toInt {ty} (n : Scalar ty) : Int := n.val
-
--- Tactic to prove that integers are in bounds
-syntax "intlit" : tactic
-
-macro_rules
-  | `(tactic| intlit) => `(tactic| apply Scalar.bound_suffices ; decide)
-
--- -- We now define a type class that subsumes the various machine integer types, so
--- -- as to write a concise definition for scalar_cast, rather than exhaustively
--- -- enumerating all of the possible pairs. We remark that Rust has sane semantics
--- -- and fails if a cast operation would involve a truncation or modulo.
-
--- class MachineInteger (t: Type) where
---   size: Nat
---   val: t -> Fin size
---   ofNatCore: (n:Nat) -> LT.lt n size -> t
-
--- set_option hygiene false in
--- run_cmd
---   for typeName in [`UInt8, `UInt16, `UInt32, `UInt64, `USize].map Lean.mkIdent do
---   Lean.Elab.Command.elabCommand (← `(
---     namespace $typeName
---     instance: MachineInteger $typeName where
---       size := size
---       val := val
---       ofNatCore := ofNatCore
---     end $typeName
---   ))
-
--- -- Aeneas only instantiates the destination type (`src` is implicit). We rely on
--- -- Lean to infer `src`.
-
--- def scalar_cast { src: Type } (dst: Type) [ MachineInteger src ] [ MachineInteger dst ] (x: src): Result dst :=
---   if h: MachineInteger.val x < MachineInteger.size dst then
---     .ret (MachineInteger.ofNatCore (MachineInteger.val x).val h)
---   else
---     .fail integerOverflow
-
--------------
--- VECTORS --
--------------
-
-def Vec (α : Type u) := { l : List α // List.length l <= Usize.max }
-
-def vec_new (α : Type u): Vec α := ⟨ [], by sorry ⟩
-
-def vec_len (α : Type u) (v : Vec α) : Usize :=
-  let ⟨ v, l ⟩ := v
-  Usize.ofIntCore (List.length v) (by sorry) l
- 
-def vec_push_fwd (α : Type u) (_ : Vec α) (_ : α) : Unit := ()
-
-def vec_push_back (α : Type u) (v : Vec α) (x : α) : Result (Vec α)
-  :=
-  if h : List.length v.val <= U32.max || List.length v.val <= Usize.max then
-    return ⟨ List.concat v.val x, by sorry ⟩
-  else
-    fail maximumSizeExceeded
-
-def vec_insert_fwd (α : Type u) (v: Vec α) (i: Usize) (_: α): Result Unit :=
-  if i.val < List.length v.val then
-    .ret ()
-  else
-    .fail arrayOutOfBounds
-
-def vec_insert_back (α : Type u) (v: Vec α) (i: Usize) (x: α): Result (Vec α) :=
-  if i.val < List.length v.val then
-    -- TODO: maybe we should redefine a list library which uses integers
-    -- (instead of natural numbers)
-    let i : Nat :=
-      match i.val with
-      | .ofNat n => n
-      | .negSucc n => by sorry -- TODO: we can't get here
-    let isLt: i < USize.size := by sorry
-    let i : Fin USize.size := { val := i, isLt := isLt }
-    .ret ⟨ List.set v.val i.val x, by
-      have h: List.length v.val <= Usize.max := v.property
-      rewrite [ List.length_set v.val i.val x ]
-      assumption
-    ⟩
-  else
-    .fail arrayOutOfBounds
-
-def vec_index_fwd (α : Type u) (v: Vec α) (i: Usize): Result α :=
-  if i.val < List.length v.val then
-    let i : Nat :=
-      match i.val with
-      | .ofNat n => n
-      | .negSucc n => by sorry -- TODO: we can't get here
-    let isLt: i < USize.size := by sorry
-    let i : Fin USize.size := { val := i, isLt := isLt }
-    let h: i < List.length v.val := by sorry
-    .ret (List.get v.val ⟨i.val, h⟩)
-  else
-    .fail arrayOutOfBounds
-
-def vec_index_back (α : Type u) (v: Vec α) (i: Usize) (_: α): Result Unit :=
-  if i.val < List.length v.val then
-    .ret ()
-  else
-    .fail arrayOutOfBounds
-
-def vec_index_mut_fwd (α : Type u) (v: Vec α) (i: Usize): Result α :=
-  if i.val < List.length v.val then
-    let i : Nat :=
-      match i.val with
-      | .ofNat n => n
-      | .negSucc n => by sorry -- TODO: we can't get here
-    let isLt: i < USize.size := by sorry
-    let i : Fin USize.size := { val := i, isLt := isLt }
-    let h: i < List.length v.val := by sorry
-    .ret (List.get v.val ⟨i.val, h⟩)
-  else
-    .fail arrayOutOfBounds
-
-def vec_index_mut_back (α : Type u) (v: Vec α) (i: Usize) (x: α): Result (Vec α) :=
-  if i.val < List.length v.val then
-    let i : Nat :=
-      match i.val with
-      | .ofNat n => n
-      | .negSucc n => by sorry -- TODO: we can't get here
-    let isLt: i < USize.size := by sorry
-    let i : Fin USize.size := { val := i, isLt := isLt }
-    .ret ⟨ List.set v.val i.val x, by
-      have h: List.length v.val <= Usize.max := v.property
-      rewrite [ List.length_set v.val i.val x ]
-      assumption
-    ⟩
-  else
-    .fail arrayOutOfBounds
-
-----------
--- MISC --
-----------
-
-def mem_replace_fwd (a : Type) (x : a) (_ : a) : a :=
-  x
-
-def mem_replace_back (a : Type) (_ : a) (y : a) : a :=
-  y
-
-/-- Aeneas-translated function -- useful to reduce non-recursive definitions.
- Use with `simp [ aeneas ]` -/
-register_simp_attr aeneas
diff --git a/tests/lean/hashmap_on_disk/HashmapMain/Clauses/Clauses.lean b/tests/lean/hashmap_on_disk/HashmapMain/Clauses/Clauses.lean
deleted file mode 100644
index a4dc996a..00000000
--- a/tests/lean/hashmap_on_disk/HashmapMain/Clauses/Clauses.lean
+++ /dev/null
@@ -1,110 +0,0 @@
-import Base.Primitives
-import HashmapMain.Types
-
-/- [hashmap_main::hashmap::HashMap::{0}::allocate_slots]: termination measure -/
-@[simp]
-def hashmap_hash_map_allocate_slots_loop_terminates (T : Type)
-  (slots : Vec (hashmap_list_t T)) (n : Usize) :=
-  (slots, n)
-
-/- [hashmap_main::hashmap::HashMap::{0}::allocate_slots]: decreases_by tactic -/
-syntax "hashmap_hash_map_allocate_slots_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| hashmap_hash_map_allocate_slots_loop_decreases $slots $n) =>
-  `(tactic| sorry)
-
-/- [hashmap_main::hashmap::HashMap::{0}::clear]: termination measure -/
-@[simp]
-def hashmap_hash_map_clear_loop_terminates (T : Type)
-  (slots : Vec (hashmap_list_t T)) (i : Usize) :=
-  (slots, i)
-
-/- [hashmap_main::hashmap::HashMap::{0}::clear]: decreases_by tactic -/
-syntax "hashmap_hash_map_clear_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| hashmap_hash_map_clear_loop_decreases $slots $i) =>`(tactic| sorry)
-
-/- [hashmap_main::hashmap::HashMap::{0}::insert_in_list]: termination measure -/
-@[simp]
-def hashmap_hash_map_insert_in_list_loop_terminates (T : Type) (key : Usize)
-  (value : T) (ls : hashmap_list_t T) :=
-  (key, value, ls)
-
-/- [hashmap_main::hashmap::HashMap::{0}::insert_in_list]: decreases_by tactic -/
-syntax "hashmap_hash_map_insert_in_list_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| hashmap_hash_map_insert_in_list_loop_decreases $key $value $ls) =>
-  `(tactic| sorry)
-
-/- [hashmap_main::hashmap::HashMap::{0}::move_elements_from_list]: termination measure -/
-@[simp]
-def hashmap_hash_map_move_elements_from_list_loop_terminates (T : Type)
-  (ntable : hashmap_hash_map_t T) (ls : hashmap_list_t T) :=
-  (ntable, ls)
-
-/- [hashmap_main::hashmap::HashMap::{0}::move_elements_from_list]: decreases_by tactic -/
-syntax "hashmap_hash_map_move_elements_from_list_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| hashmap_hash_map_move_elements_from_list_loop_decreases $ntable
-$ls) =>`(tactic| sorry)
-
-/- [hashmap_main::hashmap::HashMap::{0}::move_elements]: termination measure -/
-@[simp]
-def hashmap_hash_map_move_elements_loop_terminates (T : Type)
-  (ntable : hashmap_hash_map_t T) (slots : Vec (hashmap_list_t T)) (i : Usize)
-  :=
-  (ntable, slots, i)
-
-/- [hashmap_main::hashmap::HashMap::{0}::move_elements]: decreases_by tactic -/
-syntax "hashmap_hash_map_move_elements_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| hashmap_hash_map_move_elements_loop_decreases $ntable $slots $i) =>
-  `(tactic| sorry)
-
-/- [hashmap_main::hashmap::HashMap::{0}::contains_key_in_list]: termination measure -/
-@[simp]
-def hashmap_hash_map_contains_key_in_list_loop_terminates (T : Type)
-  (key : Usize) (ls : hashmap_list_t T) :=
-  (key, ls)
-
-/- [hashmap_main::hashmap::HashMap::{0}::contains_key_in_list]: decreases_by tactic -/
-syntax "hashmap_hash_map_contains_key_in_list_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| hashmap_hash_map_contains_key_in_list_loop_decreases $key $ls) =>
-  `(tactic| sorry)
-
-/- [hashmap_main::hashmap::HashMap::{0}::get_in_list]: termination measure -/
-@[simp]
-def hashmap_hash_map_get_in_list_loop_terminates (T : Type) (key : Usize)
-  (ls : hashmap_list_t T) :=
-  (key, ls)
-
-/- [hashmap_main::hashmap::HashMap::{0}::get_in_list]: decreases_by tactic -/
-syntax "hashmap_hash_map_get_in_list_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| hashmap_hash_map_get_in_list_loop_decreases $key $ls) =>`(tactic| sorry)
-
-/- [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list]: termination measure -/
-@[simp]
-def hashmap_hash_map_get_mut_in_list_loop_terminates (T : Type)
-  (ls : hashmap_list_t T) (key : Usize) :=
-  (ls, key)
-
-/- [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list]: decreases_by tactic -/
-syntax "hashmap_hash_map_get_mut_in_list_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| hashmap_hash_map_get_mut_in_list_loop_decreases $ls $key) =>
-  `(tactic| sorry)
-
-/- [hashmap_main::hashmap::HashMap::{0}::remove_from_list]: termination measure -/
-@[simp]
-def hashmap_hash_map_remove_from_list_loop_terminates (T : Type) (key : Usize)
-  (ls : hashmap_list_t T) :=
-  (key, ls)
-
-/- [hashmap_main::hashmap::HashMap::{0}::remove_from_list]: decreases_by tactic -/
-syntax "hashmap_hash_map_remove_from_list_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| hashmap_hash_map_remove_from_list_loop_decreases $key $ls) =>
-  `(tactic| sorry)
-
diff --git a/tests/lean/hashmap_on_disk/HashmapMain/Clauses/Template.lean b/tests/lean/hashmap_on_disk/HashmapMain/Clauses/Template.lean
deleted file mode 100644
index 33802597..00000000
--- a/tests/lean/hashmap_on_disk/HashmapMain/Clauses/Template.lean
+++ /dev/null
@@ -1,112 +0,0 @@
--- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
--- [hashmap_main]: templates for the decreases clauses
-import Base.Primitives
-import HashmapMain.Types
-
-/- [hashmap_main::hashmap::HashMap::{0}::allocate_slots]: termination measure -/
-@[simp]
-def hashmap_hash_map_allocate_slots_loop_terminates (T : Type)
-  (slots : Vec (hashmap_list_t T)) (n : Usize) :=
-  (slots, n)
-
-/- [hashmap_main::hashmap::HashMap::{0}::allocate_slots]: decreases_by tactic -/
-syntax "hashmap_hash_map_allocate_slots_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| hashmap_hash_map_allocate_slots_loop_decreases $slots $n) =>
-  `(tactic| sorry)
-
-/- [hashmap_main::hashmap::HashMap::{0}::clear]: termination measure -/
-@[simp]
-def hashmap_hash_map_clear_loop_terminates (T : Type)
-  (slots : Vec (hashmap_list_t T)) (i : Usize) :=
-  (slots, i)
-
-/- [hashmap_main::hashmap::HashMap::{0}::clear]: decreases_by tactic -/
-syntax "hashmap_hash_map_clear_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| hashmap_hash_map_clear_loop_decreases $slots $i) =>`(tactic| sorry)
-
-/- [hashmap_main::hashmap::HashMap::{0}::insert_in_list]: termination measure -/
-@[simp]
-def hashmap_hash_map_insert_in_list_loop_terminates (T : Type) (key : Usize)
-  (value : T) (ls : hashmap_list_t T) :=
-  (key, value, ls)
-
-/- [hashmap_main::hashmap::HashMap::{0}::insert_in_list]: decreases_by tactic -/
-syntax "hashmap_hash_map_insert_in_list_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| hashmap_hash_map_insert_in_list_loop_decreases $key $value $ls) =>
-  `(tactic| sorry)
-
-/- [hashmap_main::hashmap::HashMap::{0}::move_elements_from_list]: termination measure -/
-@[simp]
-def hashmap_hash_map_move_elements_from_list_loop_terminates (T : Type)
-  (ntable : hashmap_hash_map_t T) (ls : hashmap_list_t T) :=
-  (ntable, ls)
-
-/- [hashmap_main::hashmap::HashMap::{0}::move_elements_from_list]: decreases_by tactic -/
-syntax "hashmap_hash_map_move_elements_from_list_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| hashmap_hash_map_move_elements_from_list_loop_decreases $ntable
-$ls) =>`(tactic| sorry)
-
-/- [hashmap_main::hashmap::HashMap::{0}::move_elements]: termination measure -/
-@[simp]
-def hashmap_hash_map_move_elements_loop_terminates (T : Type)
-  (ntable : hashmap_hash_map_t T) (slots : Vec (hashmap_list_t T)) (i : Usize)
-  :=
-  (ntable, slots, i)
-
-/- [hashmap_main::hashmap::HashMap::{0}::move_elements]: decreases_by tactic -/
-syntax "hashmap_hash_map_move_elements_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| hashmap_hash_map_move_elements_loop_decreases $ntable $slots $i) =>
-  `(tactic| sorry)
-
-/- [hashmap_main::hashmap::HashMap::{0}::contains_key_in_list]: termination measure -/
-@[simp]
-def hashmap_hash_map_contains_key_in_list_loop_terminates (T : Type)
-  (key : Usize) (ls : hashmap_list_t T) :=
-  (key, ls)
-
-/- [hashmap_main::hashmap::HashMap::{0}::contains_key_in_list]: decreases_by tactic -/
-syntax "hashmap_hash_map_contains_key_in_list_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| hashmap_hash_map_contains_key_in_list_loop_decreases $key $ls) =>
-  `(tactic| sorry)
-
-/- [hashmap_main::hashmap::HashMap::{0}::get_in_list]: termination measure -/
-@[simp]
-def hashmap_hash_map_get_in_list_loop_terminates (T : Type) (key : Usize)
-  (ls : hashmap_list_t T) :=
-  (key, ls)
-
-/- [hashmap_main::hashmap::HashMap::{0}::get_in_list]: decreases_by tactic -/
-syntax "hashmap_hash_map_get_in_list_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| hashmap_hash_map_get_in_list_loop_decreases $key $ls) =>`(tactic| sorry)
-
-/- [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list]: termination measure -/
-@[simp]
-def hashmap_hash_map_get_mut_in_list_loop_terminates (T : Type)
-  (ls : hashmap_list_t T) (key : Usize) :=
-  (ls, key)
-
-/- [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list]: decreases_by tactic -/
-syntax "hashmap_hash_map_get_mut_in_list_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| hashmap_hash_map_get_mut_in_list_loop_decreases $ls $key) =>
-  `(tactic| sorry)
-
-/- [hashmap_main::hashmap::HashMap::{0}::remove_from_list]: termination measure -/
-@[simp]
-def hashmap_hash_map_remove_from_list_loop_terminates (T : Type) (key : Usize)
-  (ls : hashmap_list_t T) :=
-  (key, ls)
-
-/- [hashmap_main::hashmap::HashMap::{0}::remove_from_list]: decreases_by tactic -/
-syntax "hashmap_hash_map_remove_from_list_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| hashmap_hash_map_remove_from_list_loop_decreases $key $ls) =>
-  `(tactic| sorry)
-
diff --git a/tests/lean/hashmap_on_disk/HashmapMain/ExternalFuns.lean b/tests/lean/hashmap_on_disk/HashmapMain/ExternalFuns.lean
deleted file mode 100644
index a5103acc..00000000
--- a/tests/lean/hashmap_on_disk/HashmapMain/ExternalFuns.lean
+++ /dev/null
@@ -1,5 +0,0 @@
-import Base.Primitives
-import HashmapMain.Types
-import HashmapMain.Opaque
-
-def opaque_defs : OpaqueDefs := by sorry
diff --git a/tests/lean/hashmap_on_disk/HashmapMain/Funs.lean b/tests/lean/hashmap_on_disk/HashmapMain/Funs.lean
deleted file mode 100644
index 342c3833..00000000
--- a/tests/lean/hashmap_on_disk/HashmapMain/Funs.lean
+++ /dev/null
@@ -1,590 +0,0 @@
--- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
--- [hashmap_main]: function definitions
-import Base.Primitives
-import HashmapMain.Types
-import HashmapMain.ExternalFuns
-import HashmapMain.Clauses.Clauses
-
-/- [hashmap_main::hashmap::hash_key] -/
-def hashmap_hash_key_fwd (k : Usize) : Result Usize :=
-  Result.ret k
-
-/- [hashmap_main::hashmap::HashMap::{0}::allocate_slots] -/
-def hashmap_hash_map_allocate_slots_loop_fwd
-  (T : Type) (slots : Vec (hashmap_list_t T)) (n : Usize) :
-  (Result (Vec (hashmap_list_t T)))
-  :=
-  if h: n > (Usize.ofInt 0 (by intlit))
-  then
-    do
-      let slots0 ← vec_push_back (hashmap_list_t T) slots hashmap_list_t.Nil
-      let n0 ← n - (Usize.ofInt 1 (by intlit))
-      hashmap_hash_map_allocate_slots_loop_fwd T slots0 n0
-  else Result.ret slots
-termination_by hashmap_hash_map_allocate_slots_loop_fwd slots n =>
-  hashmap_hash_map_allocate_slots_loop_terminates T slots n
-decreasing_by hashmap_hash_map_allocate_slots_loop_decreases slots n
-
-/- [hashmap_main::hashmap::HashMap::{0}::allocate_slots] -/
-def hashmap_hash_map_allocate_slots_fwd
-  (T : Type) (slots : Vec (hashmap_list_t T)) (n : Usize) :
-  Result (Vec (hashmap_list_t T))
-  :=
-  hashmap_hash_map_allocate_slots_loop_fwd T slots n
-
-/- [hashmap_main::hashmap::HashMap::{0}::new_with_capacity] -/
-def hashmap_hash_map_new_with_capacity_fwd
-  (T : Type) (capacity : Usize) (max_load_dividend : Usize)
-  (max_load_divisor : Usize) :
-  Result (hashmap_hash_map_t T)
-  :=
-  do
-    let v := vec_new (hashmap_list_t T)
-    let slots ← hashmap_hash_map_allocate_slots_fwd T v capacity
-    let i ← capacity * max_load_dividend
-    let i0 ← i / max_load_divisor
-    Result.ret
-      {
-        hashmap_hash_map_num_entries := (Usize.ofInt 0 (by intlit)),
-        hashmap_hash_map_max_load_factor :=
-          (max_load_dividend, max_load_divisor),
-        hashmap_hash_map_max_load := i0,
-        hashmap_hash_map_slots := slots
-      }
-
-/- [hashmap_main::hashmap::HashMap::{0}::new] -/
-def hashmap_hash_map_new_fwd (T : Type) : Result (hashmap_hash_map_t T) :=
-  hashmap_hash_map_new_with_capacity_fwd T (Usize.ofInt 32 (by intlit))
-    (Usize.ofInt 4 (by intlit)) (Usize.ofInt 5 (by intlit))
-
-/- [hashmap_main::hashmap::HashMap::{0}::clear] -/
-def hashmap_hash_map_clear_loop_fwd_back
-  (T : Type) (slots : Vec (hashmap_list_t T)) (i : Usize) :
-  (Result (Vec (hashmap_list_t T)))
-  :=
-  let i0 := vec_len (hashmap_list_t T) slots
-  if h: i < i0
-  then
-    do
-      let i1 ← i + (Usize.ofInt 1 (by intlit))
-      let slots0 ←
-        vec_index_mut_back (hashmap_list_t T) slots i hashmap_list_t.Nil
-      hashmap_hash_map_clear_loop_fwd_back T slots0 i1
-  else Result.ret slots
-termination_by hashmap_hash_map_clear_loop_fwd_back slots i =>
-  hashmap_hash_map_clear_loop_terminates T slots i
-decreasing_by hashmap_hash_map_clear_loop_decreases slots i
-
-/- [hashmap_main::hashmap::HashMap::{0}::clear] -/
-def hashmap_hash_map_clear_fwd_back
-  (T : Type) (self : hashmap_hash_map_t T) : Result (hashmap_hash_map_t T) :=
-  do
-    let v ←
-      hashmap_hash_map_clear_loop_fwd_back T self.hashmap_hash_map_slots
-        (Usize.ofInt 0 (by intlit))
-    Result.ret
-      {
-        self
-          with
-          hashmap_hash_map_num_entries := (Usize.ofInt 0 (by intlit)),
-          hashmap_hash_map_slots := v
-      }
-
-/- [hashmap_main::hashmap::HashMap::{0}::len] -/
-def hashmap_hash_map_len_fwd
-  (T : Type) (self : hashmap_hash_map_t T) : Result Usize :=
-  Result.ret self.hashmap_hash_map_num_entries
-
-/- [hashmap_main::hashmap::HashMap::{0}::insert_in_list] -/
-def hashmap_hash_map_insert_in_list_loop_fwd
-  (T : Type) (key : Usize) (value : T) (ls : hashmap_list_t T) :
-  (Result Bool)
-  :=
-  match h: ls with
-  | hashmap_list_t.Cons ckey cvalue tl =>
-    if h: ckey = key
-    then Result.ret false
-    else hashmap_hash_map_insert_in_list_loop_fwd T key value tl
-  | hashmap_list_t.Nil => Result.ret true
-termination_by hashmap_hash_map_insert_in_list_loop_fwd key value ls =>
-  hashmap_hash_map_insert_in_list_loop_terminates T key value ls
-decreasing_by hashmap_hash_map_insert_in_list_loop_decreases key value ls
-
-/- [hashmap_main::hashmap::HashMap::{0}::insert_in_list] -/
-def hashmap_hash_map_insert_in_list_fwd
-  (T : Type) (key : Usize) (value : T) (ls : hashmap_list_t T) : Result Bool :=
-  hashmap_hash_map_insert_in_list_loop_fwd T key value ls
-
-/- [hashmap_main::hashmap::HashMap::{0}::insert_in_list] -/
-def hashmap_hash_map_insert_in_list_loop_back
-  (T : Type) (key : Usize) (value : T) (ls : hashmap_list_t T) :
-  (Result (hashmap_list_t T))
-  :=
-  match h: ls with
-  | hashmap_list_t.Cons ckey cvalue tl =>
-    if h: ckey = key
-    then Result.ret (hashmap_list_t.Cons ckey value tl)
-    else
-      do
-        let tl0 ← hashmap_hash_map_insert_in_list_loop_back T key value tl
-        Result.ret (hashmap_list_t.Cons ckey cvalue tl0)
-  | hashmap_list_t.Nil =>
-    let l := hashmap_list_t.Nil
-    Result.ret (hashmap_list_t.Cons key value l)
-termination_by hashmap_hash_map_insert_in_list_loop_back key value ls =>
-  hashmap_hash_map_insert_in_list_loop_terminates T key value ls
-decreasing_by hashmap_hash_map_insert_in_list_loop_decreases key value ls
-
-/- [hashmap_main::hashmap::HashMap::{0}::insert_in_list] -/
-def hashmap_hash_map_insert_in_list_back
-  (T : Type) (key : Usize) (value : T) (ls : hashmap_list_t T) :
-  Result (hashmap_list_t T)
-  :=
-  hashmap_hash_map_insert_in_list_loop_back T key value ls
-
-/- [hashmap_main::hashmap::HashMap::{0}::insert_no_resize] -/
-def hashmap_hash_map_insert_no_resize_fwd_back
-  (T : Type) (self : hashmap_hash_map_t T) (key : Usize) (value : T) :
-  Result (hashmap_hash_map_t T)
-  :=
-  do
-    let hash ← hashmap_hash_key_fwd key
-    let i := vec_len (hashmap_list_t T) self.hashmap_hash_map_slots
-    let hash_mod ← hash % i
-    let l ←
-      vec_index_mut_fwd (hashmap_list_t T) self.hashmap_hash_map_slots hash_mod
-    let inserted ← hashmap_hash_map_insert_in_list_fwd T key value l
-    if h: inserted
-    then
-      do
-        let i0 ← self.hashmap_hash_map_num_entries +
-          (Usize.ofInt 1 (by intlit))
-        let l0 ← hashmap_hash_map_insert_in_list_back T key value l
-        let v ←
-          vec_index_mut_back (hashmap_list_t T) self.hashmap_hash_map_slots
-            hash_mod l0
-        Result.ret
-          {
-            self
-              with
-              hashmap_hash_map_num_entries := i0, hashmap_hash_map_slots := v
-          }
-    else
-      do
-        let l0 ← hashmap_hash_map_insert_in_list_back T key value l
-        let v ←
-          vec_index_mut_back (hashmap_list_t T) self.hashmap_hash_map_slots
-            hash_mod l0
-        Result.ret { self with hashmap_hash_map_slots := v }
-
-/- [core::num::u32::{9}::MAX] -/
-def core_num_u32_max_body : Result U32 :=
-  Result.ret (U32.ofInt 4294967295 (by intlit))
-def core_num_u32_max_c : U32 := eval_global core_num_u32_max_body (by simp)
-
-/- [hashmap_main::hashmap::HashMap::{0}::move_elements_from_list] -/
-def hashmap_hash_map_move_elements_from_list_loop_fwd_back
-  (T : Type) (ntable : hashmap_hash_map_t T) (ls : hashmap_list_t T) :
-  (Result (hashmap_hash_map_t T))
-  :=
-  match h: ls with
-  | hashmap_list_t.Cons k v tl =>
-    do
-      let ntable0 ← hashmap_hash_map_insert_no_resize_fwd_back T ntable k v
-      hashmap_hash_map_move_elements_from_list_loop_fwd_back T ntable0 tl
-  | hashmap_list_t.Nil => Result.ret ntable
-termination_by hashmap_hash_map_move_elements_from_list_loop_fwd_back ntable ls
-  =>
-  hashmap_hash_map_move_elements_from_list_loop_terminates T ntable ls
-decreasing_by hashmap_hash_map_move_elements_from_list_loop_decreases ntable ls
-
-/- [hashmap_main::hashmap::HashMap::{0}::move_elements_from_list] -/
-def hashmap_hash_map_move_elements_from_list_fwd_back
-  (T : Type) (ntable : hashmap_hash_map_t T) (ls : hashmap_list_t T) :
-  Result (hashmap_hash_map_t T)
-  :=
-  hashmap_hash_map_move_elements_from_list_loop_fwd_back T ntable ls
-
-/- [hashmap_main::hashmap::HashMap::{0}::move_elements] -/
-def hashmap_hash_map_move_elements_loop_fwd_back
-  (T : Type) (ntable : hashmap_hash_map_t T) (slots : Vec (hashmap_list_t T))
-  (i : Usize) :
-  (Result ((hashmap_hash_map_t T) × (Vec (hashmap_list_t T))))
-  :=
-  let i0 := vec_len (hashmap_list_t T) slots
-  if h: i < i0
-  then
-    do
-      let l ← vec_index_mut_fwd (hashmap_list_t T) slots i
-      let ls := mem_replace_fwd (hashmap_list_t T) l hashmap_list_t.Nil
-      let ntable0 ←
-        hashmap_hash_map_move_elements_from_list_fwd_back T ntable ls
-      let i1 ← i + (Usize.ofInt 1 (by intlit))
-      let l0 := mem_replace_back (hashmap_list_t T) l hashmap_list_t.Nil
-      let slots0 ← vec_index_mut_back (hashmap_list_t T) slots i l0
-      hashmap_hash_map_move_elements_loop_fwd_back T ntable0 slots0 i1
-  else Result.ret (ntable, slots)
-termination_by hashmap_hash_map_move_elements_loop_fwd_back ntable slots i =>
-  hashmap_hash_map_move_elements_loop_terminates T ntable slots i
-decreasing_by hashmap_hash_map_move_elements_loop_decreases ntable slots i
-
-/- [hashmap_main::hashmap::HashMap::{0}::move_elements] -/
-def hashmap_hash_map_move_elements_fwd_back
-  (T : Type) (ntable : hashmap_hash_map_t T) (slots : Vec (hashmap_list_t T))
-  (i : Usize) :
-  Result ((hashmap_hash_map_t T) × (Vec (hashmap_list_t T)))
-  :=
-  hashmap_hash_map_move_elements_loop_fwd_back T ntable slots i
-
-/- [hashmap_main::hashmap::HashMap::{0}::try_resize] -/
-def hashmap_hash_map_try_resize_fwd_back
-  (T : Type) (self : hashmap_hash_map_t T) : Result (hashmap_hash_map_t T) :=
-  do
-    let max_usize ← Scalar.cast .Usize core_num_u32_max_c
-    let capacity := vec_len (hashmap_list_t T) self.hashmap_hash_map_slots
-    let n1 ← max_usize / (Usize.ofInt 2 (by intlit))
-    let (i, i0) := self.hashmap_hash_map_max_load_factor
-    let i1 ← n1 / i
-    if h: capacity <= i1
-    then
-      do
-        let i2 ← capacity * (Usize.ofInt 2 (by intlit))
-        let ntable ← hashmap_hash_map_new_with_capacity_fwd T i2 i i0
-        let (ntable0, _) ←
-          hashmap_hash_map_move_elements_fwd_back T ntable
-            self.hashmap_hash_map_slots (Usize.ofInt 0 (by intlit))
-        Result.ret
-          {
-            ntable0
-              with
-              hashmap_hash_map_num_entries := self.hashmap_hash_map_num_entries,
-              hashmap_hash_map_max_load_factor := (i, i0)
-          }
-    else Result.ret { self with hashmap_hash_map_max_load_factor := (i, i0) }
-
-/- [hashmap_main::hashmap::HashMap::{0}::insert] -/
-def hashmap_hash_map_insert_fwd_back
-  (T : Type) (self : hashmap_hash_map_t T) (key : Usize) (value : T) :
-  Result (hashmap_hash_map_t T)
-  :=
-  do
-    let self0 ← hashmap_hash_map_insert_no_resize_fwd_back T self key value
-    let i ← hashmap_hash_map_len_fwd T self0
-    if h: i > self0.hashmap_hash_map_max_load
-    then hashmap_hash_map_try_resize_fwd_back T self0
-    else Result.ret self0
-
-/- [hashmap_main::hashmap::HashMap::{0}::contains_key_in_list] -/
-def hashmap_hash_map_contains_key_in_list_loop_fwd
-  (T : Type) (key : Usize) (ls : hashmap_list_t T) : (Result Bool) :=
-  match h: ls with
-  | hashmap_list_t.Cons ckey t tl =>
-    if h: ckey = key
-    then Result.ret true
-    else hashmap_hash_map_contains_key_in_list_loop_fwd T key tl
-  | hashmap_list_t.Nil => Result.ret false
-termination_by hashmap_hash_map_contains_key_in_list_loop_fwd key ls =>
-  hashmap_hash_map_contains_key_in_list_loop_terminates T key ls
-decreasing_by hashmap_hash_map_contains_key_in_list_loop_decreases key ls
-
-/- [hashmap_main::hashmap::HashMap::{0}::contains_key_in_list] -/
-def hashmap_hash_map_contains_key_in_list_fwd
-  (T : Type) (key : Usize) (ls : hashmap_list_t T) : Result Bool :=
-  hashmap_hash_map_contains_key_in_list_loop_fwd T key ls
-
-/- [hashmap_main::hashmap::HashMap::{0}::contains_key] -/
-def hashmap_hash_map_contains_key_fwd
-  (T : Type) (self : hashmap_hash_map_t T) (key : Usize) : Result Bool :=
-  do
-    let hash ← hashmap_hash_key_fwd key
-    let i := vec_len (hashmap_list_t T) self.hashmap_hash_map_slots
-    let hash_mod ← hash % i
-    let l ←
-      vec_index_fwd (hashmap_list_t T) self.hashmap_hash_map_slots hash_mod
-    hashmap_hash_map_contains_key_in_list_fwd T key l
-
-/- [hashmap_main::hashmap::HashMap::{0}::get_in_list] -/
-def hashmap_hash_map_get_in_list_loop_fwd
-  (T : Type) (key : Usize) (ls : hashmap_list_t T) : (Result T) :=
-  match h: ls with
-  | hashmap_list_t.Cons ckey cvalue tl =>
-    if h: ckey = key
-    then Result.ret cvalue
-    else hashmap_hash_map_get_in_list_loop_fwd T key tl
-  | hashmap_list_t.Nil => Result.fail Error.panic
-termination_by hashmap_hash_map_get_in_list_loop_fwd key ls =>
-  hashmap_hash_map_get_in_list_loop_terminates T key ls
-decreasing_by hashmap_hash_map_get_in_list_loop_decreases key ls
-
-/- [hashmap_main::hashmap::HashMap::{0}::get_in_list] -/
-def hashmap_hash_map_get_in_list_fwd
-  (T : Type) (key : Usize) (ls : hashmap_list_t T) : Result T :=
-  hashmap_hash_map_get_in_list_loop_fwd T key ls
-
-/- [hashmap_main::hashmap::HashMap::{0}::get] -/
-def hashmap_hash_map_get_fwd
-  (T : Type) (self : hashmap_hash_map_t T) (key : Usize) : Result T :=
-  do
-    let hash ← hashmap_hash_key_fwd key
-    let i := vec_len (hashmap_list_t T) self.hashmap_hash_map_slots
-    let hash_mod ← hash % i
-    let l ←
-      vec_index_fwd (hashmap_list_t T) self.hashmap_hash_map_slots hash_mod
-    hashmap_hash_map_get_in_list_fwd T key l
-
-/- [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list] -/
-def hashmap_hash_map_get_mut_in_list_loop_fwd
-  (T : Type) (ls : hashmap_list_t T) (key : Usize) : (Result T) :=
-  match h: ls with
-  | hashmap_list_t.Cons ckey cvalue tl =>
-    if h: ckey = key
-    then Result.ret cvalue
-    else hashmap_hash_map_get_mut_in_list_loop_fwd T tl key
-  | hashmap_list_t.Nil => Result.fail Error.panic
-termination_by hashmap_hash_map_get_mut_in_list_loop_fwd ls key =>
-  hashmap_hash_map_get_mut_in_list_loop_terminates T ls key
-decreasing_by hashmap_hash_map_get_mut_in_list_loop_decreases ls key
-
-/- [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list] -/
-def hashmap_hash_map_get_mut_in_list_fwd
-  (T : Type) (ls : hashmap_list_t T) (key : Usize) : Result T :=
-  hashmap_hash_map_get_mut_in_list_loop_fwd T ls key
-
-/- [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list] -/
-def hashmap_hash_map_get_mut_in_list_loop_back
-  (T : Type) (ls : hashmap_list_t T) (key : Usize) (ret0 : T) :
-  (Result (hashmap_list_t T))
-  :=
-  match h: ls with
-  | hashmap_list_t.Cons ckey cvalue tl =>
-    if h: ckey = key
-    then Result.ret (hashmap_list_t.Cons ckey ret0 tl)
-    else
-      do
-        let tl0 ← hashmap_hash_map_get_mut_in_list_loop_back T tl key ret0
-        Result.ret (hashmap_list_t.Cons ckey cvalue tl0)
-  | hashmap_list_t.Nil => Result.fail Error.panic
-termination_by hashmap_hash_map_get_mut_in_list_loop_back ls key ret0 =>
-  hashmap_hash_map_get_mut_in_list_loop_terminates T ls key
-decreasing_by hashmap_hash_map_get_mut_in_list_loop_decreases ls key
-
-/- [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list] -/
-def hashmap_hash_map_get_mut_in_list_back
-  (T : Type) (ls : hashmap_list_t T) (key : Usize) (ret0 : T) :
-  Result (hashmap_list_t T)
-  :=
-  hashmap_hash_map_get_mut_in_list_loop_back T ls key ret0
-
-/- [hashmap_main::hashmap::HashMap::{0}::get_mut] -/
-def hashmap_hash_map_get_mut_fwd
-  (T : Type) (self : hashmap_hash_map_t T) (key : Usize) : Result T :=
-  do
-    let hash ← hashmap_hash_key_fwd key
-    let i := vec_len (hashmap_list_t T) self.hashmap_hash_map_slots
-    let hash_mod ← hash % i
-    let l ←
-      vec_index_mut_fwd (hashmap_list_t T) self.hashmap_hash_map_slots hash_mod
-    hashmap_hash_map_get_mut_in_list_fwd T l key
-
-/- [hashmap_main::hashmap::HashMap::{0}::get_mut] -/
-def hashmap_hash_map_get_mut_back
-  (T : Type) (self : hashmap_hash_map_t T) (key : Usize) (ret0 : T) :
-  Result (hashmap_hash_map_t T)
-  :=
-  do
-    let hash ← hashmap_hash_key_fwd key
-    let i := vec_len (hashmap_list_t T) self.hashmap_hash_map_slots
-    let hash_mod ← hash % i
-    let l ←
-      vec_index_mut_fwd (hashmap_list_t T) self.hashmap_hash_map_slots hash_mod
-    let l0 ← hashmap_hash_map_get_mut_in_list_back T l key ret0
-    let v ←
-      vec_index_mut_back (hashmap_list_t T) self.hashmap_hash_map_slots
-        hash_mod l0
-    Result.ret { self with hashmap_hash_map_slots := v }
-
-/- [hashmap_main::hashmap::HashMap::{0}::remove_from_list] -/
-def hashmap_hash_map_remove_from_list_loop_fwd
-  (T : Type) (key : Usize) (ls : hashmap_list_t T) : (Result (Option T)) :=
-  match h: ls with
-  | hashmap_list_t.Cons ckey t tl =>
-    if h: ckey = key
-    then
-      let mv_ls :=
-        mem_replace_fwd (hashmap_list_t T) (hashmap_list_t.Cons ckey t tl)
-          hashmap_list_t.Nil
-      match h: mv_ls with
-      | hashmap_list_t.Cons i cvalue tl0 => Result.ret (Option.some cvalue)
-      | hashmap_list_t.Nil => Result.fail Error.panic
-    else hashmap_hash_map_remove_from_list_loop_fwd T key tl
-  | hashmap_list_t.Nil => Result.ret Option.none
-termination_by hashmap_hash_map_remove_from_list_loop_fwd key ls =>
-  hashmap_hash_map_remove_from_list_loop_terminates T key ls
-decreasing_by hashmap_hash_map_remove_from_list_loop_decreases key ls
-
-/- [hashmap_main::hashmap::HashMap::{0}::remove_from_list] -/
-def hashmap_hash_map_remove_from_list_fwd
-  (T : Type) (key : Usize) (ls : hashmap_list_t T) : Result (Option T) :=
-  hashmap_hash_map_remove_from_list_loop_fwd T key ls
-
-/- [hashmap_main::hashmap::HashMap::{0}::remove_from_list] -/
-def hashmap_hash_map_remove_from_list_loop_back
-  (T : Type) (key : Usize) (ls : hashmap_list_t T) :
-  (Result (hashmap_list_t T))
-  :=
-  match h: ls with
-  | hashmap_list_t.Cons ckey t tl =>
-    if h: ckey = key
-    then
-      let mv_ls :=
-        mem_replace_fwd (hashmap_list_t T) (hashmap_list_t.Cons ckey t tl)
-          hashmap_list_t.Nil
-      match h: mv_ls with
-      | hashmap_list_t.Cons i cvalue tl0 => Result.ret tl0
-      | hashmap_list_t.Nil => Result.fail Error.panic
-    else
-      do
-        let tl0 ← hashmap_hash_map_remove_from_list_loop_back T key tl
-        Result.ret (hashmap_list_t.Cons ckey t tl0)
-  | hashmap_list_t.Nil => Result.ret hashmap_list_t.Nil
-termination_by hashmap_hash_map_remove_from_list_loop_back key ls =>
-  hashmap_hash_map_remove_from_list_loop_terminates T key ls
-decreasing_by hashmap_hash_map_remove_from_list_loop_decreases key ls
-
-/- [hashmap_main::hashmap::HashMap::{0}::remove_from_list] -/
-def hashmap_hash_map_remove_from_list_back
-  (T : Type) (key : Usize) (ls : hashmap_list_t T) :
-  Result (hashmap_list_t T)
-  :=
-  hashmap_hash_map_remove_from_list_loop_back T key ls
-
-/- [hashmap_main::hashmap::HashMap::{0}::remove] -/
-def hashmap_hash_map_remove_fwd
-  (T : Type) (self : hashmap_hash_map_t T) (key : Usize) : Result (Option T) :=
-  do
-    let hash ← hashmap_hash_key_fwd key
-    let i := vec_len (hashmap_list_t T) self.hashmap_hash_map_slots
-    let hash_mod ← hash % i
-    let l ←
-      vec_index_mut_fwd (hashmap_list_t T) self.hashmap_hash_map_slots hash_mod
-    let x ← hashmap_hash_map_remove_from_list_fwd T key l
-    match h: x with
-    | Option.none => Result.ret Option.none
-    | Option.some x0 =>
-      do
-        let _ ← self.hashmap_hash_map_num_entries -
-          (Usize.ofInt 1 (by intlit))
-        Result.ret (Option.some x0)
-
-/- [hashmap_main::hashmap::HashMap::{0}::remove] -/
-def hashmap_hash_map_remove_back
-  (T : Type) (self : hashmap_hash_map_t T) (key : Usize) :
-  Result (hashmap_hash_map_t T)
-  :=
-  do
-    let hash ← hashmap_hash_key_fwd key
-    let i := vec_len (hashmap_list_t T) self.hashmap_hash_map_slots
-    let hash_mod ← hash % i
-    let l ←
-      vec_index_mut_fwd (hashmap_list_t T) self.hashmap_hash_map_slots hash_mod
-    let x ← hashmap_hash_map_remove_from_list_fwd T key l
-    match h: x with
-    | Option.none =>
-      do
-        let l0 ← hashmap_hash_map_remove_from_list_back T key l
-        let v ←
-          vec_index_mut_back (hashmap_list_t T) self.hashmap_hash_map_slots
-            hash_mod l0
-        Result.ret { self with hashmap_hash_map_slots := v }
-    | Option.some x0 =>
-      do
-        let i0 ← self.hashmap_hash_map_num_entries -
-          (Usize.ofInt 1 (by intlit))
-        let l0 ← hashmap_hash_map_remove_from_list_back T key l
-        let v ←
-          vec_index_mut_back (hashmap_list_t T) self.hashmap_hash_map_slots
-            hash_mod l0
-        Result.ret
-          {
-            self
-              with
-              hashmap_hash_map_num_entries := i0, hashmap_hash_map_slots := v
-          }
-
-/- [hashmap_main::hashmap::test1] -/
-def hashmap_test1_fwd : Result Unit :=
-  do
-    let hm ← hashmap_hash_map_new_fwd U64
-    let hm0 ←
-      hashmap_hash_map_insert_fwd_back U64 hm (Usize.ofInt 0 (by intlit))
-        (U64.ofInt 42 (by intlit))
-    let hm1 ←
-      hashmap_hash_map_insert_fwd_back U64 hm0 (Usize.ofInt 128 (by intlit))
-        (U64.ofInt 18 (by intlit))
-    let hm2 ←
-      hashmap_hash_map_insert_fwd_back U64 hm1 (Usize.ofInt 1024 (by intlit))
-        (U64.ofInt 138 (by intlit))
-    let hm3 ←
-      hashmap_hash_map_insert_fwd_back U64 hm2 (Usize.ofInt 1056 (by intlit))
-        (U64.ofInt 256 (by intlit))
-    let i ← hashmap_hash_map_get_fwd U64 hm3 (Usize.ofInt 128 (by intlit))
-    if h: not (i = (U64.ofInt 18 (by intlit)))
-    then Result.fail Error.panic
-    else
-      do
-        let hm4 ←
-          hashmap_hash_map_get_mut_back U64 hm3 (Usize.ofInt 1024 (by intlit))
-            (U64.ofInt 56 (by intlit))
-        let i0 ←
-          hashmap_hash_map_get_fwd U64 hm4 (Usize.ofInt 1024 (by intlit))
-        if h: not (i0 = (U64.ofInt 56 (by intlit)))
-        then Result.fail Error.panic
-        else
-          do
-            let x ←
-              hashmap_hash_map_remove_fwd U64 hm4
-                (Usize.ofInt 1024 (by intlit))
-            match h: x with
-            | Option.none => Result.fail Error.panic
-            | Option.some x0 =>
-              if h: not (x0 = (U64.ofInt 56 (by intlit)))
-              then Result.fail Error.panic
-              else
-                do
-                  let hm5 ←
-                    hashmap_hash_map_remove_back U64 hm4
-                      (Usize.ofInt 1024 (by intlit))
-                  let i1 ←
-                    hashmap_hash_map_get_fwd U64 hm5
-                      (Usize.ofInt 0 (by intlit))
-                  if h: not (i1 = (U64.ofInt 42 (by intlit)))
-                  then Result.fail Error.panic
-                  else
-                    do
-                      let i2 ←
-                        hashmap_hash_map_get_fwd U64 hm5
-                          (Usize.ofInt 128 (by intlit))
-                      if h: not (i2 = (U64.ofInt 18 (by intlit)))
-                      then Result.fail Error.panic
-                      else
-                        do
-                          let i3 ←
-                            hashmap_hash_map_get_fwd U64 hm5
-                              (Usize.ofInt 1056 (by intlit))
-                          if h: not (i3 = (U64.ofInt 256 (by intlit)))
-                          then Result.fail Error.panic
-                          else Result.ret ()
-
-/- [hashmap_main::insert_on_disk] -/
-def insert_on_disk_fwd
-  (key : Usize) (value : U64) (st : State) : Result (State × Unit) :=
-  do
-    let (st0, hm) ← opaque_defs.hashmap_utils_deserialize_fwd st
-    let hm0 ← hashmap_hash_map_insert_fwd_back U64 hm key value
-    let (st1, _) ← opaque_defs.hashmap_utils_serialize_fwd hm0 st0
-    Result.ret (st1, ())
-
-/- [hashmap_main::main] -/
-def main_fwd : Result Unit :=
-  Result.ret ()
-
diff --git a/tests/lean/hashmap_on_disk/HashmapMain/Types.lean b/tests/lean/hashmap_on_disk/HashmapMain/Types.lean
deleted file mode 100644
index 0509fbbd..00000000
--- a/tests/lean/hashmap_on_disk/HashmapMain/Types.lean
+++ /dev/null
@@ -1,19 +0,0 @@
--- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
--- [hashmap_main]: type definitions
-import Base.Primitives
-
-/- [hashmap_main::hashmap::List] -/
-inductive hashmap_list_t (T : Type) :=
-| Cons : Usize -> T -> hashmap_list_t T -> hashmap_list_t T
-| Nil : hashmap_list_t T
-
-/- [hashmap_main::hashmap::HashMap] -/
-structure hashmap_hash_map_t (T : Type) where
-  hashmap_hash_map_num_entries : Usize
-  hashmap_hash_map_max_load_factor : (Usize × Usize)
-  hashmap_hash_map_max_load : Usize
-  hashmap_hash_map_slots : Vec (hashmap_list_t T)
-
-/- The state type used in the state-error monad -/
-axiom State : Type
-
diff --git a/tests/lean/hashmap_on_disk/lake-manifest.json b/tests/lean/hashmap_on_disk/lake-manifest.json
deleted file mode 100644
index 57b071ca..00000000
--- a/tests/lean/hashmap_on_disk/lake-manifest.json
+++ /dev/null
@@ -1,27 +0,0 @@
-{"version": 4,
- "packagesDir": "./lake-packages",
- "packages":
- [{"git":
-   {"url": "https://github.com/leanprover-community/mathlib4.git",
-    "subDir?": null,
-    "rev": "4037792ead804d7bfa8868e2c4684d4223c15ece",
-    "name": "mathlib",
-    "inputRev?": null}},
-  {"git":
-   {"url": "https://github.com/gebner/quote4",
-    "subDir?": null,
-    "rev": "2412c4fdf4a8b689f4467618e5e7b371ae5014aa",
-    "name": "Qq",
-    "inputRev?": "master"}},
-  {"git":
-   {"url": "https://github.com/JLimperg/aesop",
-    "subDir?": null,
-    "rev": "7fe9ecd9339b0e1796e89d243b776849c305c690",
-    "name": "aesop",
-    "inputRev?": "master"}},
-  {"git":
-   {"url": "https://github.com/leanprover/std4",
-    "subDir?": null,
-    "rev": "24897887905b3a1254b244369f5dd2cf6174b0ee",
-    "name": "std",
-    "inputRev?": "main"}}]}
diff --git a/tests/lean/hashmap_on_disk/lakefile.lean b/tests/lean/hashmap_on_disk/lakefile.lean
deleted file mode 100644
index 70daf427..00000000
--- a/tests/lean/hashmap_on_disk/lakefile.lean
+++ /dev/null
@@ -1,12 +0,0 @@
-import Lake
-open Lake DSL
-
-require mathlib from git
-  "https://github.com/leanprover-community/mathlib4.git"
-
-package «hashmap_main» {}
-
-lean_lib «Base» {}
-
-@[default_target]
-lean_lib «HashmapMain» {}
diff --git a/tests/lean/hashmap_on_disk/lean-toolchain b/tests/lean/hashmap_on_disk/lean-toolchain
deleted file mode 100644
index bbf57f10..00000000
--- a/tests/lean/hashmap_on_disk/lean-toolchain
+++ /dev/null
@@ -1 +0,0 @@
-leanprover/lean4:nightly-2023-01-21
diff --git a/tests/lean/lake-manifest.json b/tests/lean/lake-manifest.json
new file mode 100644
index 00000000..94030cb6
--- /dev/null
+++ b/tests/lean/lake-manifest.json
@@ -0,0 +1,40 @@
+{"version": 4,
+ "packagesDir": "lake-packages",
+ "packages":
+ [{"git":
+   {"url": "https://github.com/EdAyers/ProofWidgets4",
+    "subDir?": null,
+    "rev": "c43db94a8f495dad37829e9d7ad65483d68c86b8",
+    "name": "proofwidgets",
+    "inputRev?": "v0.0.11"}},
+  {"path": {"name": "Base", "dir": "./../../backends/lean"}},
+  {"git":
+   {"url": "https://github.com/mhuisi/lean4-cli.git",
+    "subDir?": null,
+    "rev": "5a858c32963b6b19be0d477a30a1f4b6c120be7e",
+    "name": "Cli",
+    "inputRev?": "nightly"}},
+  {"git":
+   {"url": "https://github.com/leanprover-community/mathlib4.git",
+    "subDir?": null,
+    "rev": "fa05951a270fef2873666c46f138e90338cd48d6",
+    "name": "mathlib",
+    "inputRev?": null}},
+  {"git":
+   {"url": "https://github.com/gebner/quote4",
+    "subDir?": null,
+    "rev": "c0d9516f44d07feee01c1103c8f2f7c24a822b55",
+    "name": "Qq",
+    "inputRev?": "master"}},
+  {"git":
+   {"url": "https://github.com/JLimperg/aesop",
+    "subDir?": null,
+    "rev": "f04538ab6ad07642368cf11d2702acc0a9b4bcee",
+    "name": "aesop",
+    "inputRev?": "master"}},
+  {"git":
+   {"url": "https://github.com/leanprover/std4",
+    "subDir?": null,
+    "rev": "dff883c55395438ae2a5c65ad5ddba084b600feb",
+    "name": "std",
+    "inputRev?": "main"}}]}
diff --git a/tests/lean/lakefile.lean b/tests/lean/lakefile.lean
new file mode 100644
index 00000000..ae63b129
--- /dev/null
+++ b/tests/lean/lakefile.lean
@@ -0,0 +1,19 @@
+import Lake
+open Lake DSL
+
+require mathlib from git
+  "https://github.com/leanprover-community/mathlib4.git"
+
+require Base from "../../backends/lean"
+
+package «tests» {}
+
+@[default_target] lean_lib betreeMain
+@[default_target] lean_lib constants
+@[default_target] lean_lib external
+@[default_target] lean_lib hashmap
+@[default_target] lean_lib hashmapMain
+@[default_target] lean_lib loops
+@[default_target] lean_lib noNestedBorrows
+@[default_target] lean_lib paper
+@[default_target] lean_lib poloniusList
diff --git a/tests/lean/lean-toolchain b/tests/lean/lean-toolchain
index bbf57f10..334c5053 100644
--- a/tests/lean/lean-toolchain
+++ b/tests/lean/lean-toolchain
@@ -1 +1 @@
-leanprover/lean4:nightly-2023-01-21
+leanprover/lean4:nightly-2023-07-12
\ No newline at end of file
diff --git a/tests/lean/misc-constants/Base/Primitives.lean b/tests/lean/misc-constants/Base/Primitives.lean
deleted file mode 100644
index 4a66a453..00000000
--- a/tests/lean/misc-constants/Base/Primitives.lean
+++ /dev/null
@@ -1,583 +0,0 @@
-import Lean
-import Lean.Meta.Tactic.Simp
-import Init.Data.List.Basic
-import Mathlib.Tactic.RunCmd
-
---------------------
--- ASSERT COMMAND --
---------------------
-
-open Lean Elab Command Term Meta
-
-syntax (name := assert) "#assert" term: command
-
-@[command_elab assert]
-unsafe
-def assertImpl : CommandElab := fun (_stx: Syntax) => do
-  runTermElabM (fun _ => do
-    let r ← evalTerm Bool (mkConst ``Bool) _stx[1]
-    if not r then
-      logInfo "Assertion failed for: "
-      logInfo _stx[1]
-      logError "Expression reduced to false"
-    pure ())
-
-#eval 2 == 2
-#assert (2 == 2)
-
--------------
--- PRELUDE --
--------------
-
--- Results & monadic combinators
-
-inductive Error where
-   | assertionFailure: Error
-   | integerOverflow: Error
-   | divisionByZero: Error
-   | arrayOutOfBounds: Error
-   | maximumSizeExceeded: Error
-   | panic: Error
-deriving Repr, BEq
-
-open Error
-
-inductive Result (α : Type u) where
-  | ret (v: α): Result α
-  | fail (e: Error): Result α
-deriving Repr, BEq
-
-open Result
-
-instance Result_Inhabited (α : Type u) : Inhabited (Result α) :=
-  Inhabited.mk (fail panic)
-
-/- HELPERS -/
-
-def ret? {α: Type} (r: Result α): Bool :=
-  match r with
-  | Result.ret _ => true
-  | Result.fail _ => false
-
-def massert (b:Bool) : Result Unit :=
-  if b then .ret () else fail assertionFailure
-
-def eval_global {α: Type} (x: Result α) (_: ret? x): α :=
-  match x with
-  | Result.fail _ => by contradiction
-  | Result.ret x => x
-
-/- DO-DSL SUPPORT -/
-
-def bind (x: Result α) (f: α -> Result β) : Result β :=
-  match x with
-  | ret v  => f v 
-  | fail v => fail v
-
--- Allows using Result in do-blocks
-instance : Bind Result where
-  bind := bind
-
--- Allows using return x in do-blocks
-instance : Pure Result where
-  pure := fun x => ret x
-
-/- CUSTOM-DSL SUPPORT -/
-
--- Let-binding the Result of a monadic operation is oftentimes not sufficient,
--- because we may need a hypothesis for equational reasoning in the scope. We
--- rely on subtype, and a custom let-binding operator, in effect recreating our
--- own variant of the do-dsl
-
-def Result.attach {α: Type} (o : Result α): Result { x : α // o = ret x } :=
-  match o with
-  | .ret x => .ret ⟨x, rfl⟩
-  | .fail e => .fail e
-
-macro "let" e:term " ⟵ " f:term : doElem =>
-  `(doElem| let ⟨$e, h⟩ ← Result.attach $f)
-
--- TODO: any way to factorize both definitions?
-macro "let" e:term " <-- " f:term : doElem =>
-  `(doElem| let ⟨$e, h⟩ ← Result.attach $f)
-
--- We call the hypothesis `h`, in effect making it unavailable to the user
--- (because too much shadowing). But in practice, once can use the French single
--- quote notation (input with f< and f>), where `‹ h ›` finds a suitable
--- hypothesis in the context, this is equivalent to `have x: h := by assumption in x`
-#eval do
-  let y <-- .ret (0: Nat)
-  let _: y = 0 := by cases ‹ ret 0 = ret y › ; decide
-  let r: { x: Nat // x = 0 } := ⟨ y, by assumption ⟩
-  .ret r
-
-----------------------
--- MACHINE INTEGERS --
-----------------------
-
--- We redefine our machine integers types.
-
--- For Isize/Usize, we reuse `getNumBits` from `USize`. You cannot reduce `getNumBits`
--- using the simplifier, meaning that proofs do not depend on the compile-time value of
--- USize.size. (Lean assumes 32 or 64-bit platforms, and Rust doesn't really support, at
--- least officially, 16-bit microcontrollers, so this seems like a fine design decision
--- for now.)
-
--- Note from Chris Bailey: "If there's more than one salient property of your
--- definition then the subtyping strategy might get messy, and the property part
--- of a subtype is less discoverable by the simplifier or tactics like
--- library_search." So, we will not add refinements on the return values of the
--- operations defined on Primitives, but will rather rely on custom lemmas to
--- invert on possible return values of the primitive operations.
-
--- Machine integer constants, done via `ofNatCore`, which requires a proof that
--- the `Nat` fits within the desired integer type. We provide a custom tactic.
-
-open System.Platform.getNumBits
-
--- TODO: is there a way of only importing System.Platform.getNumBits?
---
-@[simp] def size_num_bits : Nat := (System.Platform.getNumBits ()).val
-
--- Remark: Lean seems to use < for the comparisons with the upper bounds by convention.
--- We keep the F* convention for now.
-@[simp] def Isize.min : Int := - (HPow.hPow 2 (size_num_bits - 1))
-@[simp] def Isize.max : Int := (HPow.hPow 2 (size_num_bits - 1)) - 1
-@[simp] def I8.min    : Int := - (HPow.hPow 2 7)
-@[simp] def I8.max    : Int := HPow.hPow 2 7 - 1
-@[simp] def I16.min   : Int := - (HPow.hPow 2 15)
-@[simp] def I16.max   : Int := HPow.hPow 2 15 - 1
-@[simp] def I32.min   : Int := -(HPow.hPow 2 31)
-@[simp] def I32.max   : Int := HPow.hPow 2 31 - 1
-@[simp] def I64.min   : Int := -(HPow.hPow 2 63)
-@[simp] def I64.max   : Int := HPow.hPow 2 63 - 1
-@[simp] def I128.min  : Int := -(HPow.hPow 2 127)
-@[simp] def I128.max  : Int := HPow.hPow 2 127 - 1
-@[simp] def Usize.min : Int := 0
-@[simp] def Usize.max : Int := HPow.hPow 2 size_num_bits - 1
-@[simp] def U8.min    : Int := 0
-@[simp] def U8.max    : Int := HPow.hPow 2 8 - 1
-@[simp] def U16.min   : Int := 0
-@[simp] def U16.max   : Int := HPow.hPow 2 16 - 1
-@[simp] def U32.min   : Int := 0
-@[simp] def U32.max   : Int := HPow.hPow 2 32 - 1
-@[simp] def U64.min   : Int := 0
-@[simp] def U64.max   : Int := HPow.hPow 2 64 - 1
-@[simp] def U128.min  : Int := 0
-@[simp] def U128.max  : Int := HPow.hPow 2 128 - 1
-
-#assert (I8.min   == -128)
-#assert (I8.max   == 127)
-#assert (I16.min  == -32768)
-#assert (I16.max  == 32767)
-#assert (I32.min  == -2147483648)
-#assert (I32.max  == 2147483647)
-#assert (I64.min  == -9223372036854775808)
-#assert (I64.max  == 9223372036854775807)
-#assert (I128.min == -170141183460469231731687303715884105728)
-#assert (I128.max == 170141183460469231731687303715884105727)
-#assert (U8.min   == 0)
-#assert (U8.max   == 255)
-#assert (U16.min  == 0)
-#assert (U16.max  == 65535)
-#assert (U32.min  == 0)
-#assert (U32.max  == 4294967295)
-#assert (U64.min  == 0)
-#assert (U64.max  == 18446744073709551615)
-#assert (U128.min == 0)
-#assert (U128.max == 340282366920938463463374607431768211455)
-
-inductive ScalarTy :=
-| Isize
-| I8
-| I16
-| I32
-| I64
-| I128
-| Usize
-| U8
-| U16
-| U32
-| U64
-| U128
-
-def Scalar.min (ty : ScalarTy) : Int :=
-  match ty with
-  | .Isize => Isize.min
-  | .I8    => I8.min
-  | .I16   => I16.min
-  | .I32   => I32.min
-  | .I64   => I64.min
-  | .I128  => I128.min
-  | .Usize => Usize.min
-  | .U8    => U8.min
-  | .U16   => U16.min
-  | .U32   => U32.min
-  | .U64   => U64.min
-  | .U128  => U128.min
-
-def Scalar.max (ty : ScalarTy) : Int :=
-  match ty with
-  | .Isize => Isize.max
-  | .I8    => I8.max
-  | .I16   => I16.max
-  | .I32   => I32.max
-  | .I64   => I64.max
-  | .I128  => I128.max
-  | .Usize => Usize.max
-  | .U8    => U8.max
-  | .U16   => U16.max
-  | .U32   => U32.max
-  | .U64   => U64.max
-  | .U128  => U128.max
-
--- "Conservative" bounds
--- We use those because we can't compare to the isize bounds (which can't
--- reduce at compile-time). Whenever we perform an arithmetic operation like
--- addition we need to check that the result is in bounds: we first compare
--- to the conservative bounds, which reduce, then compare to the real bounds.
--- This is useful for the various #asserts that we want to reduce at
--- type-checking time.
-def Scalar.cMin (ty : ScalarTy) : Int :=
-  match ty with
-  | .Isize => I32.min
-  | _ => Scalar.min ty
-
-def Scalar.cMax (ty : ScalarTy) : Int :=
-  match ty with
-  | .Isize => I32.max
-  | .Usize => U32.max
-  | _ => Scalar.max ty
-
-theorem Scalar.cMin_bound ty : Scalar.min ty <= Scalar.cMin ty := by sorry
-theorem Scalar.cMax_bound ty : Scalar.min ty <= Scalar.cMin ty := by sorry
-
-structure Scalar (ty : ScalarTy) where
-  val : Int
-  hmin : Scalar.min ty <= val
-  hmax : val <= Scalar.max ty
-
-theorem Scalar.bound_suffices (ty : ScalarTy) (x : Int) :
-  Scalar.cMin ty <= x && x <= Scalar.cMax ty ->
-  (decide (Scalar.min ty ≤ x) && decide (x ≤ Scalar.max ty)) = true
-  := by sorry
-
-def Scalar.ofIntCore {ty : ScalarTy} (x : Int)
-  (hmin : Scalar.min ty <= x) (hmax : x <= Scalar.max ty) : Scalar ty :=
-  { val := x, hmin := hmin, hmax := hmax }
-
-def Scalar.ofInt {ty : ScalarTy} (x : Int)
-  (h : Scalar.min ty <= x && x <= Scalar.max ty) : Scalar ty :=
-  let hmin: Scalar.min ty <= x := by sorry
-  let hmax: x <= Scalar.max ty := by sorry
-  Scalar.ofIntCore x hmin hmax
-
--- Further thoughts: look at what has been done here:
--- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/Fin/Basic.lean
--- and
--- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/UInt.lean
--- which both contain a fair amount of reasoning already!
-def Scalar.tryMk (ty : ScalarTy) (x : Int) : Result (Scalar ty) :=
-  -- TODO: write this with only one if then else
-  if hmin_cons: Scalar.cMin ty <= x || Scalar.min ty <= x then
-    if hmax_cons: x <= Scalar.cMax ty || x <= Scalar.max ty then
-      let hmin: Scalar.min ty <= x := by sorry
-      let hmax: x <= Scalar.max ty := by sorry
-      return Scalar.ofIntCore x hmin hmax
-    else fail integerOverflow
-  else fail integerOverflow
-
-def Scalar.neg {ty : ScalarTy} (x : Scalar ty) : Result (Scalar ty) := Scalar.tryMk ty (- x.val)
-
-def Scalar.div {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
-  if y.val != 0 then Scalar.tryMk ty (x.val / y.val) else fail divisionByZero
-
--- Checking that the % operation in Lean computes the same as the remainder operation in Rust
-#assert 1 % 2 = (1:Int)
-#assert (-1) % 2 = -1
-#assert 1 % (-2) = 1
-#assert (-1) % (-2) = -1
-
-def Scalar.rem {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
-  if y.val != 0 then Scalar.tryMk ty (x.val % y.val) else fail divisionByZero
-
-def Scalar.add {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
-  Scalar.tryMk ty (x.val + y.val)
-
-def Scalar.sub {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
-  Scalar.tryMk ty (x.val - y.val)
-
-def Scalar.mul {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
-  Scalar.tryMk ty (x.val * y.val)
-
--- TODO: instances of +, -, * etc. for scalars
-
--- Cast an integer from a [src_ty] to a [tgt_ty]
--- TODO: check the semantics of casts in Rust
-def Scalar.cast {src_ty : ScalarTy} (tgt_ty : ScalarTy) (x : Scalar src_ty) : Result (Scalar tgt_ty) :=
-  Scalar.tryMk tgt_ty x.val
-
--- The scalar types
--- We declare the definitions as reducible so that Lean can unfold them (useful
--- for type class resolution for instance).
-@[reducible] def Isize := Scalar .Isize
-@[reducible] def I8    := Scalar .I8
-@[reducible] def I16   := Scalar .I16
-@[reducible] def I32   := Scalar .I32
-@[reducible] def I64   := Scalar .I64
-@[reducible] def I128  := Scalar .I128
-@[reducible] def Usize := Scalar .Usize
-@[reducible] def U8    := Scalar .U8
-@[reducible] def U16   := Scalar .U16
-@[reducible] def U32   := Scalar .U32
-@[reducible] def U64   := Scalar .U64
-@[reducible] def U128  := Scalar .U128
-
--- TODO: below: not sure this is the best way.
--- Should we rather overload operations like +, -, etc.?
--- Also, it is possible to automate the generation of those definitions
--- with macros (but would it be a good idea? It would be less easy to
--- read the file, which is not supposed to change a lot)
-
--- Negation
-
-/--
-Remark: there is no heterogeneous negation in the Lean prelude: we thus introduce
-one here.
-
-The notation typeclass for heterogeneous addition.
-This enables the notation `- a : β` where `a : α`.
--/
-class HNeg (α : Type u) (β : outParam (Type v)) where
-  /-- `- a` computes the negation of `a`.
-  The meaning of this notation is type-dependent. -/
-  hNeg : α → β
-
-prefix:75  "-"   => HNeg.hNeg
-
-instance : HNeg Isize (Result Isize) where hNeg x := Scalar.neg x
-instance : HNeg I8 (Result I8) where hNeg x := Scalar.neg x
-instance : HNeg I16 (Result I16) where hNeg x := Scalar.neg x
-instance : HNeg I32 (Result I32) where hNeg x := Scalar.neg x
-instance : HNeg I64 (Result I64) where hNeg x := Scalar.neg x
-instance : HNeg I128 (Result I128) where hNeg x := Scalar.neg x
-
--- Addition
-instance {ty} : HAdd (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
-  hAdd x y := Scalar.add x y
-
--- Substraction
-instance {ty} : HSub (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
-  hSub x y := Scalar.sub x y
-
--- Multiplication
-instance {ty} : HMul (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
-  hMul x y := Scalar.mul x y
-
--- Division
-instance {ty} : HDiv (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
-  hDiv x y := Scalar.div x y
-
--- Remainder
-instance {ty} : HMod (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
-  hMod x y := Scalar.rem x y
-
--- ofIntCore
--- TODO: typeclass?
-def Isize.ofIntCore := @Scalar.ofIntCore .Isize
-def I8.ofIntCore    := @Scalar.ofIntCore .I8
-def I16.ofIntCore   := @Scalar.ofIntCore .I16
-def I32.ofIntCore   := @Scalar.ofIntCore .I32
-def I64.ofIntCore   := @Scalar.ofIntCore .I64
-def I128.ofIntCore  := @Scalar.ofIntCore .I128
-def Usize.ofIntCore := @Scalar.ofIntCore .Usize
-def U8.ofIntCore    := @Scalar.ofIntCore .U8
-def U16.ofIntCore   := @Scalar.ofIntCore .U16
-def U32.ofIntCore   := @Scalar.ofIntCore .U32
-def U64.ofIntCore   := @Scalar.ofIntCore .U64
-def U128.ofIntCore  := @Scalar.ofIntCore .U128
-
---  ofInt
--- TODO: typeclass?
-def Isize.ofInt := @Scalar.ofInt .Isize
-def I8.ofInt    := @Scalar.ofInt .I8
-def I16.ofInt   := @Scalar.ofInt .I16
-def I32.ofInt   := @Scalar.ofInt .I32
-def I64.ofInt   := @Scalar.ofInt .I64
-def I128.ofInt  := @Scalar.ofInt .I128
-def Usize.ofInt := @Scalar.ofInt .Usize
-def U8.ofInt    := @Scalar.ofInt .U8
-def U16.ofInt   := @Scalar.ofInt .U16
-def U32.ofInt   := @Scalar.ofInt .U32
-def U64.ofInt   := @Scalar.ofInt .U64
-def U128.ofInt  := @Scalar.ofInt .U128
-
--- Comparisons
-instance {ty} : LT (Scalar ty) where
-  lt a b := LT.lt a.val b.val
-
-instance {ty} : LE (Scalar ty) where le a b := LE.le a.val b.val
-
-instance Scalar.decLt {ty} (a b : Scalar ty) : Decidable (LT.lt a b) := Int.decLt ..
-instance Scalar.decLe {ty} (a b : Scalar ty) : Decidable (LE.le a b) := Int.decLe ..
-
-theorem Scalar.eq_of_val_eq {ty} : ∀ {i j : Scalar ty}, Eq i.val j.val → Eq i j
-  | ⟨_, _, _⟩, ⟨_, _, _⟩, rfl => rfl
-
-theorem Scalar.val_eq_of_eq {ty} {i j : Scalar ty} (h : Eq i j) : Eq i.val j.val :=
-  h ▸ rfl
-
-theorem Scalar.ne_of_val_ne {ty} {i j : Scalar ty} (h : Not (Eq i.val j.val)) : Not (Eq i j) :=
-  fun h' => absurd (val_eq_of_eq h') h
-
-instance (ty : ScalarTy) : DecidableEq (Scalar ty) :=
-  fun i j =>
-    match decEq i.val j.val with
-    | isTrue h  => isTrue (Scalar.eq_of_val_eq h)
-    | isFalse h => isFalse (Scalar.ne_of_val_ne h)
-
-def Scalar.toInt {ty} (n : Scalar ty) : Int := n.val
-
--- Tactic to prove that integers are in bounds
-syntax "intlit" : tactic
-
-macro_rules
-  | `(tactic| intlit) => `(tactic| apply Scalar.bound_suffices ; decide)
-
--- -- We now define a type class that subsumes the various machine integer types, so
--- -- as to write a concise definition for scalar_cast, rather than exhaustively
--- -- enumerating all of the possible pairs. We remark that Rust has sane semantics
--- -- and fails if a cast operation would involve a truncation or modulo.
-
--- class MachineInteger (t: Type) where
---   size: Nat
---   val: t -> Fin size
---   ofNatCore: (n:Nat) -> LT.lt n size -> t
-
--- set_option hygiene false in
--- run_cmd
---   for typeName in [`UInt8, `UInt16, `UInt32, `UInt64, `USize].map Lean.mkIdent do
---   Lean.Elab.Command.elabCommand (← `(
---     namespace $typeName
---     instance: MachineInteger $typeName where
---       size := size
---       val := val
---       ofNatCore := ofNatCore
---     end $typeName
---   ))
-
--- -- Aeneas only instantiates the destination type (`src` is implicit). We rely on
--- -- Lean to infer `src`.
-
--- def scalar_cast { src: Type } (dst: Type) [ MachineInteger src ] [ MachineInteger dst ] (x: src): Result dst :=
---   if h: MachineInteger.val x < MachineInteger.size dst then
---     .ret (MachineInteger.ofNatCore (MachineInteger.val x).val h)
---   else
---     .fail integerOverflow
-
--------------
--- VECTORS --
--------------
-
-def Vec (α : Type u) := { l : List α // List.length l <= Usize.max }
-
-def vec_new (α : Type u): Vec α := ⟨ [], by sorry ⟩
-
-def vec_len (α : Type u) (v : Vec α) : Usize :=
-  let ⟨ v, l ⟩ := v
-  Usize.ofIntCore (List.length v) (by sorry) l
- 
-def vec_push_fwd (α : Type u) (_ : Vec α) (_ : α) : Unit := ()
-
-def vec_push_back (α : Type u) (v : Vec α) (x : α) : Result (Vec α)
-  :=
-  if h : List.length v.val <= U32.max || List.length v.val <= Usize.max then
-    return ⟨ List.concat v.val x, by sorry ⟩
-  else
-    fail maximumSizeExceeded
-
-def vec_insert_fwd (α : Type u) (v: Vec α) (i: Usize) (_: α): Result Unit :=
-  if i.val < List.length v.val then
-    .ret ()
-  else
-    .fail arrayOutOfBounds
-
-def vec_insert_back (α : Type u) (v: Vec α) (i: Usize) (x: α): Result (Vec α) :=
-  if i.val < List.length v.val then
-    -- TODO: maybe we should redefine a list library which uses integers
-    -- (instead of natural numbers)
-    let i : Nat :=
-      match i.val with
-      | .ofNat n => n
-      | .negSucc n => by sorry -- TODO: we can't get here
-    let isLt: i < USize.size := by sorry
-    let i : Fin USize.size := { val := i, isLt := isLt }
-    .ret ⟨ List.set v.val i.val x, by
-      have h: List.length v.val <= Usize.max := v.property
-      rewrite [ List.length_set v.val i.val x ]
-      assumption
-    ⟩
-  else
-    .fail arrayOutOfBounds
-
-def vec_index_fwd (α : Type u) (v: Vec α) (i: Usize): Result α :=
-  if i.val < List.length v.val then
-    let i : Nat :=
-      match i.val with
-      | .ofNat n => n
-      | .negSucc n => by sorry -- TODO: we can't get here
-    let isLt: i < USize.size := by sorry
-    let i : Fin USize.size := { val := i, isLt := isLt }
-    let h: i < List.length v.val := by sorry
-    .ret (List.get v.val ⟨i.val, h⟩)
-  else
-    .fail arrayOutOfBounds
-
-def vec_index_back (α : Type u) (v: Vec α) (i: Usize) (_: α): Result Unit :=
-  if i.val < List.length v.val then
-    .ret ()
-  else
-    .fail arrayOutOfBounds
-
-def vec_index_mut_fwd (α : Type u) (v: Vec α) (i: Usize): Result α :=
-  if i.val < List.length v.val then
-    let i : Nat :=
-      match i.val with
-      | .ofNat n => n
-      | .negSucc n => by sorry -- TODO: we can't get here
-    let isLt: i < USize.size := by sorry
-    let i : Fin USize.size := { val := i, isLt := isLt }
-    let h: i < List.length v.val := by sorry
-    .ret (List.get v.val ⟨i.val, h⟩)
-  else
-    .fail arrayOutOfBounds
-
-def vec_index_mut_back (α : Type u) (v: Vec α) (i: Usize) (x: α): Result (Vec α) :=
-  if i.val < List.length v.val then
-    let i : Nat :=
-      match i.val with
-      | .ofNat n => n
-      | .negSucc n => by sorry -- TODO: we can't get here
-    let isLt: i < USize.size := by sorry
-    let i : Fin USize.size := { val := i, isLt := isLt }
-    .ret ⟨ List.set v.val i.val x, by
-      have h: List.length v.val <= Usize.max := v.property
-      rewrite [ List.length_set v.val i.val x ]
-      assumption
-    ⟩
-  else
-    .fail arrayOutOfBounds
-
-----------
--- MISC --
-----------
-
-def mem_replace_fwd (a : Type) (x : a) (_ : a) : a :=
-  x
-
-def mem_replace_back (a : Type) (_ : a) (y : a) : a :=
-  y
-
-/-- Aeneas-translated function -- useful to reduce non-recursive definitions.
- Use with `simp [ aeneas ]` -/
-register_simp_attr aeneas
diff --git a/tests/lean/misc-constants/Constants.lean b/tests/lean/misc-constants/Constants.lean
deleted file mode 100644
index 8306ed85..00000000
--- a/tests/lean/misc-constants/Constants.lean
+++ /dev/null
@@ -1,131 +0,0 @@
--- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
--- [constants]
-import Base.Primitives
-
-/- [constants::X0] -/
-def x0_body : Result U32 := Result.ret (U32.ofInt 0 (by intlit))
-def x0_c : U32 := eval_global x0_body (by simp)
-
-/- [core::num::u32::{9}::MAX] -/
-def core_num_u32_max_body : Result U32 :=
-  Result.ret (U32.ofInt 4294967295 (by intlit))
-def core_num_u32_max_c : U32 := eval_global core_num_u32_max_body (by simp)
-
-/- [constants::X1] -/
-def x1_body : Result U32 := Result.ret core_num_u32_max_c
-def x1_c : U32 := eval_global x1_body (by simp)
-
-/- [constants::X2] -/
-def x2_body : Result U32 := Result.ret (U32.ofInt 3 (by intlit))
-def x2_c : U32 := eval_global x2_body (by simp)
-
-/- [constants::incr] -/
-def incr_fwd (n : U32) : Result U32 :=
-  n + (U32.ofInt 1 (by intlit))
-
-/- [constants::X3] -/
-def x3_body : Result U32 := incr_fwd (U32.ofInt 32 (by intlit))
-def x3_c : U32 := eval_global x3_body (by simp)
-
-/- [constants::mk_pair0] -/
-def mk_pair0_fwd (x : U32) (y : U32) : Result (U32 × U32) :=
-  Result.ret (x, y)
-
-/- [constants::Pair] -/
-structure pair_t (T1 T2 : Type) where
-  pair_x : T1
-  pair_y : T2
-
-/- [constants::mk_pair1] -/
-def mk_pair1_fwd (x : U32) (y : U32) : Result (pair_t U32 U32) :=
-  Result.ret { pair_x := x, pair_y := y }
-
-/- [constants::P0] -/
-def p0_body : Result (U32 × U32) :=
-  mk_pair0_fwd (U32.ofInt 0 (by intlit)) (U32.ofInt 1 (by intlit))
-def p0_c : (U32 × U32) := eval_global p0_body (by simp)
-
-/- [constants::P1] -/
-def p1_body : Result (pair_t U32 U32) :=
-  mk_pair1_fwd (U32.ofInt 0 (by intlit)) (U32.ofInt 1 (by intlit))
-def p1_c : pair_t U32 U32 := eval_global p1_body (by simp)
-
-/- [constants::P2] -/
-def p2_body : Result (U32 × U32) :=
-  Result.ret ((U32.ofInt 0 (by intlit)), (U32.ofInt 1 (by intlit)))
-def p2_c : (U32 × U32) := eval_global p2_body (by simp)
-
-/- [constants::P3] -/
-def p3_body : Result (pair_t U32 U32) :=
-  Result.ret
-  { pair_x := (U32.ofInt 0 (by intlit)), pair_y := (U32.ofInt 1 (by intlit)) }
-def p3_c : pair_t U32 U32 := eval_global p3_body (by simp)
-
-/- [constants::Wrap] -/
-structure wrap_t (T : Type) where
-  wrap_val : T
-
-/- [constants::Wrap::{0}::new] -/
-def wrap_new_fwd (T : Type) (val : T) : Result (wrap_t T) :=
-  Result.ret { wrap_val := val }
-
-/- [constants::Y] -/
-def y_body : Result (wrap_t I32) := wrap_new_fwd I32 (I32.ofInt 2 (by intlit))
-def y_c : wrap_t I32 := eval_global y_body (by simp)
-
-/- [constants::unwrap_y] -/
-def unwrap_y_fwd : Result I32 :=
-  Result.ret y_c.wrap_val
-
-/- [constants::YVAL] -/
-def yval_body : Result I32 := unwrap_y_fwd
-def yval_c : I32 := eval_global yval_body (by simp)
-
-/- [constants::get_z1::Z1] -/
-def get_z1_z1_body : Result I32 := Result.ret (I32.ofInt 3 (by intlit))
-def get_z1_z1_c : I32 := eval_global get_z1_z1_body (by simp)
-
-/- [constants::get_z1] -/
-def get_z1_fwd : Result I32 :=
-  Result.ret get_z1_z1_c
-
-/- [constants::add] -/
-def add_fwd (a : I32) (b : I32) : Result I32 :=
-  a + b
-
-/- [constants::Q1] -/
-def q1_body : Result I32 := Result.ret (I32.ofInt 5 (by intlit))
-def q1_c : I32 := eval_global q1_body (by simp)
-
-/- [constants::Q2] -/
-def q2_body : Result I32 := Result.ret q1_c
-def q2_c : I32 := eval_global q2_body (by simp)
-
-/- [constants::Q3] -/
-def q3_body : Result I32 := add_fwd q2_c (I32.ofInt 3 (by intlit))
-def q3_c : I32 := eval_global q3_body (by simp)
-
-/- [constants::get_z2] -/
-def get_z2_fwd : Result I32 :=
-  do
-    let i ← get_z1_fwd
-    let i0 ← add_fwd i q3_c
-    add_fwd q1_c i0
-
-/- [constants::S1] -/
-def s1_body : Result U32 := Result.ret (U32.ofInt 6 (by intlit))
-def s1_c : U32 := eval_global s1_body (by simp)
-
-/- [constants::S2] -/
-def s2_body : Result U32 := incr_fwd s1_c
-def s2_c : U32 := eval_global s2_body (by simp)
-
-/- [constants::S3] -/
-def s3_body : Result (pair_t U32 U32) := Result.ret p3_c
-def s3_c : pair_t U32 U32 := eval_global s3_body (by simp)
-
-/- [constants::S4] -/
-def s4_body : Result (pair_t U32 U32) :=
-  mk_pair1_fwd (U32.ofInt 7 (by intlit)) (U32.ofInt 8 (by intlit))
-def s4_c : pair_t U32 U32 := eval_global s4_body (by simp)
-
diff --git a/tests/lean/misc-constants/lake-manifest.json b/tests/lean/misc-constants/lake-manifest.json
deleted file mode 100644
index 57b071ca..00000000
--- a/tests/lean/misc-constants/lake-manifest.json
+++ /dev/null
@@ -1,27 +0,0 @@
-{"version": 4,
- "packagesDir": "./lake-packages",
- "packages":
- [{"git":
-   {"url": "https://github.com/leanprover-community/mathlib4.git",
-    "subDir?": null,
-    "rev": "4037792ead804d7bfa8868e2c4684d4223c15ece",
-    "name": "mathlib",
-    "inputRev?": null}},
-  {"git":
-   {"url": "https://github.com/gebner/quote4",
-    "subDir?": null,
-    "rev": "2412c4fdf4a8b689f4467618e5e7b371ae5014aa",
-    "name": "Qq",
-    "inputRev?": "master"}},
-  {"git":
-   {"url": "https://github.com/JLimperg/aesop",
-    "subDir?": null,
-    "rev": "7fe9ecd9339b0e1796e89d243b776849c305c690",
-    "name": "aesop",
-    "inputRev?": "master"}},
-  {"git":
-   {"url": "https://github.com/leanprover/std4",
-    "subDir?": null,
-    "rev": "24897887905b3a1254b244369f5dd2cf6174b0ee",
-    "name": "std",
-    "inputRev?": "main"}}]}
diff --git a/tests/lean/misc-constants/lakefile.lean b/tests/lean/misc-constants/lakefile.lean
deleted file mode 100644
index 01aacb90..00000000
--- a/tests/lean/misc-constants/lakefile.lean
+++ /dev/null
@@ -1,12 +0,0 @@
-import Lake
-open Lake DSL
-
-require mathlib from git
-  "https://github.com/leanprover-community/mathlib4.git"
-
-package «constants» {}
-
-lean_lib «Base» {}
-
-@[default_target]
-lean_lib «Constants» {}
diff --git a/tests/lean/misc-constants/lean-toolchain b/tests/lean/misc-constants/lean-toolchain
deleted file mode 100644
index bbf57f10..00000000
--- a/tests/lean/misc-constants/lean-toolchain
+++ /dev/null
@@ -1 +0,0 @@
-leanprover/lean4:nightly-2023-01-21
diff --git a/tests/lean/misc-external/Base/Primitives.lean b/tests/lean/misc-external/Base/Primitives.lean
deleted file mode 100644
index 4a66a453..00000000
--- a/tests/lean/misc-external/Base/Primitives.lean
+++ /dev/null
@@ -1,583 +0,0 @@
-import Lean
-import Lean.Meta.Tactic.Simp
-import Init.Data.List.Basic
-import Mathlib.Tactic.RunCmd
-
---------------------
--- ASSERT COMMAND --
---------------------
-
-open Lean Elab Command Term Meta
-
-syntax (name := assert) "#assert" term: command
-
-@[command_elab assert]
-unsafe
-def assertImpl : CommandElab := fun (_stx: Syntax) => do
-  runTermElabM (fun _ => do
-    let r ← evalTerm Bool (mkConst ``Bool) _stx[1]
-    if not r then
-      logInfo "Assertion failed for: "
-      logInfo _stx[1]
-      logError "Expression reduced to false"
-    pure ())
-
-#eval 2 == 2
-#assert (2 == 2)
-
--------------
--- PRELUDE --
--------------
-
--- Results & monadic combinators
-
-inductive Error where
-   | assertionFailure: Error
-   | integerOverflow: Error
-   | divisionByZero: Error
-   | arrayOutOfBounds: Error
-   | maximumSizeExceeded: Error
-   | panic: Error
-deriving Repr, BEq
-
-open Error
-
-inductive Result (α : Type u) where
-  | ret (v: α): Result α
-  | fail (e: Error): Result α
-deriving Repr, BEq
-
-open Result
-
-instance Result_Inhabited (α : Type u) : Inhabited (Result α) :=
-  Inhabited.mk (fail panic)
-
-/- HELPERS -/
-
-def ret? {α: Type} (r: Result α): Bool :=
-  match r with
-  | Result.ret _ => true
-  | Result.fail _ => false
-
-def massert (b:Bool) : Result Unit :=
-  if b then .ret () else fail assertionFailure
-
-def eval_global {α: Type} (x: Result α) (_: ret? x): α :=
-  match x with
-  | Result.fail _ => by contradiction
-  | Result.ret x => x
-
-/- DO-DSL SUPPORT -/
-
-def bind (x: Result α) (f: α -> Result β) : Result β :=
-  match x with
-  | ret v  => f v 
-  | fail v => fail v
-
--- Allows using Result in do-blocks
-instance : Bind Result where
-  bind := bind
-
--- Allows using return x in do-blocks
-instance : Pure Result where
-  pure := fun x => ret x
-
-/- CUSTOM-DSL SUPPORT -/
-
--- Let-binding the Result of a monadic operation is oftentimes not sufficient,
--- because we may need a hypothesis for equational reasoning in the scope. We
--- rely on subtype, and a custom let-binding operator, in effect recreating our
--- own variant of the do-dsl
-
-def Result.attach {α: Type} (o : Result α): Result { x : α // o = ret x } :=
-  match o with
-  | .ret x => .ret ⟨x, rfl⟩
-  | .fail e => .fail e
-
-macro "let" e:term " ⟵ " f:term : doElem =>
-  `(doElem| let ⟨$e, h⟩ ← Result.attach $f)
-
--- TODO: any way to factorize both definitions?
-macro "let" e:term " <-- " f:term : doElem =>
-  `(doElem| let ⟨$e, h⟩ ← Result.attach $f)
-
--- We call the hypothesis `h`, in effect making it unavailable to the user
--- (because too much shadowing). But in practice, once can use the French single
--- quote notation (input with f< and f>), where `‹ h ›` finds a suitable
--- hypothesis in the context, this is equivalent to `have x: h := by assumption in x`
-#eval do
-  let y <-- .ret (0: Nat)
-  let _: y = 0 := by cases ‹ ret 0 = ret y › ; decide
-  let r: { x: Nat // x = 0 } := ⟨ y, by assumption ⟩
-  .ret r
-
-----------------------
--- MACHINE INTEGERS --
-----------------------
-
--- We redefine our machine integers types.
-
--- For Isize/Usize, we reuse `getNumBits` from `USize`. You cannot reduce `getNumBits`
--- using the simplifier, meaning that proofs do not depend on the compile-time value of
--- USize.size. (Lean assumes 32 or 64-bit platforms, and Rust doesn't really support, at
--- least officially, 16-bit microcontrollers, so this seems like a fine design decision
--- for now.)
-
--- Note from Chris Bailey: "If there's more than one salient property of your
--- definition then the subtyping strategy might get messy, and the property part
--- of a subtype is less discoverable by the simplifier or tactics like
--- library_search." So, we will not add refinements on the return values of the
--- operations defined on Primitives, but will rather rely on custom lemmas to
--- invert on possible return values of the primitive operations.
-
--- Machine integer constants, done via `ofNatCore`, which requires a proof that
--- the `Nat` fits within the desired integer type. We provide a custom tactic.
-
-open System.Platform.getNumBits
-
--- TODO: is there a way of only importing System.Platform.getNumBits?
---
-@[simp] def size_num_bits : Nat := (System.Platform.getNumBits ()).val
-
--- Remark: Lean seems to use < for the comparisons with the upper bounds by convention.
--- We keep the F* convention for now.
-@[simp] def Isize.min : Int := - (HPow.hPow 2 (size_num_bits - 1))
-@[simp] def Isize.max : Int := (HPow.hPow 2 (size_num_bits - 1)) - 1
-@[simp] def I8.min    : Int := - (HPow.hPow 2 7)
-@[simp] def I8.max    : Int := HPow.hPow 2 7 - 1
-@[simp] def I16.min   : Int := - (HPow.hPow 2 15)
-@[simp] def I16.max   : Int := HPow.hPow 2 15 - 1
-@[simp] def I32.min   : Int := -(HPow.hPow 2 31)
-@[simp] def I32.max   : Int := HPow.hPow 2 31 - 1
-@[simp] def I64.min   : Int := -(HPow.hPow 2 63)
-@[simp] def I64.max   : Int := HPow.hPow 2 63 - 1
-@[simp] def I128.min  : Int := -(HPow.hPow 2 127)
-@[simp] def I128.max  : Int := HPow.hPow 2 127 - 1
-@[simp] def Usize.min : Int := 0
-@[simp] def Usize.max : Int := HPow.hPow 2 size_num_bits - 1
-@[simp] def U8.min    : Int := 0
-@[simp] def U8.max    : Int := HPow.hPow 2 8 - 1
-@[simp] def U16.min   : Int := 0
-@[simp] def U16.max   : Int := HPow.hPow 2 16 - 1
-@[simp] def U32.min   : Int := 0
-@[simp] def U32.max   : Int := HPow.hPow 2 32 - 1
-@[simp] def U64.min   : Int := 0
-@[simp] def U64.max   : Int := HPow.hPow 2 64 - 1
-@[simp] def U128.min  : Int := 0
-@[simp] def U128.max  : Int := HPow.hPow 2 128 - 1
-
-#assert (I8.min   == -128)
-#assert (I8.max   == 127)
-#assert (I16.min  == -32768)
-#assert (I16.max  == 32767)
-#assert (I32.min  == -2147483648)
-#assert (I32.max  == 2147483647)
-#assert (I64.min  == -9223372036854775808)
-#assert (I64.max  == 9223372036854775807)
-#assert (I128.min == -170141183460469231731687303715884105728)
-#assert (I128.max == 170141183460469231731687303715884105727)
-#assert (U8.min   == 0)
-#assert (U8.max   == 255)
-#assert (U16.min  == 0)
-#assert (U16.max  == 65535)
-#assert (U32.min  == 0)
-#assert (U32.max  == 4294967295)
-#assert (U64.min  == 0)
-#assert (U64.max  == 18446744073709551615)
-#assert (U128.min == 0)
-#assert (U128.max == 340282366920938463463374607431768211455)
-
-inductive ScalarTy :=
-| Isize
-| I8
-| I16
-| I32
-| I64
-| I128
-| Usize
-| U8
-| U16
-| U32
-| U64
-| U128
-
-def Scalar.min (ty : ScalarTy) : Int :=
-  match ty with
-  | .Isize => Isize.min
-  | .I8    => I8.min
-  | .I16   => I16.min
-  | .I32   => I32.min
-  | .I64   => I64.min
-  | .I128  => I128.min
-  | .Usize => Usize.min
-  | .U8    => U8.min
-  | .U16   => U16.min
-  | .U32   => U32.min
-  | .U64   => U64.min
-  | .U128  => U128.min
-
-def Scalar.max (ty : ScalarTy) : Int :=
-  match ty with
-  | .Isize => Isize.max
-  | .I8    => I8.max
-  | .I16   => I16.max
-  | .I32   => I32.max
-  | .I64   => I64.max
-  | .I128  => I128.max
-  | .Usize => Usize.max
-  | .U8    => U8.max
-  | .U16   => U16.max
-  | .U32   => U32.max
-  | .U64   => U64.max
-  | .U128  => U128.max
-
--- "Conservative" bounds
--- We use those because we can't compare to the isize bounds (which can't
--- reduce at compile-time). Whenever we perform an arithmetic operation like
--- addition we need to check that the result is in bounds: we first compare
--- to the conservative bounds, which reduce, then compare to the real bounds.
--- This is useful for the various #asserts that we want to reduce at
--- type-checking time.
-def Scalar.cMin (ty : ScalarTy) : Int :=
-  match ty with
-  | .Isize => I32.min
-  | _ => Scalar.min ty
-
-def Scalar.cMax (ty : ScalarTy) : Int :=
-  match ty with
-  | .Isize => I32.max
-  | .Usize => U32.max
-  | _ => Scalar.max ty
-
-theorem Scalar.cMin_bound ty : Scalar.min ty <= Scalar.cMin ty := by sorry
-theorem Scalar.cMax_bound ty : Scalar.min ty <= Scalar.cMin ty := by sorry
-
-structure Scalar (ty : ScalarTy) where
-  val : Int
-  hmin : Scalar.min ty <= val
-  hmax : val <= Scalar.max ty
-
-theorem Scalar.bound_suffices (ty : ScalarTy) (x : Int) :
-  Scalar.cMin ty <= x && x <= Scalar.cMax ty ->
-  (decide (Scalar.min ty ≤ x) && decide (x ≤ Scalar.max ty)) = true
-  := by sorry
-
-def Scalar.ofIntCore {ty : ScalarTy} (x : Int)
-  (hmin : Scalar.min ty <= x) (hmax : x <= Scalar.max ty) : Scalar ty :=
-  { val := x, hmin := hmin, hmax := hmax }
-
-def Scalar.ofInt {ty : ScalarTy} (x : Int)
-  (h : Scalar.min ty <= x && x <= Scalar.max ty) : Scalar ty :=
-  let hmin: Scalar.min ty <= x := by sorry
-  let hmax: x <= Scalar.max ty := by sorry
-  Scalar.ofIntCore x hmin hmax
-
--- Further thoughts: look at what has been done here:
--- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/Fin/Basic.lean
--- and
--- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/UInt.lean
--- which both contain a fair amount of reasoning already!
-def Scalar.tryMk (ty : ScalarTy) (x : Int) : Result (Scalar ty) :=
-  -- TODO: write this with only one if then else
-  if hmin_cons: Scalar.cMin ty <= x || Scalar.min ty <= x then
-    if hmax_cons: x <= Scalar.cMax ty || x <= Scalar.max ty then
-      let hmin: Scalar.min ty <= x := by sorry
-      let hmax: x <= Scalar.max ty := by sorry
-      return Scalar.ofIntCore x hmin hmax
-    else fail integerOverflow
-  else fail integerOverflow
-
-def Scalar.neg {ty : ScalarTy} (x : Scalar ty) : Result (Scalar ty) := Scalar.tryMk ty (- x.val)
-
-def Scalar.div {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
-  if y.val != 0 then Scalar.tryMk ty (x.val / y.val) else fail divisionByZero
-
--- Checking that the % operation in Lean computes the same as the remainder operation in Rust
-#assert 1 % 2 = (1:Int)
-#assert (-1) % 2 = -1
-#assert 1 % (-2) = 1
-#assert (-1) % (-2) = -1
-
-def Scalar.rem {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
-  if y.val != 0 then Scalar.tryMk ty (x.val % y.val) else fail divisionByZero
-
-def Scalar.add {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
-  Scalar.tryMk ty (x.val + y.val)
-
-def Scalar.sub {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
-  Scalar.tryMk ty (x.val - y.val)
-
-def Scalar.mul {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
-  Scalar.tryMk ty (x.val * y.val)
-
--- TODO: instances of +, -, * etc. for scalars
-
--- Cast an integer from a [src_ty] to a [tgt_ty]
--- TODO: check the semantics of casts in Rust
-def Scalar.cast {src_ty : ScalarTy} (tgt_ty : ScalarTy) (x : Scalar src_ty) : Result (Scalar tgt_ty) :=
-  Scalar.tryMk tgt_ty x.val
-
--- The scalar types
--- We declare the definitions as reducible so that Lean can unfold them (useful
--- for type class resolution for instance).
-@[reducible] def Isize := Scalar .Isize
-@[reducible] def I8    := Scalar .I8
-@[reducible] def I16   := Scalar .I16
-@[reducible] def I32   := Scalar .I32
-@[reducible] def I64   := Scalar .I64
-@[reducible] def I128  := Scalar .I128
-@[reducible] def Usize := Scalar .Usize
-@[reducible] def U8    := Scalar .U8
-@[reducible] def U16   := Scalar .U16
-@[reducible] def U32   := Scalar .U32
-@[reducible] def U64   := Scalar .U64
-@[reducible] def U128  := Scalar .U128
-
--- TODO: below: not sure this is the best way.
--- Should we rather overload operations like +, -, etc.?
--- Also, it is possible to automate the generation of those definitions
--- with macros (but would it be a good idea? It would be less easy to
--- read the file, which is not supposed to change a lot)
-
--- Negation
-
-/--
-Remark: there is no heterogeneous negation in the Lean prelude: we thus introduce
-one here.
-
-The notation typeclass for heterogeneous addition.
-This enables the notation `- a : β` where `a : α`.
--/
-class HNeg (α : Type u) (β : outParam (Type v)) where
-  /-- `- a` computes the negation of `a`.
-  The meaning of this notation is type-dependent. -/
-  hNeg : α → β
-
-prefix:75  "-"   => HNeg.hNeg
-
-instance : HNeg Isize (Result Isize) where hNeg x := Scalar.neg x
-instance : HNeg I8 (Result I8) where hNeg x := Scalar.neg x
-instance : HNeg I16 (Result I16) where hNeg x := Scalar.neg x
-instance : HNeg I32 (Result I32) where hNeg x := Scalar.neg x
-instance : HNeg I64 (Result I64) where hNeg x := Scalar.neg x
-instance : HNeg I128 (Result I128) where hNeg x := Scalar.neg x
-
--- Addition
-instance {ty} : HAdd (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
-  hAdd x y := Scalar.add x y
-
--- Substraction
-instance {ty} : HSub (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
-  hSub x y := Scalar.sub x y
-
--- Multiplication
-instance {ty} : HMul (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
-  hMul x y := Scalar.mul x y
-
--- Division
-instance {ty} : HDiv (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
-  hDiv x y := Scalar.div x y
-
--- Remainder
-instance {ty} : HMod (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
-  hMod x y := Scalar.rem x y
-
--- ofIntCore
--- TODO: typeclass?
-def Isize.ofIntCore := @Scalar.ofIntCore .Isize
-def I8.ofIntCore    := @Scalar.ofIntCore .I8
-def I16.ofIntCore   := @Scalar.ofIntCore .I16
-def I32.ofIntCore   := @Scalar.ofIntCore .I32
-def I64.ofIntCore   := @Scalar.ofIntCore .I64
-def I128.ofIntCore  := @Scalar.ofIntCore .I128
-def Usize.ofIntCore := @Scalar.ofIntCore .Usize
-def U8.ofIntCore    := @Scalar.ofIntCore .U8
-def U16.ofIntCore   := @Scalar.ofIntCore .U16
-def U32.ofIntCore   := @Scalar.ofIntCore .U32
-def U64.ofIntCore   := @Scalar.ofIntCore .U64
-def U128.ofIntCore  := @Scalar.ofIntCore .U128
-
---  ofInt
--- TODO: typeclass?
-def Isize.ofInt := @Scalar.ofInt .Isize
-def I8.ofInt    := @Scalar.ofInt .I8
-def I16.ofInt   := @Scalar.ofInt .I16
-def I32.ofInt   := @Scalar.ofInt .I32
-def I64.ofInt   := @Scalar.ofInt .I64
-def I128.ofInt  := @Scalar.ofInt .I128
-def Usize.ofInt := @Scalar.ofInt .Usize
-def U8.ofInt    := @Scalar.ofInt .U8
-def U16.ofInt   := @Scalar.ofInt .U16
-def U32.ofInt   := @Scalar.ofInt .U32
-def U64.ofInt   := @Scalar.ofInt .U64
-def U128.ofInt  := @Scalar.ofInt .U128
-
--- Comparisons
-instance {ty} : LT (Scalar ty) where
-  lt a b := LT.lt a.val b.val
-
-instance {ty} : LE (Scalar ty) where le a b := LE.le a.val b.val
-
-instance Scalar.decLt {ty} (a b : Scalar ty) : Decidable (LT.lt a b) := Int.decLt ..
-instance Scalar.decLe {ty} (a b : Scalar ty) : Decidable (LE.le a b) := Int.decLe ..
-
-theorem Scalar.eq_of_val_eq {ty} : ∀ {i j : Scalar ty}, Eq i.val j.val → Eq i j
-  | ⟨_, _, _⟩, ⟨_, _, _⟩, rfl => rfl
-
-theorem Scalar.val_eq_of_eq {ty} {i j : Scalar ty} (h : Eq i j) : Eq i.val j.val :=
-  h ▸ rfl
-
-theorem Scalar.ne_of_val_ne {ty} {i j : Scalar ty} (h : Not (Eq i.val j.val)) : Not (Eq i j) :=
-  fun h' => absurd (val_eq_of_eq h') h
-
-instance (ty : ScalarTy) : DecidableEq (Scalar ty) :=
-  fun i j =>
-    match decEq i.val j.val with
-    | isTrue h  => isTrue (Scalar.eq_of_val_eq h)
-    | isFalse h => isFalse (Scalar.ne_of_val_ne h)
-
-def Scalar.toInt {ty} (n : Scalar ty) : Int := n.val
-
--- Tactic to prove that integers are in bounds
-syntax "intlit" : tactic
-
-macro_rules
-  | `(tactic| intlit) => `(tactic| apply Scalar.bound_suffices ; decide)
-
--- -- We now define a type class that subsumes the various machine integer types, so
--- -- as to write a concise definition for scalar_cast, rather than exhaustively
--- -- enumerating all of the possible pairs. We remark that Rust has sane semantics
--- -- and fails if a cast operation would involve a truncation or modulo.
-
--- class MachineInteger (t: Type) where
---   size: Nat
---   val: t -> Fin size
---   ofNatCore: (n:Nat) -> LT.lt n size -> t
-
--- set_option hygiene false in
--- run_cmd
---   for typeName in [`UInt8, `UInt16, `UInt32, `UInt64, `USize].map Lean.mkIdent do
---   Lean.Elab.Command.elabCommand (← `(
---     namespace $typeName
---     instance: MachineInteger $typeName where
---       size := size
---       val := val
---       ofNatCore := ofNatCore
---     end $typeName
---   ))
-
--- -- Aeneas only instantiates the destination type (`src` is implicit). We rely on
--- -- Lean to infer `src`.
-
--- def scalar_cast { src: Type } (dst: Type) [ MachineInteger src ] [ MachineInteger dst ] (x: src): Result dst :=
---   if h: MachineInteger.val x < MachineInteger.size dst then
---     .ret (MachineInteger.ofNatCore (MachineInteger.val x).val h)
---   else
---     .fail integerOverflow
-
--------------
--- VECTORS --
--------------
-
-def Vec (α : Type u) := { l : List α // List.length l <= Usize.max }
-
-def vec_new (α : Type u): Vec α := ⟨ [], by sorry ⟩
-
-def vec_len (α : Type u) (v : Vec α) : Usize :=
-  let ⟨ v, l ⟩ := v
-  Usize.ofIntCore (List.length v) (by sorry) l
- 
-def vec_push_fwd (α : Type u) (_ : Vec α) (_ : α) : Unit := ()
-
-def vec_push_back (α : Type u) (v : Vec α) (x : α) : Result (Vec α)
-  :=
-  if h : List.length v.val <= U32.max || List.length v.val <= Usize.max then
-    return ⟨ List.concat v.val x, by sorry ⟩
-  else
-    fail maximumSizeExceeded
-
-def vec_insert_fwd (α : Type u) (v: Vec α) (i: Usize) (_: α): Result Unit :=
-  if i.val < List.length v.val then
-    .ret ()
-  else
-    .fail arrayOutOfBounds
-
-def vec_insert_back (α : Type u) (v: Vec α) (i: Usize) (x: α): Result (Vec α) :=
-  if i.val < List.length v.val then
-    -- TODO: maybe we should redefine a list library which uses integers
-    -- (instead of natural numbers)
-    let i : Nat :=
-      match i.val with
-      | .ofNat n => n
-      | .negSucc n => by sorry -- TODO: we can't get here
-    let isLt: i < USize.size := by sorry
-    let i : Fin USize.size := { val := i, isLt := isLt }
-    .ret ⟨ List.set v.val i.val x, by
-      have h: List.length v.val <= Usize.max := v.property
-      rewrite [ List.length_set v.val i.val x ]
-      assumption
-    ⟩
-  else
-    .fail arrayOutOfBounds
-
-def vec_index_fwd (α : Type u) (v: Vec α) (i: Usize): Result α :=
-  if i.val < List.length v.val then
-    let i : Nat :=
-      match i.val with
-      | .ofNat n => n
-      | .negSucc n => by sorry -- TODO: we can't get here
-    let isLt: i < USize.size := by sorry
-    let i : Fin USize.size := { val := i, isLt := isLt }
-    let h: i < List.length v.val := by sorry
-    .ret (List.get v.val ⟨i.val, h⟩)
-  else
-    .fail arrayOutOfBounds
-
-def vec_index_back (α : Type u) (v: Vec α) (i: Usize) (_: α): Result Unit :=
-  if i.val < List.length v.val then
-    .ret ()
-  else
-    .fail arrayOutOfBounds
-
-def vec_index_mut_fwd (α : Type u) (v: Vec α) (i: Usize): Result α :=
-  if i.val < List.length v.val then
-    let i : Nat :=
-      match i.val with
-      | .ofNat n => n
-      | .negSucc n => by sorry -- TODO: we can't get here
-    let isLt: i < USize.size := by sorry
-    let i : Fin USize.size := { val := i, isLt := isLt }
-    let h: i < List.length v.val := by sorry
-    .ret (List.get v.val ⟨i.val, h⟩)
-  else
-    .fail arrayOutOfBounds
-
-def vec_index_mut_back (α : Type u) (v: Vec α) (i: Usize) (x: α): Result (Vec α) :=
-  if i.val < List.length v.val then
-    let i : Nat :=
-      match i.val with
-      | .ofNat n => n
-      | .negSucc n => by sorry -- TODO: we can't get here
-    let isLt: i < USize.size := by sorry
-    let i : Fin USize.size := { val := i, isLt := isLt }
-    .ret ⟨ List.set v.val i.val x, by
-      have h: List.length v.val <= Usize.max := v.property
-      rewrite [ List.length_set v.val i.val x ]
-      assumption
-    ⟩
-  else
-    .fail arrayOutOfBounds
-
-----------
--- MISC --
-----------
-
-def mem_replace_fwd (a : Type) (x : a) (_ : a) : a :=
-  x
-
-def mem_replace_back (a : Type) (_ : a) (y : a) : a :=
-  y
-
-/-- Aeneas-translated function -- useful to reduce non-recursive definitions.
- Use with `simp [ aeneas ]` -/
-register_simp_attr aeneas
diff --git a/tests/lean/misc-external/External/ExternalFuns.lean b/tests/lean/misc-external/External/ExternalFuns.lean
deleted file mode 100644
index 6bd4f4a9..00000000
--- a/tests/lean/misc-external/External/ExternalFuns.lean
+++ /dev/null
@@ -1,5 +0,0 @@
-import Base.Primitives
-import External.Types
-import External.Opaque
-
-def opaque_defs : OpaqueDefs := sorry
diff --git a/tests/lean/misc-external/External/Funs.lean b/tests/lean/misc-external/External/Funs.lean
deleted file mode 100644
index eeb83989..00000000
--- a/tests/lean/misc-external/External/Funs.lean
+++ /dev/null
@@ -1,84 +0,0 @@
--- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
--- [external]: function definitions
-import Base.Primitives
-import External.Types
-import External.ExternalFuns
-
-/- [external::swap] -/
-def swap_fwd
-  (T : Type) (x : T) (y : T) (st : State) : Result (State × Unit) :=
-  do
-    let (st0, _) ← opaque_defs.core_mem_swap_fwd T x y st
-    let (st1, _) ← opaque_defs.core_mem_swap_back0 T x y st st0
-    let (st2, _) ← opaque_defs.core_mem_swap_back1 T x y st st1
-    Result.ret (st2, ())
-
-/- [external::swap] -/
-def swap_back
-  (T : Type) (x : T) (y : T) (st : State) (st0 : State) :
-  Result (State × (T × T))
-  :=
-  do
-    let (st1, _) ← opaque_defs.core_mem_swap_fwd T x y st
-    let (st2, x0) ← opaque_defs.core_mem_swap_back0 T x y st st1
-    let (_, y0) ← opaque_defs.core_mem_swap_back1 T x y st st2
-    Result.ret (st0, (x0, y0))
-
-/- [external::test_new_non_zero_u32] -/
-def test_new_non_zero_u32_fwd
-  (x : U32) (st : State) : Result (State × core_num_nonzero_non_zero_u32_t) :=
-  do
-    let (st0, opt) ← opaque_defs.core_num_nonzero_non_zero_u32_new_fwd x st
-    opaque_defs.core_option_option_unwrap_fwd core_num_nonzero_non_zero_u32_t
-      opt st0
-
-/- [external::test_vec] -/
-def test_vec_fwd : Result Unit :=
-  do
-    let v := vec_new U32
-    let _ ← vec_push_back U32 v (U32.ofInt 0 (by intlit))
-    Result.ret ()
-
-/- [external::custom_swap] -/
-def custom_swap_fwd
-  (T : Type) (x : T) (y : T) (st : State) : Result (State × T) :=
-  do
-    let (st0, _) ← opaque_defs.core_mem_swap_fwd T x y st
-    let (st1, x0) ← opaque_defs.core_mem_swap_back0 T x y st st0
-    let (st2, _) ← opaque_defs.core_mem_swap_back1 T x y st st1
-    Result.ret (st2, x0)
-
-/- [external::custom_swap] -/
-def custom_swap_back
-  (T : Type) (x : T) (y : T) (st : State) (ret0 : T) (st0 : State) :
-  Result (State × (T × T))
-  :=
-  do
-    let (st1, _) ← opaque_defs.core_mem_swap_fwd T x y st
-    let (st2, _) ← opaque_defs.core_mem_swap_back0 T x y st st1
-    let (_, y0) ← opaque_defs.core_mem_swap_back1 T x y st st2
-    Result.ret (st0, (ret0, y0))
-
-/- [external::test_custom_swap] -/
-def test_custom_swap_fwd
-  (x : U32) (y : U32) (st : State) : Result (State × Unit) :=
-  do
-    let (st0, _) ← custom_swap_fwd U32 x y st
-    Result.ret (st0, ())
-
-/- [external::test_custom_swap] -/
-def test_custom_swap_back
-  (x : U32) (y : U32) (st : State) (st0 : State) :
-  Result (State × (U32 × U32))
-  :=
-  custom_swap_back U32 x y st (U32.ofInt 1 (by intlit)) st0
-
-/- [external::test_swap_non_zero] -/
-def test_swap_non_zero_fwd (x : U32) (st : State) : Result (State × U32) :=
-  do
-    let (st0, _) ← swap_fwd U32 x (U32.ofInt 0 (by intlit)) st
-    let (st1, (x0, _)) ← swap_back U32 x (U32.ofInt 0 (by intlit)) st st0
-    if h: x0 = (U32.ofInt 0 (by intlit))
-    then Result.fail Error.panic
-    else Result.ret (st1, x0)
-
diff --git a/tests/lean/misc-external/External/Opaque.lean b/tests/lean/misc-external/External/Opaque.lean
deleted file mode 100644
index d641912b..00000000
--- a/tests/lean/misc-external/External/Opaque.lean
+++ /dev/null
@@ -1,27 +0,0 @@
--- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
--- [external]: opaque function definitions
-import Base.Primitives
-import External.Types
-
-structure OpaqueDefs where
-  
-  /- [core::mem::swap] -/
-  core_mem_swap_fwd (T : Type) : T -> T -> State -> Result (State × Unit)
-  
-  /- [core::mem::swap] -/
-  core_mem_swap_back0
-    (T : Type) : T -> T -> State -> State -> Result (State × T)
-  
-  /- [core::mem::swap] -/
-  core_mem_swap_back1
-    (T : Type) : T -> T -> State -> State -> Result (State × T)
-  
-  /- [core::num::nonzero::NonZeroU32::{14}::new] -/
-  core_num_nonzero_non_zero_u32_new_fwd
-    :
-    U32 -> State -> Result (State × (Option core_num_nonzero_non_zero_u32_t))
-  
-  /- [core::option::Option::{0}::unwrap] -/
-  core_option_option_unwrap_fwd
-    (T : Type) : Option T -> State -> Result (State × T)
-  
diff --git a/tests/lean/misc-external/lake-manifest.json b/tests/lean/misc-external/lake-manifest.json
deleted file mode 100644
index 57b071ca..00000000
--- a/tests/lean/misc-external/lake-manifest.json
+++ /dev/null
@@ -1,27 +0,0 @@
-{"version": 4,
- "packagesDir": "./lake-packages",
- "packages":
- [{"git":
-   {"url": "https://github.com/leanprover-community/mathlib4.git",
-    "subDir?": null,
-    "rev": "4037792ead804d7bfa8868e2c4684d4223c15ece",
-    "name": "mathlib",
-    "inputRev?": null}},
-  {"git":
-   {"url": "https://github.com/gebner/quote4",
-    "subDir?": null,
-    "rev": "2412c4fdf4a8b689f4467618e5e7b371ae5014aa",
-    "name": "Qq",
-    "inputRev?": "master"}},
-  {"git":
-   {"url": "https://github.com/JLimperg/aesop",
-    "subDir?": null,
-    "rev": "7fe9ecd9339b0e1796e89d243b776849c305c690",
-    "name": "aesop",
-    "inputRev?": "master"}},
-  {"git":
-   {"url": "https://github.com/leanprover/std4",
-    "subDir?": null,
-    "rev": "24897887905b3a1254b244369f5dd2cf6174b0ee",
-    "name": "std",
-    "inputRev?": "main"}}]}
diff --git a/tests/lean/misc-external/lakefile.lean b/tests/lean/misc-external/lakefile.lean
deleted file mode 100644
index 6cc4aae4..00000000
--- a/tests/lean/misc-external/lakefile.lean
+++ /dev/null
@@ -1,12 +0,0 @@
-import Lake
-open Lake DSL
-
-require mathlib from git
-  "https://github.com/leanprover-community/mathlib4.git"
-
-package «external» {}
-
-lean_lib «Base» {}
-
-@[default_target]
-lean_lib «External» {}
diff --git a/tests/lean/misc-external/lean-toolchain b/tests/lean/misc-external/lean-toolchain
deleted file mode 100644
index bbf57f10..00000000
--- a/tests/lean/misc-external/lean-toolchain
+++ /dev/null
@@ -1 +0,0 @@
-leanprover/lean4:nightly-2023-01-21
diff --git a/tests/lean/misc-loops/Base/Primitives.lean b/tests/lean/misc-loops/Base/Primitives.lean
deleted file mode 100644
index 4a66a453..00000000
--- a/tests/lean/misc-loops/Base/Primitives.lean
+++ /dev/null
@@ -1,583 +0,0 @@
-import Lean
-import Lean.Meta.Tactic.Simp
-import Init.Data.List.Basic
-import Mathlib.Tactic.RunCmd
-
---------------------
--- ASSERT COMMAND --
---------------------
-
-open Lean Elab Command Term Meta
-
-syntax (name := assert) "#assert" term: command
-
-@[command_elab assert]
-unsafe
-def assertImpl : CommandElab := fun (_stx: Syntax) => do
-  runTermElabM (fun _ => do
-    let r ← evalTerm Bool (mkConst ``Bool) _stx[1]
-    if not r then
-      logInfo "Assertion failed for: "
-      logInfo _stx[1]
-      logError "Expression reduced to false"
-    pure ())
-
-#eval 2 == 2
-#assert (2 == 2)
-
--------------
--- PRELUDE --
--------------
-
--- Results & monadic combinators
-
-inductive Error where
-   | assertionFailure: Error
-   | integerOverflow: Error
-   | divisionByZero: Error
-   | arrayOutOfBounds: Error
-   | maximumSizeExceeded: Error
-   | panic: Error
-deriving Repr, BEq
-
-open Error
-
-inductive Result (α : Type u) where
-  | ret (v: α): Result α
-  | fail (e: Error): Result α
-deriving Repr, BEq
-
-open Result
-
-instance Result_Inhabited (α : Type u) : Inhabited (Result α) :=
-  Inhabited.mk (fail panic)
-
-/- HELPERS -/
-
-def ret? {α: Type} (r: Result α): Bool :=
-  match r with
-  | Result.ret _ => true
-  | Result.fail _ => false
-
-def massert (b:Bool) : Result Unit :=
-  if b then .ret () else fail assertionFailure
-
-def eval_global {α: Type} (x: Result α) (_: ret? x): α :=
-  match x with
-  | Result.fail _ => by contradiction
-  | Result.ret x => x
-
-/- DO-DSL SUPPORT -/
-
-def bind (x: Result α) (f: α -> Result β) : Result β :=
-  match x with
-  | ret v  => f v 
-  | fail v => fail v
-
--- Allows using Result in do-blocks
-instance : Bind Result where
-  bind := bind
-
--- Allows using return x in do-blocks
-instance : Pure Result where
-  pure := fun x => ret x
-
-/- CUSTOM-DSL SUPPORT -/
-
--- Let-binding the Result of a monadic operation is oftentimes not sufficient,
--- because we may need a hypothesis for equational reasoning in the scope. We
--- rely on subtype, and a custom let-binding operator, in effect recreating our
--- own variant of the do-dsl
-
-def Result.attach {α: Type} (o : Result α): Result { x : α // o = ret x } :=
-  match o with
-  | .ret x => .ret ⟨x, rfl⟩
-  | .fail e => .fail e
-
-macro "let" e:term " ⟵ " f:term : doElem =>
-  `(doElem| let ⟨$e, h⟩ ← Result.attach $f)
-
--- TODO: any way to factorize both definitions?
-macro "let" e:term " <-- " f:term : doElem =>
-  `(doElem| let ⟨$e, h⟩ ← Result.attach $f)
-
--- We call the hypothesis `h`, in effect making it unavailable to the user
--- (because too much shadowing). But in practice, once can use the French single
--- quote notation (input with f< and f>), where `‹ h ›` finds a suitable
--- hypothesis in the context, this is equivalent to `have x: h := by assumption in x`
-#eval do
-  let y <-- .ret (0: Nat)
-  let _: y = 0 := by cases ‹ ret 0 = ret y › ; decide
-  let r: { x: Nat // x = 0 } := ⟨ y, by assumption ⟩
-  .ret r
-
-----------------------
--- MACHINE INTEGERS --
-----------------------
-
--- We redefine our machine integers types.
-
--- For Isize/Usize, we reuse `getNumBits` from `USize`. You cannot reduce `getNumBits`
--- using the simplifier, meaning that proofs do not depend on the compile-time value of
--- USize.size. (Lean assumes 32 or 64-bit platforms, and Rust doesn't really support, at
--- least officially, 16-bit microcontrollers, so this seems like a fine design decision
--- for now.)
-
--- Note from Chris Bailey: "If there's more than one salient property of your
--- definition then the subtyping strategy might get messy, and the property part
--- of a subtype is less discoverable by the simplifier or tactics like
--- library_search." So, we will not add refinements on the return values of the
--- operations defined on Primitives, but will rather rely on custom lemmas to
--- invert on possible return values of the primitive operations.
-
--- Machine integer constants, done via `ofNatCore`, which requires a proof that
--- the `Nat` fits within the desired integer type. We provide a custom tactic.
-
-open System.Platform.getNumBits
-
--- TODO: is there a way of only importing System.Platform.getNumBits?
---
-@[simp] def size_num_bits : Nat := (System.Platform.getNumBits ()).val
-
--- Remark: Lean seems to use < for the comparisons with the upper bounds by convention.
--- We keep the F* convention for now.
-@[simp] def Isize.min : Int := - (HPow.hPow 2 (size_num_bits - 1))
-@[simp] def Isize.max : Int := (HPow.hPow 2 (size_num_bits - 1)) - 1
-@[simp] def I8.min    : Int := - (HPow.hPow 2 7)
-@[simp] def I8.max    : Int := HPow.hPow 2 7 - 1
-@[simp] def I16.min   : Int := - (HPow.hPow 2 15)
-@[simp] def I16.max   : Int := HPow.hPow 2 15 - 1
-@[simp] def I32.min   : Int := -(HPow.hPow 2 31)
-@[simp] def I32.max   : Int := HPow.hPow 2 31 - 1
-@[simp] def I64.min   : Int := -(HPow.hPow 2 63)
-@[simp] def I64.max   : Int := HPow.hPow 2 63 - 1
-@[simp] def I128.min  : Int := -(HPow.hPow 2 127)
-@[simp] def I128.max  : Int := HPow.hPow 2 127 - 1
-@[simp] def Usize.min : Int := 0
-@[simp] def Usize.max : Int := HPow.hPow 2 size_num_bits - 1
-@[simp] def U8.min    : Int := 0
-@[simp] def U8.max    : Int := HPow.hPow 2 8 - 1
-@[simp] def U16.min   : Int := 0
-@[simp] def U16.max   : Int := HPow.hPow 2 16 - 1
-@[simp] def U32.min   : Int := 0
-@[simp] def U32.max   : Int := HPow.hPow 2 32 - 1
-@[simp] def U64.min   : Int := 0
-@[simp] def U64.max   : Int := HPow.hPow 2 64 - 1
-@[simp] def U128.min  : Int := 0
-@[simp] def U128.max  : Int := HPow.hPow 2 128 - 1
-
-#assert (I8.min   == -128)
-#assert (I8.max   == 127)
-#assert (I16.min  == -32768)
-#assert (I16.max  == 32767)
-#assert (I32.min  == -2147483648)
-#assert (I32.max  == 2147483647)
-#assert (I64.min  == -9223372036854775808)
-#assert (I64.max  == 9223372036854775807)
-#assert (I128.min == -170141183460469231731687303715884105728)
-#assert (I128.max == 170141183460469231731687303715884105727)
-#assert (U8.min   == 0)
-#assert (U8.max   == 255)
-#assert (U16.min  == 0)
-#assert (U16.max  == 65535)
-#assert (U32.min  == 0)
-#assert (U32.max  == 4294967295)
-#assert (U64.min  == 0)
-#assert (U64.max  == 18446744073709551615)
-#assert (U128.min == 0)
-#assert (U128.max == 340282366920938463463374607431768211455)
-
-inductive ScalarTy :=
-| Isize
-| I8
-| I16
-| I32
-| I64
-| I128
-| Usize
-| U8
-| U16
-| U32
-| U64
-| U128
-
-def Scalar.min (ty : ScalarTy) : Int :=
-  match ty with
-  | .Isize => Isize.min
-  | .I8    => I8.min
-  | .I16   => I16.min
-  | .I32   => I32.min
-  | .I64   => I64.min
-  | .I128  => I128.min
-  | .Usize => Usize.min
-  | .U8    => U8.min
-  | .U16   => U16.min
-  | .U32   => U32.min
-  | .U64   => U64.min
-  | .U128  => U128.min
-
-def Scalar.max (ty : ScalarTy) : Int :=
-  match ty with
-  | .Isize => Isize.max
-  | .I8    => I8.max
-  | .I16   => I16.max
-  | .I32   => I32.max
-  | .I64   => I64.max
-  | .I128  => I128.max
-  | .Usize => Usize.max
-  | .U8    => U8.max
-  | .U16   => U16.max
-  | .U32   => U32.max
-  | .U64   => U64.max
-  | .U128  => U128.max
-
--- "Conservative" bounds
--- We use those because we can't compare to the isize bounds (which can't
--- reduce at compile-time). Whenever we perform an arithmetic operation like
--- addition we need to check that the result is in bounds: we first compare
--- to the conservative bounds, which reduce, then compare to the real bounds.
--- This is useful for the various #asserts that we want to reduce at
--- type-checking time.
-def Scalar.cMin (ty : ScalarTy) : Int :=
-  match ty with
-  | .Isize => I32.min
-  | _ => Scalar.min ty
-
-def Scalar.cMax (ty : ScalarTy) : Int :=
-  match ty with
-  | .Isize => I32.max
-  | .Usize => U32.max
-  | _ => Scalar.max ty
-
-theorem Scalar.cMin_bound ty : Scalar.min ty <= Scalar.cMin ty := by sorry
-theorem Scalar.cMax_bound ty : Scalar.min ty <= Scalar.cMin ty := by sorry
-
-structure Scalar (ty : ScalarTy) where
-  val : Int
-  hmin : Scalar.min ty <= val
-  hmax : val <= Scalar.max ty
-
-theorem Scalar.bound_suffices (ty : ScalarTy) (x : Int) :
-  Scalar.cMin ty <= x && x <= Scalar.cMax ty ->
-  (decide (Scalar.min ty ≤ x) && decide (x ≤ Scalar.max ty)) = true
-  := by sorry
-
-def Scalar.ofIntCore {ty : ScalarTy} (x : Int)
-  (hmin : Scalar.min ty <= x) (hmax : x <= Scalar.max ty) : Scalar ty :=
-  { val := x, hmin := hmin, hmax := hmax }
-
-def Scalar.ofInt {ty : ScalarTy} (x : Int)
-  (h : Scalar.min ty <= x && x <= Scalar.max ty) : Scalar ty :=
-  let hmin: Scalar.min ty <= x := by sorry
-  let hmax: x <= Scalar.max ty := by sorry
-  Scalar.ofIntCore x hmin hmax
-
--- Further thoughts: look at what has been done here:
--- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/Fin/Basic.lean
--- and
--- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/UInt.lean
--- which both contain a fair amount of reasoning already!
-def Scalar.tryMk (ty : ScalarTy) (x : Int) : Result (Scalar ty) :=
-  -- TODO: write this with only one if then else
-  if hmin_cons: Scalar.cMin ty <= x || Scalar.min ty <= x then
-    if hmax_cons: x <= Scalar.cMax ty || x <= Scalar.max ty then
-      let hmin: Scalar.min ty <= x := by sorry
-      let hmax: x <= Scalar.max ty := by sorry
-      return Scalar.ofIntCore x hmin hmax
-    else fail integerOverflow
-  else fail integerOverflow
-
-def Scalar.neg {ty : ScalarTy} (x : Scalar ty) : Result (Scalar ty) := Scalar.tryMk ty (- x.val)
-
-def Scalar.div {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
-  if y.val != 0 then Scalar.tryMk ty (x.val / y.val) else fail divisionByZero
-
--- Checking that the % operation in Lean computes the same as the remainder operation in Rust
-#assert 1 % 2 = (1:Int)
-#assert (-1) % 2 = -1
-#assert 1 % (-2) = 1
-#assert (-1) % (-2) = -1
-
-def Scalar.rem {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
-  if y.val != 0 then Scalar.tryMk ty (x.val % y.val) else fail divisionByZero
-
-def Scalar.add {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
-  Scalar.tryMk ty (x.val + y.val)
-
-def Scalar.sub {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
-  Scalar.tryMk ty (x.val - y.val)
-
-def Scalar.mul {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
-  Scalar.tryMk ty (x.val * y.val)
-
--- TODO: instances of +, -, * etc. for scalars
-
--- Cast an integer from a [src_ty] to a [tgt_ty]
--- TODO: check the semantics of casts in Rust
-def Scalar.cast {src_ty : ScalarTy} (tgt_ty : ScalarTy) (x : Scalar src_ty) : Result (Scalar tgt_ty) :=
-  Scalar.tryMk tgt_ty x.val
-
--- The scalar types
--- We declare the definitions as reducible so that Lean can unfold them (useful
--- for type class resolution for instance).
-@[reducible] def Isize := Scalar .Isize
-@[reducible] def I8    := Scalar .I8
-@[reducible] def I16   := Scalar .I16
-@[reducible] def I32   := Scalar .I32
-@[reducible] def I64   := Scalar .I64
-@[reducible] def I128  := Scalar .I128
-@[reducible] def Usize := Scalar .Usize
-@[reducible] def U8    := Scalar .U8
-@[reducible] def U16   := Scalar .U16
-@[reducible] def U32   := Scalar .U32
-@[reducible] def U64   := Scalar .U64
-@[reducible] def U128  := Scalar .U128
-
--- TODO: below: not sure this is the best way.
--- Should we rather overload operations like +, -, etc.?
--- Also, it is possible to automate the generation of those definitions
--- with macros (but would it be a good idea? It would be less easy to
--- read the file, which is not supposed to change a lot)
-
--- Negation
-
-/--
-Remark: there is no heterogeneous negation in the Lean prelude: we thus introduce
-one here.
-
-The notation typeclass for heterogeneous addition.
-This enables the notation `- a : β` where `a : α`.
--/
-class HNeg (α : Type u) (β : outParam (Type v)) where
-  /-- `- a` computes the negation of `a`.
-  The meaning of this notation is type-dependent. -/
-  hNeg : α → β
-
-prefix:75  "-"   => HNeg.hNeg
-
-instance : HNeg Isize (Result Isize) where hNeg x := Scalar.neg x
-instance : HNeg I8 (Result I8) where hNeg x := Scalar.neg x
-instance : HNeg I16 (Result I16) where hNeg x := Scalar.neg x
-instance : HNeg I32 (Result I32) where hNeg x := Scalar.neg x
-instance : HNeg I64 (Result I64) where hNeg x := Scalar.neg x
-instance : HNeg I128 (Result I128) where hNeg x := Scalar.neg x
-
--- Addition
-instance {ty} : HAdd (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
-  hAdd x y := Scalar.add x y
-
--- Substraction
-instance {ty} : HSub (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
-  hSub x y := Scalar.sub x y
-
--- Multiplication
-instance {ty} : HMul (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
-  hMul x y := Scalar.mul x y
-
--- Division
-instance {ty} : HDiv (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
-  hDiv x y := Scalar.div x y
-
--- Remainder
-instance {ty} : HMod (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
-  hMod x y := Scalar.rem x y
-
--- ofIntCore
--- TODO: typeclass?
-def Isize.ofIntCore := @Scalar.ofIntCore .Isize
-def I8.ofIntCore    := @Scalar.ofIntCore .I8
-def I16.ofIntCore   := @Scalar.ofIntCore .I16
-def I32.ofIntCore   := @Scalar.ofIntCore .I32
-def I64.ofIntCore   := @Scalar.ofIntCore .I64
-def I128.ofIntCore  := @Scalar.ofIntCore .I128
-def Usize.ofIntCore := @Scalar.ofIntCore .Usize
-def U8.ofIntCore    := @Scalar.ofIntCore .U8
-def U16.ofIntCore   := @Scalar.ofIntCore .U16
-def U32.ofIntCore   := @Scalar.ofIntCore .U32
-def U64.ofIntCore   := @Scalar.ofIntCore .U64
-def U128.ofIntCore  := @Scalar.ofIntCore .U128
-
---  ofInt
--- TODO: typeclass?
-def Isize.ofInt := @Scalar.ofInt .Isize
-def I8.ofInt    := @Scalar.ofInt .I8
-def I16.ofInt   := @Scalar.ofInt .I16
-def I32.ofInt   := @Scalar.ofInt .I32
-def I64.ofInt   := @Scalar.ofInt .I64
-def I128.ofInt  := @Scalar.ofInt .I128
-def Usize.ofInt := @Scalar.ofInt .Usize
-def U8.ofInt    := @Scalar.ofInt .U8
-def U16.ofInt   := @Scalar.ofInt .U16
-def U32.ofInt   := @Scalar.ofInt .U32
-def U64.ofInt   := @Scalar.ofInt .U64
-def U128.ofInt  := @Scalar.ofInt .U128
-
--- Comparisons
-instance {ty} : LT (Scalar ty) where
-  lt a b := LT.lt a.val b.val
-
-instance {ty} : LE (Scalar ty) where le a b := LE.le a.val b.val
-
-instance Scalar.decLt {ty} (a b : Scalar ty) : Decidable (LT.lt a b) := Int.decLt ..
-instance Scalar.decLe {ty} (a b : Scalar ty) : Decidable (LE.le a b) := Int.decLe ..
-
-theorem Scalar.eq_of_val_eq {ty} : ∀ {i j : Scalar ty}, Eq i.val j.val → Eq i j
-  | ⟨_, _, _⟩, ⟨_, _, _⟩, rfl => rfl
-
-theorem Scalar.val_eq_of_eq {ty} {i j : Scalar ty} (h : Eq i j) : Eq i.val j.val :=
-  h ▸ rfl
-
-theorem Scalar.ne_of_val_ne {ty} {i j : Scalar ty} (h : Not (Eq i.val j.val)) : Not (Eq i j) :=
-  fun h' => absurd (val_eq_of_eq h') h
-
-instance (ty : ScalarTy) : DecidableEq (Scalar ty) :=
-  fun i j =>
-    match decEq i.val j.val with
-    | isTrue h  => isTrue (Scalar.eq_of_val_eq h)
-    | isFalse h => isFalse (Scalar.ne_of_val_ne h)
-
-def Scalar.toInt {ty} (n : Scalar ty) : Int := n.val
-
--- Tactic to prove that integers are in bounds
-syntax "intlit" : tactic
-
-macro_rules
-  | `(tactic| intlit) => `(tactic| apply Scalar.bound_suffices ; decide)
-
--- -- We now define a type class that subsumes the various machine integer types, so
--- -- as to write a concise definition for scalar_cast, rather than exhaustively
--- -- enumerating all of the possible pairs. We remark that Rust has sane semantics
--- -- and fails if a cast operation would involve a truncation or modulo.
-
--- class MachineInteger (t: Type) where
---   size: Nat
---   val: t -> Fin size
---   ofNatCore: (n:Nat) -> LT.lt n size -> t
-
--- set_option hygiene false in
--- run_cmd
---   for typeName in [`UInt8, `UInt16, `UInt32, `UInt64, `USize].map Lean.mkIdent do
---   Lean.Elab.Command.elabCommand (← `(
---     namespace $typeName
---     instance: MachineInteger $typeName where
---       size := size
---       val := val
---       ofNatCore := ofNatCore
---     end $typeName
---   ))
-
--- -- Aeneas only instantiates the destination type (`src` is implicit). We rely on
--- -- Lean to infer `src`.
-
--- def scalar_cast { src: Type } (dst: Type) [ MachineInteger src ] [ MachineInteger dst ] (x: src): Result dst :=
---   if h: MachineInteger.val x < MachineInteger.size dst then
---     .ret (MachineInteger.ofNatCore (MachineInteger.val x).val h)
---   else
---     .fail integerOverflow
-
--------------
--- VECTORS --
--------------
-
-def Vec (α : Type u) := { l : List α // List.length l <= Usize.max }
-
-def vec_new (α : Type u): Vec α := ⟨ [], by sorry ⟩
-
-def vec_len (α : Type u) (v : Vec α) : Usize :=
-  let ⟨ v, l ⟩ := v
-  Usize.ofIntCore (List.length v) (by sorry) l
- 
-def vec_push_fwd (α : Type u) (_ : Vec α) (_ : α) : Unit := ()
-
-def vec_push_back (α : Type u) (v : Vec α) (x : α) : Result (Vec α)
-  :=
-  if h : List.length v.val <= U32.max || List.length v.val <= Usize.max then
-    return ⟨ List.concat v.val x, by sorry ⟩
-  else
-    fail maximumSizeExceeded
-
-def vec_insert_fwd (α : Type u) (v: Vec α) (i: Usize) (_: α): Result Unit :=
-  if i.val < List.length v.val then
-    .ret ()
-  else
-    .fail arrayOutOfBounds
-
-def vec_insert_back (α : Type u) (v: Vec α) (i: Usize) (x: α): Result (Vec α) :=
-  if i.val < List.length v.val then
-    -- TODO: maybe we should redefine a list library which uses integers
-    -- (instead of natural numbers)
-    let i : Nat :=
-      match i.val with
-      | .ofNat n => n
-      | .negSucc n => by sorry -- TODO: we can't get here
-    let isLt: i < USize.size := by sorry
-    let i : Fin USize.size := { val := i, isLt := isLt }
-    .ret ⟨ List.set v.val i.val x, by
-      have h: List.length v.val <= Usize.max := v.property
-      rewrite [ List.length_set v.val i.val x ]
-      assumption
-    ⟩
-  else
-    .fail arrayOutOfBounds
-
-def vec_index_fwd (α : Type u) (v: Vec α) (i: Usize): Result α :=
-  if i.val < List.length v.val then
-    let i : Nat :=
-      match i.val with
-      | .ofNat n => n
-      | .negSucc n => by sorry -- TODO: we can't get here
-    let isLt: i < USize.size := by sorry
-    let i : Fin USize.size := { val := i, isLt := isLt }
-    let h: i < List.length v.val := by sorry
-    .ret (List.get v.val ⟨i.val, h⟩)
-  else
-    .fail arrayOutOfBounds
-
-def vec_index_back (α : Type u) (v: Vec α) (i: Usize) (_: α): Result Unit :=
-  if i.val < List.length v.val then
-    .ret ()
-  else
-    .fail arrayOutOfBounds
-
-def vec_index_mut_fwd (α : Type u) (v: Vec α) (i: Usize): Result α :=
-  if i.val < List.length v.val then
-    let i : Nat :=
-      match i.val with
-      | .ofNat n => n
-      | .negSucc n => by sorry -- TODO: we can't get here
-    let isLt: i < USize.size := by sorry
-    let i : Fin USize.size := { val := i, isLt := isLt }
-    let h: i < List.length v.val := by sorry
-    .ret (List.get v.val ⟨i.val, h⟩)
-  else
-    .fail arrayOutOfBounds
-
-def vec_index_mut_back (α : Type u) (v: Vec α) (i: Usize) (x: α): Result (Vec α) :=
-  if i.val < List.length v.val then
-    let i : Nat :=
-      match i.val with
-      | .ofNat n => n
-      | .negSucc n => by sorry -- TODO: we can't get here
-    let isLt: i < USize.size := by sorry
-    let i : Fin USize.size := { val := i, isLt := isLt }
-    .ret ⟨ List.set v.val i.val x, by
-      have h: List.length v.val <= Usize.max := v.property
-      rewrite [ List.length_set v.val i.val x ]
-      assumption
-    ⟩
-  else
-    .fail arrayOutOfBounds
-
-----------
--- MISC --
-----------
-
-def mem_replace_fwd (a : Type) (x : a) (_ : a) : a :=
-  x
-
-def mem_replace_back (a : Type) (_ : a) (y : a) : a :=
-  y
-
-/-- Aeneas-translated function -- useful to reduce non-recursive definitions.
- Use with `simp [ aeneas ]` -/
-register_simp_attr aeneas
diff --git a/tests/lean/misc-loops/Loops/Clauses/Clauses.lean b/tests/lean/misc-loops/Loops/Clauses/Clauses.lean
deleted file mode 100644
index 89a7ce34..00000000
--- a/tests/lean/misc-loops/Loops/Clauses/Clauses.lean
+++ /dev/null
@@ -1,205 +0,0 @@
--- [loops]: decreases clauses
-import Base.Primitives
-import Loops.Types
-
-/- [loops::sum]: termination measure -/
-@[simp]
-def sum_loop_terminates (max : U32) (i : U32) (s : U32) := (max, i, s)
-
-syntax "sum_loop_decreases" term+ : tactic
-
-macro_rules
-| `(tactic| sum_loop_decreases $max $i $s) =>`(tactic| sorry)
-
-/- [loops::sum_with_mut_borrows]: termination measure -/
-@[simp]
-def sum_with_mut_borrows_loop_terminates (max : U32) (mi : U32) (ms : U32) :=
-  (max, mi, ms)
-
-syntax "sum_with_mut_borrows_loop_decreases" term+ : tactic
-
-macro_rules
-| `(tactic| sum_with_mut_borrows_loop_decreases $max $mi $ms) =>`(tactic| sorry)
-
-/- [loops::sum_with_shared_borrows]: termination measure -/
-@[simp]
-def sum_with_shared_borrows_loop_terminates (max : U32) (i : U32) (s : U32) :=
-  (max, i, s)
-
-syntax "sum_with_shared_borrows_loop_decreases" term+ : tactic
-
-macro_rules
-| `(tactic| sum_with_shared_borrows_loop_decreases $max $i $s) =>`(tactic| sorry)
-
-/- [loops::clear]: termination measure -/
-@[simp] def clear_loop_terminates (v : Vec U32) (i : Usize) := (v, i)
-
-syntax "clear_loop_decreases" term+ : tactic
-
-macro_rules
-| `(tactic| clear_loop_decreases $v $i) =>`(tactic| sorry)
-
-/- [loops::list_mem]: termination measure -/
-@[simp]
-def list_mem_loop_terminates (x : U32) (ls : list_t U32) := (x, ls)
-
-syntax "list_mem_loop_decreases" term+ : tactic
-
-macro_rules
-| `(tactic| list_mem_loop_decreases $x $ls) =>`(tactic| sorry)
-
-/- [loops::list_nth_mut_loop]: termination measure -/
-@[simp]
-def list_nth_mut_loop_loop_terminates (T : Type) (ls : list_t T) (i : U32) :=
-  (ls, i)
-
-syntax "list_nth_mut_loop_loop_decreases" term+ : tactic
-
-macro_rules
-| `(tactic| list_nth_mut_loop_loop_decreases $ls $i) =>`(tactic| sorry)
-
-/- [loops::list_nth_shared_loop]: termination measure -/
-@[simp]
-def list_nth_shared_loop_loop_terminates (T : Type) (ls : list_t T) (i : U32) :=
-  (ls, i)
-
-syntax "list_nth_shared_loop_loop_decreases" term+ : tactic
-
-macro_rules
-| `(tactic| list_nth_shared_loop_loop_decreases $ls $i) =>`(tactic| sorry)
-
-/- [loops::get_elem_mut]: termination measure -/
-@[simp]
-def get_elem_mut_loop_terminates (x : Usize) (ls : list_t Usize) := (x, ls)
-
-syntax "get_elem_mut_loop_decreases" term+ : tactic
-
-macro_rules
-| `(tactic| get_elem_mut_loop_decreases $x $ls) =>`(tactic| sorry)
-
-/- [loops::get_elem_shared]: termination measure -/
-@[simp]
-def get_elem_shared_loop_terminates (x : Usize) (ls : list_t Usize) := (x, ls)
-
-syntax "get_elem_shared_loop_decreases" term+ : tactic
-
-macro_rules
-| `(tactic| get_elem_shared_loop_decreases $x $ls) =>`(tactic| sorry)
-
-/- [loops::list_nth_mut_loop_with_id]: termination measure -/
-@[simp]
-def list_nth_mut_loop_with_id_loop_terminates (T : Type) (i : U32)
-  (ls : list_t T) :=
-  (i, ls)
-
-syntax "list_nth_mut_loop_with_id_loop_decreases" term+ : tactic
-
-macro_rules
-| `(tactic| list_nth_mut_loop_with_id_loop_decreases $i $ls) =>`(tactic| sorry)
-
-/- [loops::list_nth_shared_loop_with_id]: termination measure -/
-@[simp]
-def list_nth_shared_loop_with_id_loop_terminates (T : Type) (i : U32)
-  (ls : list_t T) :=
-  (i, ls)
-
-syntax "list_nth_shared_loop_with_id_loop_decreases" term+ : tactic
-
-macro_rules
-| `(tactic| list_nth_shared_loop_with_id_loop_decreases $i $ls) =>`(tactic| sorry)
-
-/- [loops::list_nth_mut_loop_pair]: termination measure -/
-@[simp]
-def list_nth_mut_loop_pair_loop_terminates (T : Type) (ls0 : list_t T)
-  (ls1 : list_t T) (i : U32) :=
-  (ls0, ls1, i)
-
-syntax "list_nth_mut_loop_pair_loop_decreases" term+ : tactic
-
-macro_rules
-| `(tactic| list_nth_mut_loop_pair_loop_decreases $ls0 $ls1 $i) =>`(tactic| sorry)
-
-/- [loops::list_nth_shared_loop_pair]: termination measure -/
-@[simp]
-def list_nth_shared_loop_pair_loop_terminates (T : Type) (ls0 : list_t T)
-  (ls1 : list_t T) (i : U32) :=
-  (ls0, ls1, i)
-
-syntax "list_nth_shared_loop_pair_loop_decreases" term+ : tactic
-
-macro_rules
-| `(tactic| list_nth_shared_loop_pair_loop_decreases $ls0 $ls1 $i) =>
-  `(tactic| sorry)
-
-/- [loops::list_nth_mut_loop_pair_merge]: termination measure -/
-@[simp]
-def list_nth_mut_loop_pair_merge_loop_terminates (T : Type) (ls0 : list_t T)
-  (ls1 : list_t T) (i : U32) :=
-  (ls0, ls1, i)
-
-syntax "list_nth_mut_loop_pair_merge_loop_decreases" term+ : tactic
-
-macro_rules
-| `(tactic| list_nth_mut_loop_pair_merge_loop_decreases $ls0 $ls1 $i) =>
-  `(tactic| sorry)
-
-/- [loops::list_nth_shared_loop_pair_merge]: termination measure -/
-@[simp]
-def list_nth_shared_loop_pair_merge_loop_terminates (T : Type) (ls0 : list_t T)
-  (ls1 : list_t T) (i : U32) :=
-  (ls0, ls1, i)
-
-syntax "list_nth_shared_loop_pair_merge_loop_decreases" term+ : tactic
-
-macro_rules
-| `(tactic| list_nth_shared_loop_pair_merge_loop_decreases $ls0 $ls1 $i) =>
-  `(tactic| sorry)
-
-/- [loops::list_nth_mut_shared_loop_pair]: termination measure -/
-@[simp]
-def list_nth_mut_shared_loop_pair_loop_terminates (T : Type) (ls0 : list_t T)
-  (ls1 : list_t T) (i : U32) :=
-  (ls0, ls1, i)
-
-syntax "list_nth_mut_shared_loop_pair_loop_decreases" term+ : tactic
-
-macro_rules
-| `(tactic| list_nth_mut_shared_loop_pair_loop_decreases $ls0 $ls1 $i) =>
-  `(tactic| sorry)
-
-/- [loops::list_nth_mut_shared_loop_pair_merge]: termination measure -/
-@[simp]
-def list_nth_mut_shared_loop_pair_merge_loop_terminates (T : Type)
-  (ls0 : list_t T) (ls1 : list_t T) (i : U32) :=
-  (ls0, ls1, i)
-
-syntax "list_nth_mut_shared_loop_pair_merge_loop_decreases" term+ : tactic
-
-macro_rules
-| `(tactic| list_nth_mut_shared_loop_pair_merge_loop_decreases $ls0 $ls1 $i) =>
-  `(tactic| sorry)
-
-/- [loops::list_nth_shared_mut_loop_pair]: termination measure -/
-@[simp]
-def list_nth_shared_mut_loop_pair_loop_terminates (T : Type) (ls0 : list_t T)
-  (ls1 : list_t T) (i : U32) :=
-  (ls0, ls1, i)
-
-syntax "list_nth_shared_mut_loop_pair_loop_decreases" term+ : tactic
-
-macro_rules
-| `(tactic| list_nth_shared_mut_loop_pair_loop_decreases $ls0 $ls1 $i) =>
-  `(tactic| sorry)
-
-/- [loops::list_nth_shared_mut_loop_pair_merge]: termination measure -/
-@[simp]
-def list_nth_shared_mut_loop_pair_merge_loop_terminates (T : Type)
-  (ls0 : list_t T) (ls1 : list_t T) (i : U32) :=
-  (ls0, ls1, i)
-
-syntax "list_nth_shared_mut_loop_pair_merge_loop_decreases" term+ : tactic
-
-macro_rules
-| `(tactic| list_nth_shared_mut_loop_pair_merge_loop_decreases $ls0 $ls1 $i) =>
-  `(tactic| sorry)
-
diff --git a/tests/lean/misc-loops/Loops/Clauses/Template.lean b/tests/lean/misc-loops/Loops/Clauses/Template.lean
deleted file mode 100644
index 2e28a6c0..00000000
--- a/tests/lean/misc-loops/Loops/Clauses/Template.lean
+++ /dev/null
@@ -1,205 +0,0 @@
--- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
--- [loops]: templates for the decreases clauses
-import Base.Primitives
-import Loops.Types
-
-/- [loops::sum]: termination measure -/
-@[simp] def sum_loop_terminates (max : U32) (i : U32) (s : U32) := (max, i, s)
-
-/- [loops::sum]: decreases_by tactic -/
-syntax "sum_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| sum_loop_decreases $max $i $s) =>`(tactic| sorry)
-
-/- [loops::sum_with_mut_borrows]: termination measure -/
-@[simp]
-def sum_with_mut_borrows_loop_terminates (max : U32) (mi : U32) (ms : U32) :=
-  (max, mi, ms)
-
-/- [loops::sum_with_mut_borrows]: decreases_by tactic -/
-syntax "sum_with_mut_borrows_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| sum_with_mut_borrows_loop_decreases $max $mi $ms) =>`(tactic| sorry)
-
-/- [loops::sum_with_shared_borrows]: termination measure -/
-@[simp]
-def sum_with_shared_borrows_loop_terminates (max : U32) (i : U32) (s : U32) :=
-  (max, i, s)
-
-/- [loops::sum_with_shared_borrows]: decreases_by tactic -/
-syntax "sum_with_shared_borrows_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| sum_with_shared_borrows_loop_decreases $max $i $s) =>`(tactic| sorry)
-
-/- [loops::clear]: termination measure -/
-@[simp] def clear_loop_terminates (v : Vec U32) (i : Usize) := (v, i)
-
-/- [loops::clear]: decreases_by tactic -/
-syntax "clear_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| clear_loop_decreases $v $i) =>`(tactic| sorry)
-
-/- [loops::list_mem]: termination measure -/
-@[simp] def list_mem_loop_terminates (x : U32) (ls : list_t U32) := (x, ls)
-
-/- [loops::list_mem]: decreases_by tactic -/
-syntax "list_mem_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| list_mem_loop_decreases $x $ls) =>`(tactic| sorry)
-
-/- [loops::list_nth_mut_loop]: termination measure -/
-@[simp]
-def list_nth_mut_loop_loop_terminates (T : Type) (ls : list_t T) (i : U32) :=
-  (ls, i)
-
-/- [loops::list_nth_mut_loop]: decreases_by tactic -/
-syntax "list_nth_mut_loop_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| list_nth_mut_loop_loop_decreases $ls $i) =>`(tactic| sorry)
-
-/- [loops::list_nth_shared_loop]: termination measure -/
-@[simp]
-def list_nth_shared_loop_loop_terminates (T : Type) (ls : list_t T) (i : U32)
-  :=
-  (ls, i)
-
-/- [loops::list_nth_shared_loop]: decreases_by tactic -/
-syntax "list_nth_shared_loop_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| list_nth_shared_loop_loop_decreases $ls $i) =>`(tactic| sorry)
-
-/- [loops::get_elem_mut]: termination measure -/
-@[simp]
-def get_elem_mut_loop_terminates (x : Usize) (ls : list_t Usize) := (x, ls)
-
-/- [loops::get_elem_mut]: decreases_by tactic -/
-syntax "get_elem_mut_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| get_elem_mut_loop_decreases $x $ls) =>`(tactic| sorry)
-
-/- [loops::get_elem_shared]: termination measure -/
-@[simp]
-def get_elem_shared_loop_terminates (x : Usize) (ls : list_t Usize) := (x, ls)
-
-/- [loops::get_elem_shared]: decreases_by tactic -/
-syntax "get_elem_shared_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| get_elem_shared_loop_decreases $x $ls) =>`(tactic| sorry)
-
-/- [loops::list_nth_mut_loop_with_id]: termination measure -/
-@[simp]
-def list_nth_mut_loop_with_id_loop_terminates (T : Type) (i : U32)
-  (ls : list_t T) :=
-  (i, ls)
-
-/- [loops::list_nth_mut_loop_with_id]: decreases_by tactic -/
-syntax "list_nth_mut_loop_with_id_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| list_nth_mut_loop_with_id_loop_decreases $i $ls) =>`(tactic| sorry)
-
-/- [loops::list_nth_shared_loop_with_id]: termination measure -/
-@[simp]
-def list_nth_shared_loop_with_id_loop_terminates (T : Type) (i : U32)
-  (ls : list_t T) :=
-  (i, ls)
-
-/- [loops::list_nth_shared_loop_with_id]: decreases_by tactic -/
-syntax "list_nth_shared_loop_with_id_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| list_nth_shared_loop_with_id_loop_decreases $i $ls) =>`(tactic| sorry)
-
-/- [loops::list_nth_mut_loop_pair]: termination measure -/
-@[simp]
-def list_nth_mut_loop_pair_loop_terminates (T : Type) (ls0 : list_t T)
-  (ls1 : list_t T) (i : U32) :=
-  (ls0, ls1, i)
-
-/- [loops::list_nth_mut_loop_pair]: decreases_by tactic -/
-syntax "list_nth_mut_loop_pair_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| list_nth_mut_loop_pair_loop_decreases $ls0 $ls1 $i) =>`(tactic| sorry)
-
-/- [loops::list_nth_shared_loop_pair]: termination measure -/
-@[simp]
-def list_nth_shared_loop_pair_loop_terminates (T : Type) (ls0 : list_t T)
-  (ls1 : list_t T) (i : U32) :=
-  (ls0, ls1, i)
-
-/- [loops::list_nth_shared_loop_pair]: decreases_by tactic -/
-syntax "list_nth_shared_loop_pair_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| list_nth_shared_loop_pair_loop_decreases $ls0 $ls1 $i) =>
-  `(tactic| sorry)
-
-/- [loops::list_nth_mut_loop_pair_merge]: termination measure -/
-@[simp]
-def list_nth_mut_loop_pair_merge_loop_terminates (T : Type) (ls0 : list_t T)
-  (ls1 : list_t T) (i : U32) :=
-  (ls0, ls1, i)
-
-/- [loops::list_nth_mut_loop_pair_merge]: decreases_by tactic -/
-syntax "list_nth_mut_loop_pair_merge_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| list_nth_mut_loop_pair_merge_loop_decreases $ls0 $ls1 $i) =>
-  `(tactic| sorry)
-
-/- [loops::list_nth_shared_loop_pair_merge]: termination measure -/
-@[simp]
-def list_nth_shared_loop_pair_merge_loop_terminates (T : Type) (ls0 : list_t T)
-  (ls1 : list_t T) (i : U32) :=
-  (ls0, ls1, i)
-
-/- [loops::list_nth_shared_loop_pair_merge]: decreases_by tactic -/
-syntax "list_nth_shared_loop_pair_merge_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| list_nth_shared_loop_pair_merge_loop_decreases $ls0 $ls1 $i) =>
-  `(tactic| sorry)
-
-/- [loops::list_nth_mut_shared_loop_pair]: termination measure -/
-@[simp]
-def list_nth_mut_shared_loop_pair_loop_terminates (T : Type) (ls0 : list_t T)
-  (ls1 : list_t T) (i : U32) :=
-  (ls0, ls1, i)
-
-/- [loops::list_nth_mut_shared_loop_pair]: decreases_by tactic -/
-syntax "list_nth_mut_shared_loop_pair_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| list_nth_mut_shared_loop_pair_loop_decreases $ls0 $ls1 $i) =>
-  `(tactic| sorry)
-
-/- [loops::list_nth_mut_shared_loop_pair_merge]: termination measure -/
-@[simp]
-def list_nth_mut_shared_loop_pair_merge_loop_terminates (T : Type)
-  (ls0 : list_t T) (ls1 : list_t T) (i : U32) :=
-  (ls0, ls1, i)
-
-/- [loops::list_nth_mut_shared_loop_pair_merge]: decreases_by tactic -/
-syntax "list_nth_mut_shared_loop_pair_merge_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| list_nth_mut_shared_loop_pair_merge_loop_decreases $ls0 $ls1 $i) =>
-  `(tactic| sorry)
-
-/- [loops::list_nth_shared_mut_loop_pair]: termination measure -/
-@[simp]
-def list_nth_shared_mut_loop_pair_loop_terminates (T : Type) (ls0 : list_t T)
-  (ls1 : list_t T) (i : U32) :=
-  (ls0, ls1, i)
-
-/- [loops::list_nth_shared_mut_loop_pair]: decreases_by tactic -/
-syntax "list_nth_shared_mut_loop_pair_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| list_nth_shared_mut_loop_pair_loop_decreases $ls0 $ls1 $i) =>
-  `(tactic| sorry)
-
-/- [loops::list_nth_shared_mut_loop_pair_merge]: termination measure -/
-@[simp]
-def list_nth_shared_mut_loop_pair_merge_loop_terminates (T : Type)
-  (ls0 : list_t T) (ls1 : list_t T) (i : U32) :=
-  (ls0, ls1, i)
-
-/- [loops::list_nth_shared_mut_loop_pair_merge]: decreases_by tactic -/
-syntax "list_nth_shared_mut_loop_pair_merge_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| list_nth_shared_mut_loop_pair_merge_loop_decreases $ls0 $ls1 $i) =>
-  `(tactic| sorry)
-
diff --git a/tests/lean/misc-loops/Loops/Funs.lean b/tests/lean/misc-loops/Loops/Funs.lean
deleted file mode 100644
index fd8d62d7..00000000
--- a/tests/lean/misc-loops/Loops/Funs.lean
+++ /dev/null
@@ -1,705 +0,0 @@
--- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
--- [loops]: function definitions
-import Base.Primitives
-import Loops.Types
-import Loops.Clauses.Clauses
-
-/- [loops::sum] -/
-def sum_loop_fwd (max : U32) (i : U32) (s : U32) : (Result U32) :=
-  if h: i < max
-  then
-    do
-      let s0 ← s + i
-      let i0 ← i + (U32.ofInt 1 (by intlit))
-      sum_loop_fwd max i0 s0
-  else s * (U32.ofInt 2 (by intlit))
-termination_by sum_loop_fwd max i s => sum_loop_terminates max i s
-decreasing_by sum_loop_decreases max i s
-
-/- [loops::sum] -/
-def sum_fwd (max : U32) : Result U32 :=
-  sum_loop_fwd max (U32.ofInt 0 (by intlit)) (U32.ofInt 0 (by intlit))
-
-/- [loops::sum_with_mut_borrows] -/
-def sum_with_mut_borrows_loop_fwd
-  (max : U32) (mi : U32) (ms : U32) : (Result U32) :=
-  if h: mi < max
-  then
-    do
-      let ms0 ← ms + mi
-      let mi0 ← mi + (U32.ofInt 1 (by intlit))
-      sum_with_mut_borrows_loop_fwd max mi0 ms0
-  else ms * (U32.ofInt 2 (by intlit))
-termination_by sum_with_mut_borrows_loop_fwd max mi ms =>
-  sum_with_mut_borrows_loop_terminates max mi ms
-decreasing_by sum_with_mut_borrows_loop_decreases max mi ms
-
-/- [loops::sum_with_mut_borrows] -/
-def sum_with_mut_borrows_fwd (max : U32) : Result U32 :=
-  sum_with_mut_borrows_loop_fwd max (U32.ofInt 0 (by intlit))
-    (U32.ofInt 0 (by intlit))
-
-/- [loops::sum_with_shared_borrows] -/
-def sum_with_shared_borrows_loop_fwd
-  (max : U32) (i : U32) (s : U32) : (Result U32) :=
-  if h: i < max
-  then
-    do
-      let i0 ← i + (U32.ofInt 1 (by intlit))
-      let s0 ← s + i0
-      sum_with_shared_borrows_loop_fwd max i0 s0
-  else s * (U32.ofInt 2 (by intlit))
-termination_by sum_with_shared_borrows_loop_fwd max i s =>
-  sum_with_shared_borrows_loop_terminates max i s
-decreasing_by sum_with_shared_borrows_loop_decreases max i s
-
-/- [loops::sum_with_shared_borrows] -/
-def sum_with_shared_borrows_fwd (max : U32) : Result U32 :=
-  sum_with_shared_borrows_loop_fwd max (U32.ofInt 0 (by intlit))
-    (U32.ofInt 0 (by intlit))
-
-/- [loops::clear] -/
-def clear_loop_fwd_back (v : Vec U32) (i : Usize) : (Result (Vec U32)) :=
-  let i0 := vec_len U32 v
-  if h: i < i0
-  then
-    do
-      let i1 ← i + (Usize.ofInt 1 (by intlit))
-      let v0 ← vec_index_mut_back U32 v i (U32.ofInt 0 (by intlit))
-      clear_loop_fwd_back v0 i1
-  else Result.ret v
-termination_by clear_loop_fwd_back v i => clear_loop_terminates v i
-decreasing_by clear_loop_decreases v i
-
-/- [loops::clear] -/
-def clear_fwd_back (v : Vec U32) : Result (Vec U32) :=
-  clear_loop_fwd_back v (Usize.ofInt 0 (by intlit))
-
-/- [loops::list_mem] -/
-def list_mem_loop_fwd (x : U32) (ls : list_t U32) : (Result Bool) :=
-  match h: ls with
-  | list_t.Cons y tl =>
-    if h: y = x
-    then Result.ret true
-    else list_mem_loop_fwd x tl
-  | list_t.Nil => Result.ret false
-termination_by list_mem_loop_fwd x ls => list_mem_loop_terminates x ls
-decreasing_by list_mem_loop_decreases x ls
-
-/- [loops::list_mem] -/
-def list_mem_fwd (x : U32) (ls : list_t U32) : Result Bool :=
-  list_mem_loop_fwd x ls
-
-/- [loops::list_nth_mut_loop] -/
-def list_nth_mut_loop_loop_fwd
-  (T : Type) (ls : list_t T) (i : U32) : (Result T) :=
-  match h: ls with
-  | list_t.Cons x tl =>
-    if h: i = (U32.ofInt 0 (by intlit))
-    then Result.ret x
-    else
-      do
-        let i0 ← i - (U32.ofInt 1 (by intlit))
-        list_nth_mut_loop_loop_fwd T tl i0
-  | list_t.Nil => Result.fail Error.panic
-termination_by list_nth_mut_loop_loop_fwd ls i =>
-  list_nth_mut_loop_loop_terminates T ls i
-decreasing_by list_nth_mut_loop_loop_decreases ls i
-
-/- [loops::list_nth_mut_loop] -/
-def list_nth_mut_loop_fwd (T : Type) (ls : list_t T) (i : U32) : Result T :=
-  list_nth_mut_loop_loop_fwd T ls i
-
-/- [loops::list_nth_mut_loop] -/
-def list_nth_mut_loop_loop_back
-  (T : Type) (ls : list_t T) (i : U32) (ret0 : T) : (Result (list_t T)) :=
-  match h: ls with
-  | list_t.Cons x tl =>
-    if h: i = (U32.ofInt 0 (by intlit))
-    then Result.ret (list_t.Cons ret0 tl)
-    else
-      do
-        let i0 ← i - (U32.ofInt 1 (by intlit))
-        let tl0 ← list_nth_mut_loop_loop_back T tl i0 ret0
-        Result.ret (list_t.Cons x tl0)
-  | list_t.Nil => Result.fail Error.panic
-termination_by list_nth_mut_loop_loop_back ls i ret0 =>
-  list_nth_mut_loop_loop_terminates T ls i
-decreasing_by list_nth_mut_loop_loop_decreases ls i
-
-/- [loops::list_nth_mut_loop] -/
-def list_nth_mut_loop_back
-  (T : Type) (ls : list_t T) (i : U32) (ret0 : T) : Result (list_t T) :=
-  list_nth_mut_loop_loop_back T ls i ret0
-
-/- [loops::list_nth_shared_loop] -/
-def list_nth_shared_loop_loop_fwd
-  (T : Type) (ls : list_t T) (i : U32) : (Result T) :=
-  match h: ls with
-  | list_t.Cons x tl =>
-    if h: i = (U32.ofInt 0 (by intlit))
-    then Result.ret x
-    else
-      do
-        let i0 ← i - (U32.ofInt 1 (by intlit))
-        list_nth_shared_loop_loop_fwd T tl i0
-  | list_t.Nil => Result.fail Error.panic
-termination_by list_nth_shared_loop_loop_fwd ls i =>
-  list_nth_shared_loop_loop_terminates T ls i
-decreasing_by list_nth_shared_loop_loop_decreases ls i
-
-/- [loops::list_nth_shared_loop] -/
-def list_nth_shared_loop_fwd (T : Type) (ls : list_t T) (i : U32) : Result T :=
-  list_nth_shared_loop_loop_fwd T ls i
-
-/- [loops::get_elem_mut] -/
-def get_elem_mut_loop_fwd (x : Usize) (ls : list_t Usize) : (Result Usize) :=
-  match h: ls with
-  | list_t.Cons y tl =>
-    if h: y = x
-    then Result.ret y
-    else get_elem_mut_loop_fwd x tl
-  | list_t.Nil => Result.fail Error.panic
-termination_by get_elem_mut_loop_fwd x ls => get_elem_mut_loop_terminates x ls
-decreasing_by get_elem_mut_loop_decreases x ls
-
-/- [loops::get_elem_mut] -/
-def get_elem_mut_fwd (slots : Vec (list_t Usize)) (x : Usize) : Result Usize :=
-  do
-    let l ←
-      vec_index_mut_fwd (list_t Usize) slots (Usize.ofInt 0 (by intlit))
-    get_elem_mut_loop_fwd x l
-
-/- [loops::get_elem_mut] -/
-def get_elem_mut_loop_back
-  (x : Usize) (ls : list_t Usize) (ret0 : Usize) : (Result (list_t Usize)) :=
-  match h: ls with
-  | list_t.Cons y tl =>
-    if h: y = x
-    then Result.ret (list_t.Cons ret0 tl)
-    else
-      do
-        let tl0 ← get_elem_mut_loop_back x tl ret0
-        Result.ret (list_t.Cons y tl0)
-  | list_t.Nil => Result.fail Error.panic
-termination_by get_elem_mut_loop_back x ls ret0 =>
-  get_elem_mut_loop_terminates x ls
-decreasing_by get_elem_mut_loop_decreases x ls
-
-/- [loops::get_elem_mut] -/
-def get_elem_mut_back
-  (slots : Vec (list_t Usize)) (x : Usize) (ret0 : Usize) :
-  Result (Vec (list_t Usize))
-  :=
-  do
-    let l ←
-      vec_index_mut_fwd (list_t Usize) slots (Usize.ofInt 0 (by intlit))
-    let l0 ← get_elem_mut_loop_back x l ret0
-    vec_index_mut_back (list_t Usize) slots (Usize.ofInt 0 (by intlit)) l0
-
-/- [loops::get_elem_shared] -/
-def get_elem_shared_loop_fwd
-  (x : Usize) (ls : list_t Usize) : (Result Usize) :=
-  match h: ls with
-  | list_t.Cons y tl =>
-    if h: y = x
-    then Result.ret y
-    else get_elem_shared_loop_fwd x tl
-  | list_t.Nil => Result.fail Error.panic
-termination_by get_elem_shared_loop_fwd x ls =>
-  get_elem_shared_loop_terminates x ls
-decreasing_by get_elem_shared_loop_decreases x ls
-
-/- [loops::get_elem_shared] -/
-def get_elem_shared_fwd
-  (slots : Vec (list_t Usize)) (x : Usize) : Result Usize :=
-  do
-    let l ← vec_index_fwd (list_t Usize) slots (Usize.ofInt 0 (by intlit))
-    get_elem_shared_loop_fwd x l
-
-/- [loops::id_mut] -/
-def id_mut_fwd (T : Type) (ls : list_t T) : Result (list_t T) :=
-  Result.ret ls
-
-/- [loops::id_mut] -/
-def id_mut_back
-  (T : Type) (ls : list_t T) (ret0 : list_t T) : Result (list_t T) :=
-  Result.ret ret0
-
-/- [loops::id_shared] -/
-def id_shared_fwd (T : Type) (ls : list_t T) : Result (list_t T) :=
-  Result.ret ls
-
-/- [loops::list_nth_mut_loop_with_id] -/
-def list_nth_mut_loop_with_id_loop_fwd
-  (T : Type) (i : U32) (ls : list_t T) : (Result T) :=
-  match h: ls with
-  | list_t.Cons x tl =>
-    if h: i = (U32.ofInt 0 (by intlit))
-    then Result.ret x
-    else
-      do
-        let i0 ← i - (U32.ofInt 1 (by intlit))
-        list_nth_mut_loop_with_id_loop_fwd T i0 tl
-  | list_t.Nil => Result.fail Error.panic
-termination_by list_nth_mut_loop_with_id_loop_fwd i ls =>
-  list_nth_mut_loop_with_id_loop_terminates T i ls
-decreasing_by list_nth_mut_loop_with_id_loop_decreases i ls
-
-/- [loops::list_nth_mut_loop_with_id] -/
-def list_nth_mut_loop_with_id_fwd
-  (T : Type) (ls : list_t T) (i : U32) : Result T :=
-  do
-    let ls0 ← id_mut_fwd T ls
-    list_nth_mut_loop_with_id_loop_fwd T i ls0
-
-/- [loops::list_nth_mut_loop_with_id] -/
-def list_nth_mut_loop_with_id_loop_back
-  (T : Type) (i : U32) (ls : list_t T) (ret0 : T) : (Result (list_t T)) :=
-  match h: ls with
-  | list_t.Cons x tl =>
-    if h: i = (U32.ofInt 0 (by intlit))
-    then Result.ret (list_t.Cons ret0 tl)
-    else
-      do
-        let i0 ← i - (U32.ofInt 1 (by intlit))
-        let tl0 ← list_nth_mut_loop_with_id_loop_back T i0 tl ret0
-        Result.ret (list_t.Cons x tl0)
-  | list_t.Nil => Result.fail Error.panic
-termination_by list_nth_mut_loop_with_id_loop_back i ls ret0 =>
-  list_nth_mut_loop_with_id_loop_terminates T i ls
-decreasing_by list_nth_mut_loop_with_id_loop_decreases i ls
-
-/- [loops::list_nth_mut_loop_with_id] -/
-def list_nth_mut_loop_with_id_back
-  (T : Type) (ls : list_t T) (i : U32) (ret0 : T) : Result (list_t T) :=
-  do
-    let ls0 ← id_mut_fwd T ls
-    let l ← list_nth_mut_loop_with_id_loop_back T i ls0 ret0
-    id_mut_back T ls l
-
-/- [loops::list_nth_shared_loop_with_id] -/
-def list_nth_shared_loop_with_id_loop_fwd
-  (T : Type) (i : U32) (ls : list_t T) : (Result T) :=
-  match h: ls with
-  | list_t.Cons x tl =>
-    if h: i = (U32.ofInt 0 (by intlit))
-    then Result.ret x
-    else
-      do
-        let i0 ← i - (U32.ofInt 1 (by intlit))
-        list_nth_shared_loop_with_id_loop_fwd T i0 tl
-  | list_t.Nil => Result.fail Error.panic
-termination_by list_nth_shared_loop_with_id_loop_fwd i ls =>
-  list_nth_shared_loop_with_id_loop_terminates T i ls
-decreasing_by list_nth_shared_loop_with_id_loop_decreases i ls
-
-/- [loops::list_nth_shared_loop_with_id] -/
-def list_nth_shared_loop_with_id_fwd
-  (T : Type) (ls : list_t T) (i : U32) : Result T :=
-  do
-    let ls0 ← id_shared_fwd T ls
-    list_nth_shared_loop_with_id_loop_fwd T i ls0
-
-/- [loops::list_nth_mut_loop_pair] -/
-def list_nth_mut_loop_pair_loop_fwd
-  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : (Result (T × T)) :=
-  match h: ls0 with
-  | list_t.Cons x0 tl0 =>
-    match h: ls1 with
-    | list_t.Cons x1 tl1 =>
-      if h: i = (U32.ofInt 0 (by intlit))
-      then Result.ret (x0, x1)
-      else
-        do
-          let i0 ← i - (U32.ofInt 1 (by intlit))
-          list_nth_mut_loop_pair_loop_fwd T tl0 tl1 i0
-    | list_t.Nil => Result.fail Error.panic
-  | list_t.Nil => Result.fail Error.panic
-termination_by list_nth_mut_loop_pair_loop_fwd ls0 ls1 i =>
-  list_nth_mut_loop_pair_loop_terminates T ls0 ls1 i
-decreasing_by list_nth_mut_loop_pair_loop_decreases ls0 ls1 i
-
-/- [loops::list_nth_mut_loop_pair] -/
-def list_nth_mut_loop_pair_fwd
-  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : Result (T × T) :=
-  list_nth_mut_loop_pair_loop_fwd T ls0 ls1 i
-
-/- [loops::list_nth_mut_loop_pair] -/
-def list_nth_mut_loop_pair_loop_back'a
-  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) (ret0 : T) :
-  (Result (list_t T))
-  :=
-  match h: ls0 with
-  | list_t.Cons x0 tl0 =>
-    match h: ls1 with
-    | list_t.Cons x1 tl1 =>
-      if h: i = (U32.ofInt 0 (by intlit))
-      then Result.ret (list_t.Cons ret0 tl0)
-      else
-        do
-          let i0 ← i - (U32.ofInt 1 (by intlit))
-          let tl00 ← list_nth_mut_loop_pair_loop_back'a T tl0 tl1 i0 ret0
-          Result.ret (list_t.Cons x0 tl00)
-    | list_t.Nil => Result.fail Error.panic
-  | list_t.Nil => Result.fail Error.panic
-termination_by list_nth_mut_loop_pair_loop_back'a ls0 ls1 i ret0 =>
-  list_nth_mut_loop_pair_loop_terminates T ls0 ls1 i
-decreasing_by list_nth_mut_loop_pair_loop_decreases ls0 ls1 i
-
-/- [loops::list_nth_mut_loop_pair] -/
-def list_nth_mut_loop_pair_back'a
-  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) (ret0 : T) :
-  Result (list_t T)
-  :=
-  list_nth_mut_loop_pair_loop_back'a T ls0 ls1 i ret0
-
-/- [loops::list_nth_mut_loop_pair] -/
-def list_nth_mut_loop_pair_loop_back'b
-  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) (ret0 : T) :
-  (Result (list_t T))
-  :=
-  match h: ls0 with
-  | list_t.Cons x0 tl0 =>
-    match h: ls1 with
-    | list_t.Cons x1 tl1 =>
-      if h: i = (U32.ofInt 0 (by intlit))
-      then Result.ret (list_t.Cons ret0 tl1)
-      else
-        do
-          let i0 ← i - (U32.ofInt 1 (by intlit))
-          let tl10 ← list_nth_mut_loop_pair_loop_back'b T tl0 tl1 i0 ret0
-          Result.ret (list_t.Cons x1 tl10)
-    | list_t.Nil => Result.fail Error.panic
-  | list_t.Nil => Result.fail Error.panic
-termination_by list_nth_mut_loop_pair_loop_back'b ls0 ls1 i ret0 =>
-  list_nth_mut_loop_pair_loop_terminates T ls0 ls1 i
-decreasing_by list_nth_mut_loop_pair_loop_decreases ls0 ls1 i
-
-/- [loops::list_nth_mut_loop_pair] -/
-def list_nth_mut_loop_pair_back'b
-  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) (ret0 : T) :
-  Result (list_t T)
-  :=
-  list_nth_mut_loop_pair_loop_back'b T ls0 ls1 i ret0
-
-/- [loops::list_nth_shared_loop_pair] -/
-def list_nth_shared_loop_pair_loop_fwd
-  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : (Result (T × T)) :=
-  match h: ls0 with
-  | list_t.Cons x0 tl0 =>
-    match h: ls1 with
-    | list_t.Cons x1 tl1 =>
-      if h: i = (U32.ofInt 0 (by intlit))
-      then Result.ret (x0, x1)
-      else
-        do
-          let i0 ← i - (U32.ofInt 1 (by intlit))
-          list_nth_shared_loop_pair_loop_fwd T tl0 tl1 i0
-    | list_t.Nil => Result.fail Error.panic
-  | list_t.Nil => Result.fail Error.panic
-termination_by list_nth_shared_loop_pair_loop_fwd ls0 ls1 i =>
-  list_nth_shared_loop_pair_loop_terminates T ls0 ls1 i
-decreasing_by list_nth_shared_loop_pair_loop_decreases ls0 ls1 i
-
-/- [loops::list_nth_shared_loop_pair] -/
-def list_nth_shared_loop_pair_fwd
-  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : Result (T × T) :=
-  list_nth_shared_loop_pair_loop_fwd T ls0 ls1 i
-
-/- [loops::list_nth_mut_loop_pair_merge] -/
-def list_nth_mut_loop_pair_merge_loop_fwd
-  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : (Result (T × T)) :=
-  match h: ls0 with
-  | list_t.Cons x0 tl0 =>
-    match h: ls1 with
-    | list_t.Cons x1 tl1 =>
-      if h: i = (U32.ofInt 0 (by intlit))
-      then Result.ret (x0, x1)
-      else
-        do
-          let i0 ← i - (U32.ofInt 1 (by intlit))
-          list_nth_mut_loop_pair_merge_loop_fwd T tl0 tl1 i0
-    | list_t.Nil => Result.fail Error.panic
-  | list_t.Nil => Result.fail Error.panic
-termination_by list_nth_mut_loop_pair_merge_loop_fwd ls0 ls1 i =>
-  list_nth_mut_loop_pair_merge_loop_terminates T ls0 ls1 i
-decreasing_by list_nth_mut_loop_pair_merge_loop_decreases ls0 ls1 i
-
-/- [loops::list_nth_mut_loop_pair_merge] -/
-def list_nth_mut_loop_pair_merge_fwd
-  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : Result (T × T) :=
-  list_nth_mut_loop_pair_merge_loop_fwd T ls0 ls1 i
-
-/- [loops::list_nth_mut_loop_pair_merge] -/
-def list_nth_mut_loop_pair_merge_loop_back
-  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) (ret0 : (T × T)) :
-  (Result ((list_t T) × (list_t T)))
-  :=
-  match h: ls0 with
-  | list_t.Cons x0 tl0 =>
-    match h: ls1 with
-    | list_t.Cons x1 tl1 =>
-      if h: i = (U32.ofInt 0 (by intlit))
-      then
-        let (t, t0) := ret0
-        Result.ret (list_t.Cons t tl0, list_t.Cons t0 tl1)
-      else
-        do
-          let i0 ← i - (U32.ofInt 1 (by intlit))
-          let (tl00, tl10) ←
-            list_nth_mut_loop_pair_merge_loop_back T tl0 tl1 i0 ret0
-          Result.ret (list_t.Cons x0 tl00, list_t.Cons x1 tl10)
-    | list_t.Nil => Result.fail Error.panic
-  | list_t.Nil => Result.fail Error.panic
-termination_by list_nth_mut_loop_pair_merge_loop_back ls0 ls1 i ret0 =>
-  list_nth_mut_loop_pair_merge_loop_terminates T ls0 ls1 i
-decreasing_by list_nth_mut_loop_pair_merge_loop_decreases ls0 ls1 i
-
-/- [loops::list_nth_mut_loop_pair_merge] -/
-def list_nth_mut_loop_pair_merge_back
-  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) (ret0 : (T × T)) :
-  Result ((list_t T) × (list_t T))
-  :=
-  list_nth_mut_loop_pair_merge_loop_back T ls0 ls1 i ret0
-
-/- [loops::list_nth_shared_loop_pair_merge] -/
-def list_nth_shared_loop_pair_merge_loop_fwd
-  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : (Result (T × T)) :=
-  match h: ls0 with
-  | list_t.Cons x0 tl0 =>
-    match h: ls1 with
-    | list_t.Cons x1 tl1 =>
-      if h: i = (U32.ofInt 0 (by intlit))
-      then Result.ret (x0, x1)
-      else
-        do
-          let i0 ← i - (U32.ofInt 1 (by intlit))
-          list_nth_shared_loop_pair_merge_loop_fwd T tl0 tl1 i0
-    | list_t.Nil => Result.fail Error.panic
-  | list_t.Nil => Result.fail Error.panic
-termination_by list_nth_shared_loop_pair_merge_loop_fwd ls0 ls1 i =>
-  list_nth_shared_loop_pair_merge_loop_terminates T ls0 ls1 i
-decreasing_by list_nth_shared_loop_pair_merge_loop_decreases ls0 ls1 i
-
-/- [loops::list_nth_shared_loop_pair_merge] -/
-def list_nth_shared_loop_pair_merge_fwd
-  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : Result (T × T) :=
-  list_nth_shared_loop_pair_merge_loop_fwd T ls0 ls1 i
-
-/- [loops::list_nth_mut_shared_loop_pair] -/
-def list_nth_mut_shared_loop_pair_loop_fwd
-  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : (Result (T × T)) :=
-  match h: ls0 with
-  | list_t.Cons x0 tl0 =>
-    match h: ls1 with
-    | list_t.Cons x1 tl1 =>
-      if h: i = (U32.ofInt 0 (by intlit))
-      then Result.ret (x0, x1)
-      else
-        do
-          let i0 ← i - (U32.ofInt 1 (by intlit))
-          list_nth_mut_shared_loop_pair_loop_fwd T tl0 tl1 i0
-    | list_t.Nil => Result.fail Error.panic
-  | list_t.Nil => Result.fail Error.panic
-termination_by list_nth_mut_shared_loop_pair_loop_fwd ls0 ls1 i =>
-  list_nth_mut_shared_loop_pair_loop_terminates T ls0 ls1 i
-decreasing_by list_nth_mut_shared_loop_pair_loop_decreases ls0 ls1 i
-
-/- [loops::list_nth_mut_shared_loop_pair] -/
-def list_nth_mut_shared_loop_pair_fwd
-  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : Result (T × T) :=
-  list_nth_mut_shared_loop_pair_loop_fwd T ls0 ls1 i
-
-/- [loops::list_nth_mut_shared_loop_pair] -/
-def list_nth_mut_shared_loop_pair_loop_back
-  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) (ret0 : T) :
-  (Result (list_t T))
-  :=
-  match h: ls0 with
-  | list_t.Cons x0 tl0 =>
-    match h: ls1 with
-    | list_t.Cons x1 tl1 =>
-      if h: i = (U32.ofInt 0 (by intlit))
-      then Result.ret (list_t.Cons ret0 tl0)
-      else
-        do
-          let i0 ← i - (U32.ofInt 1 (by intlit))
-          let tl00 ←
-            list_nth_mut_shared_loop_pair_loop_back T tl0 tl1 i0 ret0
-          Result.ret (list_t.Cons x0 tl00)
-    | list_t.Nil => Result.fail Error.panic
-  | list_t.Nil => Result.fail Error.panic
-termination_by list_nth_mut_shared_loop_pair_loop_back ls0 ls1 i ret0 =>
-  list_nth_mut_shared_loop_pair_loop_terminates T ls0 ls1 i
-decreasing_by list_nth_mut_shared_loop_pair_loop_decreases ls0 ls1 i
-
-/- [loops::list_nth_mut_shared_loop_pair] -/
-def list_nth_mut_shared_loop_pair_back
-  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) (ret0 : T) :
-  Result (list_t T)
-  :=
-  list_nth_mut_shared_loop_pair_loop_back T ls0 ls1 i ret0
-
-/- [loops::list_nth_mut_shared_loop_pair_merge] -/
-def list_nth_mut_shared_loop_pair_merge_loop_fwd
-  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : (Result (T × T)) :=
-  match h: ls0 with
-  | list_t.Cons x0 tl0 =>
-    match h: ls1 with
-    | list_t.Cons x1 tl1 =>
-      if h: i = (U32.ofInt 0 (by intlit))
-      then Result.ret (x0, x1)
-      else
-        do
-          let i0 ← i - (U32.ofInt 1 (by intlit))
-          list_nth_mut_shared_loop_pair_merge_loop_fwd T tl0 tl1 i0
-    | list_t.Nil => Result.fail Error.panic
-  | list_t.Nil => Result.fail Error.panic
-termination_by list_nth_mut_shared_loop_pair_merge_loop_fwd ls0 ls1 i =>
-  list_nth_mut_shared_loop_pair_merge_loop_terminates T ls0 ls1 i
-decreasing_by list_nth_mut_shared_loop_pair_merge_loop_decreases ls0 ls1 i
-
-/- [loops::list_nth_mut_shared_loop_pair_merge] -/
-def list_nth_mut_shared_loop_pair_merge_fwd
-  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : Result (T × T) :=
-  list_nth_mut_shared_loop_pair_merge_loop_fwd T ls0 ls1 i
-
-/- [loops::list_nth_mut_shared_loop_pair_merge] -/
-def list_nth_mut_shared_loop_pair_merge_loop_back
-  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) (ret0 : T) :
-  (Result (list_t T))
-  :=
-  match h: ls0 with
-  | list_t.Cons x0 tl0 =>
-    match h: ls1 with
-    | list_t.Cons x1 tl1 =>
-      if h: i = (U32.ofInt 0 (by intlit))
-      then Result.ret (list_t.Cons ret0 tl0)
-      else
-        do
-          let i0 ← i - (U32.ofInt 1 (by intlit))
-          let tl00 ←
-            list_nth_mut_shared_loop_pair_merge_loop_back T tl0 tl1 i0 ret0
-          Result.ret (list_t.Cons x0 tl00)
-    | list_t.Nil => Result.fail Error.panic
-  | list_t.Nil => Result.fail Error.panic
-termination_by list_nth_mut_shared_loop_pair_merge_loop_back ls0 ls1 i ret0 =>
-  list_nth_mut_shared_loop_pair_merge_loop_terminates T ls0 ls1 i
-decreasing_by list_nth_mut_shared_loop_pair_merge_loop_decreases ls0 ls1 i
-
-/- [loops::list_nth_mut_shared_loop_pair_merge] -/
-def list_nth_mut_shared_loop_pair_merge_back
-  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) (ret0 : T) :
-  Result (list_t T)
-  :=
-  list_nth_mut_shared_loop_pair_merge_loop_back T ls0 ls1 i ret0
-
-/- [loops::list_nth_shared_mut_loop_pair] -/
-def list_nth_shared_mut_loop_pair_loop_fwd
-  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : (Result (T × T)) :=
-  match h: ls0 with
-  | list_t.Cons x0 tl0 =>
-    match h: ls1 with
-    | list_t.Cons x1 tl1 =>
-      if h: i = (U32.ofInt 0 (by intlit))
-      then Result.ret (x0, x1)
-      else
-        do
-          let i0 ← i - (U32.ofInt 1 (by intlit))
-          list_nth_shared_mut_loop_pair_loop_fwd T tl0 tl1 i0
-    | list_t.Nil => Result.fail Error.panic
-  | list_t.Nil => Result.fail Error.panic
-termination_by list_nth_shared_mut_loop_pair_loop_fwd ls0 ls1 i =>
-  list_nth_shared_mut_loop_pair_loop_terminates T ls0 ls1 i
-decreasing_by list_nth_shared_mut_loop_pair_loop_decreases ls0 ls1 i
-
-/- [loops::list_nth_shared_mut_loop_pair] -/
-def list_nth_shared_mut_loop_pair_fwd
-  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : Result (T × T) :=
-  list_nth_shared_mut_loop_pair_loop_fwd T ls0 ls1 i
-
-/- [loops::list_nth_shared_mut_loop_pair] -/
-def list_nth_shared_mut_loop_pair_loop_back
-  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) (ret0 : T) :
-  (Result (list_t T))
-  :=
-  match h: ls0 with
-  | list_t.Cons x0 tl0 =>
-    match h: ls1 with
-    | list_t.Cons x1 tl1 =>
-      if h: i = (U32.ofInt 0 (by intlit))
-      then Result.ret (list_t.Cons ret0 tl1)
-      else
-        do
-          let i0 ← i - (U32.ofInt 1 (by intlit))
-          let tl10 ←
-            list_nth_shared_mut_loop_pair_loop_back T tl0 tl1 i0 ret0
-          Result.ret (list_t.Cons x1 tl10)
-    | list_t.Nil => Result.fail Error.panic
-  | list_t.Nil => Result.fail Error.panic
-termination_by list_nth_shared_mut_loop_pair_loop_back ls0 ls1 i ret0 =>
-  list_nth_shared_mut_loop_pair_loop_terminates T ls0 ls1 i
-decreasing_by list_nth_shared_mut_loop_pair_loop_decreases ls0 ls1 i
-
-/- [loops::list_nth_shared_mut_loop_pair] -/
-def list_nth_shared_mut_loop_pair_back
-  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) (ret0 : T) :
-  Result (list_t T)
-  :=
-  list_nth_shared_mut_loop_pair_loop_back T ls0 ls1 i ret0
-
-/- [loops::list_nth_shared_mut_loop_pair_merge] -/
-def list_nth_shared_mut_loop_pair_merge_loop_fwd
-  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : (Result (T × T)) :=
-  match h: ls0 with
-  | list_t.Cons x0 tl0 =>
-    match h: ls1 with
-    | list_t.Cons x1 tl1 =>
-      if h: i = (U32.ofInt 0 (by intlit))
-      then Result.ret (x0, x1)
-      else
-        do
-          let i0 ← i - (U32.ofInt 1 (by intlit))
-          list_nth_shared_mut_loop_pair_merge_loop_fwd T tl0 tl1 i0
-    | list_t.Nil => Result.fail Error.panic
-  | list_t.Nil => Result.fail Error.panic
-termination_by list_nth_shared_mut_loop_pair_merge_loop_fwd ls0 ls1 i =>
-  list_nth_shared_mut_loop_pair_merge_loop_terminates T ls0 ls1 i
-decreasing_by list_nth_shared_mut_loop_pair_merge_loop_decreases ls0 ls1 i
-
-/- [loops::list_nth_shared_mut_loop_pair_merge] -/
-def list_nth_shared_mut_loop_pair_merge_fwd
-  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : Result (T × T) :=
-  list_nth_shared_mut_loop_pair_merge_loop_fwd T ls0 ls1 i
-
-/- [loops::list_nth_shared_mut_loop_pair_merge] -/
-def list_nth_shared_mut_loop_pair_merge_loop_back
-  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) (ret0 : T) :
-  (Result (list_t T))
-  :=
-  match h: ls0 with
-  | list_t.Cons x0 tl0 =>
-    match h: ls1 with
-    | list_t.Cons x1 tl1 =>
-      if h: i = (U32.ofInt 0 (by intlit))
-      then Result.ret (list_t.Cons ret0 tl1)
-      else
-        do
-          let i0 ← i - (U32.ofInt 1 (by intlit))
-          let tl10 ←
-            list_nth_shared_mut_loop_pair_merge_loop_back T tl0 tl1 i0 ret0
-          Result.ret (list_t.Cons x1 tl10)
-    | list_t.Nil => Result.fail Error.panic
-  | list_t.Nil => Result.fail Error.panic
-termination_by list_nth_shared_mut_loop_pair_merge_loop_back ls0 ls1 i ret0 =>
-  list_nth_shared_mut_loop_pair_merge_loop_terminates T ls0 ls1 i
-decreasing_by list_nth_shared_mut_loop_pair_merge_loop_decreases ls0 ls1 i
-
-/- [loops::list_nth_shared_mut_loop_pair_merge] -/
-def list_nth_shared_mut_loop_pair_merge_back
-  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) (ret0 : T) :
-  Result (list_t T)
-  :=
-  list_nth_shared_mut_loop_pair_merge_loop_back T ls0 ls1 i ret0
-
diff --git a/tests/lean/misc-loops/Loops/Types.lean b/tests/lean/misc-loops/Loops/Types.lean
deleted file mode 100644
index ca43f4c8..00000000
--- a/tests/lean/misc-loops/Loops/Types.lean
+++ /dev/null
@@ -1,9 +0,0 @@
--- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
--- [loops]: type definitions
-import Base.Primitives
-
-/- [loops::List] -/
-inductive list_t (T : Type) :=
-| Cons : T -> list_t T -> list_t T
-| Nil : list_t T
-
diff --git a/tests/lean/misc-loops/lake-manifest.json b/tests/lean/misc-loops/lake-manifest.json
deleted file mode 100644
index 57b071ca..00000000
--- a/tests/lean/misc-loops/lake-manifest.json
+++ /dev/null
@@ -1,27 +0,0 @@
-{"version": 4,
- "packagesDir": "./lake-packages",
- "packages":
- [{"git":
-   {"url": "https://github.com/leanprover-community/mathlib4.git",
-    "subDir?": null,
-    "rev": "4037792ead804d7bfa8868e2c4684d4223c15ece",
-    "name": "mathlib",
-    "inputRev?": null}},
-  {"git":
-   {"url": "https://github.com/gebner/quote4",
-    "subDir?": null,
-    "rev": "2412c4fdf4a8b689f4467618e5e7b371ae5014aa",
-    "name": "Qq",
-    "inputRev?": "master"}},
-  {"git":
-   {"url": "https://github.com/JLimperg/aesop",
-    "subDir?": null,
-    "rev": "7fe9ecd9339b0e1796e89d243b776849c305c690",
-    "name": "aesop",
-    "inputRev?": "master"}},
-  {"git":
-   {"url": "https://github.com/leanprover/std4",
-    "subDir?": null,
-    "rev": "24897887905b3a1254b244369f5dd2cf6174b0ee",
-    "name": "std",
-    "inputRev?": "main"}}]}
diff --git a/tests/lean/misc-loops/lakefile.lean b/tests/lean/misc-loops/lakefile.lean
deleted file mode 100644
index 097c0a7d..00000000
--- a/tests/lean/misc-loops/lakefile.lean
+++ /dev/null
@@ -1,12 +0,0 @@
-import Lake
-open Lake DSL
-
-require mathlib from git
-  "https://github.com/leanprover-community/mathlib4.git"
-
-package «loops» {}
-
-lean_lib «Base» {}
-
-@[default_target]
-lean_lib «Loops» {}
diff --git a/tests/lean/misc-loops/lean-toolchain b/tests/lean/misc-loops/lean-toolchain
deleted file mode 100644
index bbf57f10..00000000
--- a/tests/lean/misc-loops/lean-toolchain
+++ /dev/null
@@ -1 +0,0 @@
-leanprover/lean4:nightly-2023-01-21
diff --git a/tests/lean/misc-no_nested_borrows/Base/Primitives.lean b/tests/lean/misc-no_nested_borrows/Base/Primitives.lean
deleted file mode 100644
index 4a66a453..00000000
--- a/tests/lean/misc-no_nested_borrows/Base/Primitives.lean
+++ /dev/null
@@ -1,583 +0,0 @@
-import Lean
-import Lean.Meta.Tactic.Simp
-import Init.Data.List.Basic
-import Mathlib.Tactic.RunCmd
-
---------------------
--- ASSERT COMMAND --
---------------------
-
-open Lean Elab Command Term Meta
-
-syntax (name := assert) "#assert" term: command
-
-@[command_elab assert]
-unsafe
-def assertImpl : CommandElab := fun (_stx: Syntax) => do
-  runTermElabM (fun _ => do
-    let r ← evalTerm Bool (mkConst ``Bool) _stx[1]
-    if not r then
-      logInfo "Assertion failed for: "
-      logInfo _stx[1]
-      logError "Expression reduced to false"
-    pure ())
-
-#eval 2 == 2
-#assert (2 == 2)
-
--------------
--- PRELUDE --
--------------
-
--- Results & monadic combinators
-
-inductive Error where
-   | assertionFailure: Error
-   | integerOverflow: Error
-   | divisionByZero: Error
-   | arrayOutOfBounds: Error
-   | maximumSizeExceeded: Error
-   | panic: Error
-deriving Repr, BEq
-
-open Error
-
-inductive Result (α : Type u) where
-  | ret (v: α): Result α
-  | fail (e: Error): Result α
-deriving Repr, BEq
-
-open Result
-
-instance Result_Inhabited (α : Type u) : Inhabited (Result α) :=
-  Inhabited.mk (fail panic)
-
-/- HELPERS -/
-
-def ret? {α: Type} (r: Result α): Bool :=
-  match r with
-  | Result.ret _ => true
-  | Result.fail _ => false
-
-def massert (b:Bool) : Result Unit :=
-  if b then .ret () else fail assertionFailure
-
-def eval_global {α: Type} (x: Result α) (_: ret? x): α :=
-  match x with
-  | Result.fail _ => by contradiction
-  | Result.ret x => x
-
-/- DO-DSL SUPPORT -/
-
-def bind (x: Result α) (f: α -> Result β) : Result β :=
-  match x with
-  | ret v  => f v 
-  | fail v => fail v
-
--- Allows using Result in do-blocks
-instance : Bind Result where
-  bind := bind
-
--- Allows using return x in do-blocks
-instance : Pure Result where
-  pure := fun x => ret x
-
-/- CUSTOM-DSL SUPPORT -/
-
--- Let-binding the Result of a monadic operation is oftentimes not sufficient,
--- because we may need a hypothesis for equational reasoning in the scope. We
--- rely on subtype, and a custom let-binding operator, in effect recreating our
--- own variant of the do-dsl
-
-def Result.attach {α: Type} (o : Result α): Result { x : α // o = ret x } :=
-  match o with
-  | .ret x => .ret ⟨x, rfl⟩
-  | .fail e => .fail e
-
-macro "let" e:term " ⟵ " f:term : doElem =>
-  `(doElem| let ⟨$e, h⟩ ← Result.attach $f)
-
--- TODO: any way to factorize both definitions?
-macro "let" e:term " <-- " f:term : doElem =>
-  `(doElem| let ⟨$e, h⟩ ← Result.attach $f)
-
--- We call the hypothesis `h`, in effect making it unavailable to the user
--- (because too much shadowing). But in practice, once can use the French single
--- quote notation (input with f< and f>), where `‹ h ›` finds a suitable
--- hypothesis in the context, this is equivalent to `have x: h := by assumption in x`
-#eval do
-  let y <-- .ret (0: Nat)
-  let _: y = 0 := by cases ‹ ret 0 = ret y › ; decide
-  let r: { x: Nat // x = 0 } := ⟨ y, by assumption ⟩
-  .ret r
-
-----------------------
--- MACHINE INTEGERS --
-----------------------
-
--- We redefine our machine integers types.
-
--- For Isize/Usize, we reuse `getNumBits` from `USize`. You cannot reduce `getNumBits`
--- using the simplifier, meaning that proofs do not depend on the compile-time value of
--- USize.size. (Lean assumes 32 or 64-bit platforms, and Rust doesn't really support, at
--- least officially, 16-bit microcontrollers, so this seems like a fine design decision
--- for now.)
-
--- Note from Chris Bailey: "If there's more than one salient property of your
--- definition then the subtyping strategy might get messy, and the property part
--- of a subtype is less discoverable by the simplifier or tactics like
--- library_search." So, we will not add refinements on the return values of the
--- operations defined on Primitives, but will rather rely on custom lemmas to
--- invert on possible return values of the primitive operations.
-
--- Machine integer constants, done via `ofNatCore`, which requires a proof that
--- the `Nat` fits within the desired integer type. We provide a custom tactic.
-
-open System.Platform.getNumBits
-
--- TODO: is there a way of only importing System.Platform.getNumBits?
---
-@[simp] def size_num_bits : Nat := (System.Platform.getNumBits ()).val
-
--- Remark: Lean seems to use < for the comparisons with the upper bounds by convention.
--- We keep the F* convention for now.
-@[simp] def Isize.min : Int := - (HPow.hPow 2 (size_num_bits - 1))
-@[simp] def Isize.max : Int := (HPow.hPow 2 (size_num_bits - 1)) - 1
-@[simp] def I8.min    : Int := - (HPow.hPow 2 7)
-@[simp] def I8.max    : Int := HPow.hPow 2 7 - 1
-@[simp] def I16.min   : Int := - (HPow.hPow 2 15)
-@[simp] def I16.max   : Int := HPow.hPow 2 15 - 1
-@[simp] def I32.min   : Int := -(HPow.hPow 2 31)
-@[simp] def I32.max   : Int := HPow.hPow 2 31 - 1
-@[simp] def I64.min   : Int := -(HPow.hPow 2 63)
-@[simp] def I64.max   : Int := HPow.hPow 2 63 - 1
-@[simp] def I128.min  : Int := -(HPow.hPow 2 127)
-@[simp] def I128.max  : Int := HPow.hPow 2 127 - 1
-@[simp] def Usize.min : Int := 0
-@[simp] def Usize.max : Int := HPow.hPow 2 size_num_bits - 1
-@[simp] def U8.min    : Int := 0
-@[simp] def U8.max    : Int := HPow.hPow 2 8 - 1
-@[simp] def U16.min   : Int := 0
-@[simp] def U16.max   : Int := HPow.hPow 2 16 - 1
-@[simp] def U32.min   : Int := 0
-@[simp] def U32.max   : Int := HPow.hPow 2 32 - 1
-@[simp] def U64.min   : Int := 0
-@[simp] def U64.max   : Int := HPow.hPow 2 64 - 1
-@[simp] def U128.min  : Int := 0
-@[simp] def U128.max  : Int := HPow.hPow 2 128 - 1
-
-#assert (I8.min   == -128)
-#assert (I8.max   == 127)
-#assert (I16.min  == -32768)
-#assert (I16.max  == 32767)
-#assert (I32.min  == -2147483648)
-#assert (I32.max  == 2147483647)
-#assert (I64.min  == -9223372036854775808)
-#assert (I64.max  == 9223372036854775807)
-#assert (I128.min == -170141183460469231731687303715884105728)
-#assert (I128.max == 170141183460469231731687303715884105727)
-#assert (U8.min   == 0)
-#assert (U8.max   == 255)
-#assert (U16.min  == 0)
-#assert (U16.max  == 65535)
-#assert (U32.min  == 0)
-#assert (U32.max  == 4294967295)
-#assert (U64.min  == 0)
-#assert (U64.max  == 18446744073709551615)
-#assert (U128.min == 0)
-#assert (U128.max == 340282366920938463463374607431768211455)
-
-inductive ScalarTy :=
-| Isize
-| I8
-| I16
-| I32
-| I64
-| I128
-| Usize
-| U8
-| U16
-| U32
-| U64
-| U128
-
-def Scalar.min (ty : ScalarTy) : Int :=
-  match ty with
-  | .Isize => Isize.min
-  | .I8    => I8.min
-  | .I16   => I16.min
-  | .I32   => I32.min
-  | .I64   => I64.min
-  | .I128  => I128.min
-  | .Usize => Usize.min
-  | .U8    => U8.min
-  | .U16   => U16.min
-  | .U32   => U32.min
-  | .U64   => U64.min
-  | .U128  => U128.min
-
-def Scalar.max (ty : ScalarTy) : Int :=
-  match ty with
-  | .Isize => Isize.max
-  | .I8    => I8.max
-  | .I16   => I16.max
-  | .I32   => I32.max
-  | .I64   => I64.max
-  | .I128  => I128.max
-  | .Usize => Usize.max
-  | .U8    => U8.max
-  | .U16   => U16.max
-  | .U32   => U32.max
-  | .U64   => U64.max
-  | .U128  => U128.max
-
--- "Conservative" bounds
--- We use those because we can't compare to the isize bounds (which can't
--- reduce at compile-time). Whenever we perform an arithmetic operation like
--- addition we need to check that the result is in bounds: we first compare
--- to the conservative bounds, which reduce, then compare to the real bounds.
--- This is useful for the various #asserts that we want to reduce at
--- type-checking time.
-def Scalar.cMin (ty : ScalarTy) : Int :=
-  match ty with
-  | .Isize => I32.min
-  | _ => Scalar.min ty
-
-def Scalar.cMax (ty : ScalarTy) : Int :=
-  match ty with
-  | .Isize => I32.max
-  | .Usize => U32.max
-  | _ => Scalar.max ty
-
-theorem Scalar.cMin_bound ty : Scalar.min ty <= Scalar.cMin ty := by sorry
-theorem Scalar.cMax_bound ty : Scalar.min ty <= Scalar.cMin ty := by sorry
-
-structure Scalar (ty : ScalarTy) where
-  val : Int
-  hmin : Scalar.min ty <= val
-  hmax : val <= Scalar.max ty
-
-theorem Scalar.bound_suffices (ty : ScalarTy) (x : Int) :
-  Scalar.cMin ty <= x && x <= Scalar.cMax ty ->
-  (decide (Scalar.min ty ≤ x) && decide (x ≤ Scalar.max ty)) = true
-  := by sorry
-
-def Scalar.ofIntCore {ty : ScalarTy} (x : Int)
-  (hmin : Scalar.min ty <= x) (hmax : x <= Scalar.max ty) : Scalar ty :=
-  { val := x, hmin := hmin, hmax := hmax }
-
-def Scalar.ofInt {ty : ScalarTy} (x : Int)
-  (h : Scalar.min ty <= x && x <= Scalar.max ty) : Scalar ty :=
-  let hmin: Scalar.min ty <= x := by sorry
-  let hmax: x <= Scalar.max ty := by sorry
-  Scalar.ofIntCore x hmin hmax
-
--- Further thoughts: look at what has been done here:
--- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/Fin/Basic.lean
--- and
--- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/UInt.lean
--- which both contain a fair amount of reasoning already!
-def Scalar.tryMk (ty : ScalarTy) (x : Int) : Result (Scalar ty) :=
-  -- TODO: write this with only one if then else
-  if hmin_cons: Scalar.cMin ty <= x || Scalar.min ty <= x then
-    if hmax_cons: x <= Scalar.cMax ty || x <= Scalar.max ty then
-      let hmin: Scalar.min ty <= x := by sorry
-      let hmax: x <= Scalar.max ty := by sorry
-      return Scalar.ofIntCore x hmin hmax
-    else fail integerOverflow
-  else fail integerOverflow
-
-def Scalar.neg {ty : ScalarTy} (x : Scalar ty) : Result (Scalar ty) := Scalar.tryMk ty (- x.val)
-
-def Scalar.div {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
-  if y.val != 0 then Scalar.tryMk ty (x.val / y.val) else fail divisionByZero
-
--- Checking that the % operation in Lean computes the same as the remainder operation in Rust
-#assert 1 % 2 = (1:Int)
-#assert (-1) % 2 = -1
-#assert 1 % (-2) = 1
-#assert (-1) % (-2) = -1
-
-def Scalar.rem {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
-  if y.val != 0 then Scalar.tryMk ty (x.val % y.val) else fail divisionByZero
-
-def Scalar.add {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
-  Scalar.tryMk ty (x.val + y.val)
-
-def Scalar.sub {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
-  Scalar.tryMk ty (x.val - y.val)
-
-def Scalar.mul {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
-  Scalar.tryMk ty (x.val * y.val)
-
--- TODO: instances of +, -, * etc. for scalars
-
--- Cast an integer from a [src_ty] to a [tgt_ty]
--- TODO: check the semantics of casts in Rust
-def Scalar.cast {src_ty : ScalarTy} (tgt_ty : ScalarTy) (x : Scalar src_ty) : Result (Scalar tgt_ty) :=
-  Scalar.tryMk tgt_ty x.val
-
--- The scalar types
--- We declare the definitions as reducible so that Lean can unfold them (useful
--- for type class resolution for instance).
-@[reducible] def Isize := Scalar .Isize
-@[reducible] def I8    := Scalar .I8
-@[reducible] def I16   := Scalar .I16
-@[reducible] def I32   := Scalar .I32
-@[reducible] def I64   := Scalar .I64
-@[reducible] def I128  := Scalar .I128
-@[reducible] def Usize := Scalar .Usize
-@[reducible] def U8    := Scalar .U8
-@[reducible] def U16   := Scalar .U16
-@[reducible] def U32   := Scalar .U32
-@[reducible] def U64   := Scalar .U64
-@[reducible] def U128  := Scalar .U128
-
--- TODO: below: not sure this is the best way.
--- Should we rather overload operations like +, -, etc.?
--- Also, it is possible to automate the generation of those definitions
--- with macros (but would it be a good idea? It would be less easy to
--- read the file, which is not supposed to change a lot)
-
--- Negation
-
-/--
-Remark: there is no heterogeneous negation in the Lean prelude: we thus introduce
-one here.
-
-The notation typeclass for heterogeneous addition.
-This enables the notation `- a : β` where `a : α`.
--/
-class HNeg (α : Type u) (β : outParam (Type v)) where
-  /-- `- a` computes the negation of `a`.
-  The meaning of this notation is type-dependent. -/
-  hNeg : α → β
-
-prefix:75  "-"   => HNeg.hNeg
-
-instance : HNeg Isize (Result Isize) where hNeg x := Scalar.neg x
-instance : HNeg I8 (Result I8) where hNeg x := Scalar.neg x
-instance : HNeg I16 (Result I16) where hNeg x := Scalar.neg x
-instance : HNeg I32 (Result I32) where hNeg x := Scalar.neg x
-instance : HNeg I64 (Result I64) where hNeg x := Scalar.neg x
-instance : HNeg I128 (Result I128) where hNeg x := Scalar.neg x
-
--- Addition
-instance {ty} : HAdd (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
-  hAdd x y := Scalar.add x y
-
--- Substraction
-instance {ty} : HSub (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
-  hSub x y := Scalar.sub x y
-
--- Multiplication
-instance {ty} : HMul (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
-  hMul x y := Scalar.mul x y
-
--- Division
-instance {ty} : HDiv (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
-  hDiv x y := Scalar.div x y
-
--- Remainder
-instance {ty} : HMod (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
-  hMod x y := Scalar.rem x y
-
--- ofIntCore
--- TODO: typeclass?
-def Isize.ofIntCore := @Scalar.ofIntCore .Isize
-def I8.ofIntCore    := @Scalar.ofIntCore .I8
-def I16.ofIntCore   := @Scalar.ofIntCore .I16
-def I32.ofIntCore   := @Scalar.ofIntCore .I32
-def I64.ofIntCore   := @Scalar.ofIntCore .I64
-def I128.ofIntCore  := @Scalar.ofIntCore .I128
-def Usize.ofIntCore := @Scalar.ofIntCore .Usize
-def U8.ofIntCore    := @Scalar.ofIntCore .U8
-def U16.ofIntCore   := @Scalar.ofIntCore .U16
-def U32.ofIntCore   := @Scalar.ofIntCore .U32
-def U64.ofIntCore   := @Scalar.ofIntCore .U64
-def U128.ofIntCore  := @Scalar.ofIntCore .U128
-
---  ofInt
--- TODO: typeclass?
-def Isize.ofInt := @Scalar.ofInt .Isize
-def I8.ofInt    := @Scalar.ofInt .I8
-def I16.ofInt   := @Scalar.ofInt .I16
-def I32.ofInt   := @Scalar.ofInt .I32
-def I64.ofInt   := @Scalar.ofInt .I64
-def I128.ofInt  := @Scalar.ofInt .I128
-def Usize.ofInt := @Scalar.ofInt .Usize
-def U8.ofInt    := @Scalar.ofInt .U8
-def U16.ofInt   := @Scalar.ofInt .U16
-def U32.ofInt   := @Scalar.ofInt .U32
-def U64.ofInt   := @Scalar.ofInt .U64
-def U128.ofInt  := @Scalar.ofInt .U128
-
--- Comparisons
-instance {ty} : LT (Scalar ty) where
-  lt a b := LT.lt a.val b.val
-
-instance {ty} : LE (Scalar ty) where le a b := LE.le a.val b.val
-
-instance Scalar.decLt {ty} (a b : Scalar ty) : Decidable (LT.lt a b) := Int.decLt ..
-instance Scalar.decLe {ty} (a b : Scalar ty) : Decidable (LE.le a b) := Int.decLe ..
-
-theorem Scalar.eq_of_val_eq {ty} : ∀ {i j : Scalar ty}, Eq i.val j.val → Eq i j
-  | ⟨_, _, _⟩, ⟨_, _, _⟩, rfl => rfl
-
-theorem Scalar.val_eq_of_eq {ty} {i j : Scalar ty} (h : Eq i j) : Eq i.val j.val :=
-  h ▸ rfl
-
-theorem Scalar.ne_of_val_ne {ty} {i j : Scalar ty} (h : Not (Eq i.val j.val)) : Not (Eq i j) :=
-  fun h' => absurd (val_eq_of_eq h') h
-
-instance (ty : ScalarTy) : DecidableEq (Scalar ty) :=
-  fun i j =>
-    match decEq i.val j.val with
-    | isTrue h  => isTrue (Scalar.eq_of_val_eq h)
-    | isFalse h => isFalse (Scalar.ne_of_val_ne h)
-
-def Scalar.toInt {ty} (n : Scalar ty) : Int := n.val
-
--- Tactic to prove that integers are in bounds
-syntax "intlit" : tactic
-
-macro_rules
-  | `(tactic| intlit) => `(tactic| apply Scalar.bound_suffices ; decide)
-
--- -- We now define a type class that subsumes the various machine integer types, so
--- -- as to write a concise definition for scalar_cast, rather than exhaustively
--- -- enumerating all of the possible pairs. We remark that Rust has sane semantics
--- -- and fails if a cast operation would involve a truncation or modulo.
-
--- class MachineInteger (t: Type) where
---   size: Nat
---   val: t -> Fin size
---   ofNatCore: (n:Nat) -> LT.lt n size -> t
-
--- set_option hygiene false in
--- run_cmd
---   for typeName in [`UInt8, `UInt16, `UInt32, `UInt64, `USize].map Lean.mkIdent do
---   Lean.Elab.Command.elabCommand (← `(
---     namespace $typeName
---     instance: MachineInteger $typeName where
---       size := size
---       val := val
---       ofNatCore := ofNatCore
---     end $typeName
---   ))
-
--- -- Aeneas only instantiates the destination type (`src` is implicit). We rely on
--- -- Lean to infer `src`.
-
--- def scalar_cast { src: Type } (dst: Type) [ MachineInteger src ] [ MachineInteger dst ] (x: src): Result dst :=
---   if h: MachineInteger.val x < MachineInteger.size dst then
---     .ret (MachineInteger.ofNatCore (MachineInteger.val x).val h)
---   else
---     .fail integerOverflow
-
--------------
--- VECTORS --
--------------
-
-def Vec (α : Type u) := { l : List α // List.length l <= Usize.max }
-
-def vec_new (α : Type u): Vec α := ⟨ [], by sorry ⟩
-
-def vec_len (α : Type u) (v : Vec α) : Usize :=
-  let ⟨ v, l ⟩ := v
-  Usize.ofIntCore (List.length v) (by sorry) l
- 
-def vec_push_fwd (α : Type u) (_ : Vec α) (_ : α) : Unit := ()
-
-def vec_push_back (α : Type u) (v : Vec α) (x : α) : Result (Vec α)
-  :=
-  if h : List.length v.val <= U32.max || List.length v.val <= Usize.max then
-    return ⟨ List.concat v.val x, by sorry ⟩
-  else
-    fail maximumSizeExceeded
-
-def vec_insert_fwd (α : Type u) (v: Vec α) (i: Usize) (_: α): Result Unit :=
-  if i.val < List.length v.val then
-    .ret ()
-  else
-    .fail arrayOutOfBounds
-
-def vec_insert_back (α : Type u) (v: Vec α) (i: Usize) (x: α): Result (Vec α) :=
-  if i.val < List.length v.val then
-    -- TODO: maybe we should redefine a list library which uses integers
-    -- (instead of natural numbers)
-    let i : Nat :=
-      match i.val with
-      | .ofNat n => n
-      | .negSucc n => by sorry -- TODO: we can't get here
-    let isLt: i < USize.size := by sorry
-    let i : Fin USize.size := { val := i, isLt := isLt }
-    .ret ⟨ List.set v.val i.val x, by
-      have h: List.length v.val <= Usize.max := v.property
-      rewrite [ List.length_set v.val i.val x ]
-      assumption
-    ⟩
-  else
-    .fail arrayOutOfBounds
-
-def vec_index_fwd (α : Type u) (v: Vec α) (i: Usize): Result α :=
-  if i.val < List.length v.val then
-    let i : Nat :=
-      match i.val with
-      | .ofNat n => n
-      | .negSucc n => by sorry -- TODO: we can't get here
-    let isLt: i < USize.size := by sorry
-    let i : Fin USize.size := { val := i, isLt := isLt }
-    let h: i < List.length v.val := by sorry
-    .ret (List.get v.val ⟨i.val, h⟩)
-  else
-    .fail arrayOutOfBounds
-
-def vec_index_back (α : Type u) (v: Vec α) (i: Usize) (_: α): Result Unit :=
-  if i.val < List.length v.val then
-    .ret ()
-  else
-    .fail arrayOutOfBounds
-
-def vec_index_mut_fwd (α : Type u) (v: Vec α) (i: Usize): Result α :=
-  if i.val < List.length v.val then
-    let i : Nat :=
-      match i.val with
-      | .ofNat n => n
-      | .negSucc n => by sorry -- TODO: we can't get here
-    let isLt: i < USize.size := by sorry
-    let i : Fin USize.size := { val := i, isLt := isLt }
-    let h: i < List.length v.val := by sorry
-    .ret (List.get v.val ⟨i.val, h⟩)
-  else
-    .fail arrayOutOfBounds
-
-def vec_index_mut_back (α : Type u) (v: Vec α) (i: Usize) (x: α): Result (Vec α) :=
-  if i.val < List.length v.val then
-    let i : Nat :=
-      match i.val with
-      | .ofNat n => n
-      | .negSucc n => by sorry -- TODO: we can't get here
-    let isLt: i < USize.size := by sorry
-    let i : Fin USize.size := { val := i, isLt := isLt }
-    .ret ⟨ List.set v.val i.val x, by
-      have h: List.length v.val <= Usize.max := v.property
-      rewrite [ List.length_set v.val i.val x ]
-      assumption
-    ⟩
-  else
-    .fail arrayOutOfBounds
-
-----------
--- MISC --
-----------
-
-def mem_replace_fwd (a : Type) (x : a) (_ : a) : a :=
-  x
-
-def mem_replace_back (a : Type) (_ : a) (y : a) : a :=
-  y
-
-/-- Aeneas-translated function -- useful to reduce non-recursive definitions.
- Use with `simp [ aeneas ]` -/
-register_simp_attr aeneas
diff --git a/tests/lean/misc-no_nested_borrows/NoNestedBorrows.lean b/tests/lean/misc-no_nested_borrows/NoNestedBorrows.lean
deleted file mode 100644
index 12c7d8f7..00000000
--- a/tests/lean/misc-no_nested_borrows/NoNestedBorrows.lean
+++ /dev/null
@@ -1,538 +0,0 @@
--- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
--- [no_nested_borrows]
-import Base.Primitives
-
-/- [no_nested_borrows::Pair] -/
-structure pair_t (T1 T2 : Type) where
-  pair_x : T1
-  pair_y : T2
-
-/- [no_nested_borrows::List] -/
-inductive list_t (T : Type) :=
-| Cons : T -> list_t T -> list_t T
-| Nil : list_t T
-
-/- [no_nested_borrows::One] -/
-inductive one_t (T1 : Type) :=
-| One : T1 -> one_t T1
-
-/- [no_nested_borrows::EmptyEnum] -/
-inductive empty_enum_t :=
-| Empty : empty_enum_t
-
-/- [no_nested_borrows::Enum] -/
-inductive enum_t :=
-| Variant1 : enum_t
-| Variant2 : enum_t
-
-/- [no_nested_borrows::EmptyStruct] -/
-structure empty_struct_t where
-
-/- [no_nested_borrows::Sum] -/
-inductive sum_t (T1 T2 : Type) :=
-| Left : T1 -> sum_t T1 T2
-| Right : T2 -> sum_t T1 T2
-
-/- [no_nested_borrows::neg_test] -/
-def neg_test_fwd (x : I32) : Result I32 :=
-  - x
-
-/- [no_nested_borrows::add_test] -/
-def add_test_fwd (x : U32) (y : U32) : Result U32 :=
-  x + y
-
-/- [no_nested_borrows::subs_test] -/
-def subs_test_fwd (x : U32) (y : U32) : Result U32 :=
-  x - y
-
-/- [no_nested_borrows::div_test] -/
-def div_test_fwd (x : U32) (y : U32) : Result U32 :=
-  x / y
-
-/- [no_nested_borrows::div_test1] -/
-def div_test1_fwd (x : U32) : Result U32 :=
-  x / (U32.ofInt 2 (by intlit))
-
-/- [no_nested_borrows::rem_test] -/
-def rem_test_fwd (x : U32) (y : U32) : Result U32 :=
-  x % y
-
-/- [no_nested_borrows::cast_test] -/
-def cast_test_fwd (x : U32) : Result I32 :=
-  Scalar.cast .I32 x
-
-/- [no_nested_borrows::test2] -/
-def test2_fwd : Result Unit :=
-  do
-    let _ ← (U32.ofInt 23 (by intlit)) + (U32.ofInt 44 (by intlit))
-    Result.ret ()
-
-/- Unit test for [no_nested_borrows::test2] -/
-#assert (test2_fwd == .ret ())
-
-/- [no_nested_borrows::get_max] -/
-def get_max_fwd (x : U32) (y : U32) : Result U32 :=
-  if h: x >= y
-  then Result.ret x
-  else Result.ret y
-
-/- [no_nested_borrows::test3] -/
-def test3_fwd : Result Unit :=
-  do
-    let x ← get_max_fwd (U32.ofInt 4 (by intlit)) (U32.ofInt 3 (by intlit))
-    let y ← get_max_fwd (U32.ofInt 10 (by intlit)) (U32.ofInt 11 (by intlit))
-    let z ← x + y
-    if h: not (z = (U32.ofInt 15 (by intlit)))
-    then Result.fail Error.panic
-    else Result.ret ()
-
-/- Unit test for [no_nested_borrows::test3] -/
-#assert (test3_fwd == .ret ())
-
-/- [no_nested_borrows::test_neg1] -/
-def test_neg1_fwd : Result Unit :=
-  do
-    let y ← - (I32.ofInt 3 (by intlit))
-    if h: not (y = (I32.ofInt (-(3:Int)) (by intlit)))
-    then Result.fail Error.panic
-    else Result.ret ()
-
-/- Unit test for [no_nested_borrows::test_neg1] -/
-#assert (test_neg1_fwd == .ret ())
-
-/- [no_nested_borrows::refs_test1] -/
-def refs_test1_fwd : Result Unit :=
-  if h: not ((I32.ofInt 1 (by intlit)) = (I32.ofInt 1 (by intlit)))
-  then Result.fail Error.panic
-  else Result.ret ()
-
-/- Unit test for [no_nested_borrows::refs_test1] -/
-#assert (refs_test1_fwd == .ret ())
-
-/- [no_nested_borrows::refs_test2] -/
-def refs_test2_fwd : Result Unit :=
-  if h: not ((I32.ofInt 2 (by intlit)) = (I32.ofInt 2 (by intlit)))
-  then Result.fail Error.panic
-  else
-    if h: not ((I32.ofInt 0 (by intlit)) = (I32.ofInt 0 (by intlit)))
-    then Result.fail Error.panic
-    else
-      if h: not ((I32.ofInt 2 (by intlit)) = (I32.ofInt 2 (by intlit)))
-      then Result.fail Error.panic
-      else
-        if h: not ((I32.ofInt 2 (by intlit)) = (I32.ofInt 2 (by intlit)))
-        then Result.fail Error.panic
-        else Result.ret ()
-
-/- Unit test for [no_nested_borrows::refs_test2] -/
-#assert (refs_test2_fwd == .ret ())
-
-/- [no_nested_borrows::test_list1] -/
-def test_list1_fwd : Result Unit :=
-  Result.ret ()
-
-/- Unit test for [no_nested_borrows::test_list1] -/
-#assert (test_list1_fwd == .ret ())
-
-/- [no_nested_borrows::test_box1] -/
-def test_box1_fwd : Result Unit :=
-  let b := (I32.ofInt 1 (by intlit))
-  let x := b
-  if h: not (x = (I32.ofInt 1 (by intlit)))
-  then Result.fail Error.panic
-  else Result.ret ()
-
-/- Unit test for [no_nested_borrows::test_box1] -/
-#assert (test_box1_fwd == .ret ())
-
-/- [no_nested_borrows::copy_int] -/
-def copy_int_fwd (x : I32) : Result I32 :=
-  Result.ret x
-
-/- [no_nested_borrows::test_unreachable] -/
-def test_unreachable_fwd (b : Bool) : Result Unit :=
-  if h: b
-  then Result.fail Error.panic
-  else Result.ret ()
-
-/- [no_nested_borrows::test_panic] -/
-def test_panic_fwd (b : Bool) : Result Unit :=
-  if h: b
-  then Result.fail Error.panic
-  else Result.ret ()
-
-/- [no_nested_borrows::test_copy_int] -/
-def test_copy_int_fwd : Result Unit :=
-  do
-    let y ← copy_int_fwd (I32.ofInt 0 (by intlit))
-    if h: not ((I32.ofInt 0 (by intlit)) = y)
-    then Result.fail Error.panic
-    else Result.ret ()
-
-/- Unit test for [no_nested_borrows::test_copy_int] -/
-#assert (test_copy_int_fwd == .ret ())
-
-/- [no_nested_borrows::is_cons] -/
-def is_cons_fwd (T : Type) (l : list_t T) : Result Bool :=
-  match h: l with
-  | list_t.Cons t l0 => Result.ret true
-  | list_t.Nil => Result.ret false
-
-/- [no_nested_borrows::test_is_cons] -/
-def test_is_cons_fwd : Result Unit :=
-  do
-    let l := list_t.Nil
-    let b ← is_cons_fwd I32 (list_t.Cons (I32.ofInt 0 (by intlit)) l)
-    if h: not b
-    then Result.fail Error.panic
-    else Result.ret ()
-
-/- Unit test for [no_nested_borrows::test_is_cons] -/
-#assert (test_is_cons_fwd == .ret ())
-
-/- [no_nested_borrows::split_list] -/
-def split_list_fwd (T : Type) (l : list_t T) : Result (T × (list_t T)) :=
-  match h: l with
-  | list_t.Cons hd tl => Result.ret (hd, tl)
-  | list_t.Nil => Result.fail Error.panic
-
-/- [no_nested_borrows::test_split_list] -/
-def test_split_list_fwd : Result Unit :=
-  do
-    let l := list_t.Nil
-    let p ← split_list_fwd I32 (list_t.Cons (I32.ofInt 0 (by intlit)) l)
-    let (hd, _) := p
-    if h: not (hd = (I32.ofInt 0 (by intlit)))
-    then Result.fail Error.panic
-    else Result.ret ()
-
-/- Unit test for [no_nested_borrows::test_split_list] -/
-#assert (test_split_list_fwd == .ret ())
-
-/- [no_nested_borrows::choose] -/
-def choose_fwd (T : Type) (b : Bool) (x : T) (y : T) : Result T :=
-  if h: b
-  then Result.ret x
-  else Result.ret y
-
-/- [no_nested_borrows::choose] -/
-def choose_back
-  (T : Type) (b : Bool) (x : T) (y : T) (ret0 : T) : Result (T × T) :=
-  if h: b
-  then Result.ret (ret0, y)
-  else Result.ret (x, ret0)
-
-/- [no_nested_borrows::choose_test] -/
-def choose_test_fwd : Result Unit :=
-  do
-    let z ←
-      choose_fwd I32 true (I32.ofInt 0 (by intlit)) (I32.ofInt 0 (by intlit))
-    let z0 ← z + (I32.ofInt 1 (by intlit))
-    if h: not (z0 = (I32.ofInt 1 (by intlit)))
-    then Result.fail Error.panic
-    else
-      do
-        let (x, y) ←
-          choose_back I32 true (I32.ofInt 0 (by intlit))
-            (I32.ofInt 0 (by intlit)) z0
-        if h: not (x = (I32.ofInt 1 (by intlit)))
-        then Result.fail Error.panic
-        else
-          if h: not (y = (I32.ofInt 0 (by intlit)))
-          then Result.fail Error.panic
-          else Result.ret ()
-
-/- Unit test for [no_nested_borrows::choose_test] -/
-#assert (choose_test_fwd == .ret ())
-
-/- [no_nested_borrows::test_char] -/
-def test_char_fwd : Result Char :=
-  Result.ret 'a'
-
-mutual
-
-/- [no_nested_borrows::NodeElem] -/
-inductive node_elem_t (T : Type) :=
-| Cons : tree_t T -> node_elem_t T -> node_elem_t T
-| Nil : node_elem_t T
-
-/- [no_nested_borrows::Tree] -/
-inductive tree_t (T : Type) :=
-| Leaf : T -> tree_t T
-| Node : T -> node_elem_t T -> tree_t T -> tree_t T
-
-end
-
-/- [no_nested_borrows::list_length] -/
-def list_length_fwd (T : Type) (l : list_t T) : Result U32 :=
-  match h: l with
-  | list_t.Cons t l1 =>
-    do
-      let i ← list_length_fwd T l1
-      (U32.ofInt 1 (by intlit)) + i
-  | list_t.Nil => Result.ret (U32.ofInt 0 (by intlit))
-
-/- [no_nested_borrows::list_nth_shared] -/
-def list_nth_shared_fwd (T : Type) (l : list_t T) (i : U32) : Result T :=
-  match h: l with
-  | list_t.Cons x tl =>
-    if h: i = (U32.ofInt 0 (by intlit))
-    then Result.ret x
-    else
-      do
-        let i0 ← i - (U32.ofInt 1 (by intlit))
-        list_nth_shared_fwd T tl i0
-  | list_t.Nil => Result.fail Error.panic
-
-/- [no_nested_borrows::list_nth_mut] -/
-def list_nth_mut_fwd (T : Type) (l : list_t T) (i : U32) : Result T :=
-  match h: l with
-  | list_t.Cons x tl =>
-    if h: i = (U32.ofInt 0 (by intlit))
-    then Result.ret x
-    else do
-           let i0 ← i - (U32.ofInt 1 (by intlit))
-           list_nth_mut_fwd T tl i0
-  | list_t.Nil => Result.fail Error.panic
-
-/- [no_nested_borrows::list_nth_mut] -/
-def list_nth_mut_back
-  (T : Type) (l : list_t T) (i : U32) (ret0 : T) : Result (list_t T) :=
-  match h: l with
-  | list_t.Cons x tl =>
-    if h: i = (U32.ofInt 0 (by intlit))
-    then Result.ret (list_t.Cons ret0 tl)
-    else
-      do
-        let i0 ← i - (U32.ofInt 1 (by intlit))
-        let tl0 ← list_nth_mut_back T tl i0 ret0
-        Result.ret (list_t.Cons x tl0)
-  | list_t.Nil => Result.fail Error.panic
-
-/- [no_nested_borrows::list_rev_aux] -/
-def list_rev_aux_fwd
-  (T : Type) (li : list_t T) (lo : list_t T) : Result (list_t T) :=
-  match h: li with
-  | list_t.Cons hd tl => list_rev_aux_fwd T tl (list_t.Cons hd lo)
-  | list_t.Nil => Result.ret lo
-
-/- [no_nested_borrows::list_rev] -/
-def list_rev_fwd_back (T : Type) (l : list_t T) : Result (list_t T) :=
-  let li := mem_replace_fwd (list_t T) l list_t.Nil
-  list_rev_aux_fwd T li list_t.Nil
-
-/- [no_nested_borrows::test_list_functions] -/
-def test_list_functions_fwd : Result Unit :=
-  do
-    let l := list_t.Nil
-    let l0 := list_t.Cons (I32.ofInt 2 (by intlit)) l
-    let l1 := list_t.Cons (I32.ofInt 1 (by intlit)) l0
-    let i ← list_length_fwd I32 (list_t.Cons (I32.ofInt 0 (by intlit)) l1)
-    if h: not (i = (U32.ofInt 3 (by intlit)))
-    then Result.fail Error.panic
-    else
-      do
-        let i0 ←
-          list_nth_shared_fwd I32 (list_t.Cons (I32.ofInt 0 (by intlit)) l1)
-            (U32.ofInt 0 (by intlit))
-        if h: not (i0 = (I32.ofInt 0 (by intlit)))
-        then Result.fail Error.panic
-        else
-          do
-            let i1 ←
-              list_nth_shared_fwd I32 (list_t.Cons (I32.ofInt 0 (by intlit))
-                l1) (U32.ofInt 1 (by intlit))
-            if h: not (i1 = (I32.ofInt 1 (by intlit)))
-            then Result.fail Error.panic
-            else
-              do
-                let i2 ←
-                  list_nth_shared_fwd I32 (list_t.Cons
-                    (I32.ofInt 0 (by intlit)) l1) (U32.ofInt 2 (by intlit))
-                if h: not (i2 = (I32.ofInt 2 (by intlit)))
-                then Result.fail Error.panic
-                else
-                  do
-                    let ls ←
-                      list_nth_mut_back I32 (list_t.Cons
-                        (I32.ofInt 0 (by intlit)) l1) (U32.ofInt 1 (by intlit))
-                        (I32.ofInt 3 (by intlit))
-                    let i3 ←
-                      list_nth_shared_fwd I32 ls (U32.ofInt 0 (by intlit))
-                    if h: not (i3 = (I32.ofInt 0 (by intlit)))
-                    then Result.fail Error.panic
-                    else
-                      do
-                        let i4 ←
-                          list_nth_shared_fwd I32 ls (U32.ofInt 1 (by intlit))
-                        if h: not (i4 = (I32.ofInt 3 (by intlit)))
-                        then Result.fail Error.panic
-                        else
-                          do
-                            let i5 ←
-                              list_nth_shared_fwd I32 ls
-                                (U32.ofInt 2 (by intlit))
-                            if h: not (i5 = (I32.ofInt 2 (by intlit)))
-                            then Result.fail Error.panic
-                            else Result.ret ()
-
-/- Unit test for [no_nested_borrows::test_list_functions] -/
-#assert (test_list_functions_fwd == .ret ())
-
-/- [no_nested_borrows::id_mut_pair1] -/
-def id_mut_pair1_fwd (T1 T2 : Type) (x : T1) (y : T2) : Result (T1 × T2) :=
-  Result.ret (x, y)
-
-/- [no_nested_borrows::id_mut_pair1] -/
-def id_mut_pair1_back
-  (T1 T2 : Type) (x : T1) (y : T2) (ret0 : (T1 × T2)) : Result (T1 × T2) :=
-  let (t, t0) := ret0
-  Result.ret (t, t0)
-
-/- [no_nested_borrows::id_mut_pair2] -/
-def id_mut_pair2_fwd (T1 T2 : Type) (p : (T1 × T2)) : Result (T1 × T2) :=
-  let (t, t0) := p
-  Result.ret (t, t0)
-
-/- [no_nested_borrows::id_mut_pair2] -/
-def id_mut_pair2_back
-  (T1 T2 : Type) (p : (T1 × T2)) (ret0 : (T1 × T2)) : Result (T1 × T2) :=
-  let (t, t0) := ret0
-  Result.ret (t, t0)
-
-/- [no_nested_borrows::id_mut_pair3] -/
-def id_mut_pair3_fwd (T1 T2 : Type) (x : T1) (y : T2) : Result (T1 × T2) :=
-  Result.ret (x, y)
-
-/- [no_nested_borrows::id_mut_pair3] -/
-def id_mut_pair3_back'a
-  (T1 T2 : Type) (x : T1) (y : T2) (ret0 : T1) : Result T1 :=
-  Result.ret ret0
-
-/- [no_nested_borrows::id_mut_pair3] -/
-def id_mut_pair3_back'b
-  (T1 T2 : Type) (x : T1) (y : T2) (ret0 : T2) : Result T2 :=
-  Result.ret ret0
-
-/- [no_nested_borrows::id_mut_pair4] -/
-def id_mut_pair4_fwd (T1 T2 : Type) (p : (T1 × T2)) : Result (T1 × T2) :=
-  let (t, t0) := p
-  Result.ret (t, t0)
-
-/- [no_nested_borrows::id_mut_pair4] -/
-def id_mut_pair4_back'a
-  (T1 T2 : Type) (p : (T1 × T2)) (ret0 : T1) : Result T1 :=
-  Result.ret ret0
-
-/- [no_nested_borrows::id_mut_pair4] -/
-def id_mut_pair4_back'b
-  (T1 T2 : Type) (p : (T1 × T2)) (ret0 : T2) : Result T2 :=
-  Result.ret ret0
-
-/- [no_nested_borrows::StructWithTuple] -/
-structure struct_with_tuple_t (T1 T2 : Type) where
-  struct_with_tuple_p : (T1 × T2)
-
-/- [no_nested_borrows::new_tuple1] -/
-def new_tuple1_fwd : Result (struct_with_tuple_t U32 U32) :=
-  Result.ret
-  {
-    struct_with_tuple_p :=
-      ((U32.ofInt 1 (by intlit)), (U32.ofInt 2 (by intlit)))
-  }
-
-/- [no_nested_borrows::new_tuple2] -/
-def new_tuple2_fwd : Result (struct_with_tuple_t I16 I16) :=
-  Result.ret
-  {
-    struct_with_tuple_p :=
-      ((I16.ofInt 1 (by intlit)), (I16.ofInt 2 (by intlit)))
-  }
-
-/- [no_nested_borrows::new_tuple3] -/
-def new_tuple3_fwd : Result (struct_with_tuple_t U64 I64) :=
-  Result.ret
-  {
-    struct_with_tuple_p :=
-      ((U64.ofInt 1 (by intlit)), (I64.ofInt 2 (by intlit)))
-  }
-
-/- [no_nested_borrows::StructWithPair] -/
-structure struct_with_pair_t (T1 T2 : Type) where
-  struct_with_pair_p : pair_t T1 T2
-
-/- [no_nested_borrows::new_pair1] -/
-def new_pair1_fwd : Result (struct_with_pair_t U32 U32) :=
-  Result.ret
-  {
-    struct_with_pair_p :=
-      {
-        pair_x := (U32.ofInt 1 (by intlit)),
-        pair_y := (U32.ofInt 2 (by intlit))
-      }
-  }
-
-/- [no_nested_borrows::test_constants] -/
-def test_constants_fwd : Result Unit :=
-  do
-    let swt ← new_tuple1_fwd
-    let (i, _) := swt.struct_with_tuple_p
-    if h: not (i = (U32.ofInt 1 (by intlit)))
-    then Result.fail Error.panic
-    else
-      do
-        let swt0 ← new_tuple2_fwd
-        let (i0, _) := swt0.struct_with_tuple_p
-        if h: not (i0 = (I16.ofInt 1 (by intlit)))
-        then Result.fail Error.panic
-        else
-          do
-            let swt1 ← new_tuple3_fwd
-            let (i1, _) := swt1.struct_with_tuple_p
-            if h: not (i1 = (U64.ofInt 1 (by intlit)))
-            then Result.fail Error.panic
-            else
-              do
-                let swp ← new_pair1_fwd
-                if h: not (swp.struct_with_pair_p.pair_x =
-                  (U32.ofInt 1 (by intlit)))
-                then Result.fail Error.panic
-                else Result.ret ()
-
-/- Unit test for [no_nested_borrows::test_constants] -/
-#assert (test_constants_fwd == .ret ())
-
-/- [no_nested_borrows::test_weird_borrows1] -/
-def test_weird_borrows1_fwd : Result Unit :=
-  Result.ret ()
-
-/- Unit test for [no_nested_borrows::test_weird_borrows1] -/
-#assert (test_weird_borrows1_fwd == .ret ())
-
-/- [no_nested_borrows::test_mem_replace] -/
-def test_mem_replace_fwd_back (px : U32) : Result U32 :=
-  let y := mem_replace_fwd U32 px (U32.ofInt 1 (by intlit))
-  if h: not (y = (U32.ofInt 0 (by intlit)))
-  then Result.fail Error.panic
-  else Result.ret (U32.ofInt 2 (by intlit))
-
-/- [no_nested_borrows::test_shared_borrow_bool1] -/
-def test_shared_borrow_bool1_fwd (b : Bool) : Result U32 :=
-  if h: b
-  then Result.ret (U32.ofInt 0 (by intlit))
-  else Result.ret (U32.ofInt 1 (by intlit))
-
-/- [no_nested_borrows::test_shared_borrow_bool2] -/
-def test_shared_borrow_bool2_fwd : Result U32 :=
-  Result.ret (U32.ofInt 0 (by intlit))
-
-/- [no_nested_borrows::test_shared_borrow_enum1] -/
-def test_shared_borrow_enum1_fwd (l : list_t U32) : Result U32 :=
-  match h: l with
-  | list_t.Cons i l0 => Result.ret (U32.ofInt 1 (by intlit))
-  | list_t.Nil => Result.ret (U32.ofInt 0 (by intlit))
-
-/- [no_nested_borrows::test_shared_borrow_enum2] -/
-def test_shared_borrow_enum2_fwd : Result U32 :=
-  Result.ret (U32.ofInt 0 (by intlit))
-
diff --git a/tests/lean/misc-no_nested_borrows/lake-manifest.json b/tests/lean/misc-no_nested_borrows/lake-manifest.json
deleted file mode 100644
index 57b071ca..00000000
--- a/tests/lean/misc-no_nested_borrows/lake-manifest.json
+++ /dev/null
@@ -1,27 +0,0 @@
-{"version": 4,
- "packagesDir": "./lake-packages",
- "packages":
- [{"git":
-   {"url": "https://github.com/leanprover-community/mathlib4.git",
-    "subDir?": null,
-    "rev": "4037792ead804d7bfa8868e2c4684d4223c15ece",
-    "name": "mathlib",
-    "inputRev?": null}},
-  {"git":
-   {"url": "https://github.com/gebner/quote4",
-    "subDir?": null,
-    "rev": "2412c4fdf4a8b689f4467618e5e7b371ae5014aa",
-    "name": "Qq",
-    "inputRev?": "master"}},
-  {"git":
-   {"url": "https://github.com/JLimperg/aesop",
-    "subDir?": null,
-    "rev": "7fe9ecd9339b0e1796e89d243b776849c305c690",
-    "name": "aesop",
-    "inputRev?": "master"}},
-  {"git":
-   {"url": "https://github.com/leanprover/std4",
-    "subDir?": null,
-    "rev": "24897887905b3a1254b244369f5dd2cf6174b0ee",
-    "name": "std",
-    "inputRev?": "main"}}]}
diff --git a/tests/lean/misc-no_nested_borrows/lakefile.lean b/tests/lean/misc-no_nested_borrows/lakefile.lean
deleted file mode 100644
index 58619110..00000000
--- a/tests/lean/misc-no_nested_borrows/lakefile.lean
+++ /dev/null
@@ -1,12 +0,0 @@
-import Lake
-open Lake DSL
-
-require mathlib from git
-  "https://github.com/leanprover-community/mathlib4.git"
-
-package «no_nested_borrows» {}
-
-lean_lib «Base» {}
-
-@[default_target]
-lean_lib «NoNestedBorrows» {}
diff --git a/tests/lean/misc-no_nested_borrows/lean-toolchain b/tests/lean/misc-no_nested_borrows/lean-toolchain
deleted file mode 100644
index bbf57f10..00000000
--- a/tests/lean/misc-no_nested_borrows/lean-toolchain
+++ /dev/null
@@ -1 +0,0 @@
-leanprover/lean4:nightly-2023-01-21
diff --git a/tests/lean/misc-paper/Base/Primitives.lean b/tests/lean/misc-paper/Base/Primitives.lean
deleted file mode 100644
index 4a66a453..00000000
--- a/tests/lean/misc-paper/Base/Primitives.lean
+++ /dev/null
@@ -1,583 +0,0 @@
-import Lean
-import Lean.Meta.Tactic.Simp
-import Init.Data.List.Basic
-import Mathlib.Tactic.RunCmd
-
---------------------
--- ASSERT COMMAND --
---------------------
-
-open Lean Elab Command Term Meta
-
-syntax (name := assert) "#assert" term: command
-
-@[command_elab assert]
-unsafe
-def assertImpl : CommandElab := fun (_stx: Syntax) => do
-  runTermElabM (fun _ => do
-    let r ← evalTerm Bool (mkConst ``Bool) _stx[1]
-    if not r then
-      logInfo "Assertion failed for: "
-      logInfo _stx[1]
-      logError "Expression reduced to false"
-    pure ())
-
-#eval 2 == 2
-#assert (2 == 2)
-
--------------
--- PRELUDE --
--------------
-
--- Results & monadic combinators
-
-inductive Error where
-   | assertionFailure: Error
-   | integerOverflow: Error
-   | divisionByZero: Error
-   | arrayOutOfBounds: Error
-   | maximumSizeExceeded: Error
-   | panic: Error
-deriving Repr, BEq
-
-open Error
-
-inductive Result (α : Type u) where
-  | ret (v: α): Result α
-  | fail (e: Error): Result α
-deriving Repr, BEq
-
-open Result
-
-instance Result_Inhabited (α : Type u) : Inhabited (Result α) :=
-  Inhabited.mk (fail panic)
-
-/- HELPERS -/
-
-def ret? {α: Type} (r: Result α): Bool :=
-  match r with
-  | Result.ret _ => true
-  | Result.fail _ => false
-
-def massert (b:Bool) : Result Unit :=
-  if b then .ret () else fail assertionFailure
-
-def eval_global {α: Type} (x: Result α) (_: ret? x): α :=
-  match x with
-  | Result.fail _ => by contradiction
-  | Result.ret x => x
-
-/- DO-DSL SUPPORT -/
-
-def bind (x: Result α) (f: α -> Result β) : Result β :=
-  match x with
-  | ret v  => f v 
-  | fail v => fail v
-
--- Allows using Result in do-blocks
-instance : Bind Result where
-  bind := bind
-
--- Allows using return x in do-blocks
-instance : Pure Result where
-  pure := fun x => ret x
-
-/- CUSTOM-DSL SUPPORT -/
-
--- Let-binding the Result of a monadic operation is oftentimes not sufficient,
--- because we may need a hypothesis for equational reasoning in the scope. We
--- rely on subtype, and a custom let-binding operator, in effect recreating our
--- own variant of the do-dsl
-
-def Result.attach {α: Type} (o : Result α): Result { x : α // o = ret x } :=
-  match o with
-  | .ret x => .ret ⟨x, rfl⟩
-  | .fail e => .fail e
-
-macro "let" e:term " ⟵ " f:term : doElem =>
-  `(doElem| let ⟨$e, h⟩ ← Result.attach $f)
-
--- TODO: any way to factorize both definitions?
-macro "let" e:term " <-- " f:term : doElem =>
-  `(doElem| let ⟨$e, h⟩ ← Result.attach $f)
-
--- We call the hypothesis `h`, in effect making it unavailable to the user
--- (because too much shadowing). But in practice, once can use the French single
--- quote notation (input with f< and f>), where `‹ h ›` finds a suitable
--- hypothesis in the context, this is equivalent to `have x: h := by assumption in x`
-#eval do
-  let y <-- .ret (0: Nat)
-  let _: y = 0 := by cases ‹ ret 0 = ret y › ; decide
-  let r: { x: Nat // x = 0 } := ⟨ y, by assumption ⟩
-  .ret r
-
-----------------------
--- MACHINE INTEGERS --
-----------------------
-
--- We redefine our machine integers types.
-
--- For Isize/Usize, we reuse `getNumBits` from `USize`. You cannot reduce `getNumBits`
--- using the simplifier, meaning that proofs do not depend on the compile-time value of
--- USize.size. (Lean assumes 32 or 64-bit platforms, and Rust doesn't really support, at
--- least officially, 16-bit microcontrollers, so this seems like a fine design decision
--- for now.)
-
--- Note from Chris Bailey: "If there's more than one salient property of your
--- definition then the subtyping strategy might get messy, and the property part
--- of a subtype is less discoverable by the simplifier or tactics like
--- library_search." So, we will not add refinements on the return values of the
--- operations defined on Primitives, but will rather rely on custom lemmas to
--- invert on possible return values of the primitive operations.
-
--- Machine integer constants, done via `ofNatCore`, which requires a proof that
--- the `Nat` fits within the desired integer type. We provide a custom tactic.
-
-open System.Platform.getNumBits
-
--- TODO: is there a way of only importing System.Platform.getNumBits?
---
-@[simp] def size_num_bits : Nat := (System.Platform.getNumBits ()).val
-
--- Remark: Lean seems to use < for the comparisons with the upper bounds by convention.
--- We keep the F* convention for now.
-@[simp] def Isize.min : Int := - (HPow.hPow 2 (size_num_bits - 1))
-@[simp] def Isize.max : Int := (HPow.hPow 2 (size_num_bits - 1)) - 1
-@[simp] def I8.min    : Int := - (HPow.hPow 2 7)
-@[simp] def I8.max    : Int := HPow.hPow 2 7 - 1
-@[simp] def I16.min   : Int := - (HPow.hPow 2 15)
-@[simp] def I16.max   : Int := HPow.hPow 2 15 - 1
-@[simp] def I32.min   : Int := -(HPow.hPow 2 31)
-@[simp] def I32.max   : Int := HPow.hPow 2 31 - 1
-@[simp] def I64.min   : Int := -(HPow.hPow 2 63)
-@[simp] def I64.max   : Int := HPow.hPow 2 63 - 1
-@[simp] def I128.min  : Int := -(HPow.hPow 2 127)
-@[simp] def I128.max  : Int := HPow.hPow 2 127 - 1
-@[simp] def Usize.min : Int := 0
-@[simp] def Usize.max : Int := HPow.hPow 2 size_num_bits - 1
-@[simp] def U8.min    : Int := 0
-@[simp] def U8.max    : Int := HPow.hPow 2 8 - 1
-@[simp] def U16.min   : Int := 0
-@[simp] def U16.max   : Int := HPow.hPow 2 16 - 1
-@[simp] def U32.min   : Int := 0
-@[simp] def U32.max   : Int := HPow.hPow 2 32 - 1
-@[simp] def U64.min   : Int := 0
-@[simp] def U64.max   : Int := HPow.hPow 2 64 - 1
-@[simp] def U128.min  : Int := 0
-@[simp] def U128.max  : Int := HPow.hPow 2 128 - 1
-
-#assert (I8.min   == -128)
-#assert (I8.max   == 127)
-#assert (I16.min  == -32768)
-#assert (I16.max  == 32767)
-#assert (I32.min  == -2147483648)
-#assert (I32.max  == 2147483647)
-#assert (I64.min  == -9223372036854775808)
-#assert (I64.max  == 9223372036854775807)
-#assert (I128.min == -170141183460469231731687303715884105728)
-#assert (I128.max == 170141183460469231731687303715884105727)
-#assert (U8.min   == 0)
-#assert (U8.max   == 255)
-#assert (U16.min  == 0)
-#assert (U16.max  == 65535)
-#assert (U32.min  == 0)
-#assert (U32.max  == 4294967295)
-#assert (U64.min  == 0)
-#assert (U64.max  == 18446744073709551615)
-#assert (U128.min == 0)
-#assert (U128.max == 340282366920938463463374607431768211455)
-
-inductive ScalarTy :=
-| Isize
-| I8
-| I16
-| I32
-| I64
-| I128
-| Usize
-| U8
-| U16
-| U32
-| U64
-| U128
-
-def Scalar.min (ty : ScalarTy) : Int :=
-  match ty with
-  | .Isize => Isize.min
-  | .I8    => I8.min
-  | .I16   => I16.min
-  | .I32   => I32.min
-  | .I64   => I64.min
-  | .I128  => I128.min
-  | .Usize => Usize.min
-  | .U8    => U8.min
-  | .U16   => U16.min
-  | .U32   => U32.min
-  | .U64   => U64.min
-  | .U128  => U128.min
-
-def Scalar.max (ty : ScalarTy) : Int :=
-  match ty with
-  | .Isize => Isize.max
-  | .I8    => I8.max
-  | .I16   => I16.max
-  | .I32   => I32.max
-  | .I64   => I64.max
-  | .I128  => I128.max
-  | .Usize => Usize.max
-  | .U8    => U8.max
-  | .U16   => U16.max
-  | .U32   => U32.max
-  | .U64   => U64.max
-  | .U128  => U128.max
-
--- "Conservative" bounds
--- We use those because we can't compare to the isize bounds (which can't
--- reduce at compile-time). Whenever we perform an arithmetic operation like
--- addition we need to check that the result is in bounds: we first compare
--- to the conservative bounds, which reduce, then compare to the real bounds.
--- This is useful for the various #asserts that we want to reduce at
--- type-checking time.
-def Scalar.cMin (ty : ScalarTy) : Int :=
-  match ty with
-  | .Isize => I32.min
-  | _ => Scalar.min ty
-
-def Scalar.cMax (ty : ScalarTy) : Int :=
-  match ty with
-  | .Isize => I32.max
-  | .Usize => U32.max
-  | _ => Scalar.max ty
-
-theorem Scalar.cMin_bound ty : Scalar.min ty <= Scalar.cMin ty := by sorry
-theorem Scalar.cMax_bound ty : Scalar.min ty <= Scalar.cMin ty := by sorry
-
-structure Scalar (ty : ScalarTy) where
-  val : Int
-  hmin : Scalar.min ty <= val
-  hmax : val <= Scalar.max ty
-
-theorem Scalar.bound_suffices (ty : ScalarTy) (x : Int) :
-  Scalar.cMin ty <= x && x <= Scalar.cMax ty ->
-  (decide (Scalar.min ty ≤ x) && decide (x ≤ Scalar.max ty)) = true
-  := by sorry
-
-def Scalar.ofIntCore {ty : ScalarTy} (x : Int)
-  (hmin : Scalar.min ty <= x) (hmax : x <= Scalar.max ty) : Scalar ty :=
-  { val := x, hmin := hmin, hmax := hmax }
-
-def Scalar.ofInt {ty : ScalarTy} (x : Int)
-  (h : Scalar.min ty <= x && x <= Scalar.max ty) : Scalar ty :=
-  let hmin: Scalar.min ty <= x := by sorry
-  let hmax: x <= Scalar.max ty := by sorry
-  Scalar.ofIntCore x hmin hmax
-
--- Further thoughts: look at what has been done here:
--- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/Fin/Basic.lean
--- and
--- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/UInt.lean
--- which both contain a fair amount of reasoning already!
-def Scalar.tryMk (ty : ScalarTy) (x : Int) : Result (Scalar ty) :=
-  -- TODO: write this with only one if then else
-  if hmin_cons: Scalar.cMin ty <= x || Scalar.min ty <= x then
-    if hmax_cons: x <= Scalar.cMax ty || x <= Scalar.max ty then
-      let hmin: Scalar.min ty <= x := by sorry
-      let hmax: x <= Scalar.max ty := by sorry
-      return Scalar.ofIntCore x hmin hmax
-    else fail integerOverflow
-  else fail integerOverflow
-
-def Scalar.neg {ty : ScalarTy} (x : Scalar ty) : Result (Scalar ty) := Scalar.tryMk ty (- x.val)
-
-def Scalar.div {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
-  if y.val != 0 then Scalar.tryMk ty (x.val / y.val) else fail divisionByZero
-
--- Checking that the % operation in Lean computes the same as the remainder operation in Rust
-#assert 1 % 2 = (1:Int)
-#assert (-1) % 2 = -1
-#assert 1 % (-2) = 1
-#assert (-1) % (-2) = -1
-
-def Scalar.rem {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
-  if y.val != 0 then Scalar.tryMk ty (x.val % y.val) else fail divisionByZero
-
-def Scalar.add {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
-  Scalar.tryMk ty (x.val + y.val)
-
-def Scalar.sub {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
-  Scalar.tryMk ty (x.val - y.val)
-
-def Scalar.mul {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
-  Scalar.tryMk ty (x.val * y.val)
-
--- TODO: instances of +, -, * etc. for scalars
-
--- Cast an integer from a [src_ty] to a [tgt_ty]
--- TODO: check the semantics of casts in Rust
-def Scalar.cast {src_ty : ScalarTy} (tgt_ty : ScalarTy) (x : Scalar src_ty) : Result (Scalar tgt_ty) :=
-  Scalar.tryMk tgt_ty x.val
-
--- The scalar types
--- We declare the definitions as reducible so that Lean can unfold them (useful
--- for type class resolution for instance).
-@[reducible] def Isize := Scalar .Isize
-@[reducible] def I8    := Scalar .I8
-@[reducible] def I16   := Scalar .I16
-@[reducible] def I32   := Scalar .I32
-@[reducible] def I64   := Scalar .I64
-@[reducible] def I128  := Scalar .I128
-@[reducible] def Usize := Scalar .Usize
-@[reducible] def U8    := Scalar .U8
-@[reducible] def U16   := Scalar .U16
-@[reducible] def U32   := Scalar .U32
-@[reducible] def U64   := Scalar .U64
-@[reducible] def U128  := Scalar .U128
-
--- TODO: below: not sure this is the best way.
--- Should we rather overload operations like +, -, etc.?
--- Also, it is possible to automate the generation of those definitions
--- with macros (but would it be a good idea? It would be less easy to
--- read the file, which is not supposed to change a lot)
-
--- Negation
-
-/--
-Remark: there is no heterogeneous negation in the Lean prelude: we thus introduce
-one here.
-
-The notation typeclass for heterogeneous addition.
-This enables the notation `- a : β` where `a : α`.
--/
-class HNeg (α : Type u) (β : outParam (Type v)) where
-  /-- `- a` computes the negation of `a`.
-  The meaning of this notation is type-dependent. -/
-  hNeg : α → β
-
-prefix:75  "-"   => HNeg.hNeg
-
-instance : HNeg Isize (Result Isize) where hNeg x := Scalar.neg x
-instance : HNeg I8 (Result I8) where hNeg x := Scalar.neg x
-instance : HNeg I16 (Result I16) where hNeg x := Scalar.neg x
-instance : HNeg I32 (Result I32) where hNeg x := Scalar.neg x
-instance : HNeg I64 (Result I64) where hNeg x := Scalar.neg x
-instance : HNeg I128 (Result I128) where hNeg x := Scalar.neg x
-
--- Addition
-instance {ty} : HAdd (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
-  hAdd x y := Scalar.add x y
-
--- Substraction
-instance {ty} : HSub (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
-  hSub x y := Scalar.sub x y
-
--- Multiplication
-instance {ty} : HMul (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
-  hMul x y := Scalar.mul x y
-
--- Division
-instance {ty} : HDiv (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
-  hDiv x y := Scalar.div x y
-
--- Remainder
-instance {ty} : HMod (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
-  hMod x y := Scalar.rem x y
-
--- ofIntCore
--- TODO: typeclass?
-def Isize.ofIntCore := @Scalar.ofIntCore .Isize
-def I8.ofIntCore    := @Scalar.ofIntCore .I8
-def I16.ofIntCore   := @Scalar.ofIntCore .I16
-def I32.ofIntCore   := @Scalar.ofIntCore .I32
-def I64.ofIntCore   := @Scalar.ofIntCore .I64
-def I128.ofIntCore  := @Scalar.ofIntCore .I128
-def Usize.ofIntCore := @Scalar.ofIntCore .Usize
-def U8.ofIntCore    := @Scalar.ofIntCore .U8
-def U16.ofIntCore   := @Scalar.ofIntCore .U16
-def U32.ofIntCore   := @Scalar.ofIntCore .U32
-def U64.ofIntCore   := @Scalar.ofIntCore .U64
-def U128.ofIntCore  := @Scalar.ofIntCore .U128
-
---  ofInt
--- TODO: typeclass?
-def Isize.ofInt := @Scalar.ofInt .Isize
-def I8.ofInt    := @Scalar.ofInt .I8
-def I16.ofInt   := @Scalar.ofInt .I16
-def I32.ofInt   := @Scalar.ofInt .I32
-def I64.ofInt   := @Scalar.ofInt .I64
-def I128.ofInt  := @Scalar.ofInt .I128
-def Usize.ofInt := @Scalar.ofInt .Usize
-def U8.ofInt    := @Scalar.ofInt .U8
-def U16.ofInt   := @Scalar.ofInt .U16
-def U32.ofInt   := @Scalar.ofInt .U32
-def U64.ofInt   := @Scalar.ofInt .U64
-def U128.ofInt  := @Scalar.ofInt .U128
-
--- Comparisons
-instance {ty} : LT (Scalar ty) where
-  lt a b := LT.lt a.val b.val
-
-instance {ty} : LE (Scalar ty) where le a b := LE.le a.val b.val
-
-instance Scalar.decLt {ty} (a b : Scalar ty) : Decidable (LT.lt a b) := Int.decLt ..
-instance Scalar.decLe {ty} (a b : Scalar ty) : Decidable (LE.le a b) := Int.decLe ..
-
-theorem Scalar.eq_of_val_eq {ty} : ∀ {i j : Scalar ty}, Eq i.val j.val → Eq i j
-  | ⟨_, _, _⟩, ⟨_, _, _⟩, rfl => rfl
-
-theorem Scalar.val_eq_of_eq {ty} {i j : Scalar ty} (h : Eq i j) : Eq i.val j.val :=
-  h ▸ rfl
-
-theorem Scalar.ne_of_val_ne {ty} {i j : Scalar ty} (h : Not (Eq i.val j.val)) : Not (Eq i j) :=
-  fun h' => absurd (val_eq_of_eq h') h
-
-instance (ty : ScalarTy) : DecidableEq (Scalar ty) :=
-  fun i j =>
-    match decEq i.val j.val with
-    | isTrue h  => isTrue (Scalar.eq_of_val_eq h)
-    | isFalse h => isFalse (Scalar.ne_of_val_ne h)
-
-def Scalar.toInt {ty} (n : Scalar ty) : Int := n.val
-
--- Tactic to prove that integers are in bounds
-syntax "intlit" : tactic
-
-macro_rules
-  | `(tactic| intlit) => `(tactic| apply Scalar.bound_suffices ; decide)
-
--- -- We now define a type class that subsumes the various machine integer types, so
--- -- as to write a concise definition for scalar_cast, rather than exhaustively
--- -- enumerating all of the possible pairs. We remark that Rust has sane semantics
--- -- and fails if a cast operation would involve a truncation or modulo.
-
--- class MachineInteger (t: Type) where
---   size: Nat
---   val: t -> Fin size
---   ofNatCore: (n:Nat) -> LT.lt n size -> t
-
--- set_option hygiene false in
--- run_cmd
---   for typeName in [`UInt8, `UInt16, `UInt32, `UInt64, `USize].map Lean.mkIdent do
---   Lean.Elab.Command.elabCommand (← `(
---     namespace $typeName
---     instance: MachineInteger $typeName where
---       size := size
---       val := val
---       ofNatCore := ofNatCore
---     end $typeName
---   ))
-
--- -- Aeneas only instantiates the destination type (`src` is implicit). We rely on
--- -- Lean to infer `src`.
-
--- def scalar_cast { src: Type } (dst: Type) [ MachineInteger src ] [ MachineInteger dst ] (x: src): Result dst :=
---   if h: MachineInteger.val x < MachineInteger.size dst then
---     .ret (MachineInteger.ofNatCore (MachineInteger.val x).val h)
---   else
---     .fail integerOverflow
-
--------------
--- VECTORS --
--------------
-
-def Vec (α : Type u) := { l : List α // List.length l <= Usize.max }
-
-def vec_new (α : Type u): Vec α := ⟨ [], by sorry ⟩
-
-def vec_len (α : Type u) (v : Vec α) : Usize :=
-  let ⟨ v, l ⟩ := v
-  Usize.ofIntCore (List.length v) (by sorry) l
- 
-def vec_push_fwd (α : Type u) (_ : Vec α) (_ : α) : Unit := ()
-
-def vec_push_back (α : Type u) (v : Vec α) (x : α) : Result (Vec α)
-  :=
-  if h : List.length v.val <= U32.max || List.length v.val <= Usize.max then
-    return ⟨ List.concat v.val x, by sorry ⟩
-  else
-    fail maximumSizeExceeded
-
-def vec_insert_fwd (α : Type u) (v: Vec α) (i: Usize) (_: α): Result Unit :=
-  if i.val < List.length v.val then
-    .ret ()
-  else
-    .fail arrayOutOfBounds
-
-def vec_insert_back (α : Type u) (v: Vec α) (i: Usize) (x: α): Result (Vec α) :=
-  if i.val < List.length v.val then
-    -- TODO: maybe we should redefine a list library which uses integers
-    -- (instead of natural numbers)
-    let i : Nat :=
-      match i.val with
-      | .ofNat n => n
-      | .negSucc n => by sorry -- TODO: we can't get here
-    let isLt: i < USize.size := by sorry
-    let i : Fin USize.size := { val := i, isLt := isLt }
-    .ret ⟨ List.set v.val i.val x, by
-      have h: List.length v.val <= Usize.max := v.property
-      rewrite [ List.length_set v.val i.val x ]
-      assumption
-    ⟩
-  else
-    .fail arrayOutOfBounds
-
-def vec_index_fwd (α : Type u) (v: Vec α) (i: Usize): Result α :=
-  if i.val < List.length v.val then
-    let i : Nat :=
-      match i.val with
-      | .ofNat n => n
-      | .negSucc n => by sorry -- TODO: we can't get here
-    let isLt: i < USize.size := by sorry
-    let i : Fin USize.size := { val := i, isLt := isLt }
-    let h: i < List.length v.val := by sorry
-    .ret (List.get v.val ⟨i.val, h⟩)
-  else
-    .fail arrayOutOfBounds
-
-def vec_index_back (α : Type u) (v: Vec α) (i: Usize) (_: α): Result Unit :=
-  if i.val < List.length v.val then
-    .ret ()
-  else
-    .fail arrayOutOfBounds
-
-def vec_index_mut_fwd (α : Type u) (v: Vec α) (i: Usize): Result α :=
-  if i.val < List.length v.val then
-    let i : Nat :=
-      match i.val with
-      | .ofNat n => n
-      | .negSucc n => by sorry -- TODO: we can't get here
-    let isLt: i < USize.size := by sorry
-    let i : Fin USize.size := { val := i, isLt := isLt }
-    let h: i < List.length v.val := by sorry
-    .ret (List.get v.val ⟨i.val, h⟩)
-  else
-    .fail arrayOutOfBounds
-
-def vec_index_mut_back (α : Type u) (v: Vec α) (i: Usize) (x: α): Result (Vec α) :=
-  if i.val < List.length v.val then
-    let i : Nat :=
-      match i.val with
-      | .ofNat n => n
-      | .negSucc n => by sorry -- TODO: we can't get here
-    let isLt: i < USize.size := by sorry
-    let i : Fin USize.size := { val := i, isLt := isLt }
-    .ret ⟨ List.set v.val i.val x, by
-      have h: List.length v.val <= Usize.max := v.property
-      rewrite [ List.length_set v.val i.val x ]
-      assumption
-    ⟩
-  else
-    .fail arrayOutOfBounds
-
-----------
--- MISC --
-----------
-
-def mem_replace_fwd (a : Type) (x : a) (_ : a) : a :=
-  x
-
-def mem_replace_back (a : Type) (_ : a) (y : a) : a :=
-  y
-
-/-- Aeneas-translated function -- useful to reduce non-recursive definitions.
- Use with `simp [ aeneas ]` -/
-register_simp_attr aeneas
diff --git a/tests/lean/misc-paper/Paper.lean b/tests/lean/misc-paper/Paper.lean
deleted file mode 100644
index 0b16fb8e..00000000
--- a/tests/lean/misc-paper/Paper.lean
+++ /dev/null
@@ -1,123 +0,0 @@
--- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
--- [paper]
-import Base.Primitives
-
-/- [paper::ref_incr] -/
-def ref_incr_fwd_back (x : I32) : Result I32 :=
-  x + (I32.ofInt 1 (by intlit))
-
-/- [paper::test_incr] -/
-def test_incr_fwd : Result Unit :=
-  do
-    let x ← ref_incr_fwd_back (I32.ofInt 0 (by intlit))
-    if h: not (x = (I32.ofInt 1 (by intlit)))
-    then Result.fail Error.panic
-    else Result.ret ()
-
-/- Unit test for [paper::test_incr] -/
-#assert (test_incr_fwd == .ret ())
-
-/- [paper::choose] -/
-def choose_fwd (T : Type) (b : Bool) (x : T) (y : T) : Result T :=
-  if h: b
-  then Result.ret x
-  else Result.ret y
-
-/- [paper::choose] -/
-def choose_back
-  (T : Type) (b : Bool) (x : T) (y : T) (ret0 : T) : Result (T × T) :=
-  if h: b
-  then Result.ret (ret0, y)
-  else Result.ret (x, ret0)
-
-/- [paper::test_choose] -/
-def test_choose_fwd : Result Unit :=
-  do
-    let z ←
-      choose_fwd I32 true (I32.ofInt 0 (by intlit)) (I32.ofInt 0 (by intlit))
-    let z0 ← z + (I32.ofInt 1 (by intlit))
-    if h: not (z0 = (I32.ofInt 1 (by intlit)))
-    then Result.fail Error.panic
-    else
-      do
-        let (x, y) ←
-          choose_back I32 true (I32.ofInt 0 (by intlit))
-            (I32.ofInt 0 (by intlit)) z0
-        if h: not (x = (I32.ofInt 1 (by intlit)))
-        then Result.fail Error.panic
-        else
-          if h: not (y = (I32.ofInt 0 (by intlit)))
-          then Result.fail Error.panic
-          else Result.ret ()
-
-/- Unit test for [paper::test_choose] -/
-#assert (test_choose_fwd == .ret ())
-
-/- [paper::List] -/
-inductive list_t (T : Type) :=
-| Cons : T -> list_t T -> list_t T
-| Nil : list_t T
-
-/- [paper::list_nth_mut] -/
-def list_nth_mut_fwd (T : Type) (l : list_t T) (i : U32) : Result T :=
-  match h: l with
-  | list_t.Cons x tl =>
-    if h: i = (U32.ofInt 0 (by intlit))
-    then Result.ret x
-    else do
-           let i0 ← i - (U32.ofInt 1 (by intlit))
-           list_nth_mut_fwd T tl i0
-  | list_t.Nil => Result.fail Error.panic
-
-/- [paper::list_nth_mut] -/
-def list_nth_mut_back
-  (T : Type) (l : list_t T) (i : U32) (ret0 : T) : Result (list_t T) :=
-  match h: l with
-  | list_t.Cons x tl =>
-    if h: i = (U32.ofInt 0 (by intlit))
-    then Result.ret (list_t.Cons ret0 tl)
-    else
-      do
-        let i0 ← i - (U32.ofInt 1 (by intlit))
-        let tl0 ← list_nth_mut_back T tl i0 ret0
-        Result.ret (list_t.Cons x tl0)
-  | list_t.Nil => Result.fail Error.panic
-
-/- [paper::sum] -/
-def sum_fwd (l : list_t I32) : Result I32 :=
-  match h: l with
-  | list_t.Cons x tl => do
-                          let i ← sum_fwd tl
-                          x + i
-  | list_t.Nil => Result.ret (I32.ofInt 0 (by intlit))
-
-/- [paper::test_nth] -/
-def test_nth_fwd : Result Unit :=
-  do
-    let l := list_t.Nil
-    let l0 := list_t.Cons (I32.ofInt 3 (by intlit)) l
-    let l1 := list_t.Cons (I32.ofInt 2 (by intlit)) l0
-    let x ←
-      list_nth_mut_fwd I32 (list_t.Cons (I32.ofInt 1 (by intlit)) l1)
-        (U32.ofInt 2 (by intlit))
-    let x0 ← x + (I32.ofInt 1 (by intlit))
-    let l2 ←
-      list_nth_mut_back I32 (list_t.Cons (I32.ofInt 1 (by intlit)) l1)
-        (U32.ofInt 2 (by intlit)) x0
-    let i ← sum_fwd l2
-    if h: not (i = (I32.ofInt 7 (by intlit)))
-    then Result.fail Error.panic
-    else Result.ret ()
-
-/- Unit test for [paper::test_nth] -/
-#assert (test_nth_fwd == .ret ())
-
-/- [paper::call_choose] -/
-def call_choose_fwd (p : (U32 × U32)) : Result U32 :=
-  do
-    let (px, py) := p
-    let pz ← choose_fwd U32 true px py
-    let pz0 ← pz + (U32.ofInt 1 (by intlit))
-    let (px0, _) ← choose_back U32 true px py pz0
-    Result.ret px0
-
diff --git a/tests/lean/misc-paper/lake-manifest.json b/tests/lean/misc-paper/lake-manifest.json
deleted file mode 100644
index 57b071ca..00000000
--- a/tests/lean/misc-paper/lake-manifest.json
+++ /dev/null
@@ -1,27 +0,0 @@
-{"version": 4,
- "packagesDir": "./lake-packages",
- "packages":
- [{"git":
-   {"url": "https://github.com/leanprover-community/mathlib4.git",
-    "subDir?": null,
-    "rev": "4037792ead804d7bfa8868e2c4684d4223c15ece",
-    "name": "mathlib",
-    "inputRev?": null}},
-  {"git":
-   {"url": "https://github.com/gebner/quote4",
-    "subDir?": null,
-    "rev": "2412c4fdf4a8b689f4467618e5e7b371ae5014aa",
-    "name": "Qq",
-    "inputRev?": "master"}},
-  {"git":
-   {"url": "https://github.com/JLimperg/aesop",
-    "subDir?": null,
-    "rev": "7fe9ecd9339b0e1796e89d243b776849c305c690",
-    "name": "aesop",
-    "inputRev?": "master"}},
-  {"git":
-   {"url": "https://github.com/leanprover/std4",
-    "subDir?": null,
-    "rev": "24897887905b3a1254b244369f5dd2cf6174b0ee",
-    "name": "std",
-    "inputRev?": "main"}}]}
diff --git a/tests/lean/misc-paper/lakefile.lean b/tests/lean/misc-paper/lakefile.lean
deleted file mode 100644
index 75d7208e..00000000
--- a/tests/lean/misc-paper/lakefile.lean
+++ /dev/null
@@ -1,12 +0,0 @@
-import Lake
-open Lake DSL
-
-require mathlib from git
-  "https://github.com/leanprover-community/mathlib4.git"
-
-package «paper» {}
-
-lean_lib «Base» {}
-
-@[default_target]
-lean_lib «Paper» {}
diff --git a/tests/lean/misc-paper/lean-toolchain b/tests/lean/misc-paper/lean-toolchain
deleted file mode 100644
index bbf57f10..00000000
--- a/tests/lean/misc-paper/lean-toolchain
+++ /dev/null
@@ -1 +0,0 @@
-leanprover/lean4:nightly-2023-01-21
diff --git a/tests/lean/misc-polonius_list/Base/Primitives.lean b/tests/lean/misc-polonius_list/Base/Primitives.lean
deleted file mode 100644
index 4a66a453..00000000
--- a/tests/lean/misc-polonius_list/Base/Primitives.lean
+++ /dev/null
@@ -1,583 +0,0 @@
-import Lean
-import Lean.Meta.Tactic.Simp
-import Init.Data.List.Basic
-import Mathlib.Tactic.RunCmd
-
---------------------
--- ASSERT COMMAND --
---------------------
-
-open Lean Elab Command Term Meta
-
-syntax (name := assert) "#assert" term: command
-
-@[command_elab assert]
-unsafe
-def assertImpl : CommandElab := fun (_stx: Syntax) => do
-  runTermElabM (fun _ => do
-    let r ← evalTerm Bool (mkConst ``Bool) _stx[1]
-    if not r then
-      logInfo "Assertion failed for: "
-      logInfo _stx[1]
-      logError "Expression reduced to false"
-    pure ())
-
-#eval 2 == 2
-#assert (2 == 2)
-
--------------
--- PRELUDE --
--------------
-
--- Results & monadic combinators
-
-inductive Error where
-   | assertionFailure: Error
-   | integerOverflow: Error
-   | divisionByZero: Error
-   | arrayOutOfBounds: Error
-   | maximumSizeExceeded: Error
-   | panic: Error
-deriving Repr, BEq
-
-open Error
-
-inductive Result (α : Type u) where
-  | ret (v: α): Result α
-  | fail (e: Error): Result α
-deriving Repr, BEq
-
-open Result
-
-instance Result_Inhabited (α : Type u) : Inhabited (Result α) :=
-  Inhabited.mk (fail panic)
-
-/- HELPERS -/
-
-def ret? {α: Type} (r: Result α): Bool :=
-  match r with
-  | Result.ret _ => true
-  | Result.fail _ => false
-
-def massert (b:Bool) : Result Unit :=
-  if b then .ret () else fail assertionFailure
-
-def eval_global {α: Type} (x: Result α) (_: ret? x): α :=
-  match x with
-  | Result.fail _ => by contradiction
-  | Result.ret x => x
-
-/- DO-DSL SUPPORT -/
-
-def bind (x: Result α) (f: α -> Result β) : Result β :=
-  match x with
-  | ret v  => f v 
-  | fail v => fail v
-
--- Allows using Result in do-blocks
-instance : Bind Result where
-  bind := bind
-
--- Allows using return x in do-blocks
-instance : Pure Result where
-  pure := fun x => ret x
-
-/- CUSTOM-DSL SUPPORT -/
-
--- Let-binding the Result of a monadic operation is oftentimes not sufficient,
--- because we may need a hypothesis for equational reasoning in the scope. We
--- rely on subtype, and a custom let-binding operator, in effect recreating our
--- own variant of the do-dsl
-
-def Result.attach {α: Type} (o : Result α): Result { x : α // o = ret x } :=
-  match o with
-  | .ret x => .ret ⟨x, rfl⟩
-  | .fail e => .fail e
-
-macro "let" e:term " ⟵ " f:term : doElem =>
-  `(doElem| let ⟨$e, h⟩ ← Result.attach $f)
-
--- TODO: any way to factorize both definitions?
-macro "let" e:term " <-- " f:term : doElem =>
-  `(doElem| let ⟨$e, h⟩ ← Result.attach $f)
-
--- We call the hypothesis `h`, in effect making it unavailable to the user
--- (because too much shadowing). But in practice, once can use the French single
--- quote notation (input with f< and f>), where `‹ h ›` finds a suitable
--- hypothesis in the context, this is equivalent to `have x: h := by assumption in x`
-#eval do
-  let y <-- .ret (0: Nat)
-  let _: y = 0 := by cases ‹ ret 0 = ret y › ; decide
-  let r: { x: Nat // x = 0 } := ⟨ y, by assumption ⟩
-  .ret r
-
-----------------------
--- MACHINE INTEGERS --
-----------------------
-
--- We redefine our machine integers types.
-
--- For Isize/Usize, we reuse `getNumBits` from `USize`. You cannot reduce `getNumBits`
--- using the simplifier, meaning that proofs do not depend on the compile-time value of
--- USize.size. (Lean assumes 32 or 64-bit platforms, and Rust doesn't really support, at
--- least officially, 16-bit microcontrollers, so this seems like a fine design decision
--- for now.)
-
--- Note from Chris Bailey: "If there's more than one salient property of your
--- definition then the subtyping strategy might get messy, and the property part
--- of a subtype is less discoverable by the simplifier or tactics like
--- library_search." So, we will not add refinements on the return values of the
--- operations defined on Primitives, but will rather rely on custom lemmas to
--- invert on possible return values of the primitive operations.
-
--- Machine integer constants, done via `ofNatCore`, which requires a proof that
--- the `Nat` fits within the desired integer type. We provide a custom tactic.
-
-open System.Platform.getNumBits
-
--- TODO: is there a way of only importing System.Platform.getNumBits?
---
-@[simp] def size_num_bits : Nat := (System.Platform.getNumBits ()).val
-
--- Remark: Lean seems to use < for the comparisons with the upper bounds by convention.
--- We keep the F* convention for now.
-@[simp] def Isize.min : Int := - (HPow.hPow 2 (size_num_bits - 1))
-@[simp] def Isize.max : Int := (HPow.hPow 2 (size_num_bits - 1)) - 1
-@[simp] def I8.min    : Int := - (HPow.hPow 2 7)
-@[simp] def I8.max    : Int := HPow.hPow 2 7 - 1
-@[simp] def I16.min   : Int := - (HPow.hPow 2 15)
-@[simp] def I16.max   : Int := HPow.hPow 2 15 - 1
-@[simp] def I32.min   : Int := -(HPow.hPow 2 31)
-@[simp] def I32.max   : Int := HPow.hPow 2 31 - 1
-@[simp] def I64.min   : Int := -(HPow.hPow 2 63)
-@[simp] def I64.max   : Int := HPow.hPow 2 63 - 1
-@[simp] def I128.min  : Int := -(HPow.hPow 2 127)
-@[simp] def I128.max  : Int := HPow.hPow 2 127 - 1
-@[simp] def Usize.min : Int := 0
-@[simp] def Usize.max : Int := HPow.hPow 2 size_num_bits - 1
-@[simp] def U8.min    : Int := 0
-@[simp] def U8.max    : Int := HPow.hPow 2 8 - 1
-@[simp] def U16.min   : Int := 0
-@[simp] def U16.max   : Int := HPow.hPow 2 16 - 1
-@[simp] def U32.min   : Int := 0
-@[simp] def U32.max   : Int := HPow.hPow 2 32 - 1
-@[simp] def U64.min   : Int := 0
-@[simp] def U64.max   : Int := HPow.hPow 2 64 - 1
-@[simp] def U128.min  : Int := 0
-@[simp] def U128.max  : Int := HPow.hPow 2 128 - 1
-
-#assert (I8.min   == -128)
-#assert (I8.max   == 127)
-#assert (I16.min  == -32768)
-#assert (I16.max  == 32767)
-#assert (I32.min  == -2147483648)
-#assert (I32.max  == 2147483647)
-#assert (I64.min  == -9223372036854775808)
-#assert (I64.max  == 9223372036854775807)
-#assert (I128.min == -170141183460469231731687303715884105728)
-#assert (I128.max == 170141183460469231731687303715884105727)
-#assert (U8.min   == 0)
-#assert (U8.max   == 255)
-#assert (U16.min  == 0)
-#assert (U16.max  == 65535)
-#assert (U32.min  == 0)
-#assert (U32.max  == 4294967295)
-#assert (U64.min  == 0)
-#assert (U64.max  == 18446744073709551615)
-#assert (U128.min == 0)
-#assert (U128.max == 340282366920938463463374607431768211455)
-
-inductive ScalarTy :=
-| Isize
-| I8
-| I16
-| I32
-| I64
-| I128
-| Usize
-| U8
-| U16
-| U32
-| U64
-| U128
-
-def Scalar.min (ty : ScalarTy) : Int :=
-  match ty with
-  | .Isize => Isize.min
-  | .I8    => I8.min
-  | .I16   => I16.min
-  | .I32   => I32.min
-  | .I64   => I64.min
-  | .I128  => I128.min
-  | .Usize => Usize.min
-  | .U8    => U8.min
-  | .U16   => U16.min
-  | .U32   => U32.min
-  | .U64   => U64.min
-  | .U128  => U128.min
-
-def Scalar.max (ty : ScalarTy) : Int :=
-  match ty with
-  | .Isize => Isize.max
-  | .I8    => I8.max
-  | .I16   => I16.max
-  | .I32   => I32.max
-  | .I64   => I64.max
-  | .I128  => I128.max
-  | .Usize => Usize.max
-  | .U8    => U8.max
-  | .U16   => U16.max
-  | .U32   => U32.max
-  | .U64   => U64.max
-  | .U128  => U128.max
-
--- "Conservative" bounds
--- We use those because we can't compare to the isize bounds (which can't
--- reduce at compile-time). Whenever we perform an arithmetic operation like
--- addition we need to check that the result is in bounds: we first compare
--- to the conservative bounds, which reduce, then compare to the real bounds.
--- This is useful for the various #asserts that we want to reduce at
--- type-checking time.
-def Scalar.cMin (ty : ScalarTy) : Int :=
-  match ty with
-  | .Isize => I32.min
-  | _ => Scalar.min ty
-
-def Scalar.cMax (ty : ScalarTy) : Int :=
-  match ty with
-  | .Isize => I32.max
-  | .Usize => U32.max
-  | _ => Scalar.max ty
-
-theorem Scalar.cMin_bound ty : Scalar.min ty <= Scalar.cMin ty := by sorry
-theorem Scalar.cMax_bound ty : Scalar.min ty <= Scalar.cMin ty := by sorry
-
-structure Scalar (ty : ScalarTy) where
-  val : Int
-  hmin : Scalar.min ty <= val
-  hmax : val <= Scalar.max ty
-
-theorem Scalar.bound_suffices (ty : ScalarTy) (x : Int) :
-  Scalar.cMin ty <= x && x <= Scalar.cMax ty ->
-  (decide (Scalar.min ty ≤ x) && decide (x ≤ Scalar.max ty)) = true
-  := by sorry
-
-def Scalar.ofIntCore {ty : ScalarTy} (x : Int)
-  (hmin : Scalar.min ty <= x) (hmax : x <= Scalar.max ty) : Scalar ty :=
-  { val := x, hmin := hmin, hmax := hmax }
-
-def Scalar.ofInt {ty : ScalarTy} (x : Int)
-  (h : Scalar.min ty <= x && x <= Scalar.max ty) : Scalar ty :=
-  let hmin: Scalar.min ty <= x := by sorry
-  let hmax: x <= Scalar.max ty := by sorry
-  Scalar.ofIntCore x hmin hmax
-
--- Further thoughts: look at what has been done here:
--- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/Fin/Basic.lean
--- and
--- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/UInt.lean
--- which both contain a fair amount of reasoning already!
-def Scalar.tryMk (ty : ScalarTy) (x : Int) : Result (Scalar ty) :=
-  -- TODO: write this with only one if then else
-  if hmin_cons: Scalar.cMin ty <= x || Scalar.min ty <= x then
-    if hmax_cons: x <= Scalar.cMax ty || x <= Scalar.max ty then
-      let hmin: Scalar.min ty <= x := by sorry
-      let hmax: x <= Scalar.max ty := by sorry
-      return Scalar.ofIntCore x hmin hmax
-    else fail integerOverflow
-  else fail integerOverflow
-
-def Scalar.neg {ty : ScalarTy} (x : Scalar ty) : Result (Scalar ty) := Scalar.tryMk ty (- x.val)
-
-def Scalar.div {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
-  if y.val != 0 then Scalar.tryMk ty (x.val / y.val) else fail divisionByZero
-
--- Checking that the % operation in Lean computes the same as the remainder operation in Rust
-#assert 1 % 2 = (1:Int)
-#assert (-1) % 2 = -1
-#assert 1 % (-2) = 1
-#assert (-1) % (-2) = -1
-
-def Scalar.rem {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
-  if y.val != 0 then Scalar.tryMk ty (x.val % y.val) else fail divisionByZero
-
-def Scalar.add {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
-  Scalar.tryMk ty (x.val + y.val)
-
-def Scalar.sub {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
-  Scalar.tryMk ty (x.val - y.val)
-
-def Scalar.mul {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
-  Scalar.tryMk ty (x.val * y.val)
-
--- TODO: instances of +, -, * etc. for scalars
-
--- Cast an integer from a [src_ty] to a [tgt_ty]
--- TODO: check the semantics of casts in Rust
-def Scalar.cast {src_ty : ScalarTy} (tgt_ty : ScalarTy) (x : Scalar src_ty) : Result (Scalar tgt_ty) :=
-  Scalar.tryMk tgt_ty x.val
-
--- The scalar types
--- We declare the definitions as reducible so that Lean can unfold them (useful
--- for type class resolution for instance).
-@[reducible] def Isize := Scalar .Isize
-@[reducible] def I8    := Scalar .I8
-@[reducible] def I16   := Scalar .I16
-@[reducible] def I32   := Scalar .I32
-@[reducible] def I64   := Scalar .I64
-@[reducible] def I128  := Scalar .I128
-@[reducible] def Usize := Scalar .Usize
-@[reducible] def U8    := Scalar .U8
-@[reducible] def U16   := Scalar .U16
-@[reducible] def U32   := Scalar .U32
-@[reducible] def U64   := Scalar .U64
-@[reducible] def U128  := Scalar .U128
-
--- TODO: below: not sure this is the best way.
--- Should we rather overload operations like +, -, etc.?
--- Also, it is possible to automate the generation of those definitions
--- with macros (but would it be a good idea? It would be less easy to
--- read the file, which is not supposed to change a lot)
-
--- Negation
-
-/--
-Remark: there is no heterogeneous negation in the Lean prelude: we thus introduce
-one here.
-
-The notation typeclass for heterogeneous addition.
-This enables the notation `- a : β` where `a : α`.
--/
-class HNeg (α : Type u) (β : outParam (Type v)) where
-  /-- `- a` computes the negation of `a`.
-  The meaning of this notation is type-dependent. -/
-  hNeg : α → β
-
-prefix:75  "-"   => HNeg.hNeg
-
-instance : HNeg Isize (Result Isize) where hNeg x := Scalar.neg x
-instance : HNeg I8 (Result I8) where hNeg x := Scalar.neg x
-instance : HNeg I16 (Result I16) where hNeg x := Scalar.neg x
-instance : HNeg I32 (Result I32) where hNeg x := Scalar.neg x
-instance : HNeg I64 (Result I64) where hNeg x := Scalar.neg x
-instance : HNeg I128 (Result I128) where hNeg x := Scalar.neg x
-
--- Addition
-instance {ty} : HAdd (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
-  hAdd x y := Scalar.add x y
-
--- Substraction
-instance {ty} : HSub (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
-  hSub x y := Scalar.sub x y
-
--- Multiplication
-instance {ty} : HMul (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
-  hMul x y := Scalar.mul x y
-
--- Division
-instance {ty} : HDiv (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
-  hDiv x y := Scalar.div x y
-
--- Remainder
-instance {ty} : HMod (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
-  hMod x y := Scalar.rem x y
-
--- ofIntCore
--- TODO: typeclass?
-def Isize.ofIntCore := @Scalar.ofIntCore .Isize
-def I8.ofIntCore    := @Scalar.ofIntCore .I8
-def I16.ofIntCore   := @Scalar.ofIntCore .I16
-def I32.ofIntCore   := @Scalar.ofIntCore .I32
-def I64.ofIntCore   := @Scalar.ofIntCore .I64
-def I128.ofIntCore  := @Scalar.ofIntCore .I128
-def Usize.ofIntCore := @Scalar.ofIntCore .Usize
-def U8.ofIntCore    := @Scalar.ofIntCore .U8
-def U16.ofIntCore   := @Scalar.ofIntCore .U16
-def U32.ofIntCore   := @Scalar.ofIntCore .U32
-def U64.ofIntCore   := @Scalar.ofIntCore .U64
-def U128.ofIntCore  := @Scalar.ofIntCore .U128
-
---  ofInt
--- TODO: typeclass?
-def Isize.ofInt := @Scalar.ofInt .Isize
-def I8.ofInt    := @Scalar.ofInt .I8
-def I16.ofInt   := @Scalar.ofInt .I16
-def I32.ofInt   := @Scalar.ofInt .I32
-def I64.ofInt   := @Scalar.ofInt .I64
-def I128.ofInt  := @Scalar.ofInt .I128
-def Usize.ofInt := @Scalar.ofInt .Usize
-def U8.ofInt    := @Scalar.ofInt .U8
-def U16.ofInt   := @Scalar.ofInt .U16
-def U32.ofInt   := @Scalar.ofInt .U32
-def U64.ofInt   := @Scalar.ofInt .U64
-def U128.ofInt  := @Scalar.ofInt .U128
-
--- Comparisons
-instance {ty} : LT (Scalar ty) where
-  lt a b := LT.lt a.val b.val
-
-instance {ty} : LE (Scalar ty) where le a b := LE.le a.val b.val
-
-instance Scalar.decLt {ty} (a b : Scalar ty) : Decidable (LT.lt a b) := Int.decLt ..
-instance Scalar.decLe {ty} (a b : Scalar ty) : Decidable (LE.le a b) := Int.decLe ..
-
-theorem Scalar.eq_of_val_eq {ty} : ∀ {i j : Scalar ty}, Eq i.val j.val → Eq i j
-  | ⟨_, _, _⟩, ⟨_, _, _⟩, rfl => rfl
-
-theorem Scalar.val_eq_of_eq {ty} {i j : Scalar ty} (h : Eq i j) : Eq i.val j.val :=
-  h ▸ rfl
-
-theorem Scalar.ne_of_val_ne {ty} {i j : Scalar ty} (h : Not (Eq i.val j.val)) : Not (Eq i j) :=
-  fun h' => absurd (val_eq_of_eq h') h
-
-instance (ty : ScalarTy) : DecidableEq (Scalar ty) :=
-  fun i j =>
-    match decEq i.val j.val with
-    | isTrue h  => isTrue (Scalar.eq_of_val_eq h)
-    | isFalse h => isFalse (Scalar.ne_of_val_ne h)
-
-def Scalar.toInt {ty} (n : Scalar ty) : Int := n.val
-
--- Tactic to prove that integers are in bounds
-syntax "intlit" : tactic
-
-macro_rules
-  | `(tactic| intlit) => `(tactic| apply Scalar.bound_suffices ; decide)
-
--- -- We now define a type class that subsumes the various machine integer types, so
--- -- as to write a concise definition for scalar_cast, rather than exhaustively
--- -- enumerating all of the possible pairs. We remark that Rust has sane semantics
--- -- and fails if a cast operation would involve a truncation or modulo.
-
--- class MachineInteger (t: Type) where
---   size: Nat
---   val: t -> Fin size
---   ofNatCore: (n:Nat) -> LT.lt n size -> t
-
--- set_option hygiene false in
--- run_cmd
---   for typeName in [`UInt8, `UInt16, `UInt32, `UInt64, `USize].map Lean.mkIdent do
---   Lean.Elab.Command.elabCommand (← `(
---     namespace $typeName
---     instance: MachineInteger $typeName where
---       size := size
---       val := val
---       ofNatCore := ofNatCore
---     end $typeName
---   ))
-
--- -- Aeneas only instantiates the destination type (`src` is implicit). We rely on
--- -- Lean to infer `src`.
-
--- def scalar_cast { src: Type } (dst: Type) [ MachineInteger src ] [ MachineInteger dst ] (x: src): Result dst :=
---   if h: MachineInteger.val x < MachineInteger.size dst then
---     .ret (MachineInteger.ofNatCore (MachineInteger.val x).val h)
---   else
---     .fail integerOverflow
-
--------------
--- VECTORS --
--------------
-
-def Vec (α : Type u) := { l : List α // List.length l <= Usize.max }
-
-def vec_new (α : Type u): Vec α := ⟨ [], by sorry ⟩
-
-def vec_len (α : Type u) (v : Vec α) : Usize :=
-  let ⟨ v, l ⟩ := v
-  Usize.ofIntCore (List.length v) (by sorry) l
- 
-def vec_push_fwd (α : Type u) (_ : Vec α) (_ : α) : Unit := ()
-
-def vec_push_back (α : Type u) (v : Vec α) (x : α) : Result (Vec α)
-  :=
-  if h : List.length v.val <= U32.max || List.length v.val <= Usize.max then
-    return ⟨ List.concat v.val x, by sorry ⟩
-  else
-    fail maximumSizeExceeded
-
-def vec_insert_fwd (α : Type u) (v: Vec α) (i: Usize) (_: α): Result Unit :=
-  if i.val < List.length v.val then
-    .ret ()
-  else
-    .fail arrayOutOfBounds
-
-def vec_insert_back (α : Type u) (v: Vec α) (i: Usize) (x: α): Result (Vec α) :=
-  if i.val < List.length v.val then
-    -- TODO: maybe we should redefine a list library which uses integers
-    -- (instead of natural numbers)
-    let i : Nat :=
-      match i.val with
-      | .ofNat n => n
-      | .negSucc n => by sorry -- TODO: we can't get here
-    let isLt: i < USize.size := by sorry
-    let i : Fin USize.size := { val := i, isLt := isLt }
-    .ret ⟨ List.set v.val i.val x, by
-      have h: List.length v.val <= Usize.max := v.property
-      rewrite [ List.length_set v.val i.val x ]
-      assumption
-    ⟩
-  else
-    .fail arrayOutOfBounds
-
-def vec_index_fwd (α : Type u) (v: Vec α) (i: Usize): Result α :=
-  if i.val < List.length v.val then
-    let i : Nat :=
-      match i.val with
-      | .ofNat n => n
-      | .negSucc n => by sorry -- TODO: we can't get here
-    let isLt: i < USize.size := by sorry
-    let i : Fin USize.size := { val := i, isLt := isLt }
-    let h: i < List.length v.val := by sorry
-    .ret (List.get v.val ⟨i.val, h⟩)
-  else
-    .fail arrayOutOfBounds
-
-def vec_index_back (α : Type u) (v: Vec α) (i: Usize) (_: α): Result Unit :=
-  if i.val < List.length v.val then
-    .ret ()
-  else
-    .fail arrayOutOfBounds
-
-def vec_index_mut_fwd (α : Type u) (v: Vec α) (i: Usize): Result α :=
-  if i.val < List.length v.val then
-    let i : Nat :=
-      match i.val with
-      | .ofNat n => n
-      | .negSucc n => by sorry -- TODO: we can't get here
-    let isLt: i < USize.size := by sorry
-    let i : Fin USize.size := { val := i, isLt := isLt }
-    let h: i < List.length v.val := by sorry
-    .ret (List.get v.val ⟨i.val, h⟩)
-  else
-    .fail arrayOutOfBounds
-
-def vec_index_mut_back (α : Type u) (v: Vec α) (i: Usize) (x: α): Result (Vec α) :=
-  if i.val < List.length v.val then
-    let i : Nat :=
-      match i.val with
-      | .ofNat n => n
-      | .negSucc n => by sorry -- TODO: we can't get here
-    let isLt: i < USize.size := by sorry
-    let i : Fin USize.size := { val := i, isLt := isLt }
-    .ret ⟨ List.set v.val i.val x, by
-      have h: List.length v.val <= Usize.max := v.property
-      rewrite [ List.length_set v.val i.val x ]
-      assumption
-    ⟩
-  else
-    .fail arrayOutOfBounds
-
-----------
--- MISC --
-----------
-
-def mem_replace_fwd (a : Type) (x : a) (_ : a) : a :=
-  x
-
-def mem_replace_back (a : Type) (_ : a) (y : a) : a :=
-  y
-
-/-- Aeneas-translated function -- useful to reduce non-recursive definitions.
- Use with `simp [ aeneas ]` -/
-register_simp_attr aeneas
diff --git a/tests/lean/misc-polonius_list/PoloniusList.lean b/tests/lean/misc-polonius_list/PoloniusList.lean
deleted file mode 100644
index 79696996..00000000
--- a/tests/lean/misc-polonius_list/PoloniusList.lean
+++ /dev/null
@@ -1,31 +0,0 @@
--- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
--- [polonius_list]
-import Base.Primitives
-
-/- [polonius_list::List] -/
-inductive list_t (T : Type) :=
-| Cons : T -> list_t T -> list_t T
-| Nil : list_t T
-
-/- [polonius_list::get_list_at_x] -/
-def get_list_at_x_fwd (ls : list_t U32) (x : U32) : Result (list_t U32) :=
-  match h: ls with
-  | list_t.Cons hd tl =>
-    if h: hd = x
-    then Result.ret (list_t.Cons hd tl)
-    else get_list_at_x_fwd tl x
-  | list_t.Nil => Result.ret list_t.Nil
-
-/- [polonius_list::get_list_at_x] -/
-def get_list_at_x_back
-  (ls : list_t U32) (x : U32) (ret0 : list_t U32) : Result (list_t U32) :=
-  match h: ls with
-  | list_t.Cons hd tl =>
-    if h: hd = x
-    then Result.ret ret0
-    else
-      do
-        let tl0 ← get_list_at_x_back tl x ret0
-        Result.ret (list_t.Cons hd tl0)
-  | list_t.Nil => Result.ret ret0
-
diff --git a/tests/lean/misc-polonius_list/lake-manifest.json b/tests/lean/misc-polonius_list/lake-manifest.json
deleted file mode 100644
index 57b071ca..00000000
--- a/tests/lean/misc-polonius_list/lake-manifest.json
+++ /dev/null
@@ -1,27 +0,0 @@
-{"version": 4,
- "packagesDir": "./lake-packages",
- "packages":
- [{"git":
-   {"url": "https://github.com/leanprover-community/mathlib4.git",
-    "subDir?": null,
-    "rev": "4037792ead804d7bfa8868e2c4684d4223c15ece",
-    "name": "mathlib",
-    "inputRev?": null}},
-  {"git":
-   {"url": "https://github.com/gebner/quote4",
-    "subDir?": null,
-    "rev": "2412c4fdf4a8b689f4467618e5e7b371ae5014aa",
-    "name": "Qq",
-    "inputRev?": "master"}},
-  {"git":
-   {"url": "https://github.com/JLimperg/aesop",
-    "subDir?": null,
-    "rev": "7fe9ecd9339b0e1796e89d243b776849c305c690",
-    "name": "aesop",
-    "inputRev?": "master"}},
-  {"git":
-   {"url": "https://github.com/leanprover/std4",
-    "subDir?": null,
-    "rev": "24897887905b3a1254b244369f5dd2cf6174b0ee",
-    "name": "std",
-    "inputRev?": "main"}}]}
diff --git a/tests/lean/misc-polonius_list/lakefile.lean b/tests/lean/misc-polonius_list/lakefile.lean
deleted file mode 100644
index e89d4259..00000000
--- a/tests/lean/misc-polonius_list/lakefile.lean
+++ /dev/null
@@ -1,12 +0,0 @@
-import Lake
-open Lake DSL
-
-require mathlib from git
-  "https://github.com/leanprover-community/mathlib4.git"
-
-package «polonius_list» {}
-
-lean_lib «Base» {}
-
-@[default_target]
-lean_lib «PoloniusList» {}
diff --git a/tests/lean/misc-polonius_list/lean-toolchain b/tests/lean/misc-polonius_list/lean-toolchain
deleted file mode 100644
index bbf57f10..00000000
--- a/tests/lean/misc-polonius_list/lean-toolchain
+++ /dev/null
@@ -1 +0,0 @@
-leanprover/lean4:nightly-2023-01-21