Make minor fixes, improve formatting for Lean and generate code for all the test suite

23 files changed, 5431 insertions, 129 deletions

diff --git a/tests/lean/hashmap/Base/Primitives.lean b/tests/lean/hashmap/Base/Primitives.lean
new file mode 100644
index 00000000..79958d94
--- /dev/null
+++ b/tests/lean/hashmap/Base/Primitives.lean
@@ -0,0 +1,373 @@
+import Lean
+import Lean.Meta.Tactic.Simp
+import Init.Data.List.Basic
+import Mathlib.Tactic.RunCmd
+
+-------------
+-- PRELUDE --
+-------------
+
+-- Results & monadic combinators
+
+-- TODO: use syntactic conventions and capitalize error, result, etc.
+
+inductive error where
+   | assertionFailure: error
+   | integerOverflow: 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
+
+/- HELPERS -/
+
+-- TODO: is there automated syntax for these discriminators?
+def is_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) (_: is_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 : (o : result α) → result { x : α // o = ret x }
+  | .ret x => .ret ⟨x, rfl⟩
+  | .fail e   => .fail e
+
+macro "let" h:ident " : " e:term " <-- " f:term : doElem =>
+  `(doElem| let ⟨$e, $h⟩ ← result.attach $f)
+
+-- Silly example of the kind of reasoning that this notation enables
+#eval do
+  let h: y <-- .ret (0: Nat)
+  let _: y = 0 := by cases h; decide
+  let r: { x: Nat // x = 0 } := ⟨ y, by assumption ⟩
+  .ret r
+
+----------------------
+-- MACHINE INTEGERS --
+----------------------
+
+-- NOTE: we reuse the USize type from prelude.lean, because at least we know
+-- it's defined in an idiomatic style that is going to make proofs easy (and
+-- indeed, several proofs here are much shortened compared to Aymeric's earlier
+-- attempt.) This is not stricto sensu the *correct* thing to do, because one
+-- can query at run-time the value of USize, which we do *not* want to do (we
+-- don't know what target we'll run on!), but when the day comes, we'll just
+-- define our own USize.
+-- ANOTHER NOTE: there is USize.sub but it has wraparound semantics, which is
+-- not something we want to define (I think), so we use our own monadic sub (but
+-- is it in line with the Rust behavior?)
+
+-- TODO: I am somewhat under the impression that subtraction is defined as a
+-- total function over nats...? the hypothesis in the if condition is not used
+-- in the then-branch which confuses me quite a bit
+
+-- TODO: add a refinement for the result (just like vec_push_back below) that
+-- explains that the toNat of the result (in the case of success) is the sub of
+-- the toNat of the arguments (i.e. intrinsic specification)
+-- ... do we want intrinsic specifications for the builtins? that might require
+-- some careful type annotations in the monadic notation for clients, but may
+-- give us more "for free"
+
+-- 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." Try to settle this with a Lean expert on what is the most
+-- productive way to go about this?
+
+-- One needs to perform a little bit of reasoning in order to successfully
+-- inject constants into USize, so we provide a general-purpose macro
+
+syntax "intlit" : tactic
+
+macro_rules
+  | `(tactic| intlit) => `(tactic|
+    match USize.size, usize_size_eq with
+    | _, Or.inl rfl => decide
+    | _, Or.inr rfl => decide)
+
+-- This is how the macro is expected to be used
+#eval USize.ofNatCore 0 (by intlit)
+
+-- Also works for other integer types (at the expense of a needless disjunction)
+#eval UInt32.ofNatCore 0 (by intlit)
+
+-- 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 USize.checked_sub (n: USize) (m: USize): result USize :=
+  -- NOTE: the test USize.toNat n - m >= 0 seems to always succeed?
+  if n >= m then
+    let n' := USize.toNat n
+    let m' := USize.toNat n
+    let r := USize.ofNatCore (n' - m') (by
+      have h: n' - m' <= n' := by
+        apply Nat.sub_le_of_le_add
+        case h => rewrite [ Nat.add_comm ]; apply Nat.le_add_left
+      apply Nat.lt_of_le_of_lt h
+      apply n.val.isLt
+    )
+    return r
+  else
+    fail integerOverflow
+
+def USize.checked_add (n: USize) (m: USize): result USize :=
+  if h: n.val.val + m.val.val <= 4294967295 then
+    .ret ⟨ n.val.val + m.val.val, by
+      have h': 4294967295 < USize.size := by intlit
+      apply Nat.lt_of_le_of_lt h h'
+    ⟩
+  else if h: n.val + m.val < USize.size then
+    .ret ⟨ n.val + m.val, h ⟩
+  else
+    .fail integerOverflow
+
+def USize.checked_rem (n: USize) (m: USize): result USize :=
+  if h: m > 0 then
+    .ret ⟨ n.val % m.val, by
+      have h1: ↑m.val < USize.size := m.val.isLt
+      have h2: n.val.val % m.val.val < m.val.val := @Nat.mod_lt n.val m.val h
+      apply Nat.lt_trans h2 h1
+    ⟩
+  else
+    .fail integerOverflow
+
+def USize.checked_mul (n: USize) (m: USize): result USize :=
+    if h: n.val.val * m.val.val <= 4294967295 then
+    .ret ⟨ n.val.val * m.val.val, by
+      have h': 4294967295 < USize.size := by intlit
+      apply Nat.lt_of_le_of_lt h h'
+    ⟩
+  else if h: n.val * m.val < USize.size then
+    .ret ⟨ n.val * m.val, h ⟩
+  else
+    .fail integerOverflow
+
+def USize.checked_div (n: USize) (m: USize): result USize :=
+  if m > 0 then
+    .ret ⟨ n.val / m.val, by
+      have h1: ↑n.val < USize.size := n.val.isLt
+      have h2: n.val.val / m.val.val <= n.val.val := @Nat.div_le_self n.val m.val
+      apply Nat.lt_of_le_of_lt h2 h1
+    ⟩
+  else
+    .fail integerOverflow
+
+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
+  ))
+
+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
+
+
+-- Test behavior...
+#eval assert! USize.checked_sub 10 20 == fail integerOverflow; 0
+
+#eval USize.checked_sub 20 10
+-- NOTE: compare with concrete behavior here, which I do not think we want
+#eval USize.sub 0 1
+#eval UInt8.add 255 255
+
+-------------
+-- VECTORS --
+-------------
+
+-- Note: unlike F*, Lean seems to use strict upper bounds (e.g. USize.size)
+-- rather than maximum values (usize_max).
+def vec (α : Type u) := { l : List α // List.length l < USize.size }
+
+def vec_new (α : Type u): vec α := ⟨ [], by {
+  match USize.size, usize_size_eq with
+  | _, Or.inl rfl => simp
+  | _, Or.inr rfl => simp
+  } ⟩
+
+#check vec_new
+
+def vec_len (α : Type u) (v : vec α) : USize :=
+  let ⟨ v, l ⟩ := v
+  USize.ofNatCore (List.length v) l
+
+#eval vec_len Nat (vec_new Nat)
+ 
+def vec_push_fwd (α : Type u) (_ : vec α) (_ : α) : Unit := ()
+
+-- NOTE: old version trying to use a subtype notation, but probably better to
+-- leave result elimination to auxiliary lemmas with suitable preconditions
+-- TODO: I originally wrote `List.length v.val < USize.size - 1`; how can one
+-- make the proof work in that case? Probably need to import tactics from
+-- mathlib to deal with inequalities... would love to see an example.
+def vec_push_back_old (α : Type u) (v : vec α) (x : α) : { res: result (vec α) //
+  match res with | fail _ => True | ret v' => List.length v'.val = List.length v.val + 1}
+  :=
+  if h : List.length v.val + 1 < USize.size then
+    ⟨ return ⟨List.concat v.val x,
+      by
+        rw [List.length_concat]
+        assumption
+     ⟩, by simp ⟩
+  else
+    ⟨ fail maximumSizeExceeded, by simp ⟩
+
+#eval do
+  -- NOTE: the // notation is syntactic sugar for Subtype, a refinement with
+  -- fields val and property. However, Lean's elaborator can automatically
+  -- select the `val` field if the context provides a type annotation. We
+  -- annotate `x`, which relieves us of having to write `.val` on the right-hand
+  -- side of the monadic let.
+  let v := vec_new Nat
+  let x: vec Nat ← (vec_push_back_old Nat v 1: result (vec Nat)) -- WHY do we need the type annotation here?
+  -- TODO: strengthen post-condition above and do a demo to show that we can
+  -- safely eliminate the `fail` case
+  return (vec_len Nat x)
+
+def vec_push_back (α : Type u) (v : vec α) (x : α) : result (vec α)
+  :=
+  if h : List.length v.val + 1 <= 4294967295 then
+    return ⟨ List.concat v.val x,
+      by
+        rw [List.length_concat]
+        have h': 4294967295 < USize.size := by intlit
+        apply Nat.lt_of_le_of_lt h h'
+    ⟩
+  else if h: List.length v.val + 1 < USize.size then
+    return ⟨List.concat v.val x,
+      by
+        rw [List.length_concat]
+        assumption
+     ⟩
+  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
+    .ret ⟨ List.set v.val i.val x, by
+      have h: List.length v.val < USize.size := 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 h: i.val < List.length v.val then
+    .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 h: i.val < List.length v.val then
+    .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
+    .ret ⟨ List.set v.val i.val x, by
+      have h: List.length v.val < USize.size := 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
+
+--------------------
+-- ASSERT COMMAND --
+--------------------
+
+open Lean Elab Command Term Meta
+
+syntax (name := assert) "#assert" term: command
+
+@[command_elab assert]
+def assertImpl : CommandElab := fun (_stx: Syntax) => do
+  logInfo "Reducing and asserting: "
+  logInfo _stx[1]
+  runTermElabM (fun _ => do
+    let e ← Term.elabTerm _stx[1] none
+    logInfo (Expr.dbgToString e)
+    -- How to evaluate the term and compare the result to true?
+    pure ())
+  -- logInfo (Expr.dbgToString (``true))
+  -- throwError "TODO: assert"
+
+#eval 2 == 2
+#assert (2 == 2)
diff --git a/tests/lean/hashmap/Hashmap/Clauses/Clauses.lean b/tests/lean/hashmap/Hashmap/Clauses/Clauses.lean
new file mode 100644
index 00000000..eec8ef96
--- /dev/null
+++ b/tests/lean/hashmap/Hashmap/Clauses/Clauses.lean
@@ -0,0 +1,107 @@
+-- [hashmap]: 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)
+
+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)
+
+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)
+
+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)
+
+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)
+
+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)
+
+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)
+
+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)
+
+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)
+
+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
new file mode 100644
index 00000000..2bc92153
--- /dev/null
+++ b/tests/lean/hashmap/Hashmap/Clauses/Template.lean
@@ -0,0 +1,108 @@
+-- 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)
+
+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)
+
+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)
+
+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)
+
+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)
+
+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)
+
+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)
+
+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)
+
+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)
+
+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
new file mode 100644
index 00000000..030b335a
--- /dev/null
+++ b/tests/lean/hashmap/Hashmap/Funs.lean
@@ -0,0 +1,580 @@
+-- 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 n > (USize.ofNatCore 0 (by intlit))
+  then
+    do
+      let slots0 <- vec_push_back (list_t T) slots list_t.ListNil
+      let n0 <- USize.checked_sub n (USize.ofNatCore 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 <- USize.checked_mul capacity max_load_dividend
+    let i0 <- USize.checked_div i max_load_divisor
+    result.ret
+      {
+        hash_map_num_entries := (USize.ofNatCore 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.ofNatCore 32 (by intlit))
+    (USize.ofNatCore 4 (by intlit)) (USize.ofNatCore 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 i < i0
+  then
+    do
+      let i1 <- USize.checked_add i (USize.ofNatCore 1 (by intlit))
+      let slots0 <- vec_index_mut_back (list_t T) slots i list_t.ListNil
+      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.ofNatCore 0 (by intlit))
+    result.ret
+      {
+        hash_map_num_entries := (USize.ofNatCore 0 (by intlit)),
+        hash_map_max_load_factor := self.hash_map_max_load_factor,
+        hash_map_max_load := self.hash_map_max_load,
+        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 ls with
+  | list_t.ListCons ckey cvalue tl =>
+    if ckey = key
+    then result.ret false
+    else hash_map_insert_in_list_loop_fwd T key value tl
+  | list_t.ListNil => 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 ls with
+  | list_t.ListCons ckey cvalue tl =>
+    if ckey = key
+    then result.ret (list_t.ListCons ckey value tl)
+    else
+      do
+        let tl0 <- hash_map_insert_in_list_loop_back T key value tl
+        result.ret (list_t.ListCons ckey cvalue tl0)
+  | list_t.ListNil =>
+    let l := list_t.ListNil result.ret (list_t.ListCons 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 <- USize.checked_rem 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 inserted
+    then
+      do
+        let i0 <- USize.checked_add self.hash_map_num_entries
+          (USize.ofNatCore 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
+          {
+            hash_map_num_entries := i0,
+            hash_map_max_load_factor := self.hash_map_max_load_factor,
+            hash_map_max_load := self.hash_map_max_load,
+            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
+          {
+            hash_map_num_entries := self.hash_map_num_entries,
+            hash_map_max_load_factor := self.hash_map_max_load_factor,
+            hash_map_max_load := self.hash_map_max_load,
+            hash_map_slots := v
+          }
+
+/- [core::num::u32::{9}::MAX] -/
+def core_num_u32_max_body : result UInt32 :=
+  result.ret (UInt32.ofNatCore 4294967295 (by intlit))
+def core_num_u32_max_c : UInt32 := 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 ls with
+  | list_t.ListCons 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.ListNil => 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 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.ListNil
+      let ntable0 <- hash_map_move_elements_from_list_fwd_back T ntable ls
+      let i1 <- USize.checked_add i (USize.ofNatCore 1 (by intlit))
+      let l0 := mem_replace_back (list_t T) l list_t.ListNil
+      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 <- USize.checked_div max_usize (USize.ofNatCore 2 (by intlit))
+    let (i, i0) := self.hash_map_max_load_factor
+    let i1 <- USize.checked_div n1 i
+    if capacity <= i1
+    then
+      do
+        let i2 <- USize.checked_mul capacity (USize.ofNatCore 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.ofNatCore 0 (by intlit))
+        result.ret
+          {
+            hash_map_num_entries := self.hash_map_num_entries,
+            hash_map_max_load_factor := (i, i0),
+            hash_map_max_load := ntable0.hash_map_max_load,
+            hash_map_slots := ntable0.hash_map_slots
+          }
+    else
+      result.ret
+        {
+          hash_map_num_entries := self.hash_map_num_entries,
+          hash_map_max_load_factor := (i, i0),
+          hash_map_max_load := self.hash_map_max_load,
+          hash_map_slots := self.hash_map_slots
+        }
+
+/- [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 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 ls with
+  | list_t.ListCons ckey t tl =>
+    if ckey = key
+    then result.ret true
+    else hash_map_contains_key_in_list_loop_fwd T key tl
+  | list_t.ListNil => 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 <- USize.checked_rem 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 ls with
+  | list_t.ListCons ckey cvalue tl =>
+    if ckey = key
+    then result.ret cvalue
+    else hash_map_get_in_list_loop_fwd T key tl
+  | list_t.ListNil => 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 <- USize.checked_rem 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 ls with
+  | list_t.ListCons ckey cvalue tl =>
+    if ckey = key
+    then result.ret cvalue
+    else hash_map_get_mut_in_list_loop_fwd T tl key
+  | list_t.ListNil => 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 ls with
+  | list_t.ListCons ckey cvalue tl =>
+    if ckey = key
+    then result.ret (list_t.ListCons ckey ret0 tl)
+    else
+      do
+        let tl0 <- hash_map_get_mut_in_list_loop_back T tl key ret0
+        result.ret (list_t.ListCons ckey cvalue tl0)
+  | list_t.ListNil => 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 <- USize.checked_rem 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 <- USize.checked_rem 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
+      {
+        hash_map_num_entries := self.hash_map_num_entries,
+        hash_map_max_load_factor := self.hash_map_max_load_factor,
+        hash_map_max_load := self.hash_map_max_load,
+        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 ls with
+  | list_t.ListCons ckey t tl =>
+    if ckey = key
+    then
+      let mv_ls :=
+        mem_replace_fwd (list_t T) (list_t.ListCons ckey t tl) list_t.ListNil
+      match mv_ls with
+      | list_t.ListCons i cvalue tl0 => result.ret (Option.some cvalue)
+      | list_t.ListNil => result.fail error.panic
+      
+    else hash_map_remove_from_list_loop_fwd T key tl
+  | list_t.ListNil => 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 ls with
+  | list_t.ListCons ckey t tl =>
+    if ckey = key
+    then
+      let mv_ls :=
+        mem_replace_fwd (list_t T) (list_t.ListCons ckey t tl) list_t.ListNil
+      match mv_ls with
+      | list_t.ListCons i cvalue tl0 => result.ret tl0
+      | list_t.ListNil => result.fail error.panic
+      
+    else
+      do
+        let tl0 <- hash_map_remove_from_list_loop_back T key tl
+        result.ret (list_t.ListCons ckey t tl0)
+  | list_t.ListNil => result.ret list_t.ListNil
+  
+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 <- USize.checked_rem 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 x with
+    | Option.none => result.ret Option.none
+    | Option.some x0 =>
+      do
+        let _ <- USize.checked_sub self.hash_map_num_entries
+          (USize.ofNatCore 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 <- USize.checked_rem 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 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
+          {
+            hash_map_num_entries := self.hash_map_num_entries,
+            hash_map_max_load_factor := self.hash_map_max_load_factor,
+            hash_map_max_load := self.hash_map_max_load,
+            hash_map_slots := v
+          }
+    | Option.some x0 =>
+      do
+        let i0 <- USize.checked_sub self.hash_map_num_entries
+          (USize.ofNatCore 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
+          {
+            hash_map_num_entries := i0,
+            hash_map_max_load_factor := self.hash_map_max_load_factor,
+            hash_map_max_load := self.hash_map_max_load,
+            hash_map_slots := v
+          }
+    
+
+/- [hashmap::test1] -/
+def test1_fwd : result Unit :=
+  do
+    let hm <- hash_map_new_fwd UInt64
+    let hm0 <-
+      hash_map_insert_fwd_back UInt64 hm (USize.ofNatCore 0 (by intlit))
+        (UInt64.ofNatCore 42 (by intlit))
+    let hm1 <-
+      hash_map_insert_fwd_back UInt64 hm0 (USize.ofNatCore 128 (by intlit))
+        (UInt64.ofNatCore 18 (by intlit))
+    let hm2 <-
+      hash_map_insert_fwd_back UInt64 hm1 (USize.ofNatCore 1024 (by intlit))
+        (UInt64.ofNatCore 138 (by intlit))
+    let hm3 <-
+      hash_map_insert_fwd_back UInt64 hm2 (USize.ofNatCore 1056 (by intlit))
+        (UInt64.ofNatCore 256 (by intlit))
+    let i <- hash_map_get_fwd UInt64 hm3 (USize.ofNatCore 128 (by intlit))
+    if not (i = (UInt64.ofNatCore 18 (by intlit)))
+    then result.fail error.panic
+    else
+      do
+        let hm4 <-
+          hash_map_get_mut_back UInt64 hm3 (USize.ofNatCore 1024 (by intlit))
+            (UInt64.ofNatCore 56 (by intlit))
+        let i0 <-
+          hash_map_get_fwd UInt64 hm4 (USize.ofNatCore 1024 (by intlit))
+        if not (i0 = (UInt64.ofNatCore 56 (by intlit)))
+        then result.fail error.panic
+        else
+          do
+            let x <-
+              hash_map_remove_fwd UInt64 hm4 (USize.ofNatCore 1024 (by intlit))
+            match x with
+            | Option.none => result.fail error.panic
+            | Option.some x0 =>
+              if not (x0 = (UInt64.ofNatCore 56 (by intlit)))
+              then result.fail error.panic
+              else
+                do
+                  let hm5 <-
+                    hash_map_remove_back UInt64 hm4
+                      (USize.ofNatCore 1024 (by intlit))
+                  let i1 <-
+                    hash_map_get_fwd UInt64 hm5 (USize.ofNatCore 0 (by intlit))
+                  if not (i1 = (UInt64.ofNatCore 42 (by intlit)))
+                  then result.fail error.panic
+                  else
+                    do
+                      let i2 <-
+                        hash_map_get_fwd UInt64 hm5
+                          (USize.ofNatCore 128 (by intlit))
+                      if not (i2 = (UInt64.ofNatCore 18 (by intlit)))
+                      then result.fail error.panic
+                      else
+                        do
+                          let i3 <-
+                            hash_map_get_fwd UInt64 hm5
+                              (USize.ofNatCore 1056 (by intlit))
+                          if not (i3 = (UInt64.ofNatCore 256 (by intlit)))
+                          then result.fail error.panic
+                          else result.ret ()
+            
+
+/- Unit test for [hashmap::test1] -/
+#assert (test1_fwd = .ret ())
+
diff --git a/tests/lean/hashmap/Hashmap/Types.lean b/tests/lean/hashmap/Hashmap/Types.lean
new file mode 100644
index 00000000..9f08bd60
--- /dev/null
+++ b/tests/lean/hashmap/Hashmap/Types.lean
@@ -0,0 +1,18 @@
+-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
+-- [hashmap]: type definitions
+import Base.Primitives
+
+/- [hashmap::List] -/
+inductive list_t (T : Type) :=
+| ListCons : USize -> T -> list_t T -> list_t T
+| ListNil : 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_on_disk/HashmapMain/Clauses/Clauses.lean b/tests/lean/hashmap_on_disk/HashmapMain/Clauses/Clauses.lean
new file mode 100644
index 00000000..16a4ea4c
--- /dev/null
+++ b/tests/lean/hashmap_on_disk/HashmapMain/Clauses/Clauses.lean
@@ -0,0 +1,111 @@
+-- [hashmap_main]: 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)
+
+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)
+
+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)
+
+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)
+
+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)
+
+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)
+
+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)
+
+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)
+
+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)
+
+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
index bf331d6e..3466e7e0 100644
--- a/tests/lean/hashmap_on_disk/HashmapMain/Clauses/Template.lean
+++ b/tests/lean/hashmap_on_disk/HashmapMain/Clauses/Template.lean
@@ -15,17 +15,16 @@ macro_rules
 | `(tactic| hashmap_hash_map_allocate_slots_loop_decreases $slots $n) =>
   `(tactic| sorry)
 
-/- [hashmap_main::hashmap::HashMap::{0}::clear_slots]: termination measure -/
+/- [hashmap_main::hashmap::HashMap::{0}::clear]: termination measure -/
 @[simp]
-def hashmap_hash_map_clear_slots_loop_terminates (T : Type)
+def hashmap_hash_map_clear_loop_terminates (T : Type)
   (slots : vec (hashmap_list_t T)) (i : USize) :=
   (slots, i)
 
-syntax "hashmap_hash_map_clear_slots_loop_decreases" term+ : tactic
+syntax "hashmap_hash_map_clear_loop_decreases" term+ : tactic
 
 macro_rules
-| `(tactic| hashmap_hash_map_clear_slots_loop_decreases $slots $i) =>
-  `(tactic| sorry)
+| `(tactic| hashmap_hash_map_clear_loop_decreases $slots $i) =>`(tactic| sorry)
 
 /- [hashmap_main::hashmap::HashMap::{0}::insert_in_list]: termination measure -/
 @[simp]
diff --git a/tests/lean/hashmap_on_disk/HashmapMain/Funs.lean b/tests/lean/hashmap_on_disk/HashmapMain/Funs.lean
index b0c4d683..5134f483 100644
--- a/tests/lean/hashmap_on_disk/HashmapMain/Funs.lean
+++ b/tests/lean/hashmap_on_disk/HashmapMain/Funs.lean
@@ -3,7 +3,7 @@
 import Base.Primitives
 import HashmapMain.Types
 import HashmapMain.Opaque
-import HashmapMain.Clauses.Template
+import HashmapMain.Clauses.Clauses
 
 section variable (opaque_defs: OpaqueDefs)
 
@@ -19,13 +19,13 @@ def hashmap_hash_map_allocate_slots_loop_fwd
   then
     do
       let slots0 <-
-        vec_push_back (hashmap_list_t T) slots hashmap_list_t.HashmapListNil 
-      let n0 <- USize.checked_sub n (USize.ofNatCore 1 (by intlit)) 
+        vec_push_back (hashmap_list_t T) slots hashmap_list_t.HashmapListNil
+      let n0 <- USize.checked_sub n (USize.ofNatCore 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 
+                                                                  T slots n
 decreasing_by hashmap_hash_map_allocate_slots_loop_decreases slots n
 
 /- [hashmap_main::hashmap::HashMap::{0}::allocate_slots] -/
@@ -42,10 +42,10 @@ def hashmap_hash_map_new_with_capacity_fwd
   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 <- USize.checked_mul capacity max_load_dividend 
-    let i0 <- USize.checked_div i max_load_divisor 
+    let v := vec_new (hashmap_list_t T)
+    let slots <- hashmap_hash_map_allocate_slots_fwd T v capacity
+    let i <- USize.checked_mul capacity max_load_dividend
+    let i0 <- USize.checked_div i max_load_divisor
     result.ret
       {
         hashmap_hash_map_num_entries := (USize.ofNatCore 0 (by intlit)),
@@ -60,40 +60,33 @@ def hashmap_hash_map_new_fwd (T : Type) : result (hashmap_hash_map_t T) :=
   hashmap_hash_map_new_with_capacity_fwd T (USize.ofNatCore 32 (by intlit))
     (USize.ofNatCore 4 (by intlit)) (USize.ofNatCore 5 (by intlit))
 
-/- [hashmap_main::hashmap::HashMap::{0}::clear_slots] -/
-def hashmap_hash_map_clear_slots_loop_fwd_back
+/- [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 
+  let i0 := vec_len (hashmap_list_t T) slots
   if i < i0
   then
     do
-      let i1 <- USize.checked_add i (USize.ofNatCore 1 (by intlit)) 
+      let i1 <- USize.checked_add i (USize.ofNatCore 1 (by intlit))
       let slots0 <-
         vec_index_mut_back (hashmap_list_t T) slots i
-          hashmap_list_t.HashmapListNil 
-      hashmap_hash_map_clear_slots_loop_fwd_back T slots0 i1
+          hashmap_list_t.HashmapListNil
+      hashmap_hash_map_clear_loop_fwd_back T slots0 i1
   else result.ret slots
-termination_by hashmap_hash_map_clear_slots_loop_fwd_back slots i =>
-                                                                    hashmap_hash_map_clear_slots_loop_terminates
-                                                                    T slots i 
-decreasing_by hashmap_hash_map_clear_slots_loop_decreases slots i
-
-/- [hashmap_main::hashmap::HashMap::{0}::clear_slots] -/
-def hashmap_hash_map_clear_slots_fwd_back
-  (T : Type) (slots : vec (hashmap_list_t T)) :
-  result (vec (hashmap_list_t T))
-  :=
-  hashmap_hash_map_clear_slots_loop_fwd_back T slots
-    (USize.ofNatCore 0 (by intlit))
+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_slots_fwd_back T self.hashmap_hash_map_slots 
+      hashmap_hash_map_clear_loop_fwd_back T self.hashmap_hash_map_slots
+        (USize.ofNatCore 0 (by intlit))
     result.ret
       {
         hashmap_hash_map_num_entries := (USize.ofNatCore 0 (by intlit)),
@@ -120,7 +113,7 @@ def hashmap_hash_map_insert_in_list_loop_fwd
   | hashmap_list_t.HashmapListNil => 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 
+   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] -/
@@ -139,14 +132,14 @@ def hashmap_hash_map_insert_in_list_loop_back
     then result.ret (hashmap_list_t.HashmapListCons ckey value tl)
     else
       do
-        let l <- hashmap_hash_map_insert_in_list_loop_back T key value tl 
-        result.ret (hashmap_list_t.HashmapListCons ckey cvalue l)
+        let tl0 <- hashmap_hash_map_insert_in_list_loop_back T key value tl
+        result.ret (hashmap_list_t.HashmapListCons ckey cvalue tl0)
   | hashmap_list_t.HashmapListNil =>
-    let l := hashmap_list_t.HashmapListNil 
+    let l := hashmap_list_t.HashmapListNil
     result.ret (hashmap_list_t.HashmapListCons 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 
+   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] -/
@@ -162,21 +155,21 @@ def hashmap_hash_map_insert_no_resize_fwd_back
   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 <- USize.checked_rem hash i 
+    let hash <- hashmap_hash_key_fwd key
+    let i := vec_len (hashmap_list_t T) self.hashmap_hash_map_slots
+    let hash_mod <- USize.checked_rem 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 
+      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 inserted
     then
       do
         let i0 <- USize.checked_add self.hashmap_hash_map_num_entries
-          (USize.ofNatCore 1 (by intlit)) 
-        let l0 <- hashmap_hash_map_insert_in_list_back T key value l 
+          (USize.ofNatCore 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 
+            hash_mod l0
         result.ret
           {
             hashmap_hash_map_num_entries := i0,
@@ -186,10 +179,10 @@ def hashmap_hash_map_insert_no_resize_fwd_back
           }
     else
       do
-        let l0 <- hashmap_hash_map_insert_in_list_back T key value l 
+        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 
+            hash_mod l0
         result.ret
           {
             hashmap_hash_map_num_entries := self.hashmap_hash_map_num_entries,
@@ -211,13 +204,13 @@ def hashmap_hash_map_move_elements_from_list_loop_fwd_back
   match ls with
   | hashmap_list_t.HashmapListCons k v tl =>
     do
-      let ntable0 <- hashmap_hash_map_insert_no_resize_fwd_back T ntable k v 
+      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.HashmapListNil => 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 
+                ntable ls
 decreasing_by hashmap_hash_map_move_elements_from_list_loop_decreases ntable ls
 
 /- [hashmap_main::hashmap::HashMap::{0}::move_elements_from_list] -/
@@ -233,23 +226,23 @@ def hashmap_hash_map_move_elements_loop_fwd_back
   (i : USize) :
   (result ((hashmap_hash_map_t T) × (vec (hashmap_list_t T))))
   :=
-  let i0 := vec_len (hashmap_list_t T) slots 
+  let i0 := vec_len (hashmap_list_t T) slots
   if i < i0
   then
     do
-      let l <- vec_index_mut_fwd (hashmap_list_t T) slots i 
+      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.HashmapListNil 
+        mem_replace_fwd (hashmap_list_t T) l hashmap_list_t.HashmapListNil
       let ntable0 <-
-        hashmap_hash_map_move_elements_from_list_fwd_back T ntable ls 
-      let i1 <- USize.checked_add i (USize.ofNatCore 1 (by intlit)) 
+        hashmap_hash_map_move_elements_from_list_fwd_back T ntable ls
+      let i1 <- USize.checked_add i (USize.ofNatCore 1 (by intlit))
       let l0 :=
-        mem_replace_back (hashmap_list_t T) l hashmap_list_t.HashmapListNil 
-      let slots0 <- vec_index_mut_back (hashmap_list_t T) slots i l0 
+        mem_replace_back (hashmap_list_t T) l hashmap_list_t.HashmapListNil
+      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 
+   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] -/
@@ -264,19 +257,19 @@ def hashmap_hash_map_move_elements_fwd_back
 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 <- USize.checked_div max_usize (USize.ofNatCore 2 (by intlit)) 
-    let (i, i0) := self.hashmap_hash_map_max_load_factor 
-    let i1 <- USize.checked_div n1 i 
+    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 <- USize.checked_div max_usize (USize.ofNatCore 2 (by intlit))
+    let (i, i0) := self.hashmap_hash_map_max_load_factor
+    let i1 <- USize.checked_div n1 i
     if capacity <= i1
     then
       do
-        let i2 <- USize.checked_mul capacity (USize.ofNatCore 2 (by intlit)) 
-        let ntable <- hashmap_hash_map_new_with_capacity_fwd T i2 i i0 
+        let i2 <- USize.checked_mul capacity (USize.ofNatCore 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.ofNatCore 0 (by intlit)) 
+            self.hashmap_hash_map_slots (USize.ofNatCore 0 (by intlit))
         result.ret
           {
             hashmap_hash_map_num_entries := self.hashmap_hash_map_num_entries,
@@ -299,8 +292,8 @@ def hashmap_hash_map_insert_fwd_back
   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 
+    let self0 <- hashmap_hash_map_insert_no_resize_fwd_back T self key value
+    let i <- hashmap_hash_map_len_fwd T self0
     if i > self0.hashmap_hash_map_max_load
     then hashmap_hash_map_try_resize_fwd_back T self0
     else result.ret self0
@@ -316,7 +309,7 @@ def hashmap_hash_map_contains_key_in_list_loop_fwd
   | hashmap_list_t.HashmapListNil => 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 
+   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] -/
@@ -328,11 +321,11 @@ def hashmap_hash_map_contains_key_in_list_fwd
 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 <- USize.checked_rem hash i 
+    let hash <- hashmap_hash_key_fwd key
+    let i := vec_len (hashmap_list_t T) self.hashmap_hash_map_slots
+    let hash_mod <- USize.checked_rem hash i
     let l <-
-      vec_index_fwd (hashmap_list_t T) self.hashmap_hash_map_slots hash_mod 
+      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] -/
@@ -347,7 +340,7 @@ def hashmap_hash_map_get_in_list_loop_fwd
   
 termination_by hashmap_hash_map_get_in_list_loop_fwd key ls =>
                                                               hashmap_hash_map_get_in_list_loop_terminates
-                                                              T key ls 
+                                                              T key ls
 decreasing_by hashmap_hash_map_get_in_list_loop_decreases key ls
 
 /- [hashmap_main::hashmap::HashMap::{0}::get_in_list] -/
@@ -359,11 +352,11 @@ def hashmap_hash_map_get_in_list_fwd
 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 <- USize.checked_rem hash i 
+    let hash <- hashmap_hash_key_fwd key
+    let i := vec_len (hashmap_list_t T) self.hashmap_hash_map_slots
+    let hash_mod <- USize.checked_rem hash i
     let l <-
-      vec_index_fwd (hashmap_list_t T) self.hashmap_hash_map_slots hash_mod 
+      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] -/
@@ -378,7 +371,7 @@ def hashmap_hash_map_get_mut_in_list_loop_fwd
   
 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 
+                                                                  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] -/
@@ -397,12 +390,12 @@ def hashmap_hash_map_get_mut_in_list_loop_back
     then result.ret (hashmap_list_t.HashmapListCons ckey ret0 tl)
     else
       do
-        let l <- hashmap_hash_map_get_mut_in_list_loop_back T tl key ret0 
-        result.ret (hashmap_list_t.HashmapListCons ckey cvalue l)
+        let tl0 <- hashmap_hash_map_get_mut_in_list_loop_back T tl key ret0
+        result.ret (hashmap_list_t.HashmapListCons ckey cvalue tl0)
   | hashmap_list_t.HashmapListNil => 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 
+   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] -/
@@ -416,11 +409,11 @@ def hashmap_hash_map_get_mut_in_list_back
 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 <- USize.checked_rem hash i 
+    let hash <- hashmap_hash_key_fwd key
+    let i := vec_len (hashmap_list_t T) self.hashmap_hash_map_slots
+    let hash_mod <- USize.checked_rem hash i
     let l <-
-      vec_index_mut_fwd (hashmap_list_t T) self.hashmap_hash_map_slots hash_mod 
+      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] -/
@@ -429,15 +422,15 @@ def hashmap_hash_map_get_mut_back
   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 <- USize.checked_rem hash i 
+    let hash <- hashmap_hash_key_fwd key
+    let i := vec_len (hashmap_list_t T) self.hashmap_hash_map_slots
+    let hash_mod <- USize.checked_rem 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 
+      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 
+        hash_mod l0
     result.ret
       {
         hashmap_hash_map_num_entries := self.hashmap_hash_map_num_entries,
@@ -455,7 +448,7 @@ def hashmap_hash_map_remove_from_list_loop_fwd
     then
       let mv_ls :=
         mem_replace_fwd (hashmap_list_t T) (hashmap_list_t.HashmapListCons ckey
-          t tl) hashmap_list_t.HashmapListNil 
+          t tl) hashmap_list_t.HashmapListNil
       match mv_ls with
       | hashmap_list_t.HashmapListCons i cvalue tl0 =>
         result.ret (Option.some cvalue)
@@ -466,7 +459,7 @@ def hashmap_hash_map_remove_from_list_loop_fwd
   
 termination_by hashmap_hash_map_remove_from_list_loop_fwd key ls =>
                                                                    hashmap_hash_map_remove_from_list_loop_terminates
-                                                                   T key ls 
+                                                                   T key ls
 decreasing_by hashmap_hash_map_remove_from_list_loop_decreases key ls
 
 /- [hashmap_main::hashmap::HashMap::{0}::remove_from_list] -/
@@ -485,20 +478,20 @@ def hashmap_hash_map_remove_from_list_loop_back
     then
       let mv_ls :=
         mem_replace_fwd (hashmap_list_t T) (hashmap_list_t.HashmapListCons ckey
-          t tl) hashmap_list_t.HashmapListNil 
+          t tl) hashmap_list_t.HashmapListNil
       match mv_ls with
       | hashmap_list_t.HashmapListCons i cvalue tl0 => result.ret tl0
       | hashmap_list_t.HashmapListNil => result.fail error.panic
       
     else
       do
-        let l <- hashmap_hash_map_remove_from_list_loop_back T key tl 
-        result.ret (hashmap_list_t.HashmapListCons ckey t l)
+        let tl0 <- hashmap_hash_map_remove_from_list_loop_back T key tl
+        result.ret (hashmap_list_t.HashmapListCons ckey t tl0)
   | hashmap_list_t.HashmapListNil => result.ret hashmap_list_t.HashmapListNil
   
 termination_by hashmap_hash_map_remove_from_list_loop_back key ls =>
                                                                     hashmap_hash_map_remove_from_list_loop_terminates
-                                                                    T key ls 
+                                                                    T key ls
 decreasing_by hashmap_hash_map_remove_from_list_loop_decreases key ls
 
 /- [hashmap_main::hashmap::HashMap::{0}::remove_from_list] -/
@@ -512,18 +505,18 @@ def hashmap_hash_map_remove_from_list_back
 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 <- USize.checked_rem hash i 
+    let hash <- hashmap_hash_key_fwd key
+    let i := vec_len (hashmap_list_t T) self.hashmap_hash_map_slots
+    let hash_mod <- USize.checked_rem 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 
+      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 x with
     | Option.none => result.ret Option.none
     | Option.some x0 =>
       do
         let _ <- USize.checked_sub self.hashmap_hash_map_num_entries
-          (USize.ofNatCore 1 (by intlit)) 
+          (USize.ofNatCore 1 (by intlit))
         result.ret (Option.some x0)
     
 
@@ -533,19 +526,19 @@ def hashmap_hash_map_remove_back
   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 <- USize.checked_rem hash i 
+    let hash <- hashmap_hash_key_fwd key
+    let i := vec_len (hashmap_list_t T) self.hashmap_hash_map_slots
+    let hash_mod <- USize.checked_rem 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 
+      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 x with
     | Option.none =>
       do
-        let l0 <- hashmap_hash_map_remove_from_list_back T key l 
+        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 
+            hash_mod l0
         result.ret
           {
             hashmap_hash_map_num_entries := self.hashmap_hash_map_num_entries,
@@ -556,11 +549,11 @@ def hashmap_hash_map_remove_back
     | Option.some x0 =>
       do
         let i0 <- USize.checked_sub self.hashmap_hash_map_num_entries
-          (USize.ofNatCore 1 (by intlit)) 
-        let l0 <- hashmap_hash_map_remove_from_list_back T key l 
+          (USize.ofNatCore 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 
+            hash_mod l0
         result.ret
           {
             hashmap_hash_map_num_entries := i0,
@@ -573,21 +566,21 @@ def hashmap_hash_map_remove_back
 /- [hashmap_main::hashmap::test1] -/
 def hashmap_test1_fwd : result Unit :=
   do
-    let hm <- hashmap_hash_map_new_fwd UInt64 
+    let hm <- hashmap_hash_map_new_fwd UInt64
     let hm0 <-
       hashmap_hash_map_insert_fwd_back UInt64 hm
-        (USize.ofNatCore 0 (by intlit)) (UInt64.ofNatCore 42 (by intlit)) 
+        (USize.ofNatCore 0 (by intlit)) (UInt64.ofNatCore 42 (by intlit))
     let hm1 <-
       hashmap_hash_map_insert_fwd_back UInt64 hm0
-        (USize.ofNatCore 128 (by intlit)) (UInt64.ofNatCore 18 (by intlit)) 
+        (USize.ofNatCore 128 (by intlit)) (UInt64.ofNatCore 18 (by intlit))
     let hm2 <-
       hashmap_hash_map_insert_fwd_back UInt64 hm1
-        (USize.ofNatCore 1024 (by intlit)) (UInt64.ofNatCore 138 (by intlit)) 
+        (USize.ofNatCore 1024 (by intlit)) (UInt64.ofNatCore 138 (by intlit))
     let hm3 <-
       hashmap_hash_map_insert_fwd_back UInt64 hm2
-        (USize.ofNatCore 1056 (by intlit)) (UInt64.ofNatCore 256 (by intlit)) 
+        (USize.ofNatCore 1056 (by intlit)) (UInt64.ofNatCore 256 (by intlit))
     let i <-
-      hashmap_hash_map_get_fwd UInt64 hm3 (USize.ofNatCore 128 (by intlit)) 
+      hashmap_hash_map_get_fwd UInt64 hm3 (USize.ofNatCore 128 (by intlit))
     if not (i = (UInt64.ofNatCore 18 (by intlit)))
     then result.fail error.panic
     else
@@ -595,17 +588,17 @@ def hashmap_test1_fwd : result Unit :=
         let hm4 <-
           hashmap_hash_map_get_mut_back UInt64 hm3
             (USize.ofNatCore 1024 (by intlit))
-            (UInt64.ofNatCore 56 (by intlit)) 
+            (UInt64.ofNatCore 56 (by intlit))
         let i0 <-
           hashmap_hash_map_get_fwd UInt64 hm4
-            (USize.ofNatCore 1024 (by intlit)) 
+            (USize.ofNatCore 1024 (by intlit))
         if not (i0 = (UInt64.ofNatCore 56 (by intlit)))
         then result.fail error.panic
         else
           do
             let x <-
               hashmap_hash_map_remove_fwd UInt64 hm4
-                (USize.ofNatCore 1024 (by intlit)) 
+                (USize.ofNatCore 1024 (by intlit))
             match x with
             | Option.none => result.fail error.panic
             | Option.some x0 =>
@@ -615,24 +608,24 @@ def hashmap_test1_fwd : result Unit :=
                 do
                   let hm5 <-
                     hashmap_hash_map_remove_back UInt64 hm4
-                      (USize.ofNatCore 1024 (by intlit)) 
+                      (USize.ofNatCore 1024 (by intlit))
                   let i1 <-
                     hashmap_hash_map_get_fwd UInt64 hm5
-                      (USize.ofNatCore 0 (by intlit)) 
+                      (USize.ofNatCore 0 (by intlit))
                   if not (i1 = (UInt64.ofNatCore 42 (by intlit)))
                   then result.fail error.panic
                   else
                     do
                       let i2 <-
                         hashmap_hash_map_get_fwd UInt64 hm5
-                          (USize.ofNatCore 128 (by intlit)) 
+                          (USize.ofNatCore 128 (by intlit))
                       if not (i2 = (UInt64.ofNatCore 18 (by intlit)))
                       then result.fail error.panic
                       else
                         do
                           let i3 <-
                             hashmap_hash_map_get_fwd UInt64 hm5
-                              (USize.ofNatCore 1056 (by intlit)) 
+                              (USize.ofNatCore 1056 (by intlit))
                           if not (i3 = (UInt64.ofNatCore 256 (by intlit)))
                           then result.fail error.panic
                           else result.ret ()
@@ -645,9 +638,9 @@ def hashmap_test1_fwd : result Unit :=
 def insert_on_disk_fwd
   (key : USize) (value : UInt64) (st : state) : result (state × Unit) :=
   do
-    let (st0, hm) <- opaque_defs.hashmap_utils_deserialize_fwd st 
-    let hm0 <- hashmap_hash_map_insert_fwd_back UInt64 hm key value 
-    let (st1, _) <- opaque_defs.hashmap_utils_serialize_fwd hm0 st0 
+    let (st0, hm) <- opaque_defs.hashmap_utils_deserialize_fwd st
+    let hm0 <- hashmap_hash_map_insert_fwd_back UInt64 hm key value
+    let (st1, _) <- opaque_defs.hashmap_utils_serialize_fwd hm0 st0
     result.ret (st1, ())
 
 /- [hashmap_main::main] -/
diff --git a/tests/lean/misc/constants/Base/Primitives.lean b/tests/lean/misc/constants/Base/Primitives.lean
new file mode 100644
index 00000000..79958d94
--- /dev/null
+++ b/tests/lean/misc/constants/Base/Primitives.lean
@@ -0,0 +1,373 @@
+import Lean
+import Lean.Meta.Tactic.Simp
+import Init.Data.List.Basic
+import Mathlib.Tactic.RunCmd
+
+-------------
+-- PRELUDE --
+-------------
+
+-- Results & monadic combinators
+
+-- TODO: use syntactic conventions and capitalize error, result, etc.
+
+inductive error where
+   | assertionFailure: error
+   | integerOverflow: 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
+
+/- HELPERS -/
+
+-- TODO: is there automated syntax for these discriminators?
+def is_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) (_: is_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 : (o : result α) → result { x : α // o = ret x }
+  | .ret x => .ret ⟨x, rfl⟩
+  | .fail e   => .fail e
+
+macro "let" h:ident " : " e:term " <-- " f:term : doElem =>
+  `(doElem| let ⟨$e, $h⟩ ← result.attach $f)
+
+-- Silly example of the kind of reasoning that this notation enables
+#eval do
+  let h: y <-- .ret (0: Nat)
+  let _: y = 0 := by cases h; decide
+  let r: { x: Nat // x = 0 } := ⟨ y, by assumption ⟩
+  .ret r
+
+----------------------
+-- MACHINE INTEGERS --
+----------------------
+
+-- NOTE: we reuse the USize type from prelude.lean, because at least we know
+-- it's defined in an idiomatic style that is going to make proofs easy (and
+-- indeed, several proofs here are much shortened compared to Aymeric's earlier
+-- attempt.) This is not stricto sensu the *correct* thing to do, because one
+-- can query at run-time the value of USize, which we do *not* want to do (we
+-- don't know what target we'll run on!), but when the day comes, we'll just
+-- define our own USize.
+-- ANOTHER NOTE: there is USize.sub but it has wraparound semantics, which is
+-- not something we want to define (I think), so we use our own monadic sub (but
+-- is it in line with the Rust behavior?)
+
+-- TODO: I am somewhat under the impression that subtraction is defined as a
+-- total function over nats...? the hypothesis in the if condition is not used
+-- in the then-branch which confuses me quite a bit
+
+-- TODO: add a refinement for the result (just like vec_push_back below) that
+-- explains that the toNat of the result (in the case of success) is the sub of
+-- the toNat of the arguments (i.e. intrinsic specification)
+-- ... do we want intrinsic specifications for the builtins? that might require
+-- some careful type annotations in the monadic notation for clients, but may
+-- give us more "for free"
+
+-- 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." Try to settle this with a Lean expert on what is the most
+-- productive way to go about this?
+
+-- One needs to perform a little bit of reasoning in order to successfully
+-- inject constants into USize, so we provide a general-purpose macro
+
+syntax "intlit" : tactic
+
+macro_rules
+  | `(tactic| intlit) => `(tactic|
+    match USize.size, usize_size_eq with
+    | _, Or.inl rfl => decide
+    | _, Or.inr rfl => decide)
+
+-- This is how the macro is expected to be used
+#eval USize.ofNatCore 0 (by intlit)
+
+-- Also works for other integer types (at the expense of a needless disjunction)
+#eval UInt32.ofNatCore 0 (by intlit)
+
+-- 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 USize.checked_sub (n: USize) (m: USize): result USize :=
+  -- NOTE: the test USize.toNat n - m >= 0 seems to always succeed?
+  if n >= m then
+    let n' := USize.toNat n
+    let m' := USize.toNat n
+    let r := USize.ofNatCore (n' - m') (by
+      have h: n' - m' <= n' := by
+        apply Nat.sub_le_of_le_add
+        case h => rewrite [ Nat.add_comm ]; apply Nat.le_add_left
+      apply Nat.lt_of_le_of_lt h
+      apply n.val.isLt
+    )
+    return r
+  else
+    fail integerOverflow
+
+def USize.checked_add (n: USize) (m: USize): result USize :=
+  if h: n.val.val + m.val.val <= 4294967295 then
+    .ret ⟨ n.val.val + m.val.val, by
+      have h': 4294967295 < USize.size := by intlit
+      apply Nat.lt_of_le_of_lt h h'
+    ⟩
+  else if h: n.val + m.val < USize.size then
+    .ret ⟨ n.val + m.val, h ⟩
+  else
+    .fail integerOverflow
+
+def USize.checked_rem (n: USize) (m: USize): result USize :=
+  if h: m > 0 then
+    .ret ⟨ n.val % m.val, by
+      have h1: ↑m.val < USize.size := m.val.isLt
+      have h2: n.val.val % m.val.val < m.val.val := @Nat.mod_lt n.val m.val h
+      apply Nat.lt_trans h2 h1
+    ⟩
+  else
+    .fail integerOverflow
+
+def USize.checked_mul (n: USize) (m: USize): result USize :=
+    if h: n.val.val * m.val.val <= 4294967295 then
+    .ret ⟨ n.val.val * m.val.val, by
+      have h': 4294967295 < USize.size := by intlit
+      apply Nat.lt_of_le_of_lt h h'
+    ⟩
+  else if h: n.val * m.val < USize.size then
+    .ret ⟨ n.val * m.val, h ⟩
+  else
+    .fail integerOverflow
+
+def USize.checked_div (n: USize) (m: USize): result USize :=
+  if m > 0 then
+    .ret ⟨ n.val / m.val, by
+      have h1: ↑n.val < USize.size := n.val.isLt
+      have h2: n.val.val / m.val.val <= n.val.val := @Nat.div_le_self n.val m.val
+      apply Nat.lt_of_le_of_lt h2 h1
+    ⟩
+  else
+    .fail integerOverflow
+
+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
+  ))
+
+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
+
+
+-- Test behavior...
+#eval assert! USize.checked_sub 10 20 == fail integerOverflow; 0
+
+#eval USize.checked_sub 20 10
+-- NOTE: compare with concrete behavior here, which I do not think we want
+#eval USize.sub 0 1
+#eval UInt8.add 255 255
+
+-------------
+-- VECTORS --
+-------------
+
+-- Note: unlike F*, Lean seems to use strict upper bounds (e.g. USize.size)
+-- rather than maximum values (usize_max).
+def vec (α : Type u) := { l : List α // List.length l < USize.size }
+
+def vec_new (α : Type u): vec α := ⟨ [], by {
+  match USize.size, usize_size_eq with
+  | _, Or.inl rfl => simp
+  | _, Or.inr rfl => simp
+  } ⟩
+
+#check vec_new
+
+def vec_len (α : Type u) (v : vec α) : USize :=
+  let ⟨ v, l ⟩ := v
+  USize.ofNatCore (List.length v) l
+
+#eval vec_len Nat (vec_new Nat)
+ 
+def vec_push_fwd (α : Type u) (_ : vec α) (_ : α) : Unit := ()
+
+-- NOTE: old version trying to use a subtype notation, but probably better to
+-- leave result elimination to auxiliary lemmas with suitable preconditions
+-- TODO: I originally wrote `List.length v.val < USize.size - 1`; how can one
+-- make the proof work in that case? Probably need to import tactics from
+-- mathlib to deal with inequalities... would love to see an example.
+def vec_push_back_old (α : Type u) (v : vec α) (x : α) : { res: result (vec α) //
+  match res with | fail _ => True | ret v' => List.length v'.val = List.length v.val + 1}
+  :=
+  if h : List.length v.val + 1 < USize.size then
+    ⟨ return ⟨List.concat v.val x,
+      by
+        rw [List.length_concat]
+        assumption
+     ⟩, by simp ⟩
+  else
+    ⟨ fail maximumSizeExceeded, by simp ⟩
+
+#eval do
+  -- NOTE: the // notation is syntactic sugar for Subtype, a refinement with
+  -- fields val and property. However, Lean's elaborator can automatically
+  -- select the `val` field if the context provides a type annotation. We
+  -- annotate `x`, which relieves us of having to write `.val` on the right-hand
+  -- side of the monadic let.
+  let v := vec_new Nat
+  let x: vec Nat ← (vec_push_back_old Nat v 1: result (vec Nat)) -- WHY do we need the type annotation here?
+  -- TODO: strengthen post-condition above and do a demo to show that we can
+  -- safely eliminate the `fail` case
+  return (vec_len Nat x)
+
+def vec_push_back (α : Type u) (v : vec α) (x : α) : result (vec α)
+  :=
+  if h : List.length v.val + 1 <= 4294967295 then
+    return ⟨ List.concat v.val x,
+      by
+        rw [List.length_concat]
+        have h': 4294967295 < USize.size := by intlit
+        apply Nat.lt_of_le_of_lt h h'
+    ⟩
+  else if h: List.length v.val + 1 < USize.size then
+    return ⟨List.concat v.val x,
+      by
+        rw [List.length_concat]
+        assumption
+     ⟩
+  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
+    .ret ⟨ List.set v.val i.val x, by
+      have h: List.length v.val < USize.size := 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 h: i.val < List.length v.val then
+    .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 h: i.val < List.length v.val then
+    .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
+    .ret ⟨ List.set v.val i.val x, by
+      have h: List.length v.val < USize.size := 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
+
+--------------------
+-- ASSERT COMMAND --
+--------------------
+
+open Lean Elab Command Term Meta
+
+syntax (name := assert) "#assert" term: command
+
+@[command_elab assert]
+def assertImpl : CommandElab := fun (_stx: Syntax) => do
+  logInfo "Reducing and asserting: "
+  logInfo _stx[1]
+  runTermElabM (fun _ => do
+    let e ← Term.elabTerm _stx[1] none
+    logInfo (Expr.dbgToString e)
+    -- How to evaluate the term and compare the result to true?
+    pure ())
+  -- logInfo (Expr.dbgToString (``true))
+  -- throwError "TODO: assert"
+
+#eval 2 == 2
+#assert (2 == 2)
diff --git a/tests/lean/misc/constants/Constants.lean b/tests/lean/misc/constants/Constants.lean
new file mode 100644
index 00000000..a5cbe363
--- /dev/null
+++ b/tests/lean/misc/constants/Constants.lean
@@ -0,0 +1,138 @@
+-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
+-- [constants]
+import Base.Primitives
+
+structure OpaqueDefs where
+  
+  /- [constants::X0] -/
+  def x0_body : result UInt32 := result.ret (UInt32.ofNatCore 0 (by intlit))
+  def x0_c : UInt32 := eval_global x0_body (by simp)
+  
+  /- [core::num::u32::{9}::MAX] -/
+  def core_num_u32_max_body : result UInt32 :=
+    result.ret (UInt32.ofNatCore 4294967295 (by intlit))
+  def core_num_u32_max_c : UInt32 :=
+    eval_global core_num_u32_max_body (by simp)
+  
+  /- [constants::X1] -/
+  def x1_body : result UInt32 := result.ret core_num_u32_max_c
+  def x1_c : UInt32 := eval_global x1_body (by simp)
+  
+  /- [constants::X2] -/
+  def x2_body : result UInt32 := result.ret (UInt32.ofNatCore 3 (by intlit))
+  def x2_c : UInt32 := eval_global x2_body (by simp)
+  
+  /- [constants::incr] -/
+  def incr_fwd (n : UInt32) : result UInt32 :=
+    UInt32.checked_add n (UInt32.ofNatCore 1 (by intlit))
+  
+  /- [constants::X3] -/
+  def x3_body : result UInt32 := incr_fwd (UInt32.ofNatCore 32 (by intlit))
+  def x3_c : UInt32 := eval_global x3_body (by simp)
+  
+  /- [constants::mk_pair0] -/
+  def mk_pair0_fwd (x : UInt32) (y : UInt32) : result (UInt32 × UInt32) :=
+    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 : UInt32) (y : UInt32) : result (pair_t UInt32 UInt32) :=
+    result.ret { pair_x := x, pair_y := y }
+  
+  /- [constants::P0] -/
+  def p0_body : result (UInt32 × UInt32) :=
+    mk_pair0_fwd (UInt32.ofNatCore 0 (by intlit))
+      (UInt32.ofNatCore 1 (by intlit))
+  def p0_c : (UInt32 × UInt32) := eval_global p0_body (by simp)
+  
+  /- [constants::P1] -/
+  def p1_body : result (pair_t UInt32 UInt32) :=
+    mk_pair1_fwd (UInt32.ofNatCore 0 (by intlit))
+      (UInt32.ofNatCore 1 (by intlit))
+  def p1_c : pair_t UInt32 UInt32 := eval_global p1_body (by simp)
+  
+  /- [constants::P2] -/
+  def p2_body : result (UInt32 × UInt32) :=
+    result.ret
+    ((UInt32.ofNatCore 0 (by intlit)),
+    (UInt32.ofNatCore 1 (by intlit)))
+  def p2_c : (UInt32 × UInt32) := eval_global p2_body (by simp)
+  
+  /- [constants::P3] -/
+  def p3_body : result (pair_t UInt32 UInt32) :=
+    result.ret
+    {
+      pair_x := (UInt32.ofNatCore 0 (by intlit)),
+      pair_y := (UInt32.ofNatCore 1 (by intlit))
+    }
+  def p3_c : pair_t UInt32 UInt32 := 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 Int32) :=
+    wrap_new_fwd Int32 (Int32.ofNatCore 2 (by intlit))
+  def y_c : wrap_t Int32 := eval_global y_body (by simp)
+  
+  /- [constants::unwrap_y] -/
+  def unwrap_y_fwd : result Int32 := result.ret y_c.wrap_val
+  
+  /- [constants::YVAL] -/
+  def yval_body : result Int32 := unwrap_y_fwd
+  def yval_c : Int32 := eval_global yval_body (by simp)
+  
+  /- [constants::get_z1::Z1] -/
+  def get_z1_z1_body : result Int32 :=
+    result.ret (Int32.ofNatCore 3 (by intlit))
+  def get_z1_z1_c : Int32 := eval_global get_z1_z1_body (by simp)
+  
+  /- [constants::get_z1] -/
+  def get_z1_fwd : result Int32 := result.ret get_z1_z1_c
+  
+  /- [constants::add] -/
+  def add_fwd (a : Int32) (b : Int32) : result Int32 := Int32.checked_add a b
+  
+  /- [constants::Q1] -/
+  def q1_body : result Int32 := result.ret (Int32.ofNatCore 5 (by intlit))
+  def q1_c : Int32 := eval_global q1_body (by simp)
+  
+  /- [constants::Q2] -/
+  def q2_body : result Int32 := result.ret q1_c
+  def q2_c : Int32 := eval_global q2_body (by simp)
+  
+  /- [constants::Q3] -/
+  def q3_body : result Int32 := add_fwd q2_c (Int32.ofNatCore 3 (by intlit))
+  def q3_c : Int32 := eval_global q3_body (by simp)
+  
+  /- [constants::get_z2] -/
+  def get_z2_fwd : result Int32 :=
+    do
+      let i <- get_z1_fwd
+      let i0 <- add_fwd i q3_c
+      add_fwd q1_c i0
+  
+  /- [constants::S1] -/
+  def s1_body : result UInt32 := result.ret (UInt32.ofNatCore 6 (by intlit))
+  def s1_c : UInt32 := eval_global s1_body (by simp)
+  
+  /- [constants::S2] -/
+  def s2_body : result UInt32 := incr_fwd s1_c
+  def s2_c : UInt32 := eval_global s2_body (by simp)
+  
+  /- [constants::S3] -/
+  def s3_body : result (pair_t UInt32 UInt32) := result.ret p3_c
+  def s3_c : pair_t UInt32 UInt32 := eval_global s3_body (by simp)
+  
+  /- [constants::S4] -/
+  def s4_body : result (pair_t UInt32 UInt32) :=
+    mk_pair1_fwd (UInt32.ofNatCore 7 (by intlit))
+      (UInt32.ofNatCore 8 (by intlit))
+  def s4_c : pair_t UInt32 UInt32 := eval_global s4_body (by simp)
+  
diff --git a/tests/lean/misc/external/Base/Primitives.lean b/tests/lean/misc/external/Base/Primitives.lean
new file mode 100644
index 00000000..79958d94
--- /dev/null
+++ b/tests/lean/misc/external/Base/Primitives.lean
@@ -0,0 +1,373 @@
+import Lean
+import Lean.Meta.Tactic.Simp
+import Init.Data.List.Basic
+import Mathlib.Tactic.RunCmd
+
+-------------
+-- PRELUDE --
+-------------
+
+-- Results & monadic combinators
+
+-- TODO: use syntactic conventions and capitalize error, result, etc.
+
+inductive error where
+   | assertionFailure: error
+   | integerOverflow: 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
+
+/- HELPERS -/
+
+-- TODO: is there automated syntax for these discriminators?
+def is_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) (_: is_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 : (o : result α) → result { x : α // o = ret x }
+  | .ret x => .ret ⟨x, rfl⟩
+  | .fail e   => .fail e
+
+macro "let" h:ident " : " e:term " <-- " f:term : doElem =>
+  `(doElem| let ⟨$e, $h⟩ ← result.attach $f)
+
+-- Silly example of the kind of reasoning that this notation enables
+#eval do
+  let h: y <-- .ret (0: Nat)
+  let _: y = 0 := by cases h; decide
+  let r: { x: Nat // x = 0 } := ⟨ y, by assumption ⟩
+  .ret r
+
+----------------------
+-- MACHINE INTEGERS --
+----------------------
+
+-- NOTE: we reuse the USize type from prelude.lean, because at least we know
+-- it's defined in an idiomatic style that is going to make proofs easy (and
+-- indeed, several proofs here are much shortened compared to Aymeric's earlier
+-- attempt.) This is not stricto sensu the *correct* thing to do, because one
+-- can query at run-time the value of USize, which we do *not* want to do (we
+-- don't know what target we'll run on!), but when the day comes, we'll just
+-- define our own USize.
+-- ANOTHER NOTE: there is USize.sub but it has wraparound semantics, which is
+-- not something we want to define (I think), so we use our own monadic sub (but
+-- is it in line with the Rust behavior?)
+
+-- TODO: I am somewhat under the impression that subtraction is defined as a
+-- total function over nats...? the hypothesis in the if condition is not used
+-- in the then-branch which confuses me quite a bit
+
+-- TODO: add a refinement for the result (just like vec_push_back below) that
+-- explains that the toNat of the result (in the case of success) is the sub of
+-- the toNat of the arguments (i.e. intrinsic specification)
+-- ... do we want intrinsic specifications for the builtins? that might require
+-- some careful type annotations in the monadic notation for clients, but may
+-- give us more "for free"
+
+-- 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." Try to settle this with a Lean expert on what is the most
+-- productive way to go about this?
+
+-- One needs to perform a little bit of reasoning in order to successfully
+-- inject constants into USize, so we provide a general-purpose macro
+
+syntax "intlit" : tactic
+
+macro_rules
+  | `(tactic| intlit) => `(tactic|
+    match USize.size, usize_size_eq with
+    | _, Or.inl rfl => decide
+    | _, Or.inr rfl => decide)
+
+-- This is how the macro is expected to be used
+#eval USize.ofNatCore 0 (by intlit)
+
+-- Also works for other integer types (at the expense of a needless disjunction)
+#eval UInt32.ofNatCore 0 (by intlit)
+
+-- 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 USize.checked_sub (n: USize) (m: USize): result USize :=
+  -- NOTE: the test USize.toNat n - m >= 0 seems to always succeed?
+  if n >= m then
+    let n' := USize.toNat n
+    let m' := USize.toNat n
+    let r := USize.ofNatCore (n' - m') (by
+      have h: n' - m' <= n' := by
+        apply Nat.sub_le_of_le_add
+        case h => rewrite [ Nat.add_comm ]; apply Nat.le_add_left
+      apply Nat.lt_of_le_of_lt h
+      apply n.val.isLt
+    )
+    return r
+  else
+    fail integerOverflow
+
+def USize.checked_add (n: USize) (m: USize): result USize :=
+  if h: n.val.val + m.val.val <= 4294967295 then
+    .ret ⟨ n.val.val + m.val.val, by
+      have h': 4294967295 < USize.size := by intlit
+      apply Nat.lt_of_le_of_lt h h'
+    ⟩
+  else if h: n.val + m.val < USize.size then
+    .ret ⟨ n.val + m.val, h ⟩
+  else
+    .fail integerOverflow
+
+def USize.checked_rem (n: USize) (m: USize): result USize :=
+  if h: m > 0 then
+    .ret ⟨ n.val % m.val, by
+      have h1: ↑m.val < USize.size := m.val.isLt
+      have h2: n.val.val % m.val.val < m.val.val := @Nat.mod_lt n.val m.val h
+      apply Nat.lt_trans h2 h1
+    ⟩
+  else
+    .fail integerOverflow
+
+def USize.checked_mul (n: USize) (m: USize): result USize :=
+    if h: n.val.val * m.val.val <= 4294967295 then
+    .ret ⟨ n.val.val * m.val.val, by
+      have h': 4294967295 < USize.size := by intlit
+      apply Nat.lt_of_le_of_lt h h'
+    ⟩
+  else if h: n.val * m.val < USize.size then
+    .ret ⟨ n.val * m.val, h ⟩
+  else
+    .fail integerOverflow
+
+def USize.checked_div (n: USize) (m: USize): result USize :=
+  if m > 0 then
+    .ret ⟨ n.val / m.val, by
+      have h1: ↑n.val < USize.size := n.val.isLt
+      have h2: n.val.val / m.val.val <= n.val.val := @Nat.div_le_self n.val m.val
+      apply Nat.lt_of_le_of_lt h2 h1
+    ⟩
+  else
+    .fail integerOverflow
+
+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
+  ))
+
+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
+
+
+-- Test behavior...
+#eval assert! USize.checked_sub 10 20 == fail integerOverflow; 0
+
+#eval USize.checked_sub 20 10
+-- NOTE: compare with concrete behavior here, which I do not think we want
+#eval USize.sub 0 1
+#eval UInt8.add 255 255
+
+-------------
+-- VECTORS --
+-------------
+
+-- Note: unlike F*, Lean seems to use strict upper bounds (e.g. USize.size)
+-- rather than maximum values (usize_max).
+def vec (α : Type u) := { l : List α // List.length l < USize.size }
+
+def vec_new (α : Type u): vec α := ⟨ [], by {
+  match USize.size, usize_size_eq with
+  | _, Or.inl rfl => simp
+  | _, Or.inr rfl => simp
+  } ⟩
+
+#check vec_new
+
+def vec_len (α : Type u) (v : vec α) : USize :=
+  let ⟨ v, l ⟩ := v
+  USize.ofNatCore (List.length v) l
+
+#eval vec_len Nat (vec_new Nat)
+ 
+def vec_push_fwd (α : Type u) (_ : vec α) (_ : α) : Unit := ()
+
+-- NOTE: old version trying to use a subtype notation, but probably better to
+-- leave result elimination to auxiliary lemmas with suitable preconditions
+-- TODO: I originally wrote `List.length v.val < USize.size - 1`; how can one
+-- make the proof work in that case? Probably need to import tactics from
+-- mathlib to deal with inequalities... would love to see an example.
+def vec_push_back_old (α : Type u) (v : vec α) (x : α) : { res: result (vec α) //
+  match res with | fail _ => True | ret v' => List.length v'.val = List.length v.val + 1}
+  :=
+  if h : List.length v.val + 1 < USize.size then
+    ⟨ return ⟨List.concat v.val x,
+      by
+        rw [List.length_concat]
+        assumption
+     ⟩, by simp ⟩
+  else
+    ⟨ fail maximumSizeExceeded, by simp ⟩
+
+#eval do
+  -- NOTE: the // notation is syntactic sugar for Subtype, a refinement with
+  -- fields val and property. However, Lean's elaborator can automatically
+  -- select the `val` field if the context provides a type annotation. We
+  -- annotate `x`, which relieves us of having to write `.val` on the right-hand
+  -- side of the monadic let.
+  let v := vec_new Nat
+  let x: vec Nat ← (vec_push_back_old Nat v 1: result (vec Nat)) -- WHY do we need the type annotation here?
+  -- TODO: strengthen post-condition above and do a demo to show that we can
+  -- safely eliminate the `fail` case
+  return (vec_len Nat x)
+
+def vec_push_back (α : Type u) (v : vec α) (x : α) : result (vec α)
+  :=
+  if h : List.length v.val + 1 <= 4294967295 then
+    return ⟨ List.concat v.val x,
+      by
+        rw [List.length_concat]
+        have h': 4294967295 < USize.size := by intlit
+        apply Nat.lt_of_le_of_lt h h'
+    ⟩
+  else if h: List.length v.val + 1 < USize.size then
+    return ⟨List.concat v.val x,
+      by
+        rw [List.length_concat]
+        assumption
+     ⟩
+  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
+    .ret ⟨ List.set v.val i.val x, by
+      have h: List.length v.val < USize.size := 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 h: i.val < List.length v.val then
+    .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 h: i.val < List.length v.val then
+    .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
+    .ret ⟨ List.set v.val i.val x, by
+      have h: List.length v.val < USize.size := 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
+
+--------------------
+-- ASSERT COMMAND --
+--------------------
+
+open Lean Elab Command Term Meta
+
+syntax (name := assert) "#assert" term: command
+
+@[command_elab assert]
+def assertImpl : CommandElab := fun (_stx: Syntax) => do
+  logInfo "Reducing and asserting: "
+  logInfo _stx[1]
+  runTermElabM (fun _ => do
+    let e ← Term.elabTerm _stx[1] none
+    logInfo (Expr.dbgToString e)
+    -- How to evaluate the term and compare the result to true?
+    pure ())
+  -- logInfo (Expr.dbgToString (``true))
+  -- throwError "TODO: assert"
+
+#eval 2 == 2
+#assert (2 == 2)
diff --git a/tests/lean/misc/external/External/Funs.lean b/tests/lean/misc/external/External/Funs.lean
new file mode 100644
index 00000000..bb1e296d
--- /dev/null
+++ b/tests/lean/misc/external/External/Funs.lean
@@ -0,0 +1,93 @@
+-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
+-- [external]: function definitions
+import Base.Primitives
+import External.Types
+import External.Opaque
+
+section variable (opaque_defs: OpaqueDefs)
+
+/- [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 : UInt32) (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 UInt32
+    let _ <- vec_push_back UInt32 v (UInt32.ofNatCore 0 (by intlit))
+    result.ret ()
+
+/- Unit test for [external::test_vec] -/
+#assert (test_vec_fwd = .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 : UInt32) (y : UInt32) (st : state) : result (state × Unit) :=
+  do
+    let (st0, _) <- custom_swap_fwd UInt32 x y st
+    result.ret (st0, ())
+
+/- [external::test_custom_swap] -/
+def test_custom_swap_back
+  (x : UInt32) (y : UInt32) (st : state) (st0 : state) :
+  result (state × (UInt32 × UInt32))
+  :=
+  custom_swap_back UInt32 x y st (UInt32.ofNatCore 1 (by intlit)) st0
+
+/- [external::test_swap_non_zero] -/
+def test_swap_non_zero_fwd
+  (x : UInt32) (st : state) : result (state × UInt32) :=
+  do
+    let (st0, _) <- swap_fwd UInt32 x (UInt32.ofNatCore 0 (by intlit)) st
+    let (st1, (x0, _)) <-
+      swap_back UInt32 x (UInt32.ofNatCore 0 (by intlit)) st st0
+    if x0 = (UInt32.ofNatCore 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
new file mode 100644
index 00000000..40ccc313
--- /dev/null
+++ b/tests/lean/misc/external/External/Opaque.lean
@@ -0,0 +1,28 @@
+-- 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
+    :
+    UInt32 -> 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/External/Types.lean b/tests/lean/misc/external/External/Types.lean
new file mode 100644
index 00000000..b6fa292b
--- /dev/null
+++ b/tests/lean/misc/external/External/Types.lean
@@ -0,0 +1,8 @@
+-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
+-- [external]: type definitions
+import Base.Primitives
+
+/- [core::num::nonzero::NonZeroU32] -/
+axiom core_num_nonzero_non_zero_u32_t : Type
+/- The state type used in the state-error monad -/ axiom state : Type
+
diff --git a/tests/lean/misc/loops/Base/Primitives.lean b/tests/lean/misc/loops/Base/Primitives.lean
new file mode 100644
index 00000000..79958d94
--- /dev/null
+++ b/tests/lean/misc/loops/Base/Primitives.lean
@@ -0,0 +1,373 @@
+import Lean
+import Lean.Meta.Tactic.Simp
+import Init.Data.List.Basic
+import Mathlib.Tactic.RunCmd
+
+-------------
+-- PRELUDE --
+-------------
+
+-- Results & monadic combinators
+
+-- TODO: use syntactic conventions and capitalize error, result, etc.
+
+inductive error where
+   | assertionFailure: error
+   | integerOverflow: 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
+
+/- HELPERS -/
+
+-- TODO: is there automated syntax for these discriminators?
+def is_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) (_: is_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 : (o : result α) → result { x : α // o = ret x }
+  | .ret x => .ret ⟨x, rfl⟩
+  | .fail e   => .fail e
+
+macro "let" h:ident " : " e:term " <-- " f:term : doElem =>
+  `(doElem| let ⟨$e, $h⟩ ← result.attach $f)
+
+-- Silly example of the kind of reasoning that this notation enables
+#eval do
+  let h: y <-- .ret (0: Nat)
+  let _: y = 0 := by cases h; decide
+  let r: { x: Nat // x = 0 } := ⟨ y, by assumption ⟩
+  .ret r
+
+----------------------
+-- MACHINE INTEGERS --
+----------------------
+
+-- NOTE: we reuse the USize type from prelude.lean, because at least we know
+-- it's defined in an idiomatic style that is going to make proofs easy (and
+-- indeed, several proofs here are much shortened compared to Aymeric's earlier
+-- attempt.) This is not stricto sensu the *correct* thing to do, because one
+-- can query at run-time the value of USize, which we do *not* want to do (we
+-- don't know what target we'll run on!), but when the day comes, we'll just
+-- define our own USize.
+-- ANOTHER NOTE: there is USize.sub but it has wraparound semantics, which is
+-- not something we want to define (I think), so we use our own monadic sub (but
+-- is it in line with the Rust behavior?)
+
+-- TODO: I am somewhat under the impression that subtraction is defined as a
+-- total function over nats...? the hypothesis in the if condition is not used
+-- in the then-branch which confuses me quite a bit
+
+-- TODO: add a refinement for the result (just like vec_push_back below) that
+-- explains that the toNat of the result (in the case of success) is the sub of
+-- the toNat of the arguments (i.e. intrinsic specification)
+-- ... do we want intrinsic specifications for the builtins? that might require
+-- some careful type annotations in the monadic notation for clients, but may
+-- give us more "for free"
+
+-- 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." Try to settle this with a Lean expert on what is the most
+-- productive way to go about this?
+
+-- One needs to perform a little bit of reasoning in order to successfully
+-- inject constants into USize, so we provide a general-purpose macro
+
+syntax "intlit" : tactic
+
+macro_rules
+  | `(tactic| intlit) => `(tactic|
+    match USize.size, usize_size_eq with
+    | _, Or.inl rfl => decide
+    | _, Or.inr rfl => decide)
+
+-- This is how the macro is expected to be used
+#eval USize.ofNatCore 0 (by intlit)
+
+-- Also works for other integer types (at the expense of a needless disjunction)
+#eval UInt32.ofNatCore 0 (by intlit)
+
+-- 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 USize.checked_sub (n: USize) (m: USize): result USize :=
+  -- NOTE: the test USize.toNat n - m >= 0 seems to always succeed?
+  if n >= m then
+    let n' := USize.toNat n
+    let m' := USize.toNat n
+    let r := USize.ofNatCore (n' - m') (by
+      have h: n' - m' <= n' := by
+        apply Nat.sub_le_of_le_add
+        case h => rewrite [ Nat.add_comm ]; apply Nat.le_add_left
+      apply Nat.lt_of_le_of_lt h
+      apply n.val.isLt
+    )
+    return r
+  else
+    fail integerOverflow
+
+def USize.checked_add (n: USize) (m: USize): result USize :=
+  if h: n.val.val + m.val.val <= 4294967295 then
+    .ret ⟨ n.val.val + m.val.val, by
+      have h': 4294967295 < USize.size := by intlit
+      apply Nat.lt_of_le_of_lt h h'
+    ⟩
+  else if h: n.val + m.val < USize.size then
+    .ret ⟨ n.val + m.val, h ⟩
+  else
+    .fail integerOverflow
+
+def USize.checked_rem (n: USize) (m: USize): result USize :=
+  if h: m > 0 then
+    .ret ⟨ n.val % m.val, by
+      have h1: ↑m.val < USize.size := m.val.isLt
+      have h2: n.val.val % m.val.val < m.val.val := @Nat.mod_lt n.val m.val h
+      apply Nat.lt_trans h2 h1
+    ⟩
+  else
+    .fail integerOverflow
+
+def USize.checked_mul (n: USize) (m: USize): result USize :=
+    if h: n.val.val * m.val.val <= 4294967295 then
+    .ret ⟨ n.val.val * m.val.val, by
+      have h': 4294967295 < USize.size := by intlit
+      apply Nat.lt_of_le_of_lt h h'
+    ⟩
+  else if h: n.val * m.val < USize.size then
+    .ret ⟨ n.val * m.val, h ⟩
+  else
+    .fail integerOverflow
+
+def USize.checked_div (n: USize) (m: USize): result USize :=
+  if m > 0 then
+    .ret ⟨ n.val / m.val, by
+      have h1: ↑n.val < USize.size := n.val.isLt
+      have h2: n.val.val / m.val.val <= n.val.val := @Nat.div_le_self n.val m.val
+      apply Nat.lt_of_le_of_lt h2 h1
+    ⟩
+  else
+    .fail integerOverflow
+
+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
+  ))
+
+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
+
+
+-- Test behavior...
+#eval assert! USize.checked_sub 10 20 == fail integerOverflow; 0
+
+#eval USize.checked_sub 20 10
+-- NOTE: compare with concrete behavior here, which I do not think we want
+#eval USize.sub 0 1
+#eval UInt8.add 255 255
+
+-------------
+-- VECTORS --
+-------------
+
+-- Note: unlike F*, Lean seems to use strict upper bounds (e.g. USize.size)
+-- rather than maximum values (usize_max).
+def vec (α : Type u) := { l : List α // List.length l < USize.size }
+
+def vec_new (α : Type u): vec α := ⟨ [], by {
+  match USize.size, usize_size_eq with
+  | _, Or.inl rfl => simp
+  | _, Or.inr rfl => simp
+  } ⟩
+
+#check vec_new
+
+def vec_len (α : Type u) (v : vec α) : USize :=
+  let ⟨ v, l ⟩ := v
+  USize.ofNatCore (List.length v) l
+
+#eval vec_len Nat (vec_new Nat)
+ 
+def vec_push_fwd (α : Type u) (_ : vec α) (_ : α) : Unit := ()
+
+-- NOTE: old version trying to use a subtype notation, but probably better to
+-- leave result elimination to auxiliary lemmas with suitable preconditions
+-- TODO: I originally wrote `List.length v.val < USize.size - 1`; how can one
+-- make the proof work in that case? Probably need to import tactics from
+-- mathlib to deal with inequalities... would love to see an example.
+def vec_push_back_old (α : Type u) (v : vec α) (x : α) : { res: result (vec α) //
+  match res with | fail _ => True | ret v' => List.length v'.val = List.length v.val + 1}
+  :=
+  if h : List.length v.val + 1 < USize.size then
+    ⟨ return ⟨List.concat v.val x,
+      by
+        rw [List.length_concat]
+        assumption
+     ⟩, by simp ⟩
+  else
+    ⟨ fail maximumSizeExceeded, by simp ⟩
+
+#eval do
+  -- NOTE: the // notation is syntactic sugar for Subtype, a refinement with
+  -- fields val and property. However, Lean's elaborator can automatically
+  -- select the `val` field if the context provides a type annotation. We
+  -- annotate `x`, which relieves us of having to write `.val` on the right-hand
+  -- side of the monadic let.
+  let v := vec_new Nat
+  let x: vec Nat ← (vec_push_back_old Nat v 1: result (vec Nat)) -- WHY do we need the type annotation here?
+  -- TODO: strengthen post-condition above and do a demo to show that we can
+  -- safely eliminate the `fail` case
+  return (vec_len Nat x)
+
+def vec_push_back (α : Type u) (v : vec α) (x : α) : result (vec α)
+  :=
+  if h : List.length v.val + 1 <= 4294967295 then
+    return ⟨ List.concat v.val x,
+      by
+        rw [List.length_concat]
+        have h': 4294967295 < USize.size := by intlit
+        apply Nat.lt_of_le_of_lt h h'
+    ⟩
+  else if h: List.length v.val + 1 < USize.size then
+    return ⟨List.concat v.val x,
+      by
+        rw [List.length_concat]
+        assumption
+     ⟩
+  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
+    .ret ⟨ List.set v.val i.val x, by
+      have h: List.length v.val < USize.size := 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 h: i.val < List.length v.val then
+    .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 h: i.val < List.length v.val then
+    .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
+    .ret ⟨ List.set v.val i.val x, by
+      have h: List.length v.val < USize.size := 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
+
+--------------------
+-- ASSERT COMMAND --
+--------------------
+
+open Lean Elab Command Term Meta
+
+syntax (name := assert) "#assert" term: command
+
+@[command_elab assert]
+def assertImpl : CommandElab := fun (_stx: Syntax) => do
+  logInfo "Reducing and asserting: "
+  logInfo _stx[1]
+  runTermElabM (fun _ => do
+    let e ← Term.elabTerm _stx[1] none
+    logInfo (Expr.dbgToString e)
+    -- How to evaluate the term and compare the result to true?
+    pure ())
+  -- logInfo (Expr.dbgToString (``true))
+  -- throwError "TODO: assert"
+
+#eval 2 == 2
+#assert (2 == 2)
diff --git a/tests/lean/misc/loops/Loops/Clauses/Clauses.lean b/tests/lean/misc/loops/Loops/Clauses/Clauses.lean
new file mode 100644
index 00000000..5ddb65ca
--- /dev/null
+++ b/tests/lean/misc/loops/Loops/Clauses/Clauses.lean
@@ -0,0 +1,209 @@
+-- [loops]: decreases clauses
+import Base.Primitives
+import Loops.Types
+
+/- [loops::sum]: termination measure -/
+@[simp]
+def sum_loop_terminates (max : UInt32) (i : UInt32) (s : UInt32) := (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 : UInt32) (mi : UInt32)
+  (ms : UInt32) :=
+  (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 : UInt32) (i : UInt32)
+  (s : UInt32) :=
+  (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 UInt32) (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 : UInt32) (ls : list_t UInt32) := (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 : UInt32)
+  :=
+  (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 : UInt32) :=
+  (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 : UInt32)
+  (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 : UInt32)
+  (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 : UInt32) :=
+  (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 : UInt32) :=
+  (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 : UInt32) :=
+  (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 : UInt32) :=
+  (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 : UInt32) :=
+  (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 : UInt32) :=
+  (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 : UInt32) :=
+  (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 : UInt32) :=
+  (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
new file mode 100644
index 00000000..3c0f2f7c
--- /dev/null
+++ b/tests/lean/misc/loops/Loops/Clauses/Template.lean
@@ -0,0 +1,210 @@
+-- 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 : UInt32) (i : UInt32) (s : UInt32) := (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 : UInt32) (mi : UInt32)
+  (ms : UInt32) :=
+  (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 : UInt32) (i : UInt32)
+  (s : UInt32) :=
+  (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 UInt32) (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 : UInt32) (ls : list_t UInt32) := (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 : UInt32)
+  :=
+  (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 : UInt32) :=
+  (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 : UInt32)
+  (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 : UInt32)
+  (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 : UInt32) :=
+  (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 : UInt32) :=
+  (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 : UInt32) :=
+  (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 : UInt32) :=
+  (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 : UInt32) :=
+  (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 : UInt32) :=
+  (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 : UInt32) :=
+  (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 : UInt32) :=
+  (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/Funs.lean b/tests/lean/misc/loops/Loops/Funs.lean
new file mode 100644
index 00000000..5fe5b4ff
--- /dev/null
+++ b/tests/lean/misc/loops/Loops/Funs.lean
@@ -0,0 +1,786 @@
+-- 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 : UInt32) (i : UInt32) (s : UInt32) : (result UInt32) :=
+  if i < max
+  then
+    do
+      let s0 <- UInt32.checked_add s i
+      let i0 <- UInt32.checked_add i (UInt32.ofNatCore 1 (by intlit))
+      sum_loop_fwd max i0 s0
+  else UInt32.checked_mul s (UInt32.ofNatCore 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 : UInt32) : result UInt32 :=
+  sum_loop_fwd max (UInt32.ofNatCore 0 (by intlit))
+    (UInt32.ofNatCore 0 (by intlit))
+
+/- [loops::sum_with_mut_borrows] -/
+def sum_with_mut_borrows_loop_fwd
+  (max : UInt32) (mi : UInt32) (ms : UInt32) : (result UInt32) :=
+  if mi < max
+  then
+    do
+      let ms0 <- UInt32.checked_add ms mi
+      let mi0 <- UInt32.checked_add mi (UInt32.ofNatCore 1 (by intlit))
+      sum_with_mut_borrows_loop_fwd max mi0 ms0
+  else UInt32.checked_mul ms (UInt32.ofNatCore 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 : UInt32) : result UInt32 :=
+  sum_with_mut_borrows_loop_fwd max (UInt32.ofNatCore 0 (by intlit))
+    (UInt32.ofNatCore 0 (by intlit))
+
+/- [loops::sum_with_shared_borrows] -/
+def sum_with_shared_borrows_loop_fwd
+  (max : UInt32) (i : UInt32) (s : UInt32) : (result UInt32) :=
+  if i < max
+  then
+    do
+      let i0 <- UInt32.checked_add i (UInt32.ofNatCore 1 (by intlit))
+      let s0 <- UInt32.checked_add s i0
+      sum_with_shared_borrows_loop_fwd max i0 s0
+  else UInt32.checked_mul s (UInt32.ofNatCore 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 : UInt32) : result UInt32 :=
+  sum_with_shared_borrows_loop_fwd max (UInt32.ofNatCore 0 (by intlit))
+    (UInt32.ofNatCore 0 (by intlit))
+
+/- [loops::clear] -/
+def clear_loop_fwd_back (v : vec UInt32) (i : USize) : (result (vec UInt32)) :=
+  let i0 := vec_len UInt32 v
+  if i < i0
+  then
+    do
+      let i1 <- USize.checked_add i (USize.ofNatCore 1 (by intlit))
+      let v0 <- vec_index_mut_back UInt32 v i (UInt32.ofNatCore 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 UInt32) : result (vec UInt32) :=
+  clear_loop_fwd_back v (USize.ofNatCore 0 (by intlit))
+
+/- [loops::list_mem] -/
+def list_mem_loop_fwd (x : UInt32) (ls : list_t UInt32) : (result Bool) :=
+  match ls with
+  | list_t.ListCons y tl =>
+    if y = x then result.ret true else list_mem_loop_fwd x tl
+  | list_t.ListNil => 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 : UInt32) (ls : list_t UInt32) : 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 : UInt32) : (result T) :=
+  match ls with
+  | list_t.ListCons x tl =>
+    if i = (UInt32.ofNatCore 0 (by intlit))
+    then result.ret x
+    else
+      do
+        let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+        list_nth_mut_loop_loop_fwd T tl i0
+  | list_t.ListNil => 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 : UInt32) : 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 : UInt32) (ret0 : T) : (result (list_t T)) :=
+  match ls with
+  | list_t.ListCons x tl =>
+    if i = (UInt32.ofNatCore 0 (by intlit))
+    then result.ret (list_t.ListCons ret0 tl)
+    else
+      do
+        let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+        let tl0 <- list_nth_mut_loop_loop_back T tl i0 ret0
+        result.ret (list_t.ListCons x tl0)
+  | list_t.ListNil => 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 : UInt32) (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 : UInt32) : (result T) :=
+  match ls with
+  | list_t.ListCons x tl =>
+    if i = (UInt32.ofNatCore 0 (by intlit))
+    then result.ret x
+    else
+      do
+        let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+        list_nth_shared_loop_loop_fwd T tl i0
+  | list_t.ListNil => 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 : UInt32) : 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 ls with
+  | list_t.ListCons y tl =>
+    if y = x then result.ret y else get_elem_mut_loop_fwd x tl
+  | list_t.ListNil => 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.ofNatCore 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 ls with
+  | list_t.ListCons y tl =>
+    if y = x
+    then result.ret (list_t.ListCons ret0 tl)
+    else
+      do
+        let tl0 <- get_elem_mut_loop_back x tl ret0
+        result.ret (list_t.ListCons y tl0)
+  | list_t.ListNil => 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.ofNatCore 0 (by intlit))
+    let l0 <- get_elem_mut_loop_back x l ret0
+    vec_index_mut_back (list_t USize) slots (USize.ofNatCore 0 (by intlit)) l0
+
+/- [loops::get_elem_shared] -/
+def get_elem_shared_loop_fwd
+  (x : USize) (ls : list_t USize) : (result USize) :=
+  match ls with
+  | list_t.ListCons y tl =>
+    if y = x then result.ret y else get_elem_shared_loop_fwd x tl
+  | list_t.ListNil => 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.ofNatCore 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 : UInt32) (ls : list_t T) : (result T) :=
+  match ls with
+  | list_t.ListCons x tl =>
+    if i = (UInt32.ofNatCore 0 (by intlit))
+    then result.ret x
+    else
+      do
+        let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+        list_nth_mut_loop_with_id_loop_fwd T i0 tl
+  | list_t.ListNil => 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 : UInt32) : 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 : UInt32) (ls : list_t T) (ret0 : T) : (result (list_t T)) :=
+  match ls with
+  | list_t.ListCons x tl =>
+    if i = (UInt32.ofNatCore 0 (by intlit))
+    then result.ret (list_t.ListCons ret0 tl)
+    else
+      do
+        let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+        let tl0 <- list_nth_mut_loop_with_id_loop_back T i0 tl ret0
+        result.ret (list_t.ListCons x tl0)
+  | list_t.ListNil => 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 : UInt32) (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 : UInt32) (ls : list_t T) : (result T) :=
+  match ls with
+  | list_t.ListCons x tl =>
+    if i = (UInt32.ofNatCore 0 (by intlit))
+    then result.ret x
+    else
+      do
+        let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+        list_nth_shared_loop_with_id_loop_fwd T i0 tl
+  | list_t.ListNil => 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 : UInt32) : 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 : UInt32) :
+  (result (T × T))
+  :=
+  match ls0 with
+  | list_t.ListCons x0 tl0 =>
+    match ls1 with
+    | list_t.ListCons x1 tl1 =>
+      if i = (UInt32.ofNatCore 0 (by intlit))
+      then result.ret (x0, x1)
+      else
+        do
+          let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+          list_nth_mut_loop_pair_loop_fwd T tl0 tl1 i0
+    | list_t.ListNil => result.fail error.panic
+    
+  | list_t.ListNil => 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 : UInt32) :
+  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 : UInt32) (ret0 : T) :
+  (result (list_t T))
+  :=
+  match ls0 with
+  | list_t.ListCons x0 tl0 =>
+    match ls1 with
+    | list_t.ListCons x1 tl1 =>
+      if i = (UInt32.ofNatCore 0 (by intlit))
+      then result.ret (list_t.ListCons ret0 tl0)
+      else
+        do
+          let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+          let tl00 <- list_nth_mut_loop_pair_loop_back'a T tl0 tl1 i0 ret0
+          result.ret (list_t.ListCons x0 tl00)
+    | list_t.ListNil => result.fail error.panic
+    
+  | list_t.ListNil => 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 : UInt32) (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 : UInt32) (ret0 : T) :
+  (result (list_t T))
+  :=
+  match ls0 with
+  | list_t.ListCons x0 tl0 =>
+    match ls1 with
+    | list_t.ListCons x1 tl1 =>
+      if i = (UInt32.ofNatCore 0 (by intlit))
+      then result.ret (list_t.ListCons ret0 tl1)
+      else
+        do
+          let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+          let tl10 <- list_nth_mut_loop_pair_loop_back'b T tl0 tl1 i0 ret0
+          result.ret (list_t.ListCons x1 tl10)
+    | list_t.ListNil => result.fail error.panic
+    
+  | list_t.ListNil => 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 : UInt32) (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 : UInt32) :
+  (result (T × T))
+  :=
+  match ls0 with
+  | list_t.ListCons x0 tl0 =>
+    match ls1 with
+    | list_t.ListCons x1 tl1 =>
+      if i = (UInt32.ofNatCore 0 (by intlit))
+      then result.ret (x0, x1)
+      else
+        do
+          let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+          list_nth_shared_loop_pair_loop_fwd T tl0 tl1 i0
+    | list_t.ListNil => result.fail error.panic
+    
+  | list_t.ListNil => 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 : UInt32) :
+  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 : UInt32) :
+  (result (T × T))
+  :=
+  match ls0 with
+  | list_t.ListCons x0 tl0 =>
+    match ls1 with
+    | list_t.ListCons x1 tl1 =>
+      if i = (UInt32.ofNatCore 0 (by intlit))
+      then result.ret (x0, x1)
+      else
+        do
+          let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+          list_nth_mut_loop_pair_merge_loop_fwd T tl0 tl1 i0
+    | list_t.ListNil => result.fail error.panic
+    
+  | list_t.ListNil => 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 : UInt32) :
+  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 : UInt32) (ret0 : (T × T)) :
+  (result ((list_t T) × (list_t T)))
+  :=
+  match ls0 with
+  | list_t.ListCons x0 tl0 =>
+    match ls1 with
+    | list_t.ListCons x1 tl1 =>
+      if i = (UInt32.ofNatCore 0 (by intlit))
+      then
+        let (t, t0) := ret0
+        result.ret (list_t.ListCons t tl0, list_t.ListCons t0 tl1)
+      else
+        do
+          let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+          let (tl00, tl10) <-
+            list_nth_mut_loop_pair_merge_loop_back T tl0 tl1 i0 ret0
+          result.ret (list_t.ListCons x0 tl00, list_t.ListCons x1 tl10)
+    | list_t.ListNil => result.fail error.panic
+    
+  | list_t.ListNil => 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 : UInt32) (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 : UInt32) :
+  (result (T × T))
+  :=
+  match ls0 with
+  | list_t.ListCons x0 tl0 =>
+    match ls1 with
+    | list_t.ListCons x1 tl1 =>
+      if i = (UInt32.ofNatCore 0 (by intlit))
+      then result.ret (x0, x1)
+      else
+        do
+          let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+          list_nth_shared_loop_pair_merge_loop_fwd T tl0 tl1 i0
+    | list_t.ListNil => result.fail error.panic
+    
+  | list_t.ListNil => 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 : UInt32) :
+  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 : UInt32) :
+  (result (T × T))
+  :=
+  match ls0 with
+  | list_t.ListCons x0 tl0 =>
+    match ls1 with
+    | list_t.ListCons x1 tl1 =>
+      if i = (UInt32.ofNatCore 0 (by intlit))
+      then result.ret (x0, x1)
+      else
+        do
+          let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+          list_nth_mut_shared_loop_pair_loop_fwd T tl0 tl1 i0
+    | list_t.ListNil => result.fail error.panic
+    
+  | list_t.ListNil => 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 : UInt32) :
+  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 : UInt32) (ret0 : T) :
+  (result (list_t T))
+  :=
+  match ls0 with
+  | list_t.ListCons x0 tl0 =>
+    match ls1 with
+    | list_t.ListCons x1 tl1 =>
+      if i = (UInt32.ofNatCore 0 (by intlit))
+      then result.ret (list_t.ListCons ret0 tl0)
+      else
+        do
+          let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+          let tl00 <- list_nth_mut_shared_loop_pair_loop_back T tl0 tl1 i0 ret0
+          result.ret (list_t.ListCons x0 tl00)
+    | list_t.ListNil => result.fail error.panic
+    
+  | list_t.ListNil => 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 : UInt32) (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 : UInt32) :
+  (result (T × T))
+  :=
+  match ls0 with
+  | list_t.ListCons x0 tl0 =>
+    match ls1 with
+    | list_t.ListCons x1 tl1 =>
+      if i = (UInt32.ofNatCore 0 (by intlit))
+      then result.ret (x0, x1)
+      else
+        do
+          let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+          list_nth_mut_shared_loop_pair_merge_loop_fwd T tl0 tl1 i0
+    | list_t.ListNil => result.fail error.panic
+    
+  | list_t.ListNil => 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 : UInt32) :
+  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 : UInt32) (ret0 : T) :
+  (result (list_t T))
+  :=
+  match ls0 with
+  | list_t.ListCons x0 tl0 =>
+    match ls1 with
+    | list_t.ListCons x1 tl1 =>
+      if i = (UInt32.ofNatCore 0 (by intlit))
+      then result.ret (list_t.ListCons ret0 tl0)
+      else
+        do
+          let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+          let tl00 <-
+            list_nth_mut_shared_loop_pair_merge_loop_back T tl0 tl1 i0 ret0
+          result.ret (list_t.ListCons x0 tl00)
+    | list_t.ListNil => result.fail error.panic
+    
+  | list_t.ListNil => 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 : UInt32) (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 : UInt32) :
+  (result (T × T))
+  :=
+  match ls0 with
+  | list_t.ListCons x0 tl0 =>
+    match ls1 with
+    | list_t.ListCons x1 tl1 =>
+      if i = (UInt32.ofNatCore 0 (by intlit))
+      then result.ret (x0, x1)
+      else
+        do
+          let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+          list_nth_shared_mut_loop_pair_loop_fwd T tl0 tl1 i0
+    | list_t.ListNil => result.fail error.panic
+    
+  | list_t.ListNil => 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 : UInt32) :
+  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 : UInt32) (ret0 : T) :
+  (result (list_t T))
+  :=
+  match ls0 with
+  | list_t.ListCons x0 tl0 =>
+    match ls1 with
+    | list_t.ListCons x1 tl1 =>
+      if i = (UInt32.ofNatCore 0 (by intlit))
+      then result.ret (list_t.ListCons ret0 tl1)
+      else
+        do
+          let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+          let tl10 <- list_nth_shared_mut_loop_pair_loop_back T tl0 tl1 i0 ret0
+          result.ret (list_t.ListCons x1 tl10)
+    | list_t.ListNil => result.fail error.panic
+    
+  | list_t.ListNil => 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 : UInt32) (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 : UInt32) :
+  (result (T × T))
+  :=
+  match ls0 with
+  | list_t.ListCons x0 tl0 =>
+    match ls1 with
+    | list_t.ListCons x1 tl1 =>
+      if i = (UInt32.ofNatCore 0 (by intlit))
+      then result.ret (x0, x1)
+      else
+        do
+          let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+          list_nth_shared_mut_loop_pair_merge_loop_fwd T tl0 tl1 i0
+    | list_t.ListNil => result.fail error.panic
+    
+  | list_t.ListNil => 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 : UInt32) :
+  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 : UInt32) (ret0 : T) :
+  (result (list_t T))
+  :=
+  match ls0 with
+  | list_t.ListCons x0 tl0 =>
+    match ls1 with
+    | list_t.ListCons x1 tl1 =>
+      if i = (UInt32.ofNatCore 0 (by intlit))
+      then result.ret (list_t.ListCons ret0 tl1)
+      else
+        do
+          let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+          let tl10 <-
+            list_nth_shared_mut_loop_pair_merge_loop_back T tl0 tl1 i0 ret0
+          result.ret (list_t.ListCons x1 tl10)
+    | list_t.ListNil => result.fail error.panic
+    
+  | list_t.ListNil => 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 : UInt32) (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
new file mode 100644
index 00000000..f4b6809e
--- /dev/null
+++ b/tests/lean/misc/loops/Loops/Types.lean
@@ -0,0 +1,9 @@
+-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
+-- [loops]: type definitions
+import Base.Primitives
+
+/- [loops::List] -/
+inductive list_t (T : Type) :=
+| ListCons : T -> list_t T -> list_t T
+| ListNil : list_t T
+
diff --git a/tests/lean/misc/no_nested_borrows/Base/Primitives.lean b/tests/lean/misc/no_nested_borrows/Base/Primitives.lean
new file mode 100644
index 00000000..79958d94
--- /dev/null
+++ b/tests/lean/misc/no_nested_borrows/Base/Primitives.lean
@@ -0,0 +1,373 @@
+import Lean
+import Lean.Meta.Tactic.Simp
+import Init.Data.List.Basic
+import Mathlib.Tactic.RunCmd
+
+-------------
+-- PRELUDE --
+-------------
+
+-- Results & monadic combinators
+
+-- TODO: use syntactic conventions and capitalize error, result, etc.
+
+inductive error where
+   | assertionFailure: error
+   | integerOverflow: 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
+
+/- HELPERS -/
+
+-- TODO: is there automated syntax for these discriminators?
+def is_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) (_: is_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 : (o : result α) → result { x : α // o = ret x }
+  | .ret x => .ret ⟨x, rfl⟩
+  | .fail e   => .fail e
+
+macro "let" h:ident " : " e:term " <-- " f:term : doElem =>
+  `(doElem| let ⟨$e, $h⟩ ← result.attach $f)
+
+-- Silly example of the kind of reasoning that this notation enables
+#eval do
+  let h: y <-- .ret (0: Nat)
+  let _: y = 0 := by cases h; decide
+  let r: { x: Nat // x = 0 } := ⟨ y, by assumption ⟩
+  .ret r
+
+----------------------
+-- MACHINE INTEGERS --
+----------------------
+
+-- NOTE: we reuse the USize type from prelude.lean, because at least we know
+-- it's defined in an idiomatic style that is going to make proofs easy (and
+-- indeed, several proofs here are much shortened compared to Aymeric's earlier
+-- attempt.) This is not stricto sensu the *correct* thing to do, because one
+-- can query at run-time the value of USize, which we do *not* want to do (we
+-- don't know what target we'll run on!), but when the day comes, we'll just
+-- define our own USize.
+-- ANOTHER NOTE: there is USize.sub but it has wraparound semantics, which is
+-- not something we want to define (I think), so we use our own monadic sub (but
+-- is it in line with the Rust behavior?)
+
+-- TODO: I am somewhat under the impression that subtraction is defined as a
+-- total function over nats...? the hypothesis in the if condition is not used
+-- in the then-branch which confuses me quite a bit
+
+-- TODO: add a refinement for the result (just like vec_push_back below) that
+-- explains that the toNat of the result (in the case of success) is the sub of
+-- the toNat of the arguments (i.e. intrinsic specification)
+-- ... do we want intrinsic specifications for the builtins? that might require
+-- some careful type annotations in the monadic notation for clients, but may
+-- give us more "for free"
+
+-- 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." Try to settle this with a Lean expert on what is the most
+-- productive way to go about this?
+
+-- One needs to perform a little bit of reasoning in order to successfully
+-- inject constants into USize, so we provide a general-purpose macro
+
+syntax "intlit" : tactic
+
+macro_rules
+  | `(tactic| intlit) => `(tactic|
+    match USize.size, usize_size_eq with
+    | _, Or.inl rfl => decide
+    | _, Or.inr rfl => decide)
+
+-- This is how the macro is expected to be used
+#eval USize.ofNatCore 0 (by intlit)
+
+-- Also works for other integer types (at the expense of a needless disjunction)
+#eval UInt32.ofNatCore 0 (by intlit)
+
+-- 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 USize.checked_sub (n: USize) (m: USize): result USize :=
+  -- NOTE: the test USize.toNat n - m >= 0 seems to always succeed?
+  if n >= m then
+    let n' := USize.toNat n
+    let m' := USize.toNat n
+    let r := USize.ofNatCore (n' - m') (by
+      have h: n' - m' <= n' := by
+        apply Nat.sub_le_of_le_add
+        case h => rewrite [ Nat.add_comm ]; apply Nat.le_add_left
+      apply Nat.lt_of_le_of_lt h
+      apply n.val.isLt
+    )
+    return r
+  else
+    fail integerOverflow
+
+def USize.checked_add (n: USize) (m: USize): result USize :=
+  if h: n.val.val + m.val.val <= 4294967295 then
+    .ret ⟨ n.val.val + m.val.val, by
+      have h': 4294967295 < USize.size := by intlit
+      apply Nat.lt_of_le_of_lt h h'
+    ⟩
+  else if h: n.val + m.val < USize.size then
+    .ret ⟨ n.val + m.val, h ⟩
+  else
+    .fail integerOverflow
+
+def USize.checked_rem (n: USize) (m: USize): result USize :=
+  if h: m > 0 then
+    .ret ⟨ n.val % m.val, by
+      have h1: ↑m.val < USize.size := m.val.isLt
+      have h2: n.val.val % m.val.val < m.val.val := @Nat.mod_lt n.val m.val h
+      apply Nat.lt_trans h2 h1
+    ⟩
+  else
+    .fail integerOverflow
+
+def USize.checked_mul (n: USize) (m: USize): result USize :=
+    if h: n.val.val * m.val.val <= 4294967295 then
+    .ret ⟨ n.val.val * m.val.val, by
+      have h': 4294967295 < USize.size := by intlit
+      apply Nat.lt_of_le_of_lt h h'
+    ⟩
+  else if h: n.val * m.val < USize.size then
+    .ret ⟨ n.val * m.val, h ⟩
+  else
+    .fail integerOverflow
+
+def USize.checked_div (n: USize) (m: USize): result USize :=
+  if m > 0 then
+    .ret ⟨ n.val / m.val, by
+      have h1: ↑n.val < USize.size := n.val.isLt
+      have h2: n.val.val / m.val.val <= n.val.val := @Nat.div_le_self n.val m.val
+      apply Nat.lt_of_le_of_lt h2 h1
+    ⟩
+  else
+    .fail integerOverflow
+
+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
+  ))
+
+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
+
+
+-- Test behavior...
+#eval assert! USize.checked_sub 10 20 == fail integerOverflow; 0
+
+#eval USize.checked_sub 20 10
+-- NOTE: compare with concrete behavior here, which I do not think we want
+#eval USize.sub 0 1
+#eval UInt8.add 255 255
+
+-------------
+-- VECTORS --
+-------------
+
+-- Note: unlike F*, Lean seems to use strict upper bounds (e.g. USize.size)
+-- rather than maximum values (usize_max).
+def vec (α : Type u) := { l : List α // List.length l < USize.size }
+
+def vec_new (α : Type u): vec α := ⟨ [], by {
+  match USize.size, usize_size_eq with
+  | _, Or.inl rfl => simp
+  | _, Or.inr rfl => simp
+  } ⟩
+
+#check vec_new
+
+def vec_len (α : Type u) (v : vec α) : USize :=
+  let ⟨ v, l ⟩ := v
+  USize.ofNatCore (List.length v) l
+
+#eval vec_len Nat (vec_new Nat)
+ 
+def vec_push_fwd (α : Type u) (_ : vec α) (_ : α) : Unit := ()
+
+-- NOTE: old version trying to use a subtype notation, but probably better to
+-- leave result elimination to auxiliary lemmas with suitable preconditions
+-- TODO: I originally wrote `List.length v.val < USize.size - 1`; how can one
+-- make the proof work in that case? Probably need to import tactics from
+-- mathlib to deal with inequalities... would love to see an example.
+def vec_push_back_old (α : Type u) (v : vec α) (x : α) : { res: result (vec α) //
+  match res with | fail _ => True | ret v' => List.length v'.val = List.length v.val + 1}
+  :=
+  if h : List.length v.val + 1 < USize.size then
+    ⟨ return ⟨List.concat v.val x,
+      by
+        rw [List.length_concat]
+        assumption
+     ⟩, by simp ⟩
+  else
+    ⟨ fail maximumSizeExceeded, by simp ⟩
+
+#eval do
+  -- NOTE: the // notation is syntactic sugar for Subtype, a refinement with
+  -- fields val and property. However, Lean's elaborator can automatically
+  -- select the `val` field if the context provides a type annotation. We
+  -- annotate `x`, which relieves us of having to write `.val` on the right-hand
+  -- side of the monadic let.
+  let v := vec_new Nat
+  let x: vec Nat ← (vec_push_back_old Nat v 1: result (vec Nat)) -- WHY do we need the type annotation here?
+  -- TODO: strengthen post-condition above and do a demo to show that we can
+  -- safely eliminate the `fail` case
+  return (vec_len Nat x)
+
+def vec_push_back (α : Type u) (v : vec α) (x : α) : result (vec α)
+  :=
+  if h : List.length v.val + 1 <= 4294967295 then
+    return ⟨ List.concat v.val x,
+      by
+        rw [List.length_concat]
+        have h': 4294967295 < USize.size := by intlit
+        apply Nat.lt_of_le_of_lt h h'
+    ⟩
+  else if h: List.length v.val + 1 < USize.size then
+    return ⟨List.concat v.val x,
+      by
+        rw [List.length_concat]
+        assumption
+     ⟩
+  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
+    .ret ⟨ List.set v.val i.val x, by
+      have h: List.length v.val < USize.size := 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 h: i.val < List.length v.val then
+    .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 h: i.val < List.length v.val then
+    .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
+    .ret ⟨ List.set v.val i.val x, by
+      have h: List.length v.val < USize.size := 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
+
+--------------------
+-- ASSERT COMMAND --
+--------------------
+
+open Lean Elab Command Term Meta
+
+syntax (name := assert) "#assert" term: command
+
+@[command_elab assert]
+def assertImpl : CommandElab := fun (_stx: Syntax) => do
+  logInfo "Reducing and asserting: "
+  logInfo _stx[1]
+  runTermElabM (fun _ => do
+    let e ← Term.elabTerm _stx[1] none
+    logInfo (Expr.dbgToString e)
+    -- How to evaluate the term and compare the result to true?
+    pure ())
+  -- logInfo (Expr.dbgToString (``true))
+  -- throwError "TODO: assert"
+
+#eval 2 == 2
+#assert (2 == 2)
diff --git a/tests/lean/misc/no_nested_borrows/NoNestedBorrows.lean b/tests/lean/misc/no_nested_borrows/NoNestedBorrows.lean
new file mode 100644
index 00000000..d871392b
--- /dev/null
+++ b/tests/lean/misc/no_nested_borrows/NoNestedBorrows.lean
@@ -0,0 +1,540 @@
+-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
+-- [no_nested_borrows]
+import Base.Primitives
+
+structure OpaqueDefs where
+  
+  /- [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) :=
+  | ListCons : T -> list_t T -> list_t T
+  | ListNil : list_t T
+  
+  /- [no_nested_borrows::One] -/
+  inductive one_t (T1 : Type) := | OneOne : T1 -> one_t T1
+  
+  /- [no_nested_borrows::EmptyEnum] -/
+  inductive empty_enum_t := | EmptyEnumEmpty : empty_enum_t
+  
+  /- [no_nested_borrows::Enum] -/
+  inductive enum_t := | EnumVariant1 : enum_t | EnumVariant2 : enum_t
+  
+  /- [no_nested_borrows::EmptyStruct] -/
+  structure empty_struct_t where   
+  
+  /- [no_nested_borrows::Sum] -/
+  inductive sum_t (T1 T2 : Type) :=
+  | SumLeft : T1 -> sum_t T1 T2
+  | SumRight : T2 -> sum_t T1 T2
+  
+  /- [no_nested_borrows::neg_test] -/
+  def neg_test_fwd (x : Int32) : result Int32 := Int32.checked_neg x
+  
+  /- [no_nested_borrows::add_test] -/
+  def add_test_fwd (x : UInt32) (y : UInt32) : result UInt32 :=
+    UInt32.checked_add x y
+  
+  /- [no_nested_borrows::subs_test] -/
+  def subs_test_fwd (x : UInt32) (y : UInt32) : result UInt32 :=
+    UInt32.checked_sub x y
+  
+  /- [no_nested_borrows::div_test] -/
+  def div_test_fwd (x : UInt32) (y : UInt32) : result UInt32 :=
+    UInt32.checked_div x y
+  
+  /- [no_nested_borrows::div_test1] -/
+  def div_test1_fwd (x : UInt32) : result UInt32 :=
+    UInt32.checked_div x (UInt32.ofNatCore 2 (by intlit))
+  
+  /- [no_nested_borrows::rem_test] -/
+  def rem_test_fwd (x : UInt32) (y : UInt32) : result UInt32 :=
+    UInt32.checked_rem x y
+  
+  /- [no_nested_borrows::cast_test] -/
+  def cast_test_fwd (x : UInt32) : result Int32 := scalar_cast Int32 x
+  
+  /- [no_nested_borrows::test2] -/
+  def test2_fwd : result Unit :=
+    do
+      let _ <- UInt32.checked_add (UInt32.ofNatCore 23 (by intlit))
+        (UInt32.ofNatCore 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 : UInt32) (y : UInt32) : result UInt32 :=
+    if 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 (UInt32.ofNatCore 4 (by intlit))
+          (UInt32.ofNatCore 3 (by intlit))
+      let y <-
+        get_max_fwd (UInt32.ofNatCore 10 (by intlit))
+          (UInt32.ofNatCore 11 (by intlit))
+      let z <- UInt32.checked_add x y
+      if not (z = (UInt32.ofNatCore 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 <- Int32.checked_neg (Int32.ofNatCore 3 (by intlit))
+      if not (y = (Int32.ofNatCore -3 (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 not ((Int32.ofNatCore 1 (by intlit)) = (Int32.ofNatCore 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 not ((Int32.ofNatCore 2 (by intlit)) = (Int32.ofNatCore 2 (by intlit)))
+    then result.fail error.panic
+    else
+      if not ((Int32.ofNatCore 0 (by intlit)) =
+        (Int32.ofNatCore 0 (by intlit)))
+      then result.fail error.panic
+      else
+        if not ((Int32.ofNatCore 2 (by intlit)) =
+          (Int32.ofNatCore 2 (by intlit)))
+        then result.fail error.panic
+        else
+          if not ((Int32.ofNatCore 2 (by intlit)) =
+            (Int32.ofNatCore 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 := (Int32.ofNatCore 1 (by intlit))
+    let x := b
+    if not (x = (Int32.ofNatCore 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 : Int32) : result Int32 := result.ret x
+  
+  /- [no_nested_borrows::test_unreachable] -/
+  def test_unreachable_fwd (b : Bool) : result Unit :=
+    if b then result.fail error.panic else result.ret ()
+  
+  /- [no_nested_borrows::test_panic] -/
+  def test_panic_fwd (b : Bool) : result Unit :=
+    if 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 (Int32.ofNatCore 0 (by intlit))
+      if not ((Int32.ofNatCore 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 l with
+    | list_t.ListCons t l0 => result.ret true
+    | list_t.ListNil => result.ret false
+    
+  
+  /- [no_nested_borrows::test_is_cons] -/
+  def test_is_cons_fwd : result Unit :=
+    do
+      let l := list_t.ListNil
+      let b <-
+        is_cons_fwd Int32 (list_t.ListCons (Int32.ofNatCore 0 (by intlit)) 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_fwd = .ret ())
+  
+  /- [no_nested_borrows::split_list] -/
+  def split_list_fwd (T : Type) (l : list_t T) : result (T × (list_t T)) :=
+    match l with
+    | list_t.ListCons hd tl => result.ret (hd, tl)
+    | list_t.ListNil => result.fail error.panic
+    
+  
+  /- [no_nested_borrows::test_split_list] -/
+  def test_split_list_fwd : result Unit :=
+    do
+      let l := list_t.ListNil
+      let p <-
+        split_list_fwd Int32 (list_t.ListCons (Int32.ofNatCore 0 (by intlit))
+          l)
+      let (hd, _) := p
+      if not (hd = (Int32.ofNatCore 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 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 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 Int32 true (Int32.ofNatCore 0 (by intlit))
+          (Int32.ofNatCore 0 (by intlit))
+      let z0 <- Int32.checked_add z (Int32.ofNatCore 1 (by intlit))
+      if not (z0 = (Int32.ofNatCore 1 (by intlit)))
+      then result.fail error.panic
+      else
+        do
+          let (x, y) <-
+            choose_back Int32 true (Int32.ofNatCore 0 (by intlit))
+              (Int32.ofNatCore 0 (by intlit)) z0
+          if not (x = (Int32.ofNatCore 1 (by intlit)))
+          then result.fail error.panic
+          else
+            if not (y = (Int32.ofNatCore 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'
+  
+  /- [no_nested_borrows::NodeElem] -/
+  mutual inductive node_elem_t (T : Type) :=
+  | NodeElemCons : tree_t T -> node_elem_t T -> node_elem_t T
+  | NodeElemNil : node_elem_t T
+  
+  /- [no_nested_borrows::Tree] -/
+  inductive tree_t (T : Type) :=
+  | TreeLeaf : T -> tree_t T
+  | TreeNode : T -> node_elem_t T -> tree_t T -> tree_t T
+  
+  /- [no_nested_borrows::list_length] -/
+  def list_length_fwd (T : Type) (l : list_t T) : result UInt32 :=
+    match l with
+    | list_t.ListCons t l1 =>
+      do
+        let i <- list_length_fwd T l1
+        UInt32.checked_add (UInt32.ofNatCore 1 (by intlit)) i
+    | list_t.ListNil => result.ret (UInt32.ofNatCore 0 (by intlit))
+    
+  
+  /- [no_nested_borrows::list_nth_shared] -/
+  def list_nth_shared_fwd (T : Type) (l : list_t T) (i : UInt32) : result T :=
+    match l with
+    | list_t.ListCons x tl =>
+      if i = (UInt32.ofNatCore 0 (by intlit))
+      then result.ret x
+      else
+        do
+          let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+          list_nth_shared_fwd T tl i0
+    | list_t.ListNil => result.fail error.panic
+    
+  
+  /- [no_nested_borrows::list_nth_mut] -/
+  def list_nth_mut_fwd (T : Type) (l : list_t T) (i : UInt32) : result T :=
+    match l with
+    | list_t.ListCons x tl =>
+      if i = (UInt32.ofNatCore 0 (by intlit))
+      then result.ret x
+      else
+        do
+          let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+          list_nth_mut_fwd T tl i0
+    | list_t.ListNil => result.fail error.panic
+    
+  
+  /- [no_nested_borrows::list_nth_mut] -/
+  def list_nth_mut_back
+    (T : Type) (l : list_t T) (i : UInt32) (ret0 : T) : result (list_t T) :=
+    match l with
+    | list_t.ListCons x tl =>
+      if i = (UInt32.ofNatCore 0 (by intlit))
+      then result.ret (list_t.ListCons ret0 tl)
+      else
+        do
+          let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+          let tl0 <- list_nth_mut_back T tl i0 ret0
+          result.ret (list_t.ListCons x tl0)
+    | list_t.ListNil => 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 li with
+    | list_t.ListCons hd tl => list_rev_aux_fwd T tl (list_t.ListCons hd lo)
+    | list_t.ListNil => 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.ListNil
+    list_rev_aux_fwd T li list_t.ListNil
+  
+  /- [no_nested_borrows::test_list_functions] -/
+  def test_list_functions_fwd : result Unit :=
+    do
+      let l := list_t.ListNil
+      let l0 := list_t.ListCons (Int32.ofNatCore 2 (by intlit)) l
+      let l1 := list_t.ListCons (Int32.ofNatCore 1 (by intlit)) l0
+      let i <-
+        list_length_fwd Int32 (list_t.ListCons (Int32.ofNatCore 0 (by intlit))
+          l1)
+      if not (i = (UInt32.ofNatCore 3 (by intlit)))
+      then result.fail error.panic
+      else
+        do
+          let i0 <-
+            list_nth_shared_fwd Int32 (list_t.ListCons
+              (Int32.ofNatCore 0 (by intlit)) l1)
+              (UInt32.ofNatCore 0 (by intlit))
+          if not (i0 = (Int32.ofNatCore 0 (by intlit)))
+          then result.fail error.panic
+          else
+            do
+              let i1 <-
+                list_nth_shared_fwd Int32 (list_t.ListCons
+                  (Int32.ofNatCore 0 (by intlit)) l1)
+                  (UInt32.ofNatCore 1 (by intlit))
+              if not (i1 = (Int32.ofNatCore 1 (by intlit)))
+              then result.fail error.panic
+              else
+                do
+                  let i2 <-
+                    list_nth_shared_fwd Int32 (list_t.ListCons
+                      (Int32.ofNatCore 0 (by intlit)) l1)
+                      (UInt32.ofNatCore 2 (by intlit))
+                  if not (i2 = (Int32.ofNatCore 2 (by intlit)))
+                  then result.fail error.panic
+                  else
+                    do
+                      let ls <-
+                        list_nth_mut_back Int32 (list_t.ListCons
+                          (Int32.ofNatCore 0 (by intlit)) l1)
+                          (UInt32.ofNatCore 1 (by intlit))
+                          (Int32.ofNatCore 3 (by intlit))
+                      let i3 <-
+                        list_nth_shared_fwd Int32 ls
+                          (UInt32.ofNatCore 0 (by intlit))
+                      if not (i3 = (Int32.ofNatCore 0 (by intlit)))
+                      then result.fail error.panic
+                      else
+                        do
+                          let i4 <-
+                            list_nth_shared_fwd Int32 ls
+                              (UInt32.ofNatCore 1 (by intlit))
+                          if not (i4 = (Int32.ofNatCore 3 (by intlit)))
+                          then result.fail error.panic
+                          else
+                            do
+                              let i5 <-
+                                list_nth_shared_fwd Int32 ls
+                                  (UInt32.ofNatCore 2 (by intlit))
+                              if not (i5 = (Int32.ofNatCore 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 UInt32 UInt32) :=
+    result.ret
+    {
+      struct_with_tuple_p := ((UInt32.ofNatCore 1 (by intlit)),
+                               (UInt32.ofNatCore 2 (by intlit)))
+    }
+  
+  /- [no_nested_borrows::new_tuple2] -/
+  def new_tuple2_fwd : result (struct_with_tuple_t Int16 Int16) :=
+    result.ret
+    {
+      struct_with_tuple_p := ((Int16.ofNatCore 1 (by intlit)),
+                               (Int16.ofNatCore 2 (by intlit)))
+    }
+  
+  /- [no_nested_borrows::new_tuple3] -/
+  def new_tuple3_fwd : result (struct_with_tuple_t UInt64 Int64) :=
+    result.ret
+    {
+      struct_with_tuple_p := ((UInt64.ofNatCore 1 (by intlit)),
+                               (Int64.ofNatCore 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 UInt32 UInt32) :=
+    result.ret
+    {
+      struct_with_pair_p := {
+                              pair_x := (UInt32.ofNatCore 1 (by intlit)),
+                              pair_y := (UInt32.ofNatCore 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 not (i = (UInt32.ofNatCore 1 (by intlit)))
+      then result.fail error.panic
+      else
+        do
+          let swt0 <- new_tuple2_fwd
+          let (i0, _) := swt0.struct_with_tuple_p
+          if not (i0 = (Int16.ofNatCore 1 (by intlit)))
+          then result.fail error.panic
+          else
+            do
+              let swt1 <- new_tuple3_fwd
+              let (i1, _) := swt1.struct_with_tuple_p
+              if not (i1 = (UInt64.ofNatCore 1 (by intlit)))
+              then result.fail error.panic
+              else
+                do
+                  let swp <- new_pair1_fwd
+                  if not (swp.struct_with_pair_p.pair_x =
+                    (UInt32.ofNatCore 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 : UInt32) : result UInt32 :=
+    let y := mem_replace_fwd UInt32 px (UInt32.ofNatCore 1 (by intlit))
+    if not (y = (UInt32.ofNatCore 0 (by intlit)))
+    then result.fail error.panic
+    else result.ret (UInt32.ofNatCore 2 (by intlit))
+  
+  /- [no_nested_borrows::test_shared_borrow_bool1] -/
+  def test_shared_borrow_bool1_fwd (b : Bool) : result UInt32 :=
+    if b
+    then result.ret (UInt32.ofNatCore 0 (by intlit))
+    else result.ret (UInt32.ofNatCore 1 (by intlit))
+  
+  /- [no_nested_borrows::test_shared_borrow_bool2] -/
+  def test_shared_borrow_bool2_fwd : result UInt32 :=
+    result.ret (UInt32.ofNatCore 0 (by intlit))
+  
+  /- [no_nested_borrows::test_shared_borrow_enum1] -/
+  def test_shared_borrow_enum1_fwd (l : list_t UInt32) : result UInt32 :=
+    match l with
+    | list_t.ListCons i l0 => result.ret (UInt32.ofNatCore 1 (by intlit))
+    | list_t.ListNil => result.ret (UInt32.ofNatCore 0 (by intlit))
+    
+  
+  /- [no_nested_borrows::test_shared_borrow_enum2] -/
+  def test_shared_borrow_enum2_fwd : result UInt32 :=
+    result.ret (UInt32.ofNatCore 0 (by intlit))
+  
diff --git a/tests/lean/misc/paper/Base/Primitives.lean b/tests/lean/misc/paper/Base/Primitives.lean
new file mode 100644
index 00000000..79958d94
--- /dev/null
+++ b/tests/lean/misc/paper/Base/Primitives.lean
@@ -0,0 +1,373 @@
+import Lean
+import Lean.Meta.Tactic.Simp
+import Init.Data.List.Basic
+import Mathlib.Tactic.RunCmd
+
+-------------
+-- PRELUDE --
+-------------
+
+-- Results & monadic combinators
+
+-- TODO: use syntactic conventions and capitalize error, result, etc.
+
+inductive error where
+   | assertionFailure: error
+   | integerOverflow: 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
+
+/- HELPERS -/
+
+-- TODO: is there automated syntax for these discriminators?
+def is_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) (_: is_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 : (o : result α) → result { x : α // o = ret x }
+  | .ret x => .ret ⟨x, rfl⟩
+  | .fail e   => .fail e
+
+macro "let" h:ident " : " e:term " <-- " f:term : doElem =>
+  `(doElem| let ⟨$e, $h⟩ ← result.attach $f)
+
+-- Silly example of the kind of reasoning that this notation enables
+#eval do
+  let h: y <-- .ret (0: Nat)
+  let _: y = 0 := by cases h; decide
+  let r: { x: Nat // x = 0 } := ⟨ y, by assumption ⟩
+  .ret r
+
+----------------------
+-- MACHINE INTEGERS --
+----------------------
+
+-- NOTE: we reuse the USize type from prelude.lean, because at least we know
+-- it's defined in an idiomatic style that is going to make proofs easy (and
+-- indeed, several proofs here are much shortened compared to Aymeric's earlier
+-- attempt.) This is not stricto sensu the *correct* thing to do, because one
+-- can query at run-time the value of USize, which we do *not* want to do (we
+-- don't know what target we'll run on!), but when the day comes, we'll just
+-- define our own USize.
+-- ANOTHER NOTE: there is USize.sub but it has wraparound semantics, which is
+-- not something we want to define (I think), so we use our own monadic sub (but
+-- is it in line with the Rust behavior?)
+
+-- TODO: I am somewhat under the impression that subtraction is defined as a
+-- total function over nats...? the hypothesis in the if condition is not used
+-- in the then-branch which confuses me quite a bit
+
+-- TODO: add a refinement for the result (just like vec_push_back below) that
+-- explains that the toNat of the result (in the case of success) is the sub of
+-- the toNat of the arguments (i.e. intrinsic specification)
+-- ... do we want intrinsic specifications for the builtins? that might require
+-- some careful type annotations in the monadic notation for clients, but may
+-- give us more "for free"
+
+-- 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." Try to settle this with a Lean expert on what is the most
+-- productive way to go about this?
+
+-- One needs to perform a little bit of reasoning in order to successfully
+-- inject constants into USize, so we provide a general-purpose macro
+
+syntax "intlit" : tactic
+
+macro_rules
+  | `(tactic| intlit) => `(tactic|
+    match USize.size, usize_size_eq with
+    | _, Or.inl rfl => decide
+    | _, Or.inr rfl => decide)
+
+-- This is how the macro is expected to be used
+#eval USize.ofNatCore 0 (by intlit)
+
+-- Also works for other integer types (at the expense of a needless disjunction)
+#eval UInt32.ofNatCore 0 (by intlit)
+
+-- 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 USize.checked_sub (n: USize) (m: USize): result USize :=
+  -- NOTE: the test USize.toNat n - m >= 0 seems to always succeed?
+  if n >= m then
+    let n' := USize.toNat n
+    let m' := USize.toNat n
+    let r := USize.ofNatCore (n' - m') (by
+      have h: n' - m' <= n' := by
+        apply Nat.sub_le_of_le_add
+        case h => rewrite [ Nat.add_comm ]; apply Nat.le_add_left
+      apply Nat.lt_of_le_of_lt h
+      apply n.val.isLt
+    )
+    return r
+  else
+    fail integerOverflow
+
+def USize.checked_add (n: USize) (m: USize): result USize :=
+  if h: n.val.val + m.val.val <= 4294967295 then
+    .ret ⟨ n.val.val + m.val.val, by
+      have h': 4294967295 < USize.size := by intlit
+      apply Nat.lt_of_le_of_lt h h'
+    ⟩
+  else if h: n.val + m.val < USize.size then
+    .ret ⟨ n.val + m.val, h ⟩
+  else
+    .fail integerOverflow
+
+def USize.checked_rem (n: USize) (m: USize): result USize :=
+  if h: m > 0 then
+    .ret ⟨ n.val % m.val, by
+      have h1: ↑m.val < USize.size := m.val.isLt
+      have h2: n.val.val % m.val.val < m.val.val := @Nat.mod_lt n.val m.val h
+      apply Nat.lt_trans h2 h1
+    ⟩
+  else
+    .fail integerOverflow
+
+def USize.checked_mul (n: USize) (m: USize): result USize :=
+    if h: n.val.val * m.val.val <= 4294967295 then
+    .ret ⟨ n.val.val * m.val.val, by
+      have h': 4294967295 < USize.size := by intlit
+      apply Nat.lt_of_le_of_lt h h'
+    ⟩
+  else if h: n.val * m.val < USize.size then
+    .ret ⟨ n.val * m.val, h ⟩
+  else
+    .fail integerOverflow
+
+def USize.checked_div (n: USize) (m: USize): result USize :=
+  if m > 0 then
+    .ret ⟨ n.val / m.val, by
+      have h1: ↑n.val < USize.size := n.val.isLt
+      have h2: n.val.val / m.val.val <= n.val.val := @Nat.div_le_self n.val m.val
+      apply Nat.lt_of_le_of_lt h2 h1
+    ⟩
+  else
+    .fail integerOverflow
+
+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
+  ))
+
+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
+
+
+-- Test behavior...
+#eval assert! USize.checked_sub 10 20 == fail integerOverflow; 0
+
+#eval USize.checked_sub 20 10
+-- NOTE: compare with concrete behavior here, which I do not think we want
+#eval USize.sub 0 1
+#eval UInt8.add 255 255
+
+-------------
+-- VECTORS --
+-------------
+
+-- Note: unlike F*, Lean seems to use strict upper bounds (e.g. USize.size)
+-- rather than maximum values (usize_max).
+def vec (α : Type u) := { l : List α // List.length l < USize.size }
+
+def vec_new (α : Type u): vec α := ⟨ [], by {
+  match USize.size, usize_size_eq with
+  | _, Or.inl rfl => simp
+  | _, Or.inr rfl => simp
+  } ⟩
+
+#check vec_new
+
+def vec_len (α : Type u) (v : vec α) : USize :=
+  let ⟨ v, l ⟩ := v
+  USize.ofNatCore (List.length v) l
+
+#eval vec_len Nat (vec_new Nat)
+ 
+def vec_push_fwd (α : Type u) (_ : vec α) (_ : α) : Unit := ()
+
+-- NOTE: old version trying to use a subtype notation, but probably better to
+-- leave result elimination to auxiliary lemmas with suitable preconditions
+-- TODO: I originally wrote `List.length v.val < USize.size - 1`; how can one
+-- make the proof work in that case? Probably need to import tactics from
+-- mathlib to deal with inequalities... would love to see an example.
+def vec_push_back_old (α : Type u) (v : vec α) (x : α) : { res: result (vec α) //
+  match res with | fail _ => True | ret v' => List.length v'.val = List.length v.val + 1}
+  :=
+  if h : List.length v.val + 1 < USize.size then
+    ⟨ return ⟨List.concat v.val x,
+      by
+        rw [List.length_concat]
+        assumption
+     ⟩, by simp ⟩
+  else
+    ⟨ fail maximumSizeExceeded, by simp ⟩
+
+#eval do
+  -- NOTE: the // notation is syntactic sugar for Subtype, a refinement with
+  -- fields val and property. However, Lean's elaborator can automatically
+  -- select the `val` field if the context provides a type annotation. We
+  -- annotate `x`, which relieves us of having to write `.val` on the right-hand
+  -- side of the monadic let.
+  let v := vec_new Nat
+  let x: vec Nat ← (vec_push_back_old Nat v 1: result (vec Nat)) -- WHY do we need the type annotation here?
+  -- TODO: strengthen post-condition above and do a demo to show that we can
+  -- safely eliminate the `fail` case
+  return (vec_len Nat x)
+
+def vec_push_back (α : Type u) (v : vec α) (x : α) : result (vec α)
+  :=
+  if h : List.length v.val + 1 <= 4294967295 then
+    return ⟨ List.concat v.val x,
+      by
+        rw [List.length_concat]
+        have h': 4294967295 < USize.size := by intlit
+        apply Nat.lt_of_le_of_lt h h'
+    ⟩
+  else if h: List.length v.val + 1 < USize.size then
+    return ⟨List.concat v.val x,
+      by
+        rw [List.length_concat]
+        assumption
+     ⟩
+  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
+    .ret ⟨ List.set v.val i.val x, by
+      have h: List.length v.val < USize.size := 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 h: i.val < List.length v.val then
+    .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 h: i.val < List.length v.val then
+    .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
+    .ret ⟨ List.set v.val i.val x, by
+      have h: List.length v.val < USize.size := 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
+
+--------------------
+-- ASSERT COMMAND --
+--------------------
+
+open Lean Elab Command Term Meta
+
+syntax (name := assert) "#assert" term: command
+
+@[command_elab assert]
+def assertImpl : CommandElab := fun (_stx: Syntax) => do
+  logInfo "Reducing and asserting: "
+  logInfo _stx[1]
+  runTermElabM (fun _ => do
+    let e ← Term.elabTerm _stx[1] none
+    logInfo (Expr.dbgToString e)
+    -- How to evaluate the term and compare the result to true?
+    pure ())
+  -- logInfo (Expr.dbgToString (``true))
+  -- throwError "TODO: assert"
+
+#eval 2 == 2
+#assert (2 == 2)
diff --git a/tests/lean/misc/paper/Paper.lean b/tests/lean/misc/paper/Paper.lean
new file mode 100644
index 00000000..2d23f394
--- /dev/null
+++ b/tests/lean/misc/paper/Paper.lean
@@ -0,0 +1,127 @@
+-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
+-- [paper]
+import Base.Primitives
+
+structure OpaqueDefs where
+  
+  /- [paper::ref_incr] -/
+  def ref_incr_fwd_back (x : Int32) : result Int32 :=
+    Int32.checked_add x (Int32.ofNatCore 1 (by intlit))
+  
+  /- [paper::test_incr] -/
+  def test_incr_fwd : result Unit :=
+    do
+      let x <- ref_incr_fwd_back (Int32.ofNatCore 0 (by intlit))
+      if not (x = (Int32.ofNatCore 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 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 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 Int32 true (Int32.ofNatCore 0 (by intlit))
+          (Int32.ofNatCore 0 (by intlit))
+      let z0 <- Int32.checked_add z (Int32.ofNatCore 1 (by intlit))
+      if not (z0 = (Int32.ofNatCore 1 (by intlit)))
+      then result.fail error.panic
+      else
+        do
+          let (x, y) <-
+            choose_back Int32 true (Int32.ofNatCore 0 (by intlit))
+              (Int32.ofNatCore 0 (by intlit)) z0
+          if not (x = (Int32.ofNatCore 1 (by intlit)))
+          then result.fail error.panic
+          else
+            if not (y = (Int32.ofNatCore 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) :=
+  | ListCons : T -> list_t T -> list_t T
+  | ListNil : list_t T
+  
+  /- [paper::list_nth_mut] -/
+  def list_nth_mut_fwd (T : Type) (l : list_t T) (i : UInt32) : result T :=
+    match l with
+    | list_t.ListCons x tl =>
+      if i = (UInt32.ofNatCore 0 (by intlit))
+      then result.ret x
+      else
+        do
+          let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+          list_nth_mut_fwd T tl i0
+    | list_t.ListNil => result.fail error.panic
+    
+  
+  /- [paper::list_nth_mut] -/
+  def list_nth_mut_back
+    (T : Type) (l : list_t T) (i : UInt32) (ret0 : T) : result (list_t T) :=
+    match l with
+    | list_t.ListCons x tl =>
+      if i = (UInt32.ofNatCore 0 (by intlit))
+      then result.ret (list_t.ListCons ret0 tl)
+      else
+        do
+          let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+          let tl0 <- list_nth_mut_back T tl i0 ret0
+          result.ret (list_t.ListCons x tl0)
+    | list_t.ListNil => result.fail error.panic
+    
+  
+  /- [paper::sum] -/
+  def sum_fwd (l : list_t Int32) : result Int32 :=
+    match l with
+    | list_t.ListCons x tl => do
+                                let i <- sum_fwd tl
+                                Int32.checked_add x i
+    | list_t.ListNil => result.ret (Int32.ofNatCore 0 (by intlit))
+    
+  
+  /- [paper::test_nth] -/
+  def test_nth_fwd : result Unit :=
+    do
+      let l := list_t.ListNil
+      let l0 := list_t.ListCons (Int32.ofNatCore 3 (by intlit)) l
+      let l1 := list_t.ListCons (Int32.ofNatCore 2 (by intlit)) l0
+      let x <-
+        list_nth_mut_fwd Int32 (list_t.ListCons (Int32.ofNatCore 1 (by intlit))
+          l1) (UInt32.ofNatCore 2 (by intlit))
+      let x0 <- Int32.checked_add x (Int32.ofNatCore 1 (by intlit))
+      let l2 <-
+        list_nth_mut_back Int32 (list_t.ListCons
+          (Int32.ofNatCore 1 (by intlit)) l1) (UInt32.ofNatCore 2 (by intlit))
+          x0
+      let i <- sum_fwd l2
+      if not (i = (Int32.ofNatCore 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 : (UInt32 × UInt32)) : result UInt32 :=
+    do
+      let (px, py) := p
+      let pz <- choose_fwd UInt32 true px py
+      let pz0 <- UInt32.checked_add pz (UInt32.ofNatCore 1 (by intlit))
+      let (px0, _) <- choose_back UInt32 true px py pz0
+      result.ret px0
+