Merge pull request #31 from AeneasVerif/son_lean_backend

Improve the Lean backend

38 files changed, 5 insertions, 5803 deletions

diff --git a/tests/lean/misc-external/External.lean b/tests/lean/External.lean
index b95db309..b95db309 100644
--- a/tests/lean/misc-external/External.lean
+++ b/tests/lean/External.lean
diff --git a/tests/lean/misc-external/External/Types.lean b/tests/lean/External/Types.lean
index ed1842be..ba984e2a 100644
--- a/tests/lean/misc-external/External/Types.lean
+++ b/tests/lean/External/Types.lean
@@ -1,10 +1,13 @@
 -- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
 -- [external]: type definitions
-import Base.Primitives
+import Base
+open Primitives
+namespace external
 
 /- [core::num::nonzero::NonZeroU32] -/
-axiom core_num_nonzero_non_zero_u32_t : Type
+axiom core.num.nonzero.NonZeroU32 : Type
 
 /- The state type used in the state-error monad -/
 axiom State : Type
 
+end external
diff --git a/tests/lean/misc-loops/Loops.lean b/tests/lean/Loops.lean
index 60c73776..60c73776 100644
--- a/tests/lean/misc-loops/Loops.lean
+++ b/tests/lean/Loops.lean
diff --git a/tests/lean/misc-constants/Base/Primitives.lean b/tests/lean/misc-constants/Base/Primitives.lean
deleted file mode 100644
index 4a66a453..00000000
--- a/tests/lean/misc-constants/Base/Primitives.lean
+++ /dev/null
@@ -1,583 +0,0 @@
-import Lean
-import Lean.Meta.Tactic.Simp
-import Init.Data.List.Basic
-import Mathlib.Tactic.RunCmd
-
---------------------
--- ASSERT COMMAND --
---------------------
-
-open Lean Elab Command Term Meta
-
-syntax (name := assert) "#assert" term: command
-
-@[command_elab assert]
-unsafe
-def assertImpl : CommandElab := fun (_stx: Syntax) => do
-  runTermElabM (fun _ => do
-    let r ← evalTerm Bool (mkConst ``Bool) _stx[1]
-    if not r then
-      logInfo "Assertion failed for: "
-      logInfo _stx[1]
-      logError "Expression reduced to false"
-    pure ())
-
-#eval 2 == 2
-#assert (2 == 2)
-
--------------
--- PRELUDE --
--------------
-
--- Results & monadic combinators
-
-inductive Error where
-   | assertionFailure: Error
-   | integerOverflow: Error
-   | divisionByZero: Error
-   | arrayOutOfBounds: Error
-   | maximumSizeExceeded: Error
-   | panic: Error
-deriving Repr, BEq
-
-open Error
-
-inductive Result (α : Type u) where
-  | ret (v: α): Result α
-  | fail (e: Error): Result α
-deriving Repr, BEq
-
-open Result
-
-instance Result_Inhabited (α : Type u) : Inhabited (Result α) :=
-  Inhabited.mk (fail panic)
-
-/- HELPERS -/
-
-def ret? {α: Type} (r: Result α): Bool :=
-  match r with
-  | Result.ret _ => true
-  | Result.fail _ => false
-
-def massert (b:Bool) : Result Unit :=
-  if b then .ret () else fail assertionFailure
-
-def eval_global {α: Type} (x: Result α) (_: ret? x): α :=
-  match x with
-  | Result.fail _ => by contradiction
-  | Result.ret x => x
-
-/- DO-DSL SUPPORT -/
-
-def bind (x: Result α) (f: α -> Result β) : Result β :=
-  match x with
-  | ret v  => f v 
-  | fail v => fail v
-
--- Allows using Result in do-blocks
-instance : Bind Result where
-  bind := bind
-
--- Allows using return x in do-blocks
-instance : Pure Result where
-  pure := fun x => ret x
-
-/- CUSTOM-DSL SUPPORT -/
-
--- Let-binding the Result of a monadic operation is oftentimes not sufficient,
--- because we may need a hypothesis for equational reasoning in the scope. We
--- rely on subtype, and a custom let-binding operator, in effect recreating our
--- own variant of the do-dsl
-
-def Result.attach {α: Type} (o : Result α): Result { x : α // o = ret x } :=
-  match o with
-  | .ret x => .ret ⟨x, rfl⟩
-  | .fail e => .fail e
-
-macro "let" e:term " ⟵ " f:term : doElem =>
-  `(doElem| let ⟨$e, h⟩ ← Result.attach $f)
-
--- TODO: any way to factorize both definitions?
-macro "let" e:term " <-- " f:term : doElem =>
-  `(doElem| let ⟨$e, h⟩ ← Result.attach $f)
-
--- We call the hypothesis `h`, in effect making it unavailable to the user
--- (because too much shadowing). But in practice, once can use the French single
--- quote notation (input with f< and f>), where `‹ h ›` finds a suitable
--- hypothesis in the context, this is equivalent to `have x: h := by assumption in x`
-#eval do
-  let y <-- .ret (0: Nat)
-  let _: y = 0 := by cases ‹ ret 0 = ret y › ; decide
-  let r: { x: Nat // x = 0 } := ⟨ y, by assumption ⟩
-  .ret r
-
-----------------------
--- MACHINE INTEGERS --
-----------------------
-
--- We redefine our machine integers types.
-
--- For Isize/Usize, we reuse `getNumBits` from `USize`. You cannot reduce `getNumBits`
--- using the simplifier, meaning that proofs do not depend on the compile-time value of
--- USize.size. (Lean assumes 32 or 64-bit platforms, and Rust doesn't really support, at
--- least officially, 16-bit microcontrollers, so this seems like a fine design decision
--- for now.)
-
--- Note from Chris Bailey: "If there's more than one salient property of your
--- definition then the subtyping strategy might get messy, and the property part
--- of a subtype is less discoverable by the simplifier or tactics like
--- library_search." So, we will not add refinements on the return values of the
--- operations defined on Primitives, but will rather rely on custom lemmas to
--- invert on possible return values of the primitive operations.
-
--- Machine integer constants, done via `ofNatCore`, which requires a proof that
--- the `Nat` fits within the desired integer type. We provide a custom tactic.
-
-open System.Platform.getNumBits
-
--- TODO: is there a way of only importing System.Platform.getNumBits?
---
-@[simp] def size_num_bits : Nat := (System.Platform.getNumBits ()).val
-
--- Remark: Lean seems to use < for the comparisons with the upper bounds by convention.
--- We keep the F* convention for now.
-@[simp] def Isize.min : Int := - (HPow.hPow 2 (size_num_bits - 1))
-@[simp] def Isize.max : Int := (HPow.hPow 2 (size_num_bits - 1)) - 1
-@[simp] def I8.min    : Int := - (HPow.hPow 2 7)
-@[simp] def I8.max    : Int := HPow.hPow 2 7 - 1
-@[simp] def I16.min   : Int := - (HPow.hPow 2 15)
-@[simp] def I16.max   : Int := HPow.hPow 2 15 - 1
-@[simp] def I32.min   : Int := -(HPow.hPow 2 31)
-@[simp] def I32.max   : Int := HPow.hPow 2 31 - 1
-@[simp] def I64.min   : Int := -(HPow.hPow 2 63)
-@[simp] def I64.max   : Int := HPow.hPow 2 63 - 1
-@[simp] def I128.min  : Int := -(HPow.hPow 2 127)
-@[simp] def I128.max  : Int := HPow.hPow 2 127 - 1
-@[simp] def Usize.min : Int := 0
-@[simp] def Usize.max : Int := HPow.hPow 2 size_num_bits - 1
-@[simp] def U8.min    : Int := 0
-@[simp] def U8.max    : Int := HPow.hPow 2 8 - 1
-@[simp] def U16.min   : Int := 0
-@[simp] def U16.max   : Int := HPow.hPow 2 16 - 1
-@[simp] def U32.min   : Int := 0
-@[simp] def U32.max   : Int := HPow.hPow 2 32 - 1
-@[simp] def U64.min   : Int := 0
-@[simp] def U64.max   : Int := HPow.hPow 2 64 - 1
-@[simp] def U128.min  : Int := 0
-@[simp] def U128.max  : Int := HPow.hPow 2 128 - 1
-
-#assert (I8.min   == -128)
-#assert (I8.max   == 127)
-#assert (I16.min  == -32768)
-#assert (I16.max  == 32767)
-#assert (I32.min  == -2147483648)
-#assert (I32.max  == 2147483647)
-#assert (I64.min  == -9223372036854775808)
-#assert (I64.max  == 9223372036854775807)
-#assert (I128.min == -170141183460469231731687303715884105728)
-#assert (I128.max == 170141183460469231731687303715884105727)
-#assert (U8.min   == 0)
-#assert (U8.max   == 255)
-#assert (U16.min  == 0)
-#assert (U16.max  == 65535)
-#assert (U32.min  == 0)
-#assert (U32.max  == 4294967295)
-#assert (U64.min  == 0)
-#assert (U64.max  == 18446744073709551615)
-#assert (U128.min == 0)
-#assert (U128.max == 340282366920938463463374607431768211455)
-
-inductive ScalarTy :=
-| Isize
-| I8
-| I16
-| I32
-| I64
-| I128
-| Usize
-| U8
-| U16
-| U32
-| U64
-| U128
-
-def Scalar.min (ty : ScalarTy) : Int :=
-  match ty with
-  | .Isize => Isize.min
-  | .I8    => I8.min
-  | .I16   => I16.min
-  | .I32   => I32.min
-  | .I64   => I64.min
-  | .I128  => I128.min
-  | .Usize => Usize.min
-  | .U8    => U8.min
-  | .U16   => U16.min
-  | .U32   => U32.min
-  | .U64   => U64.min
-  | .U128  => U128.min
-
-def Scalar.max (ty : ScalarTy) : Int :=
-  match ty with
-  | .Isize => Isize.max
-  | .I8    => I8.max
-  | .I16   => I16.max
-  | .I32   => I32.max
-  | .I64   => I64.max
-  | .I128  => I128.max
-  | .Usize => Usize.max
-  | .U8    => U8.max
-  | .U16   => U16.max
-  | .U32   => U32.max
-  | .U64   => U64.max
-  | .U128  => U128.max
-
--- "Conservative" bounds
--- We use those because we can't compare to the isize bounds (which can't
--- reduce at compile-time). Whenever we perform an arithmetic operation like
--- addition we need to check that the result is in bounds: we first compare
--- to the conservative bounds, which reduce, then compare to the real bounds.
--- This is useful for the various #asserts that we want to reduce at
--- type-checking time.
-def Scalar.cMin (ty : ScalarTy) : Int :=
-  match ty with
-  | .Isize => I32.min
-  | _ => Scalar.min ty
-
-def Scalar.cMax (ty : ScalarTy) : Int :=
-  match ty with
-  | .Isize => I32.max
-  | .Usize => U32.max
-  | _ => Scalar.max ty
-
-theorem Scalar.cMin_bound ty : Scalar.min ty <= Scalar.cMin ty := by sorry
-theorem Scalar.cMax_bound ty : Scalar.min ty <= Scalar.cMin ty := by sorry
-
-structure Scalar (ty : ScalarTy) where
-  val : Int
-  hmin : Scalar.min ty <= val
-  hmax : val <= Scalar.max ty
-
-theorem Scalar.bound_suffices (ty : ScalarTy) (x : Int) :
-  Scalar.cMin ty <= x && x <= Scalar.cMax ty ->
-  (decide (Scalar.min ty ≤ x) && decide (x ≤ Scalar.max ty)) = true
-  := by sorry
-
-def Scalar.ofIntCore {ty : ScalarTy} (x : Int)
-  (hmin : Scalar.min ty <= x) (hmax : x <= Scalar.max ty) : Scalar ty :=
-  { val := x, hmin := hmin, hmax := hmax }
-
-def Scalar.ofInt {ty : ScalarTy} (x : Int)
-  (h : Scalar.min ty <= x && x <= Scalar.max ty) : Scalar ty :=
-  let hmin: Scalar.min ty <= x := by sorry
-  let hmax: x <= Scalar.max ty := by sorry
-  Scalar.ofIntCore x hmin hmax
-
--- Further thoughts: look at what has been done here:
--- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/Fin/Basic.lean
--- and
--- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/UInt.lean
--- which both contain a fair amount of reasoning already!
-def Scalar.tryMk (ty : ScalarTy) (x : Int) : Result (Scalar ty) :=
-  -- TODO: write this with only one if then else
-  if hmin_cons: Scalar.cMin ty <= x || Scalar.min ty <= x then
-    if hmax_cons: x <= Scalar.cMax ty || x <= Scalar.max ty then
-      let hmin: Scalar.min ty <= x := by sorry
-      let hmax: x <= Scalar.max ty := by sorry
-      return Scalar.ofIntCore x hmin hmax
-    else fail integerOverflow
-  else fail integerOverflow
-
-def Scalar.neg {ty : ScalarTy} (x : Scalar ty) : Result (Scalar ty) := Scalar.tryMk ty (- x.val)
-
-def Scalar.div {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
-  if y.val != 0 then Scalar.tryMk ty (x.val / y.val) else fail divisionByZero
-
--- Checking that the % operation in Lean computes the same as the remainder operation in Rust
-#assert 1 % 2 = (1:Int)
-#assert (-1) % 2 = -1
-#assert 1 % (-2) = 1
-#assert (-1) % (-2) = -1
-
-def Scalar.rem {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
-  if y.val != 0 then Scalar.tryMk ty (x.val % y.val) else fail divisionByZero
-
-def Scalar.add {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
-  Scalar.tryMk ty (x.val + y.val)
-
-def Scalar.sub {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
-  Scalar.tryMk ty (x.val - y.val)
-
-def Scalar.mul {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
-  Scalar.tryMk ty (x.val * y.val)
-
--- TODO: instances of +, -, * etc. for scalars
-
--- Cast an integer from a [src_ty] to a [tgt_ty]
--- TODO: check the semantics of casts in Rust
-def Scalar.cast {src_ty : ScalarTy} (tgt_ty : ScalarTy) (x : Scalar src_ty) : Result (Scalar tgt_ty) :=
-  Scalar.tryMk tgt_ty x.val
-
--- The scalar types
--- We declare the definitions as reducible so that Lean can unfold them (useful
--- for type class resolution for instance).
-@[reducible] def Isize := Scalar .Isize
-@[reducible] def I8    := Scalar .I8
-@[reducible] def I16   := Scalar .I16
-@[reducible] def I32   := Scalar .I32
-@[reducible] def I64   := Scalar .I64
-@[reducible] def I128  := Scalar .I128
-@[reducible] def Usize := Scalar .Usize
-@[reducible] def U8    := Scalar .U8
-@[reducible] def U16   := Scalar .U16
-@[reducible] def U32   := Scalar .U32
-@[reducible] def U64   := Scalar .U64
-@[reducible] def U128  := Scalar .U128
-
--- TODO: below: not sure this is the best way.
--- Should we rather overload operations like +, -, etc.?
--- Also, it is possible to automate the generation of those definitions
--- with macros (but would it be a good idea? It would be less easy to
--- read the file, which is not supposed to change a lot)
-
--- Negation
-
-/--
-Remark: there is no heterogeneous negation in the Lean prelude: we thus introduce
-one here.
-
-The notation typeclass for heterogeneous addition.
-This enables the notation `- a : β` where `a : α`.
--/
-class HNeg (α : Type u) (β : outParam (Type v)) where
-  /-- `- a` computes the negation of `a`.
-  The meaning of this notation is type-dependent. -/
-  hNeg : α → β
-
-prefix:75  "-"   => HNeg.hNeg
-
-instance : HNeg Isize (Result Isize) where hNeg x := Scalar.neg x
-instance : HNeg I8 (Result I8) where hNeg x := Scalar.neg x
-instance : HNeg I16 (Result I16) where hNeg x := Scalar.neg x
-instance : HNeg I32 (Result I32) where hNeg x := Scalar.neg x
-instance : HNeg I64 (Result I64) where hNeg x := Scalar.neg x
-instance : HNeg I128 (Result I128) where hNeg x := Scalar.neg x
-
--- Addition
-instance {ty} : HAdd (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
-  hAdd x y := Scalar.add x y
-
--- Substraction
-instance {ty} : HSub (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
-  hSub x y := Scalar.sub x y
-
--- Multiplication
-instance {ty} : HMul (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
-  hMul x y := Scalar.mul x y
-
--- Division
-instance {ty} : HDiv (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
-  hDiv x y := Scalar.div x y
-
--- Remainder
-instance {ty} : HMod (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
-  hMod x y := Scalar.rem x y
-
--- ofIntCore
--- TODO: typeclass?
-def Isize.ofIntCore := @Scalar.ofIntCore .Isize
-def I8.ofIntCore    := @Scalar.ofIntCore .I8
-def I16.ofIntCore   := @Scalar.ofIntCore .I16
-def I32.ofIntCore   := @Scalar.ofIntCore .I32
-def I64.ofIntCore   := @Scalar.ofIntCore .I64
-def I128.ofIntCore  := @Scalar.ofIntCore .I128
-def Usize.ofIntCore := @Scalar.ofIntCore .Usize
-def U8.ofIntCore    := @Scalar.ofIntCore .U8
-def U16.ofIntCore   := @Scalar.ofIntCore .U16
-def U32.ofIntCore   := @Scalar.ofIntCore .U32
-def U64.ofIntCore   := @Scalar.ofIntCore .U64
-def U128.ofIntCore  := @Scalar.ofIntCore .U128
-
---  ofInt
--- TODO: typeclass?
-def Isize.ofInt := @Scalar.ofInt .Isize
-def I8.ofInt    := @Scalar.ofInt .I8
-def I16.ofInt   := @Scalar.ofInt .I16
-def I32.ofInt   := @Scalar.ofInt .I32
-def I64.ofInt   := @Scalar.ofInt .I64
-def I128.ofInt  := @Scalar.ofInt .I128
-def Usize.ofInt := @Scalar.ofInt .Usize
-def U8.ofInt    := @Scalar.ofInt .U8
-def U16.ofInt   := @Scalar.ofInt .U16
-def U32.ofInt   := @Scalar.ofInt .U32
-def U64.ofInt   := @Scalar.ofInt .U64
-def U128.ofInt  := @Scalar.ofInt .U128
-
--- Comparisons
-instance {ty} : LT (Scalar ty) where
-  lt a b := LT.lt a.val b.val
-
-instance {ty} : LE (Scalar ty) where le a b := LE.le a.val b.val
-
-instance Scalar.decLt {ty} (a b : Scalar ty) : Decidable (LT.lt a b) := Int.decLt ..
-instance Scalar.decLe {ty} (a b : Scalar ty) : Decidable (LE.le a b) := Int.decLe ..
-
-theorem Scalar.eq_of_val_eq {ty} : ∀ {i j : Scalar ty}, Eq i.val j.val → Eq i j
-  | ⟨_, _, _⟩, ⟨_, _, _⟩, rfl => rfl
-
-theorem Scalar.val_eq_of_eq {ty} {i j : Scalar ty} (h : Eq i j) : Eq i.val j.val :=
-  h ▸ rfl
-
-theorem Scalar.ne_of_val_ne {ty} {i j : Scalar ty} (h : Not (Eq i.val j.val)) : Not (Eq i j) :=
-  fun h' => absurd (val_eq_of_eq h') h
-
-instance (ty : ScalarTy) : DecidableEq (Scalar ty) :=
-  fun i j =>
-    match decEq i.val j.val with
-    | isTrue h  => isTrue (Scalar.eq_of_val_eq h)
-    | isFalse h => isFalse (Scalar.ne_of_val_ne h)
-
-def Scalar.toInt {ty} (n : Scalar ty) : Int := n.val
-
--- Tactic to prove that integers are in bounds
-syntax "intlit" : tactic
-
-macro_rules
-  | `(tactic| intlit) => `(tactic| apply Scalar.bound_suffices ; decide)
-
--- -- We now define a type class that subsumes the various machine integer types, so
--- -- as to write a concise definition for scalar_cast, rather than exhaustively
--- -- enumerating all of the possible pairs. We remark that Rust has sane semantics
--- -- and fails if a cast operation would involve a truncation or modulo.
-
--- class MachineInteger (t: Type) where
---   size: Nat
---   val: t -> Fin size
---   ofNatCore: (n:Nat) -> LT.lt n size -> t
-
--- set_option hygiene false in
--- run_cmd
---   for typeName in [`UInt8, `UInt16, `UInt32, `UInt64, `USize].map Lean.mkIdent do
---   Lean.Elab.Command.elabCommand (← `(
---     namespace $typeName
---     instance: MachineInteger $typeName where
---       size := size
---       val := val
---       ofNatCore := ofNatCore
---     end $typeName
---   ))
-
--- -- Aeneas only instantiates the destination type (`src` is implicit). We rely on
--- -- Lean to infer `src`.
-
--- def scalar_cast { src: Type } (dst: Type) [ MachineInteger src ] [ MachineInteger dst ] (x: src): Result dst :=
---   if h: MachineInteger.val x < MachineInteger.size dst then
---     .ret (MachineInteger.ofNatCore (MachineInteger.val x).val h)
---   else
---     .fail integerOverflow
-
--------------
--- VECTORS --
--------------
-
-def Vec (α : Type u) := { l : List α // List.length l <= Usize.max }
-
-def vec_new (α : Type u): Vec α := ⟨ [], by sorry ⟩
-
-def vec_len (α : Type u) (v : Vec α) : Usize :=
-  let ⟨ v, l ⟩ := v
-  Usize.ofIntCore (List.length v) (by sorry) l
- 
-def vec_push_fwd (α : Type u) (_ : Vec α) (_ : α) : Unit := ()
-
-def vec_push_back (α : Type u) (v : Vec α) (x : α) : Result (Vec α)
-  :=
-  if h : List.length v.val <= U32.max || List.length v.val <= Usize.max then
-    return ⟨ List.concat v.val x, by sorry ⟩
-  else
-    fail maximumSizeExceeded
-
-def vec_insert_fwd (α : Type u) (v: Vec α) (i: Usize) (_: α): Result Unit :=
-  if i.val < List.length v.val then
-    .ret ()
-  else
-    .fail arrayOutOfBounds
-
-def vec_insert_back (α : Type u) (v: Vec α) (i: Usize) (x: α): Result (Vec α) :=
-  if i.val < List.length v.val then
-    -- TODO: maybe we should redefine a list library which uses integers
-    -- (instead of natural numbers)
-    let i : Nat :=
-      match i.val with
-      | .ofNat n => n
-      | .negSucc n => by sorry -- TODO: we can't get here
-    let isLt: i < USize.size := by sorry
-    let i : Fin USize.size := { val := i, isLt := isLt }
-    .ret ⟨ List.set v.val i.val x, by
-      have h: List.length v.val <= Usize.max := v.property
-      rewrite [ List.length_set v.val i.val x ]
-      assumption
-    ⟩
-  else
-    .fail arrayOutOfBounds
-
-def vec_index_fwd (α : Type u) (v: Vec α) (i: Usize): Result α :=
-  if i.val < List.length v.val then
-    let i : Nat :=
-      match i.val with
-      | .ofNat n => n
-      | .negSucc n => by sorry -- TODO: we can't get here
-    let isLt: i < USize.size := by sorry
-    let i : Fin USize.size := { val := i, isLt := isLt }
-    let h: i < List.length v.val := by sorry
-    .ret (List.get v.val ⟨i.val, h⟩)
-  else
-    .fail arrayOutOfBounds
-
-def vec_index_back (α : Type u) (v: Vec α) (i: Usize) (_: α): Result Unit :=
-  if i.val < List.length v.val then
-    .ret ()
-  else
-    .fail arrayOutOfBounds
-
-def vec_index_mut_fwd (α : Type u) (v: Vec α) (i: Usize): Result α :=
-  if i.val < List.length v.val then
-    let i : Nat :=
-      match i.val with
-      | .ofNat n => n
-      | .negSucc n => by sorry -- TODO: we can't get here
-    let isLt: i < USize.size := by sorry
-    let i : Fin USize.size := { val := i, isLt := isLt }
-    let h: i < List.length v.val := by sorry
-    .ret (List.get v.val ⟨i.val, h⟩)
-  else
-    .fail arrayOutOfBounds
-
-def vec_index_mut_back (α : Type u) (v: Vec α) (i: Usize) (x: α): Result (Vec α) :=
-  if i.val < List.length v.val then
-    let i : Nat :=
-      match i.val with
-      | .ofNat n => n
-      | .negSucc n => by sorry -- TODO: we can't get here
-    let isLt: i < USize.size := by sorry
-    let i : Fin USize.size := { val := i, isLt := isLt }
-    .ret ⟨ List.set v.val i.val x, by
-      have h: List.length v.val <= Usize.max := v.property
-      rewrite [ List.length_set v.val i.val x ]
-      assumption
-    ⟩
-  else
-    .fail arrayOutOfBounds
-
-----------
--- MISC --
-----------
-
-def mem_replace_fwd (a : Type) (x : a) (_ : a) : a :=
-  x
-
-def mem_replace_back (a : Type) (_ : a) (y : a) : a :=
-  y
-
-/-- Aeneas-translated function -- useful to reduce non-recursive definitions.
- Use with `simp [ aeneas ]` -/
-register_simp_attr aeneas
diff --git a/tests/lean/misc-constants/Constants.lean b/tests/lean/misc-constants/Constants.lean
deleted file mode 100644
index 8306ed85..00000000
--- a/tests/lean/misc-constants/Constants.lean
+++ /dev/null
@@ -1,131 +0,0 @@
--- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
--- [constants]
-import Base.Primitives
-
-/- [constants::X0] -/
-def x0_body : Result U32 := Result.ret (U32.ofInt 0 (by intlit))
-def x0_c : U32 := eval_global x0_body (by simp)
-
-/- [core::num::u32::{9}::MAX] -/
-def core_num_u32_max_body : Result U32 :=
-  Result.ret (U32.ofInt 4294967295 (by intlit))
-def core_num_u32_max_c : U32 := eval_global core_num_u32_max_body (by simp)
-
-/- [constants::X1] -/
-def x1_body : Result U32 := Result.ret core_num_u32_max_c
-def x1_c : U32 := eval_global x1_body (by simp)
-
-/- [constants::X2] -/
-def x2_body : Result U32 := Result.ret (U32.ofInt 3 (by intlit))
-def x2_c : U32 := eval_global x2_body (by simp)
-
-/- [constants::incr] -/
-def incr_fwd (n : U32) : Result U32 :=
-  n + (U32.ofInt 1 (by intlit))
-
-/- [constants::X3] -/
-def x3_body : Result U32 := incr_fwd (U32.ofInt 32 (by intlit))
-def x3_c : U32 := eval_global x3_body (by simp)
-
-/- [constants::mk_pair0] -/
-def mk_pair0_fwd (x : U32) (y : U32) : Result (U32 × U32) :=
-  Result.ret (x, y)
-
-/- [constants::Pair] -/
-structure pair_t (T1 T2 : Type) where
-  pair_x : T1
-  pair_y : T2
-
-/- [constants::mk_pair1] -/
-def mk_pair1_fwd (x : U32) (y : U32) : Result (pair_t U32 U32) :=
-  Result.ret { pair_x := x, pair_y := y }
-
-/- [constants::P0] -/
-def p0_body : Result (U32 × U32) :=
-  mk_pair0_fwd (U32.ofInt 0 (by intlit)) (U32.ofInt 1 (by intlit))
-def p0_c : (U32 × U32) := eval_global p0_body (by simp)
-
-/- [constants::P1] -/
-def p1_body : Result (pair_t U32 U32) :=
-  mk_pair1_fwd (U32.ofInt 0 (by intlit)) (U32.ofInt 1 (by intlit))
-def p1_c : pair_t U32 U32 := eval_global p1_body (by simp)
-
-/- [constants::P2] -/
-def p2_body : Result (U32 × U32) :=
-  Result.ret ((U32.ofInt 0 (by intlit)), (U32.ofInt 1 (by intlit)))
-def p2_c : (U32 × U32) := eval_global p2_body (by simp)
-
-/- [constants::P3] -/
-def p3_body : Result (pair_t U32 U32) :=
-  Result.ret
-  { pair_x := (U32.ofInt 0 (by intlit)), pair_y := (U32.ofInt 1 (by intlit)) }
-def p3_c : pair_t U32 U32 := eval_global p3_body (by simp)
-
-/- [constants::Wrap] -/
-structure wrap_t (T : Type) where
-  wrap_val : T
-
-/- [constants::Wrap::{0}::new] -/
-def wrap_new_fwd (T : Type) (val : T) : Result (wrap_t T) :=
-  Result.ret { wrap_val := val }
-
-/- [constants::Y] -/
-def y_body : Result (wrap_t I32) := wrap_new_fwd I32 (I32.ofInt 2 (by intlit))
-def y_c : wrap_t I32 := eval_global y_body (by simp)
-
-/- [constants::unwrap_y] -/
-def unwrap_y_fwd : Result I32 :=
-  Result.ret y_c.wrap_val
-
-/- [constants::YVAL] -/
-def yval_body : Result I32 := unwrap_y_fwd
-def yval_c : I32 := eval_global yval_body (by simp)
-
-/- [constants::get_z1::Z1] -/
-def get_z1_z1_body : Result I32 := Result.ret (I32.ofInt 3 (by intlit))
-def get_z1_z1_c : I32 := eval_global get_z1_z1_body (by simp)
-
-/- [constants::get_z1] -/
-def get_z1_fwd : Result I32 :=
-  Result.ret get_z1_z1_c
-
-/- [constants::add] -/
-def add_fwd (a : I32) (b : I32) : Result I32 :=
-  a + b
-
-/- [constants::Q1] -/
-def q1_body : Result I32 := Result.ret (I32.ofInt 5 (by intlit))
-def q1_c : I32 := eval_global q1_body (by simp)
-
-/- [constants::Q2] -/
-def q2_body : Result I32 := Result.ret q1_c
-def q2_c : I32 := eval_global q2_body (by simp)
-
-/- [constants::Q3] -/
-def q3_body : Result I32 := add_fwd q2_c (I32.ofInt 3 (by intlit))
-def q3_c : I32 := eval_global q3_body (by simp)
-
-/- [constants::get_z2] -/
-def get_z2_fwd : Result I32 :=
-  do
-    let i ← get_z1_fwd
-    let i0 ← add_fwd i q3_c
-    add_fwd q1_c i0
-
-/- [constants::S1] -/
-def s1_body : Result U32 := Result.ret (U32.ofInt 6 (by intlit))
-def s1_c : U32 := eval_global s1_body (by simp)
-
-/- [constants::S2] -/
-def s2_body : Result U32 := incr_fwd s1_c
-def s2_c : U32 := eval_global s2_body (by simp)
-
-/- [constants::S3] -/
-def s3_body : Result (pair_t U32 U32) := Result.ret p3_c
-def s3_c : pair_t U32 U32 := eval_global s3_body (by simp)
-
-/- [constants::S4] -/
-def s4_body : Result (pair_t U32 U32) :=
-  mk_pair1_fwd (U32.ofInt 7 (by intlit)) (U32.ofInt 8 (by intlit))
-def s4_c : pair_t U32 U32 := eval_global s4_body (by simp)
-
diff --git a/tests/lean/misc-constants/lake-manifest.json b/tests/lean/misc-constants/lake-manifest.json
deleted file mode 100644
index 57b071ca..00000000
--- a/tests/lean/misc-constants/lake-manifest.json
+++ /dev/null
@@ -1,27 +0,0 @@
-{"version": 4,
- "packagesDir": "./lake-packages",
- "packages":
- [{"git":
-   {"url": "https://github.com/leanprover-community/mathlib4.git",
-    "subDir?": null,
-    "rev": "4037792ead804d7bfa8868e2c4684d4223c15ece",
-    "name": "mathlib",
-    "inputRev?": null}},
-  {"git":
-   {"url": "https://github.com/gebner/quote4",
-    "subDir?": null,
-    "rev": "2412c4fdf4a8b689f4467618e5e7b371ae5014aa",
-    "name": "Qq",
-    "inputRev?": "master"}},
-  {"git":
-   {"url": "https://github.com/JLimperg/aesop",
-    "subDir?": null,
-    "rev": "7fe9ecd9339b0e1796e89d243b776849c305c690",
-    "name": "aesop",
-    "inputRev?": "master"}},
-  {"git":
-   {"url": "https://github.com/leanprover/std4",
-    "subDir?": null,
-    "rev": "24897887905b3a1254b244369f5dd2cf6174b0ee",
-    "name": "std",
-    "inputRev?": "main"}}]}
diff --git a/tests/lean/misc-constants/lakefile.lean b/tests/lean/misc-constants/lakefile.lean
deleted file mode 100644
index 01aacb90..00000000
--- a/tests/lean/misc-constants/lakefile.lean
+++ /dev/null
@@ -1,12 +0,0 @@
-import Lake
-open Lake DSL
-
-require mathlib from git
-  "https://github.com/leanprover-community/mathlib4.git"
-
-package «constants» {}
-
-lean_lib «Base» {}
-
-@[default_target]
-lean_lib «Constants» {}
diff --git a/tests/lean/misc-constants/lean-toolchain b/tests/lean/misc-constants/lean-toolchain
deleted file mode 100644
index bbf57f10..00000000
--- a/tests/lean/misc-constants/lean-toolchain
+++ /dev/null
@@ -1 +0,0 @@
-leanprover/lean4:nightly-2023-01-21
diff --git a/tests/lean/misc-external/Base/Primitives.lean b/tests/lean/misc-external/Base/Primitives.lean
deleted file mode 100644
index 4a66a453..00000000
--- a/tests/lean/misc-external/Base/Primitives.lean
+++ /dev/null
@@ -1,583 +0,0 @@
-import Lean
-import Lean.Meta.Tactic.Simp
-import Init.Data.List.Basic
-import Mathlib.Tactic.RunCmd
-
---------------------
--- ASSERT COMMAND --
---------------------
-
-open Lean Elab Command Term Meta
-
-syntax (name := assert) "#assert" term: command
-
-@[command_elab assert]
-unsafe
-def assertImpl : CommandElab := fun (_stx: Syntax) => do
-  runTermElabM (fun _ => do
-    let r ← evalTerm Bool (mkConst ``Bool) _stx[1]
-    if not r then
-      logInfo "Assertion failed for: "
-      logInfo _stx[1]
-      logError "Expression reduced to false"
-    pure ())
-
-#eval 2 == 2
-#assert (2 == 2)
-
--------------
--- PRELUDE --
--------------
-
--- Results & monadic combinators
-
-inductive Error where
-   | assertionFailure: Error
-   | integerOverflow: Error
-   | divisionByZero: Error
-   | arrayOutOfBounds: Error
-   | maximumSizeExceeded: Error
-   | panic: Error
-deriving Repr, BEq
-
-open Error
-
-inductive Result (α : Type u) where
-  | ret (v: α): Result α
-  | fail (e: Error): Result α
-deriving Repr, BEq
-
-open Result
-
-instance Result_Inhabited (α : Type u) : Inhabited (Result α) :=
-  Inhabited.mk (fail panic)
-
-/- HELPERS -/
-
-def ret? {α: Type} (r: Result α): Bool :=
-  match r with
-  | Result.ret _ => true
-  | Result.fail _ => false
-
-def massert (b:Bool) : Result Unit :=
-  if b then .ret () else fail assertionFailure
-
-def eval_global {α: Type} (x: Result α) (_: ret? x): α :=
-  match x with
-  | Result.fail _ => by contradiction
-  | Result.ret x => x
-
-/- DO-DSL SUPPORT -/
-
-def bind (x: Result α) (f: α -> Result β) : Result β :=
-  match x with
-  | ret v  => f v 
-  | fail v => fail v
-
--- Allows using Result in do-blocks
-instance : Bind Result where
-  bind := bind
-
--- Allows using return x in do-blocks
-instance : Pure Result where
-  pure := fun x => ret x
-
-/- CUSTOM-DSL SUPPORT -/
-
--- Let-binding the Result of a monadic operation is oftentimes not sufficient,
--- because we may need a hypothesis for equational reasoning in the scope. We
--- rely on subtype, and a custom let-binding operator, in effect recreating our
--- own variant of the do-dsl
-
-def Result.attach {α: Type} (o : Result α): Result { x : α // o = ret x } :=
-  match o with
-  | .ret x => .ret ⟨x, rfl⟩
-  | .fail e => .fail e
-
-macro "let" e:term " ⟵ " f:term : doElem =>
-  `(doElem| let ⟨$e, h⟩ ← Result.attach $f)
-
--- TODO: any way to factorize both definitions?
-macro "let" e:term " <-- " f:term : doElem =>
-  `(doElem| let ⟨$e, h⟩ ← Result.attach $f)
-
--- We call the hypothesis `h`, in effect making it unavailable to the user
--- (because too much shadowing). But in practice, once can use the French single
--- quote notation (input with f< and f>), where `‹ h ›` finds a suitable
--- hypothesis in the context, this is equivalent to `have x: h := by assumption in x`
-#eval do
-  let y <-- .ret (0: Nat)
-  let _: y = 0 := by cases ‹ ret 0 = ret y › ; decide
-  let r: { x: Nat // x = 0 } := ⟨ y, by assumption ⟩
-  .ret r
-
-----------------------
--- MACHINE INTEGERS --
-----------------------
-
--- We redefine our machine integers types.
-
--- For Isize/Usize, we reuse `getNumBits` from `USize`. You cannot reduce `getNumBits`
--- using the simplifier, meaning that proofs do not depend on the compile-time value of
--- USize.size. (Lean assumes 32 or 64-bit platforms, and Rust doesn't really support, at
--- least officially, 16-bit microcontrollers, so this seems like a fine design decision
--- for now.)
-
--- Note from Chris Bailey: "If there's more than one salient property of your
--- definition then the subtyping strategy might get messy, and the property part
--- of a subtype is less discoverable by the simplifier or tactics like
--- library_search." So, we will not add refinements on the return values of the
--- operations defined on Primitives, but will rather rely on custom lemmas to
--- invert on possible return values of the primitive operations.
-
--- Machine integer constants, done via `ofNatCore`, which requires a proof that
--- the `Nat` fits within the desired integer type. We provide a custom tactic.
-
-open System.Platform.getNumBits
-
--- TODO: is there a way of only importing System.Platform.getNumBits?
---
-@[simp] def size_num_bits : Nat := (System.Platform.getNumBits ()).val
-
--- Remark: Lean seems to use < for the comparisons with the upper bounds by convention.
--- We keep the F* convention for now.
-@[simp] def Isize.min : Int := - (HPow.hPow 2 (size_num_bits - 1))
-@[simp] def Isize.max : Int := (HPow.hPow 2 (size_num_bits - 1)) - 1
-@[simp] def I8.min    : Int := - (HPow.hPow 2 7)
-@[simp] def I8.max    : Int := HPow.hPow 2 7 - 1
-@[simp] def I16.min   : Int := - (HPow.hPow 2 15)
-@[simp] def I16.max   : Int := HPow.hPow 2 15 - 1
-@[simp] def I32.min   : Int := -(HPow.hPow 2 31)
-@[simp] def I32.max   : Int := HPow.hPow 2 31 - 1
-@[simp] def I64.min   : Int := -(HPow.hPow 2 63)
-@[simp] def I64.max   : Int := HPow.hPow 2 63 - 1
-@[simp] def I128.min  : Int := -(HPow.hPow 2 127)
-@[simp] def I128.max  : Int := HPow.hPow 2 127 - 1
-@[simp] def Usize.min : Int := 0
-@[simp] def Usize.max : Int := HPow.hPow 2 size_num_bits - 1
-@[simp] def U8.min    : Int := 0
-@[simp] def U8.max    : Int := HPow.hPow 2 8 - 1
-@[simp] def U16.min   : Int := 0
-@[simp] def U16.max   : Int := HPow.hPow 2 16 - 1
-@[simp] def U32.min   : Int := 0
-@[simp] def U32.max   : Int := HPow.hPow 2 32 - 1
-@[simp] def U64.min   : Int := 0
-@[simp] def U64.max   : Int := HPow.hPow 2 64 - 1
-@[simp] def U128.min  : Int := 0
-@[simp] def U128.max  : Int := HPow.hPow 2 128 - 1
-
-#assert (I8.min   == -128)
-#assert (I8.max   == 127)
-#assert (I16.min  == -32768)
-#assert (I16.max  == 32767)
-#assert (I32.min  == -2147483648)
-#assert (I32.max  == 2147483647)
-#assert (I64.min  == -9223372036854775808)
-#assert (I64.max  == 9223372036854775807)
-#assert (I128.min == -170141183460469231731687303715884105728)
-#assert (I128.max == 170141183460469231731687303715884105727)
-#assert (U8.min   == 0)
-#assert (U8.max   == 255)
-#assert (U16.min  == 0)
-#assert (U16.max  == 65535)
-#assert (U32.min  == 0)
-#assert (U32.max  == 4294967295)
-#assert (U64.min  == 0)
-#assert (U64.max  == 18446744073709551615)
-#assert (U128.min == 0)
-#assert (U128.max == 340282366920938463463374607431768211455)
-
-inductive ScalarTy :=
-| Isize
-| I8
-| I16
-| I32
-| I64
-| I128
-| Usize
-| U8
-| U16
-| U32
-| U64
-| U128
-
-def Scalar.min (ty : ScalarTy) : Int :=
-  match ty with
-  | .Isize => Isize.min
-  | .I8    => I8.min
-  | .I16   => I16.min
-  | .I32   => I32.min
-  | .I64   => I64.min
-  | .I128  => I128.min
-  | .Usize => Usize.min
-  | .U8    => U8.min
-  | .U16   => U16.min
-  | .U32   => U32.min
-  | .U64   => U64.min
-  | .U128  => U128.min
-
-def Scalar.max (ty : ScalarTy) : Int :=
-  match ty with
-  | .Isize => Isize.max
-  | .I8    => I8.max
-  | .I16   => I16.max
-  | .I32   => I32.max
-  | .I64   => I64.max
-  | .I128  => I128.max
-  | .Usize => Usize.max
-  | .U8    => U8.max
-  | .U16   => U16.max
-  | .U32   => U32.max
-  | .U64   => U64.max
-  | .U128  => U128.max
-
--- "Conservative" bounds
--- We use those because we can't compare to the isize bounds (which can't
--- reduce at compile-time). Whenever we perform an arithmetic operation like
--- addition we need to check that the result is in bounds: we first compare
--- to the conservative bounds, which reduce, then compare to the real bounds.
--- This is useful for the various #asserts that we want to reduce at
--- type-checking time.
-def Scalar.cMin (ty : ScalarTy) : Int :=
-  match ty with
-  | .Isize => I32.min
-  | _ => Scalar.min ty
-
-def Scalar.cMax (ty : ScalarTy) : Int :=
-  match ty with
-  | .Isize => I32.max
-  | .Usize => U32.max
-  | _ => Scalar.max ty
-
-theorem Scalar.cMin_bound ty : Scalar.min ty <= Scalar.cMin ty := by sorry
-theorem Scalar.cMax_bound ty : Scalar.min ty <= Scalar.cMin ty := by sorry
-
-structure Scalar (ty : ScalarTy) where
-  val : Int
-  hmin : Scalar.min ty <= val
-  hmax : val <= Scalar.max ty
-
-theorem Scalar.bound_suffices (ty : ScalarTy) (x : Int) :
-  Scalar.cMin ty <= x && x <= Scalar.cMax ty ->
-  (decide (Scalar.min ty ≤ x) && decide (x ≤ Scalar.max ty)) = true
-  := by sorry
-
-def Scalar.ofIntCore {ty : ScalarTy} (x : Int)
-  (hmin : Scalar.min ty <= x) (hmax : x <= Scalar.max ty) : Scalar ty :=
-  { val := x, hmin := hmin, hmax := hmax }
-
-def Scalar.ofInt {ty : ScalarTy} (x : Int)
-  (h : Scalar.min ty <= x && x <= Scalar.max ty) : Scalar ty :=
-  let hmin: Scalar.min ty <= x := by sorry
-  let hmax: x <= Scalar.max ty := by sorry
-  Scalar.ofIntCore x hmin hmax
-
--- Further thoughts: look at what has been done here:
--- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/Fin/Basic.lean
--- and
--- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/UInt.lean
--- which both contain a fair amount of reasoning already!
-def Scalar.tryMk (ty : ScalarTy) (x : Int) : Result (Scalar ty) :=
-  -- TODO: write this with only one if then else
-  if hmin_cons: Scalar.cMin ty <= x || Scalar.min ty <= x then
-    if hmax_cons: x <= Scalar.cMax ty || x <= Scalar.max ty then
-      let hmin: Scalar.min ty <= x := by sorry
-      let hmax: x <= Scalar.max ty := by sorry
-      return Scalar.ofIntCore x hmin hmax
-    else fail integerOverflow
-  else fail integerOverflow
-
-def Scalar.neg {ty : ScalarTy} (x : Scalar ty) : Result (Scalar ty) := Scalar.tryMk ty (- x.val)
-
-def Scalar.div {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
-  if y.val != 0 then Scalar.tryMk ty (x.val / y.val) else fail divisionByZero
-
--- Checking that the % operation in Lean computes the same as the remainder operation in Rust
-#assert 1 % 2 = (1:Int)
-#assert (-1) % 2 = -1
-#assert 1 % (-2) = 1
-#assert (-1) % (-2) = -1
-
-def Scalar.rem {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
-  if y.val != 0 then Scalar.tryMk ty (x.val % y.val) else fail divisionByZero
-
-def Scalar.add {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
-  Scalar.tryMk ty (x.val + y.val)
-
-def Scalar.sub {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
-  Scalar.tryMk ty (x.val - y.val)
-
-def Scalar.mul {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
-  Scalar.tryMk ty (x.val * y.val)
-
--- TODO: instances of +, -, * etc. for scalars
-
--- Cast an integer from a [src_ty] to a [tgt_ty]
--- TODO: check the semantics of casts in Rust
-def Scalar.cast {src_ty : ScalarTy} (tgt_ty : ScalarTy) (x : Scalar src_ty) : Result (Scalar tgt_ty) :=
-  Scalar.tryMk tgt_ty x.val
-
--- The scalar types
--- We declare the definitions as reducible so that Lean can unfold them (useful
--- for type class resolution for instance).
-@[reducible] def Isize := Scalar .Isize
-@[reducible] def I8    := Scalar .I8
-@[reducible] def I16   := Scalar .I16
-@[reducible] def I32   := Scalar .I32
-@[reducible] def I64   := Scalar .I64
-@[reducible] def I128  := Scalar .I128
-@[reducible] def Usize := Scalar .Usize
-@[reducible] def U8    := Scalar .U8
-@[reducible] def U16   := Scalar .U16
-@[reducible] def U32   := Scalar .U32
-@[reducible] def U64   := Scalar .U64
-@[reducible] def U128  := Scalar .U128
-
--- TODO: below: not sure this is the best way.
--- Should we rather overload operations like +, -, etc.?
--- Also, it is possible to automate the generation of those definitions
--- with macros (but would it be a good idea? It would be less easy to
--- read the file, which is not supposed to change a lot)
-
--- Negation
-
-/--
-Remark: there is no heterogeneous negation in the Lean prelude: we thus introduce
-one here.
-
-The notation typeclass for heterogeneous addition.
-This enables the notation `- a : β` where `a : α`.
--/
-class HNeg (α : Type u) (β : outParam (Type v)) where
-  /-- `- a` computes the negation of `a`.
-  The meaning of this notation is type-dependent. -/
-  hNeg : α → β
-
-prefix:75  "-"   => HNeg.hNeg
-
-instance : HNeg Isize (Result Isize) where hNeg x := Scalar.neg x
-instance : HNeg I8 (Result I8) where hNeg x := Scalar.neg x
-instance : HNeg I16 (Result I16) where hNeg x := Scalar.neg x
-instance : HNeg I32 (Result I32) where hNeg x := Scalar.neg x
-instance : HNeg I64 (Result I64) where hNeg x := Scalar.neg x
-instance : HNeg I128 (Result I128) where hNeg x := Scalar.neg x
-
--- Addition
-instance {ty} : HAdd (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
-  hAdd x y := Scalar.add x y
-
--- Substraction
-instance {ty} : HSub (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
-  hSub x y := Scalar.sub x y
-
--- Multiplication
-instance {ty} : HMul (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
-  hMul x y := Scalar.mul x y
-
--- Division
-instance {ty} : HDiv (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
-  hDiv x y := Scalar.div x y
-
--- Remainder
-instance {ty} : HMod (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
-  hMod x y := Scalar.rem x y
-
--- ofIntCore
--- TODO: typeclass?
-def Isize.ofIntCore := @Scalar.ofIntCore .Isize
-def I8.ofIntCore    := @Scalar.ofIntCore .I8
-def I16.ofIntCore   := @Scalar.ofIntCore .I16
-def I32.ofIntCore   := @Scalar.ofIntCore .I32
-def I64.ofIntCore   := @Scalar.ofIntCore .I64
-def I128.ofIntCore  := @Scalar.ofIntCore .I128
-def Usize.ofIntCore := @Scalar.ofIntCore .Usize
-def U8.ofIntCore    := @Scalar.ofIntCore .U8
-def U16.ofIntCore   := @Scalar.ofIntCore .U16
-def U32.ofIntCore   := @Scalar.ofIntCore .U32
-def U64.ofIntCore   := @Scalar.ofIntCore .U64
-def U128.ofIntCore  := @Scalar.ofIntCore .U128
-
---  ofInt
--- TODO: typeclass?
-def Isize.ofInt := @Scalar.ofInt .Isize
-def I8.ofInt    := @Scalar.ofInt .I8
-def I16.ofInt   := @Scalar.ofInt .I16
-def I32.ofInt   := @Scalar.ofInt .I32
-def I64.ofInt   := @Scalar.ofInt .I64
-def I128.ofInt  := @Scalar.ofInt .I128
-def Usize.ofInt := @Scalar.ofInt .Usize
-def U8.ofInt    := @Scalar.ofInt .U8
-def U16.ofInt   := @Scalar.ofInt .U16
-def U32.ofInt   := @Scalar.ofInt .U32
-def U64.ofInt   := @Scalar.ofInt .U64
-def U128.ofInt  := @Scalar.ofInt .U128
-
--- Comparisons
-instance {ty} : LT (Scalar ty) where
-  lt a b := LT.lt a.val b.val
-
-instance {ty} : LE (Scalar ty) where le a b := LE.le a.val b.val
-
-instance Scalar.decLt {ty} (a b : Scalar ty) : Decidable (LT.lt a b) := Int.decLt ..
-instance Scalar.decLe {ty} (a b : Scalar ty) : Decidable (LE.le a b) := Int.decLe ..
-
-theorem Scalar.eq_of_val_eq {ty} : ∀ {i j : Scalar ty}, Eq i.val j.val → Eq i j
-  | ⟨_, _, _⟩, ⟨_, _, _⟩, rfl => rfl
-
-theorem Scalar.val_eq_of_eq {ty} {i j : Scalar ty} (h : Eq i j) : Eq i.val j.val :=
-  h ▸ rfl
-
-theorem Scalar.ne_of_val_ne {ty} {i j : Scalar ty} (h : Not (Eq i.val j.val)) : Not (Eq i j) :=
-  fun h' => absurd (val_eq_of_eq h') h
-
-instance (ty : ScalarTy) : DecidableEq (Scalar ty) :=
-  fun i j =>
-    match decEq i.val j.val with
-    | isTrue h  => isTrue (Scalar.eq_of_val_eq h)
-    | isFalse h => isFalse (Scalar.ne_of_val_ne h)
-
-def Scalar.toInt {ty} (n : Scalar ty) : Int := n.val
-
--- Tactic to prove that integers are in bounds
-syntax "intlit" : tactic
-
-macro_rules
-  | `(tactic| intlit) => `(tactic| apply Scalar.bound_suffices ; decide)
-
--- -- We now define a type class that subsumes the various machine integer types, so
--- -- as to write a concise definition for scalar_cast, rather than exhaustively
--- -- enumerating all of the possible pairs. We remark that Rust has sane semantics
--- -- and fails if a cast operation would involve a truncation or modulo.
-
--- class MachineInteger (t: Type) where
---   size: Nat
---   val: t -> Fin size
---   ofNatCore: (n:Nat) -> LT.lt n size -> t
-
--- set_option hygiene false in
--- run_cmd
---   for typeName in [`UInt8, `UInt16, `UInt32, `UInt64, `USize].map Lean.mkIdent do
---   Lean.Elab.Command.elabCommand (← `(
---     namespace $typeName
---     instance: MachineInteger $typeName where
---       size := size
---       val := val
---       ofNatCore := ofNatCore
---     end $typeName
---   ))
-
--- -- Aeneas only instantiates the destination type (`src` is implicit). We rely on
--- -- Lean to infer `src`.
-
--- def scalar_cast { src: Type } (dst: Type) [ MachineInteger src ] [ MachineInteger dst ] (x: src): Result dst :=
---   if h: MachineInteger.val x < MachineInteger.size dst then
---     .ret (MachineInteger.ofNatCore (MachineInteger.val x).val h)
---   else
---     .fail integerOverflow
-
--------------
--- VECTORS --
--------------
-
-def Vec (α : Type u) := { l : List α // List.length l <= Usize.max }
-
-def vec_new (α : Type u): Vec α := ⟨ [], by sorry ⟩
-
-def vec_len (α : Type u) (v : Vec α) : Usize :=
-  let ⟨ v, l ⟩ := v
-  Usize.ofIntCore (List.length v) (by sorry) l
- 
-def vec_push_fwd (α : Type u) (_ : Vec α) (_ : α) : Unit := ()
-
-def vec_push_back (α : Type u) (v : Vec α) (x : α) : Result (Vec α)
-  :=
-  if h : List.length v.val <= U32.max || List.length v.val <= Usize.max then
-    return ⟨ List.concat v.val x, by sorry ⟩
-  else
-    fail maximumSizeExceeded
-
-def vec_insert_fwd (α : Type u) (v: Vec α) (i: Usize) (_: α): Result Unit :=
-  if i.val < List.length v.val then
-    .ret ()
-  else
-    .fail arrayOutOfBounds
-
-def vec_insert_back (α : Type u) (v: Vec α) (i: Usize) (x: α): Result (Vec α) :=
-  if i.val < List.length v.val then
-    -- TODO: maybe we should redefine a list library which uses integers
-    -- (instead of natural numbers)
-    let i : Nat :=
-      match i.val with
-      | .ofNat n => n
-      | .negSucc n => by sorry -- TODO: we can't get here
-    let isLt: i < USize.size := by sorry
-    let i : Fin USize.size := { val := i, isLt := isLt }
-    .ret ⟨ List.set v.val i.val x, by
-      have h: List.length v.val <= Usize.max := v.property
-      rewrite [ List.length_set v.val i.val x ]
-      assumption
-    ⟩
-  else
-    .fail arrayOutOfBounds
-
-def vec_index_fwd (α : Type u) (v: Vec α) (i: Usize): Result α :=
-  if i.val < List.length v.val then
-    let i : Nat :=
-      match i.val with
-      | .ofNat n => n
-      | .negSucc n => by sorry -- TODO: we can't get here
-    let isLt: i < USize.size := by sorry
-    let i : Fin USize.size := { val := i, isLt := isLt }
-    let h: i < List.length v.val := by sorry
-    .ret (List.get v.val ⟨i.val, h⟩)
-  else
-    .fail arrayOutOfBounds
-
-def vec_index_back (α : Type u) (v: Vec α) (i: Usize) (_: α): Result Unit :=
-  if i.val < List.length v.val then
-    .ret ()
-  else
-    .fail arrayOutOfBounds
-
-def vec_index_mut_fwd (α : Type u) (v: Vec α) (i: Usize): Result α :=
-  if i.val < List.length v.val then
-    let i : Nat :=
-      match i.val with
-      | .ofNat n => n
-      | .negSucc n => by sorry -- TODO: we can't get here
-    let isLt: i < USize.size := by sorry
-    let i : Fin USize.size := { val := i, isLt := isLt }
-    let h: i < List.length v.val := by sorry
-    .ret (List.get v.val ⟨i.val, h⟩)
-  else
-    .fail arrayOutOfBounds
-
-def vec_index_mut_back (α : Type u) (v: Vec α) (i: Usize) (x: α): Result (Vec α) :=
-  if i.val < List.length v.val then
-    let i : Nat :=
-      match i.val with
-      | .ofNat n => n
-      | .negSucc n => by sorry -- TODO: we can't get here
-    let isLt: i < USize.size := by sorry
-    let i : Fin USize.size := { val := i, isLt := isLt }
-    .ret ⟨ List.set v.val i.val x, by
-      have h: List.length v.val <= Usize.max := v.property
-      rewrite [ List.length_set v.val i.val x ]
-      assumption
-    ⟩
-  else
-    .fail arrayOutOfBounds
-
-----------
--- MISC --
-----------
-
-def mem_replace_fwd (a : Type) (x : a) (_ : a) : a :=
-  x
-
-def mem_replace_back (a : Type) (_ : a) (y : a) : a :=
-  y
-
-/-- Aeneas-translated function -- useful to reduce non-recursive definitions.
- Use with `simp [ aeneas ]` -/
-register_simp_attr aeneas
diff --git a/tests/lean/misc-external/External/ExternalFuns.lean b/tests/lean/misc-external/External/ExternalFuns.lean
deleted file mode 100644
index 6bd4f4a9..00000000
--- a/tests/lean/misc-external/External/ExternalFuns.lean
+++ /dev/null
@@ -1,5 +0,0 @@
-import Base.Primitives
-import External.Types
-import External.Opaque
-
-def opaque_defs : OpaqueDefs := sorry
diff --git a/tests/lean/misc-external/External/Funs.lean b/tests/lean/misc-external/External/Funs.lean
deleted file mode 100644
index eeb83989..00000000
--- a/tests/lean/misc-external/External/Funs.lean
+++ /dev/null
@@ -1,84 +0,0 @@
--- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
--- [external]: function definitions
-import Base.Primitives
-import External.Types
-import External.ExternalFuns
-
-/- [external::swap] -/
-def swap_fwd
-  (T : Type) (x : T) (y : T) (st : State) : Result (State × Unit) :=
-  do
-    let (st0, _) ← opaque_defs.core_mem_swap_fwd T x y st
-    let (st1, _) ← opaque_defs.core_mem_swap_back0 T x y st st0
-    let (st2, _) ← opaque_defs.core_mem_swap_back1 T x y st st1
-    Result.ret (st2, ())
-
-/- [external::swap] -/
-def swap_back
-  (T : Type) (x : T) (y : T) (st : State) (st0 : State) :
-  Result (State × (T × T))
-  :=
-  do
-    let (st1, _) ← opaque_defs.core_mem_swap_fwd T x y st
-    let (st2, x0) ← opaque_defs.core_mem_swap_back0 T x y st st1
-    let (_, y0) ← opaque_defs.core_mem_swap_back1 T x y st st2
-    Result.ret (st0, (x0, y0))
-
-/- [external::test_new_non_zero_u32] -/
-def test_new_non_zero_u32_fwd
-  (x : U32) (st : State) : Result (State × core_num_nonzero_non_zero_u32_t) :=
-  do
-    let (st0, opt) ← opaque_defs.core_num_nonzero_non_zero_u32_new_fwd x st
-    opaque_defs.core_option_option_unwrap_fwd core_num_nonzero_non_zero_u32_t
-      opt st0
-
-/- [external::test_vec] -/
-def test_vec_fwd : Result Unit :=
-  do
-    let v := vec_new U32
-    let _ ← vec_push_back U32 v (U32.ofInt 0 (by intlit))
-    Result.ret ()
-
-/- [external::custom_swap] -/
-def custom_swap_fwd
-  (T : Type) (x : T) (y : T) (st : State) : Result (State × T) :=
-  do
-    let (st0, _) ← opaque_defs.core_mem_swap_fwd T x y st
-    let (st1, x0) ← opaque_defs.core_mem_swap_back0 T x y st st0
-    let (st2, _) ← opaque_defs.core_mem_swap_back1 T x y st st1
-    Result.ret (st2, x0)
-
-/- [external::custom_swap] -/
-def custom_swap_back
-  (T : Type) (x : T) (y : T) (st : State) (ret0 : T) (st0 : State) :
-  Result (State × (T × T))
-  :=
-  do
-    let (st1, _) ← opaque_defs.core_mem_swap_fwd T x y st
-    let (st2, _) ← opaque_defs.core_mem_swap_back0 T x y st st1
-    let (_, y0) ← opaque_defs.core_mem_swap_back1 T x y st st2
-    Result.ret (st0, (ret0, y0))
-
-/- [external::test_custom_swap] -/
-def test_custom_swap_fwd
-  (x : U32) (y : U32) (st : State) : Result (State × Unit) :=
-  do
-    let (st0, _) ← custom_swap_fwd U32 x y st
-    Result.ret (st0, ())
-
-/- [external::test_custom_swap] -/
-def test_custom_swap_back
-  (x : U32) (y : U32) (st : State) (st0 : State) :
-  Result (State × (U32 × U32))
-  :=
-  custom_swap_back U32 x y st (U32.ofInt 1 (by intlit)) st0
-
-/- [external::test_swap_non_zero] -/
-def test_swap_non_zero_fwd (x : U32) (st : State) : Result (State × U32) :=
-  do
-    let (st0, _) ← swap_fwd U32 x (U32.ofInt 0 (by intlit)) st
-    let (st1, (x0, _)) ← swap_back U32 x (U32.ofInt 0 (by intlit)) st st0
-    if h: x0 = (U32.ofInt 0 (by intlit))
-    then Result.fail Error.panic
-    else Result.ret (st1, x0)
-
diff --git a/tests/lean/misc-external/External/Opaque.lean b/tests/lean/misc-external/External/Opaque.lean
deleted file mode 100644
index d641912b..00000000
--- a/tests/lean/misc-external/External/Opaque.lean
+++ /dev/null
@@ -1,27 +0,0 @@
--- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
--- [external]: opaque function definitions
-import Base.Primitives
-import External.Types
-
-structure OpaqueDefs where
-  
-  /- [core::mem::swap] -/
-  core_mem_swap_fwd (T : Type) : T -> T -> State -> Result (State × Unit)
-  
-  /- [core::mem::swap] -/
-  core_mem_swap_back0
-    (T : Type) : T -> T -> State -> State -> Result (State × T)
-  
-  /- [core::mem::swap] -/
-  core_mem_swap_back1
-    (T : Type) : T -> T -> State -> State -> Result (State × T)
-  
-  /- [core::num::nonzero::NonZeroU32::{14}::new] -/
-  core_num_nonzero_non_zero_u32_new_fwd
-    :
-    U32 -> State -> Result (State × (Option core_num_nonzero_non_zero_u32_t))
-  
-  /- [core::option::Option::{0}::unwrap] -/
-  core_option_option_unwrap_fwd
-    (T : Type) : Option T -> State -> Result (State × T)
-  
diff --git a/tests/lean/misc-external/lake-manifest.json b/tests/lean/misc-external/lake-manifest.json
deleted file mode 100644
index 57b071ca..00000000
--- a/tests/lean/misc-external/lake-manifest.json
+++ /dev/null
@@ -1,27 +0,0 @@
-{"version": 4,
- "packagesDir": "./lake-packages",
- "packages":
- [{"git":
-   {"url": "https://github.com/leanprover-community/mathlib4.git",
-    "subDir?": null,
-    "rev": "4037792ead804d7bfa8868e2c4684d4223c15ece",
-    "name": "mathlib",
-    "inputRev?": null}},
-  {"git":
-   {"url": "https://github.com/gebner/quote4",
-    "subDir?": null,
-    "rev": "2412c4fdf4a8b689f4467618e5e7b371ae5014aa",
-    "name": "Qq",
-    "inputRev?": "master"}},
-  {"git":
-   {"url": "https://github.com/JLimperg/aesop",
-    "subDir?": null,
-    "rev": "7fe9ecd9339b0e1796e89d243b776849c305c690",
-    "name": "aesop",
-    "inputRev?": "master"}},
-  {"git":
-   {"url": "https://github.com/leanprover/std4",
-    "subDir?": null,
-    "rev": "24897887905b3a1254b244369f5dd2cf6174b0ee",
-    "name": "std",
-    "inputRev?": "main"}}]}
diff --git a/tests/lean/misc-external/lakefile.lean b/tests/lean/misc-external/lakefile.lean
deleted file mode 100644
index 6cc4aae4..00000000
--- a/tests/lean/misc-external/lakefile.lean
+++ /dev/null
@@ -1,12 +0,0 @@
-import Lake
-open Lake DSL
-
-require mathlib from git
-  "https://github.com/leanprover-community/mathlib4.git"
-
-package «external» {}
-
-lean_lib «Base» {}
-
-@[default_target]
-lean_lib «External» {}
diff --git a/tests/lean/misc-external/lean-toolchain b/tests/lean/misc-external/lean-toolchain
deleted file mode 100644
index bbf57f10..00000000
--- a/tests/lean/misc-external/lean-toolchain
+++ /dev/null
@@ -1 +0,0 @@
-leanprover/lean4:nightly-2023-01-21
diff --git a/tests/lean/misc-loops/Base/Primitives.lean b/tests/lean/misc-loops/Base/Primitives.lean
deleted file mode 100644
index 4a66a453..00000000
--- a/tests/lean/misc-loops/Base/Primitives.lean
+++ /dev/null
@@ -1,583 +0,0 @@
-import Lean
-import Lean.Meta.Tactic.Simp
-import Init.Data.List.Basic
-import Mathlib.Tactic.RunCmd
-
---------------------
--- ASSERT COMMAND --
---------------------
-
-open Lean Elab Command Term Meta
-
-syntax (name := assert) "#assert" term: command
-
-@[command_elab assert]
-unsafe
-def assertImpl : CommandElab := fun (_stx: Syntax) => do
-  runTermElabM (fun _ => do
-    let r ← evalTerm Bool (mkConst ``Bool) _stx[1]
-    if not r then
-      logInfo "Assertion failed for: "
-      logInfo _stx[1]
-      logError "Expression reduced to false"
-    pure ())
-
-#eval 2 == 2
-#assert (2 == 2)
-
--------------
--- PRELUDE --
--------------
-
--- Results & monadic combinators
-
-inductive Error where
-   | assertionFailure: Error
-   | integerOverflow: Error
-   | divisionByZero: Error
-   | arrayOutOfBounds: Error
-   | maximumSizeExceeded: Error
-   | panic: Error
-deriving Repr, BEq
-
-open Error
-
-inductive Result (α : Type u) where
-  | ret (v: α): Result α
-  | fail (e: Error): Result α
-deriving Repr, BEq
-
-open Result
-
-instance Result_Inhabited (α : Type u) : Inhabited (Result α) :=
-  Inhabited.mk (fail panic)
-
-/- HELPERS -/
-
-def ret? {α: Type} (r: Result α): Bool :=
-  match r with
-  | Result.ret _ => true
-  | Result.fail _ => false
-
-def massert (b:Bool) : Result Unit :=
-  if b then .ret () else fail assertionFailure
-
-def eval_global {α: Type} (x: Result α) (_: ret? x): α :=
-  match x with
-  | Result.fail _ => by contradiction
-  | Result.ret x => x
-
-/- DO-DSL SUPPORT -/
-
-def bind (x: Result α) (f: α -> Result β) : Result β :=
-  match x with
-  | ret v  => f v 
-  | fail v => fail v
-
--- Allows using Result in do-blocks
-instance : Bind Result where
-  bind := bind
-
--- Allows using return x in do-blocks
-instance : Pure Result where
-  pure := fun x => ret x
-
-/- CUSTOM-DSL SUPPORT -/
-
--- Let-binding the Result of a monadic operation is oftentimes not sufficient,
--- because we may need a hypothesis for equational reasoning in the scope. We
--- rely on subtype, and a custom let-binding operator, in effect recreating our
--- own variant of the do-dsl
-
-def Result.attach {α: Type} (o : Result α): Result { x : α // o = ret x } :=
-  match o with
-  | .ret x => .ret ⟨x, rfl⟩
-  | .fail e => .fail e
-
-macro "let" e:term " ⟵ " f:term : doElem =>
-  `(doElem| let ⟨$e, h⟩ ← Result.attach $f)
-
--- TODO: any way to factorize both definitions?
-macro "let" e:term " <-- " f:term : doElem =>
-  `(doElem| let ⟨$e, h⟩ ← Result.attach $f)
-
--- We call the hypothesis `h`, in effect making it unavailable to the user
--- (because too much shadowing). But in practice, once can use the French single
--- quote notation (input with f< and f>), where `‹ h ›` finds a suitable
--- hypothesis in the context, this is equivalent to `have x: h := by assumption in x`
-#eval do
-  let y <-- .ret (0: Nat)
-  let _: y = 0 := by cases ‹ ret 0 = ret y › ; decide
-  let r: { x: Nat // x = 0 } := ⟨ y, by assumption ⟩
-  .ret r
-
-----------------------
--- MACHINE INTEGERS --
-----------------------
-
--- We redefine our machine integers types.
-
--- For Isize/Usize, we reuse `getNumBits` from `USize`. You cannot reduce `getNumBits`
--- using the simplifier, meaning that proofs do not depend on the compile-time value of
--- USize.size. (Lean assumes 32 or 64-bit platforms, and Rust doesn't really support, at
--- least officially, 16-bit microcontrollers, so this seems like a fine design decision
--- for now.)
-
--- Note from Chris Bailey: "If there's more than one salient property of your
--- definition then the subtyping strategy might get messy, and the property part
--- of a subtype is less discoverable by the simplifier or tactics like
--- library_search." So, we will not add refinements on the return values of the
--- operations defined on Primitives, but will rather rely on custom lemmas to
--- invert on possible return values of the primitive operations.
-
--- Machine integer constants, done via `ofNatCore`, which requires a proof that
--- the `Nat` fits within the desired integer type. We provide a custom tactic.
-
-open System.Platform.getNumBits
-
--- TODO: is there a way of only importing System.Platform.getNumBits?
---
-@[simp] def size_num_bits : Nat := (System.Platform.getNumBits ()).val
-
--- Remark: Lean seems to use < for the comparisons with the upper bounds by convention.
--- We keep the F* convention for now.
-@[simp] def Isize.min : Int := - (HPow.hPow 2 (size_num_bits - 1))
-@[simp] def Isize.max : Int := (HPow.hPow 2 (size_num_bits - 1)) - 1
-@[simp] def I8.min    : Int := - (HPow.hPow 2 7)
-@[simp] def I8.max    : Int := HPow.hPow 2 7 - 1
-@[simp] def I16.min   : Int := - (HPow.hPow 2 15)
-@[simp] def I16.max   : Int := HPow.hPow 2 15 - 1
-@[simp] def I32.min   : Int := -(HPow.hPow 2 31)
-@[simp] def I32.max   : Int := HPow.hPow 2 31 - 1
-@[simp] def I64.min   : Int := -(HPow.hPow 2 63)
-@[simp] def I64.max   : Int := HPow.hPow 2 63 - 1
-@[simp] def I128.min  : Int := -(HPow.hPow 2 127)
-@[simp] def I128.max  : Int := HPow.hPow 2 127 - 1
-@[simp] def Usize.min : Int := 0
-@[simp] def Usize.max : Int := HPow.hPow 2 size_num_bits - 1
-@[simp] def U8.min    : Int := 0
-@[simp] def U8.max    : Int := HPow.hPow 2 8 - 1
-@[simp] def U16.min   : Int := 0
-@[simp] def U16.max   : Int := HPow.hPow 2 16 - 1
-@[simp] def U32.min   : Int := 0
-@[simp] def U32.max   : Int := HPow.hPow 2 32 - 1
-@[simp] def U64.min   : Int := 0
-@[simp] def U64.max   : Int := HPow.hPow 2 64 - 1
-@[simp] def U128.min  : Int := 0
-@[simp] def U128.max  : Int := HPow.hPow 2 128 - 1
-
-#assert (I8.min   == -128)
-#assert (I8.max   == 127)
-#assert (I16.min  == -32768)
-#assert (I16.max  == 32767)
-#assert (I32.min  == -2147483648)
-#assert (I32.max  == 2147483647)
-#assert (I64.min  == -9223372036854775808)
-#assert (I64.max  == 9223372036854775807)
-#assert (I128.min == -170141183460469231731687303715884105728)
-#assert (I128.max == 170141183460469231731687303715884105727)
-#assert (U8.min   == 0)
-#assert (U8.max   == 255)
-#assert (U16.min  == 0)
-#assert (U16.max  == 65535)
-#assert (U32.min  == 0)
-#assert (U32.max  == 4294967295)
-#assert (U64.min  == 0)
-#assert (U64.max  == 18446744073709551615)
-#assert (U128.min == 0)
-#assert (U128.max == 340282366920938463463374607431768211455)
-
-inductive ScalarTy :=
-| Isize
-| I8
-| I16
-| I32
-| I64
-| I128
-| Usize
-| U8
-| U16
-| U32
-| U64
-| U128
-
-def Scalar.min (ty : ScalarTy) : Int :=
-  match ty with
-  | .Isize => Isize.min
-  | .I8    => I8.min
-  | .I16   => I16.min
-  | .I32   => I32.min
-  | .I64   => I64.min
-  | .I128  => I128.min
-  | .Usize => Usize.min
-  | .U8    => U8.min
-  | .U16   => U16.min
-  | .U32   => U32.min
-  | .U64   => U64.min
-  | .U128  => U128.min
-
-def Scalar.max (ty : ScalarTy) : Int :=
-  match ty with
-  | .Isize => Isize.max
-  | .I8    => I8.max
-  | .I16   => I16.max
-  | .I32   => I32.max
-  | .I64   => I64.max
-  | .I128  => I128.max
-  | .Usize => Usize.max
-  | .U8    => U8.max
-  | .U16   => U16.max
-  | .U32   => U32.max
-  | .U64   => U64.max
-  | .U128  => U128.max
-
--- "Conservative" bounds
--- We use those because we can't compare to the isize bounds (which can't
--- reduce at compile-time). Whenever we perform an arithmetic operation like
--- addition we need to check that the result is in bounds: we first compare
--- to the conservative bounds, which reduce, then compare to the real bounds.
--- This is useful for the various #asserts that we want to reduce at
--- type-checking time.
-def Scalar.cMin (ty : ScalarTy) : Int :=
-  match ty with
-  | .Isize => I32.min
-  | _ => Scalar.min ty
-
-def Scalar.cMax (ty : ScalarTy) : Int :=
-  match ty with
-  | .Isize => I32.max
-  | .Usize => U32.max
-  | _ => Scalar.max ty
-
-theorem Scalar.cMin_bound ty : Scalar.min ty <= Scalar.cMin ty := by sorry
-theorem Scalar.cMax_bound ty : Scalar.min ty <= Scalar.cMin ty := by sorry
-
-structure Scalar (ty : ScalarTy) where
-  val : Int
-  hmin : Scalar.min ty <= val
-  hmax : val <= Scalar.max ty
-
-theorem Scalar.bound_suffices (ty : ScalarTy) (x : Int) :
-  Scalar.cMin ty <= x && x <= Scalar.cMax ty ->
-  (decide (Scalar.min ty ≤ x) && decide (x ≤ Scalar.max ty)) = true
-  := by sorry
-
-def Scalar.ofIntCore {ty : ScalarTy} (x : Int)
-  (hmin : Scalar.min ty <= x) (hmax : x <= Scalar.max ty) : Scalar ty :=
-  { val := x, hmin := hmin, hmax := hmax }
-
-def Scalar.ofInt {ty : ScalarTy} (x : Int)
-  (h : Scalar.min ty <= x && x <= Scalar.max ty) : Scalar ty :=
-  let hmin: Scalar.min ty <= x := by sorry
-  let hmax: x <= Scalar.max ty := by sorry
-  Scalar.ofIntCore x hmin hmax
-
--- Further thoughts: look at what has been done here:
--- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/Fin/Basic.lean
--- and
--- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/UInt.lean
--- which both contain a fair amount of reasoning already!
-def Scalar.tryMk (ty : ScalarTy) (x : Int) : Result (Scalar ty) :=
-  -- TODO: write this with only one if then else
-  if hmin_cons: Scalar.cMin ty <= x || Scalar.min ty <= x then
-    if hmax_cons: x <= Scalar.cMax ty || x <= Scalar.max ty then
-      let hmin: Scalar.min ty <= x := by sorry
-      let hmax: x <= Scalar.max ty := by sorry
-      return Scalar.ofIntCore x hmin hmax
-    else fail integerOverflow
-  else fail integerOverflow
-
-def Scalar.neg {ty : ScalarTy} (x : Scalar ty) : Result (Scalar ty) := Scalar.tryMk ty (- x.val)
-
-def Scalar.div {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
-  if y.val != 0 then Scalar.tryMk ty (x.val / y.val) else fail divisionByZero
-
--- Checking that the % operation in Lean computes the same as the remainder operation in Rust
-#assert 1 % 2 = (1:Int)
-#assert (-1) % 2 = -1
-#assert 1 % (-2) = 1
-#assert (-1) % (-2) = -1
-
-def Scalar.rem {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
-  if y.val != 0 then Scalar.tryMk ty (x.val % y.val) else fail divisionByZero
-
-def Scalar.add {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
-  Scalar.tryMk ty (x.val + y.val)
-
-def Scalar.sub {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
-  Scalar.tryMk ty (x.val - y.val)
-
-def Scalar.mul {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
-  Scalar.tryMk ty (x.val * y.val)
-
--- TODO: instances of +, -, * etc. for scalars
-
--- Cast an integer from a [src_ty] to a [tgt_ty]
--- TODO: check the semantics of casts in Rust
-def Scalar.cast {src_ty : ScalarTy} (tgt_ty : ScalarTy) (x : Scalar src_ty) : Result (Scalar tgt_ty) :=
-  Scalar.tryMk tgt_ty x.val
-
--- The scalar types
--- We declare the definitions as reducible so that Lean can unfold them (useful
--- for type class resolution for instance).
-@[reducible] def Isize := Scalar .Isize
-@[reducible] def I8    := Scalar .I8
-@[reducible] def I16   := Scalar .I16
-@[reducible] def I32   := Scalar .I32
-@[reducible] def I64   := Scalar .I64
-@[reducible] def I128  := Scalar .I128
-@[reducible] def Usize := Scalar .Usize
-@[reducible] def U8    := Scalar .U8
-@[reducible] def U16   := Scalar .U16
-@[reducible] def U32   := Scalar .U32
-@[reducible] def U64   := Scalar .U64
-@[reducible] def U128  := Scalar .U128
-
--- TODO: below: not sure this is the best way.
--- Should we rather overload operations like +, -, etc.?
--- Also, it is possible to automate the generation of those definitions
--- with macros (but would it be a good idea? It would be less easy to
--- read the file, which is not supposed to change a lot)
-
--- Negation
-
-/--
-Remark: there is no heterogeneous negation in the Lean prelude: we thus introduce
-one here.
-
-The notation typeclass for heterogeneous addition.
-This enables the notation `- a : β` where `a : α`.
--/
-class HNeg (α : Type u) (β : outParam (Type v)) where
-  /-- `- a` computes the negation of `a`.
-  The meaning of this notation is type-dependent. -/
-  hNeg : α → β
-
-prefix:75  "-"   => HNeg.hNeg
-
-instance : HNeg Isize (Result Isize) where hNeg x := Scalar.neg x
-instance : HNeg I8 (Result I8) where hNeg x := Scalar.neg x
-instance : HNeg I16 (Result I16) where hNeg x := Scalar.neg x
-instance : HNeg I32 (Result I32) where hNeg x := Scalar.neg x
-instance : HNeg I64 (Result I64) where hNeg x := Scalar.neg x
-instance : HNeg I128 (Result I128) where hNeg x := Scalar.neg x
-
--- Addition
-instance {ty} : HAdd (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
-  hAdd x y := Scalar.add x y
-
--- Substraction
-instance {ty} : HSub (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
-  hSub x y := Scalar.sub x y
-
--- Multiplication
-instance {ty} : HMul (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
-  hMul x y := Scalar.mul x y
-
--- Division
-instance {ty} : HDiv (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
-  hDiv x y := Scalar.div x y
-
--- Remainder
-instance {ty} : HMod (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
-  hMod x y := Scalar.rem x y
-
--- ofIntCore
--- TODO: typeclass?
-def Isize.ofIntCore := @Scalar.ofIntCore .Isize
-def I8.ofIntCore    := @Scalar.ofIntCore .I8
-def I16.ofIntCore   := @Scalar.ofIntCore .I16
-def I32.ofIntCore   := @Scalar.ofIntCore .I32
-def I64.ofIntCore   := @Scalar.ofIntCore .I64
-def I128.ofIntCore  := @Scalar.ofIntCore .I128
-def Usize.ofIntCore := @Scalar.ofIntCore .Usize
-def U8.ofIntCore    := @Scalar.ofIntCore .U8
-def U16.ofIntCore   := @Scalar.ofIntCore .U16
-def U32.ofIntCore   := @Scalar.ofIntCore .U32
-def U64.ofIntCore   := @Scalar.ofIntCore .U64
-def U128.ofIntCore  := @Scalar.ofIntCore .U128
-
---  ofInt
--- TODO: typeclass?
-def Isize.ofInt := @Scalar.ofInt .Isize
-def I8.ofInt    := @Scalar.ofInt .I8
-def I16.ofInt   := @Scalar.ofInt .I16
-def I32.ofInt   := @Scalar.ofInt .I32
-def I64.ofInt   := @Scalar.ofInt .I64
-def I128.ofInt  := @Scalar.ofInt .I128
-def Usize.ofInt := @Scalar.ofInt .Usize
-def U8.ofInt    := @Scalar.ofInt .U8
-def U16.ofInt   := @Scalar.ofInt .U16
-def U32.ofInt   := @Scalar.ofInt .U32
-def U64.ofInt   := @Scalar.ofInt .U64
-def U128.ofInt  := @Scalar.ofInt .U128
-
--- Comparisons
-instance {ty} : LT (Scalar ty) where
-  lt a b := LT.lt a.val b.val
-
-instance {ty} : LE (Scalar ty) where le a b := LE.le a.val b.val
-
-instance Scalar.decLt {ty} (a b : Scalar ty) : Decidable (LT.lt a b) := Int.decLt ..
-instance Scalar.decLe {ty} (a b : Scalar ty) : Decidable (LE.le a b) := Int.decLe ..
-
-theorem Scalar.eq_of_val_eq {ty} : ∀ {i j : Scalar ty}, Eq i.val j.val → Eq i j
-  | ⟨_, _, _⟩, ⟨_, _, _⟩, rfl => rfl
-
-theorem Scalar.val_eq_of_eq {ty} {i j : Scalar ty} (h : Eq i j) : Eq i.val j.val :=
-  h ▸ rfl
-
-theorem Scalar.ne_of_val_ne {ty} {i j : Scalar ty} (h : Not (Eq i.val j.val)) : Not (Eq i j) :=
-  fun h' => absurd (val_eq_of_eq h') h
-
-instance (ty : ScalarTy) : DecidableEq (Scalar ty) :=
-  fun i j =>
-    match decEq i.val j.val with
-    | isTrue h  => isTrue (Scalar.eq_of_val_eq h)
-    | isFalse h => isFalse (Scalar.ne_of_val_ne h)
-
-def Scalar.toInt {ty} (n : Scalar ty) : Int := n.val
-
--- Tactic to prove that integers are in bounds
-syntax "intlit" : tactic
-
-macro_rules
-  | `(tactic| intlit) => `(tactic| apply Scalar.bound_suffices ; decide)
-
--- -- We now define a type class that subsumes the various machine integer types, so
--- -- as to write a concise definition for scalar_cast, rather than exhaustively
--- -- enumerating all of the possible pairs. We remark that Rust has sane semantics
--- -- and fails if a cast operation would involve a truncation or modulo.
-
--- class MachineInteger (t: Type) where
---   size: Nat
---   val: t -> Fin size
---   ofNatCore: (n:Nat) -> LT.lt n size -> t
-
--- set_option hygiene false in
--- run_cmd
---   for typeName in [`UInt8, `UInt16, `UInt32, `UInt64, `USize].map Lean.mkIdent do
---   Lean.Elab.Command.elabCommand (← `(
---     namespace $typeName
---     instance: MachineInteger $typeName where
---       size := size
---       val := val
---       ofNatCore := ofNatCore
---     end $typeName
---   ))
-
--- -- Aeneas only instantiates the destination type (`src` is implicit). We rely on
--- -- Lean to infer `src`.
-
--- def scalar_cast { src: Type } (dst: Type) [ MachineInteger src ] [ MachineInteger dst ] (x: src): Result dst :=
---   if h: MachineInteger.val x < MachineInteger.size dst then
---     .ret (MachineInteger.ofNatCore (MachineInteger.val x).val h)
---   else
---     .fail integerOverflow
-
--------------
--- VECTORS --
--------------
-
-def Vec (α : Type u) := { l : List α // List.length l <= Usize.max }
-
-def vec_new (α : Type u): Vec α := ⟨ [], by sorry ⟩
-
-def vec_len (α : Type u) (v : Vec α) : Usize :=
-  let ⟨ v, l ⟩ := v
-  Usize.ofIntCore (List.length v) (by sorry) l
- 
-def vec_push_fwd (α : Type u) (_ : Vec α) (_ : α) : Unit := ()
-
-def vec_push_back (α : Type u) (v : Vec α) (x : α) : Result (Vec α)
-  :=
-  if h : List.length v.val <= U32.max || List.length v.val <= Usize.max then
-    return ⟨ List.concat v.val x, by sorry ⟩
-  else
-    fail maximumSizeExceeded
-
-def vec_insert_fwd (α : Type u) (v: Vec α) (i: Usize) (_: α): Result Unit :=
-  if i.val < List.length v.val then
-    .ret ()
-  else
-    .fail arrayOutOfBounds
-
-def vec_insert_back (α : Type u) (v: Vec α) (i: Usize) (x: α): Result (Vec α) :=
-  if i.val < List.length v.val then
-    -- TODO: maybe we should redefine a list library which uses integers
-    -- (instead of natural numbers)
-    let i : Nat :=
-      match i.val with
-      | .ofNat n => n
-      | .negSucc n => by sorry -- TODO: we can't get here
-    let isLt: i < USize.size := by sorry
-    let i : Fin USize.size := { val := i, isLt := isLt }
-    .ret ⟨ List.set v.val i.val x, by
-      have h: List.length v.val <= Usize.max := v.property
-      rewrite [ List.length_set v.val i.val x ]
-      assumption
-    ⟩
-  else
-    .fail arrayOutOfBounds
-
-def vec_index_fwd (α : Type u) (v: Vec α) (i: Usize): Result α :=
-  if i.val < List.length v.val then
-    let i : Nat :=
-      match i.val with
-      | .ofNat n => n
-      | .negSucc n => by sorry -- TODO: we can't get here
-    let isLt: i < USize.size := by sorry
-    let i : Fin USize.size := { val := i, isLt := isLt }
-    let h: i < List.length v.val := by sorry
-    .ret (List.get v.val ⟨i.val, h⟩)
-  else
-    .fail arrayOutOfBounds
-
-def vec_index_back (α : Type u) (v: Vec α) (i: Usize) (_: α): Result Unit :=
-  if i.val < List.length v.val then
-    .ret ()
-  else
-    .fail arrayOutOfBounds
-
-def vec_index_mut_fwd (α : Type u) (v: Vec α) (i: Usize): Result α :=
-  if i.val < List.length v.val then
-    let i : Nat :=
-      match i.val with
-      | .ofNat n => n
-      | .negSucc n => by sorry -- TODO: we can't get here
-    let isLt: i < USize.size := by sorry
-    let i : Fin USize.size := { val := i, isLt := isLt }
-    let h: i < List.length v.val := by sorry
-    .ret (List.get v.val ⟨i.val, h⟩)
-  else
-    .fail arrayOutOfBounds
-
-def vec_index_mut_back (α : Type u) (v: Vec α) (i: Usize) (x: α): Result (Vec α) :=
-  if i.val < List.length v.val then
-    let i : Nat :=
-      match i.val with
-      | .ofNat n => n
-      | .negSucc n => by sorry -- TODO: we can't get here
-    let isLt: i < USize.size := by sorry
-    let i : Fin USize.size := { val := i, isLt := isLt }
-    .ret ⟨ List.set v.val i.val x, by
-      have h: List.length v.val <= Usize.max := v.property
-      rewrite [ List.length_set v.val i.val x ]
-      assumption
-    ⟩
-  else
-    .fail arrayOutOfBounds
-
-----------
--- MISC --
-----------
-
-def mem_replace_fwd (a : Type) (x : a) (_ : a) : a :=
-  x
-
-def mem_replace_back (a : Type) (_ : a) (y : a) : a :=
-  y
-
-/-- Aeneas-translated function -- useful to reduce non-recursive definitions.
- Use with `simp [ aeneas ]` -/
-register_simp_attr aeneas
diff --git a/tests/lean/misc-loops/Loops/Clauses/Clauses.lean b/tests/lean/misc-loops/Loops/Clauses/Clauses.lean
deleted file mode 100644
index 89a7ce34..00000000
--- a/tests/lean/misc-loops/Loops/Clauses/Clauses.lean
+++ /dev/null
@@ -1,205 +0,0 @@
--- [loops]: decreases clauses
-import Base.Primitives
-import Loops.Types
-
-/- [loops::sum]: termination measure -/
-@[simp]
-def sum_loop_terminates (max : U32) (i : U32) (s : U32) := (max, i, s)
-
-syntax "sum_loop_decreases" term+ : tactic
-
-macro_rules
-| `(tactic| sum_loop_decreases $max $i $s) =>`(tactic| sorry)
-
-/- [loops::sum_with_mut_borrows]: termination measure -/
-@[simp]
-def sum_with_mut_borrows_loop_terminates (max : U32) (mi : U32) (ms : U32) :=
-  (max, mi, ms)
-
-syntax "sum_with_mut_borrows_loop_decreases" term+ : tactic
-
-macro_rules
-| `(tactic| sum_with_mut_borrows_loop_decreases $max $mi $ms) =>`(tactic| sorry)
-
-/- [loops::sum_with_shared_borrows]: termination measure -/
-@[simp]
-def sum_with_shared_borrows_loop_terminates (max : U32) (i : U32) (s : U32) :=
-  (max, i, s)
-
-syntax "sum_with_shared_borrows_loop_decreases" term+ : tactic
-
-macro_rules
-| `(tactic| sum_with_shared_borrows_loop_decreases $max $i $s) =>`(tactic| sorry)
-
-/- [loops::clear]: termination measure -/
-@[simp] def clear_loop_terminates (v : Vec U32) (i : Usize) := (v, i)
-
-syntax "clear_loop_decreases" term+ : tactic
-
-macro_rules
-| `(tactic| clear_loop_decreases $v $i) =>`(tactic| sorry)
-
-/- [loops::list_mem]: termination measure -/
-@[simp]
-def list_mem_loop_terminates (x : U32) (ls : list_t U32) := (x, ls)
-
-syntax "list_mem_loop_decreases" term+ : tactic
-
-macro_rules
-| `(tactic| list_mem_loop_decreases $x $ls) =>`(tactic| sorry)
-
-/- [loops::list_nth_mut_loop]: termination measure -/
-@[simp]
-def list_nth_mut_loop_loop_terminates (T : Type) (ls : list_t T) (i : U32) :=
-  (ls, i)
-
-syntax "list_nth_mut_loop_loop_decreases" term+ : tactic
-
-macro_rules
-| `(tactic| list_nth_mut_loop_loop_decreases $ls $i) =>`(tactic| sorry)
-
-/- [loops::list_nth_shared_loop]: termination measure -/
-@[simp]
-def list_nth_shared_loop_loop_terminates (T : Type) (ls : list_t T) (i : U32) :=
-  (ls, i)
-
-syntax "list_nth_shared_loop_loop_decreases" term+ : tactic
-
-macro_rules
-| `(tactic| list_nth_shared_loop_loop_decreases $ls $i) =>`(tactic| sorry)
-
-/- [loops::get_elem_mut]: termination measure -/
-@[simp]
-def get_elem_mut_loop_terminates (x : Usize) (ls : list_t Usize) := (x, ls)
-
-syntax "get_elem_mut_loop_decreases" term+ : tactic
-
-macro_rules
-| `(tactic| get_elem_mut_loop_decreases $x $ls) =>`(tactic| sorry)
-
-/- [loops::get_elem_shared]: termination measure -/
-@[simp]
-def get_elem_shared_loop_terminates (x : Usize) (ls : list_t Usize) := (x, ls)
-
-syntax "get_elem_shared_loop_decreases" term+ : tactic
-
-macro_rules
-| `(tactic| get_elem_shared_loop_decreases $x $ls) =>`(tactic| sorry)
-
-/- [loops::list_nth_mut_loop_with_id]: termination measure -/
-@[simp]
-def list_nth_mut_loop_with_id_loop_terminates (T : Type) (i : U32)
-  (ls : list_t T) :=
-  (i, ls)
-
-syntax "list_nth_mut_loop_with_id_loop_decreases" term+ : tactic
-
-macro_rules
-| `(tactic| list_nth_mut_loop_with_id_loop_decreases $i $ls) =>`(tactic| sorry)
-
-/- [loops::list_nth_shared_loop_with_id]: termination measure -/
-@[simp]
-def list_nth_shared_loop_with_id_loop_terminates (T : Type) (i : U32)
-  (ls : list_t T) :=
-  (i, ls)
-
-syntax "list_nth_shared_loop_with_id_loop_decreases" term+ : tactic
-
-macro_rules
-| `(tactic| list_nth_shared_loop_with_id_loop_decreases $i $ls) =>`(tactic| sorry)
-
-/- [loops::list_nth_mut_loop_pair]: termination measure -/
-@[simp]
-def list_nth_mut_loop_pair_loop_terminates (T : Type) (ls0 : list_t T)
-  (ls1 : list_t T) (i : U32) :=
-  (ls0, ls1, i)
-
-syntax "list_nth_mut_loop_pair_loop_decreases" term+ : tactic
-
-macro_rules
-| `(tactic| list_nth_mut_loop_pair_loop_decreases $ls0 $ls1 $i) =>`(tactic| sorry)
-
-/- [loops::list_nth_shared_loop_pair]: termination measure -/
-@[simp]
-def list_nth_shared_loop_pair_loop_terminates (T : Type) (ls0 : list_t T)
-  (ls1 : list_t T) (i : U32) :=
-  (ls0, ls1, i)
-
-syntax "list_nth_shared_loop_pair_loop_decreases" term+ : tactic
-
-macro_rules
-| `(tactic| list_nth_shared_loop_pair_loop_decreases $ls0 $ls1 $i) =>
-  `(tactic| sorry)
-
-/- [loops::list_nth_mut_loop_pair_merge]: termination measure -/
-@[simp]
-def list_nth_mut_loop_pair_merge_loop_terminates (T : Type) (ls0 : list_t T)
-  (ls1 : list_t T) (i : U32) :=
-  (ls0, ls1, i)
-
-syntax "list_nth_mut_loop_pair_merge_loop_decreases" term+ : tactic
-
-macro_rules
-| `(tactic| list_nth_mut_loop_pair_merge_loop_decreases $ls0 $ls1 $i) =>
-  `(tactic| sorry)
-
-/- [loops::list_nth_shared_loop_pair_merge]: termination measure -/
-@[simp]
-def list_nth_shared_loop_pair_merge_loop_terminates (T : Type) (ls0 : list_t T)
-  (ls1 : list_t T) (i : U32) :=
-  (ls0, ls1, i)
-
-syntax "list_nth_shared_loop_pair_merge_loop_decreases" term+ : tactic
-
-macro_rules
-| `(tactic| list_nth_shared_loop_pair_merge_loop_decreases $ls0 $ls1 $i) =>
-  `(tactic| sorry)
-
-/- [loops::list_nth_mut_shared_loop_pair]: termination measure -/
-@[simp]
-def list_nth_mut_shared_loop_pair_loop_terminates (T : Type) (ls0 : list_t T)
-  (ls1 : list_t T) (i : U32) :=
-  (ls0, ls1, i)
-
-syntax "list_nth_mut_shared_loop_pair_loop_decreases" term+ : tactic
-
-macro_rules
-| `(tactic| list_nth_mut_shared_loop_pair_loop_decreases $ls0 $ls1 $i) =>
-  `(tactic| sorry)
-
-/- [loops::list_nth_mut_shared_loop_pair_merge]: termination measure -/
-@[simp]
-def list_nth_mut_shared_loop_pair_merge_loop_terminates (T : Type)
-  (ls0 : list_t T) (ls1 : list_t T) (i : U32) :=
-  (ls0, ls1, i)
-
-syntax "list_nth_mut_shared_loop_pair_merge_loop_decreases" term+ : tactic
-
-macro_rules
-| `(tactic| list_nth_mut_shared_loop_pair_merge_loop_decreases $ls0 $ls1 $i) =>
-  `(tactic| sorry)
-
-/- [loops::list_nth_shared_mut_loop_pair]: termination measure -/
-@[simp]
-def list_nth_shared_mut_loop_pair_loop_terminates (T : Type) (ls0 : list_t T)
-  (ls1 : list_t T) (i : U32) :=
-  (ls0, ls1, i)
-
-syntax "list_nth_shared_mut_loop_pair_loop_decreases" term+ : tactic
-
-macro_rules
-| `(tactic| list_nth_shared_mut_loop_pair_loop_decreases $ls0 $ls1 $i) =>
-  `(tactic| sorry)
-
-/- [loops::list_nth_shared_mut_loop_pair_merge]: termination measure -/
-@[simp]
-def list_nth_shared_mut_loop_pair_merge_loop_terminates (T : Type)
-  (ls0 : list_t T) (ls1 : list_t T) (i : U32) :=
-  (ls0, ls1, i)
-
-syntax "list_nth_shared_mut_loop_pair_merge_loop_decreases" term+ : tactic
-
-macro_rules
-| `(tactic| list_nth_shared_mut_loop_pair_merge_loop_decreases $ls0 $ls1 $i) =>
-  `(tactic| sorry)
-
diff --git a/tests/lean/misc-loops/Loops/Clauses/Template.lean b/tests/lean/misc-loops/Loops/Clauses/Template.lean
deleted file mode 100644
index 2e28a6c0..00000000
--- a/tests/lean/misc-loops/Loops/Clauses/Template.lean
+++ /dev/null
@@ -1,205 +0,0 @@
--- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
--- [loops]: templates for the decreases clauses
-import Base.Primitives
-import Loops.Types
-
-/- [loops::sum]: termination measure -/
-@[simp] def sum_loop_terminates (max : U32) (i : U32) (s : U32) := (max, i, s)
-
-/- [loops::sum]: decreases_by tactic -/
-syntax "sum_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| sum_loop_decreases $max $i $s) =>`(tactic| sorry)
-
-/- [loops::sum_with_mut_borrows]: termination measure -/
-@[simp]
-def sum_with_mut_borrows_loop_terminates (max : U32) (mi : U32) (ms : U32) :=
-  (max, mi, ms)
-
-/- [loops::sum_with_mut_borrows]: decreases_by tactic -/
-syntax "sum_with_mut_borrows_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| sum_with_mut_borrows_loop_decreases $max $mi $ms) =>`(tactic| sorry)
-
-/- [loops::sum_with_shared_borrows]: termination measure -/
-@[simp]
-def sum_with_shared_borrows_loop_terminates (max : U32) (i : U32) (s : U32) :=
-  (max, i, s)
-
-/- [loops::sum_with_shared_borrows]: decreases_by tactic -/
-syntax "sum_with_shared_borrows_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| sum_with_shared_borrows_loop_decreases $max $i $s) =>`(tactic| sorry)
-
-/- [loops::clear]: termination measure -/
-@[simp] def clear_loop_terminates (v : Vec U32) (i : Usize) := (v, i)
-
-/- [loops::clear]: decreases_by tactic -/
-syntax "clear_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| clear_loop_decreases $v $i) =>`(tactic| sorry)
-
-/- [loops::list_mem]: termination measure -/
-@[simp] def list_mem_loop_terminates (x : U32) (ls : list_t U32) := (x, ls)
-
-/- [loops::list_mem]: decreases_by tactic -/
-syntax "list_mem_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| list_mem_loop_decreases $x $ls) =>`(tactic| sorry)
-
-/- [loops::list_nth_mut_loop]: termination measure -/
-@[simp]
-def list_nth_mut_loop_loop_terminates (T : Type) (ls : list_t T) (i : U32) :=
-  (ls, i)
-
-/- [loops::list_nth_mut_loop]: decreases_by tactic -/
-syntax "list_nth_mut_loop_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| list_nth_mut_loop_loop_decreases $ls $i) =>`(tactic| sorry)
-
-/- [loops::list_nth_shared_loop]: termination measure -/
-@[simp]
-def list_nth_shared_loop_loop_terminates (T : Type) (ls : list_t T) (i : U32)
-  :=
-  (ls, i)
-
-/- [loops::list_nth_shared_loop]: decreases_by tactic -/
-syntax "list_nth_shared_loop_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| list_nth_shared_loop_loop_decreases $ls $i) =>`(tactic| sorry)
-
-/- [loops::get_elem_mut]: termination measure -/
-@[simp]
-def get_elem_mut_loop_terminates (x : Usize) (ls : list_t Usize) := (x, ls)
-
-/- [loops::get_elem_mut]: decreases_by tactic -/
-syntax "get_elem_mut_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| get_elem_mut_loop_decreases $x $ls) =>`(tactic| sorry)
-
-/- [loops::get_elem_shared]: termination measure -/
-@[simp]
-def get_elem_shared_loop_terminates (x : Usize) (ls : list_t Usize) := (x, ls)
-
-/- [loops::get_elem_shared]: decreases_by tactic -/
-syntax "get_elem_shared_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| get_elem_shared_loop_decreases $x $ls) =>`(tactic| sorry)
-
-/- [loops::list_nth_mut_loop_with_id]: termination measure -/
-@[simp]
-def list_nth_mut_loop_with_id_loop_terminates (T : Type) (i : U32)
-  (ls : list_t T) :=
-  (i, ls)
-
-/- [loops::list_nth_mut_loop_with_id]: decreases_by tactic -/
-syntax "list_nth_mut_loop_with_id_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| list_nth_mut_loop_with_id_loop_decreases $i $ls) =>`(tactic| sorry)
-
-/- [loops::list_nth_shared_loop_with_id]: termination measure -/
-@[simp]
-def list_nth_shared_loop_with_id_loop_terminates (T : Type) (i : U32)
-  (ls : list_t T) :=
-  (i, ls)
-
-/- [loops::list_nth_shared_loop_with_id]: decreases_by tactic -/
-syntax "list_nth_shared_loop_with_id_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| list_nth_shared_loop_with_id_loop_decreases $i $ls) =>`(tactic| sorry)
-
-/- [loops::list_nth_mut_loop_pair]: termination measure -/
-@[simp]
-def list_nth_mut_loop_pair_loop_terminates (T : Type) (ls0 : list_t T)
-  (ls1 : list_t T) (i : U32) :=
-  (ls0, ls1, i)
-
-/- [loops::list_nth_mut_loop_pair]: decreases_by tactic -/
-syntax "list_nth_mut_loop_pair_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| list_nth_mut_loop_pair_loop_decreases $ls0 $ls1 $i) =>`(tactic| sorry)
-
-/- [loops::list_nth_shared_loop_pair]: termination measure -/
-@[simp]
-def list_nth_shared_loop_pair_loop_terminates (T : Type) (ls0 : list_t T)
-  (ls1 : list_t T) (i : U32) :=
-  (ls0, ls1, i)
-
-/- [loops::list_nth_shared_loop_pair]: decreases_by tactic -/
-syntax "list_nth_shared_loop_pair_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| list_nth_shared_loop_pair_loop_decreases $ls0 $ls1 $i) =>
-  `(tactic| sorry)
-
-/- [loops::list_nth_mut_loop_pair_merge]: termination measure -/
-@[simp]
-def list_nth_mut_loop_pair_merge_loop_terminates (T : Type) (ls0 : list_t T)
-  (ls1 : list_t T) (i : U32) :=
-  (ls0, ls1, i)
-
-/- [loops::list_nth_mut_loop_pair_merge]: decreases_by tactic -/
-syntax "list_nth_mut_loop_pair_merge_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| list_nth_mut_loop_pair_merge_loop_decreases $ls0 $ls1 $i) =>
-  `(tactic| sorry)
-
-/- [loops::list_nth_shared_loop_pair_merge]: termination measure -/
-@[simp]
-def list_nth_shared_loop_pair_merge_loop_terminates (T : Type) (ls0 : list_t T)
-  (ls1 : list_t T) (i : U32) :=
-  (ls0, ls1, i)
-
-/- [loops::list_nth_shared_loop_pair_merge]: decreases_by tactic -/
-syntax "list_nth_shared_loop_pair_merge_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| list_nth_shared_loop_pair_merge_loop_decreases $ls0 $ls1 $i) =>
-  `(tactic| sorry)
-
-/- [loops::list_nth_mut_shared_loop_pair]: termination measure -/
-@[simp]
-def list_nth_mut_shared_loop_pair_loop_terminates (T : Type) (ls0 : list_t T)
-  (ls1 : list_t T) (i : U32) :=
-  (ls0, ls1, i)
-
-/- [loops::list_nth_mut_shared_loop_pair]: decreases_by tactic -/
-syntax "list_nth_mut_shared_loop_pair_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| list_nth_mut_shared_loop_pair_loop_decreases $ls0 $ls1 $i) =>
-  `(tactic| sorry)
-
-/- [loops::list_nth_mut_shared_loop_pair_merge]: termination measure -/
-@[simp]
-def list_nth_mut_shared_loop_pair_merge_loop_terminates (T : Type)
-  (ls0 : list_t T) (ls1 : list_t T) (i : U32) :=
-  (ls0, ls1, i)
-
-/- [loops::list_nth_mut_shared_loop_pair_merge]: decreases_by tactic -/
-syntax "list_nth_mut_shared_loop_pair_merge_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| list_nth_mut_shared_loop_pair_merge_loop_decreases $ls0 $ls1 $i) =>
-  `(tactic| sorry)
-
-/- [loops::list_nth_shared_mut_loop_pair]: termination measure -/
-@[simp]
-def list_nth_shared_mut_loop_pair_loop_terminates (T : Type) (ls0 : list_t T)
-  (ls1 : list_t T) (i : U32) :=
-  (ls0, ls1, i)
-
-/- [loops::list_nth_shared_mut_loop_pair]: decreases_by tactic -/
-syntax "list_nth_shared_mut_loop_pair_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| list_nth_shared_mut_loop_pair_loop_decreases $ls0 $ls1 $i) =>
-  `(tactic| sorry)
-
-/- [loops::list_nth_shared_mut_loop_pair_merge]: termination measure -/
-@[simp]
-def list_nth_shared_mut_loop_pair_merge_loop_terminates (T : Type)
-  (ls0 : list_t T) (ls1 : list_t T) (i : U32) :=
-  (ls0, ls1, i)
-
-/- [loops::list_nth_shared_mut_loop_pair_merge]: decreases_by tactic -/
-syntax "list_nth_shared_mut_loop_pair_merge_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| list_nth_shared_mut_loop_pair_merge_loop_decreases $ls0 $ls1 $i) =>
-  `(tactic| sorry)
-
diff --git a/tests/lean/misc-loops/Loops/Funs.lean b/tests/lean/misc-loops/Loops/Funs.lean
deleted file mode 100644
index fd8d62d7..00000000
--- a/tests/lean/misc-loops/Loops/Funs.lean
+++ /dev/null
@@ -1,705 +0,0 @@
--- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
--- [loops]: function definitions
-import Base.Primitives
-import Loops.Types
-import Loops.Clauses.Clauses
-
-/- [loops::sum] -/
-def sum_loop_fwd (max : U32) (i : U32) (s : U32) : (Result U32) :=
-  if h: i < max
-  then
-    do
-      let s0 ← s + i
-      let i0 ← i + (U32.ofInt 1 (by intlit))
-      sum_loop_fwd max i0 s0
-  else s * (U32.ofInt 2 (by intlit))
-termination_by sum_loop_fwd max i s => sum_loop_terminates max i s
-decreasing_by sum_loop_decreases max i s
-
-/- [loops::sum] -/
-def sum_fwd (max : U32) : Result U32 :=
-  sum_loop_fwd max (U32.ofInt 0 (by intlit)) (U32.ofInt 0 (by intlit))
-
-/- [loops::sum_with_mut_borrows] -/
-def sum_with_mut_borrows_loop_fwd
-  (max : U32) (mi : U32) (ms : U32) : (Result U32) :=
-  if h: mi < max
-  then
-    do
-      let ms0 ← ms + mi
-      let mi0 ← mi + (U32.ofInt 1 (by intlit))
-      sum_with_mut_borrows_loop_fwd max mi0 ms0
-  else ms * (U32.ofInt 2 (by intlit))
-termination_by sum_with_mut_borrows_loop_fwd max mi ms =>
-  sum_with_mut_borrows_loop_terminates max mi ms
-decreasing_by sum_with_mut_borrows_loop_decreases max mi ms
-
-/- [loops::sum_with_mut_borrows] -/
-def sum_with_mut_borrows_fwd (max : U32) : Result U32 :=
-  sum_with_mut_borrows_loop_fwd max (U32.ofInt 0 (by intlit))
-    (U32.ofInt 0 (by intlit))
-
-/- [loops::sum_with_shared_borrows] -/
-def sum_with_shared_borrows_loop_fwd
-  (max : U32) (i : U32) (s : U32) : (Result U32) :=
-  if h: i < max
-  then
-    do
-      let i0 ← i + (U32.ofInt 1 (by intlit))
-      let s0 ← s + i0
-      sum_with_shared_borrows_loop_fwd max i0 s0
-  else s * (U32.ofInt 2 (by intlit))
-termination_by sum_with_shared_borrows_loop_fwd max i s =>
-  sum_with_shared_borrows_loop_terminates max i s
-decreasing_by sum_with_shared_borrows_loop_decreases max i s
-
-/- [loops::sum_with_shared_borrows] -/
-def sum_with_shared_borrows_fwd (max : U32) : Result U32 :=
-  sum_with_shared_borrows_loop_fwd max (U32.ofInt 0 (by intlit))
-    (U32.ofInt 0 (by intlit))
-
-/- [loops::clear] -/
-def clear_loop_fwd_back (v : Vec U32) (i : Usize) : (Result (Vec U32)) :=
-  let i0 := vec_len U32 v
-  if h: i < i0
-  then
-    do
-      let i1 ← i + (Usize.ofInt 1 (by intlit))
-      let v0 ← vec_index_mut_back U32 v i (U32.ofInt 0 (by intlit))
-      clear_loop_fwd_back v0 i1
-  else Result.ret v
-termination_by clear_loop_fwd_back v i => clear_loop_terminates v i
-decreasing_by clear_loop_decreases v i
-
-/- [loops::clear] -/
-def clear_fwd_back (v : Vec U32) : Result (Vec U32) :=
-  clear_loop_fwd_back v (Usize.ofInt 0 (by intlit))
-
-/- [loops::list_mem] -/
-def list_mem_loop_fwd (x : U32) (ls : list_t U32) : (Result Bool) :=
-  match h: ls with
-  | list_t.Cons y tl =>
-    if h: y = x
-    then Result.ret true
-    else list_mem_loop_fwd x tl
-  | list_t.Nil => Result.ret false
-termination_by list_mem_loop_fwd x ls => list_mem_loop_terminates x ls
-decreasing_by list_mem_loop_decreases x ls
-
-/- [loops::list_mem] -/
-def list_mem_fwd (x : U32) (ls : list_t U32) : Result Bool :=
-  list_mem_loop_fwd x ls
-
-/- [loops::list_nth_mut_loop] -/
-def list_nth_mut_loop_loop_fwd
-  (T : Type) (ls : list_t T) (i : U32) : (Result T) :=
-  match h: ls with
-  | list_t.Cons x tl =>
-    if h: i = (U32.ofInt 0 (by intlit))
-    then Result.ret x
-    else
-      do
-        let i0 ← i - (U32.ofInt 1 (by intlit))
-        list_nth_mut_loop_loop_fwd T tl i0
-  | list_t.Nil => Result.fail Error.panic
-termination_by list_nth_mut_loop_loop_fwd ls i =>
-  list_nth_mut_loop_loop_terminates T ls i
-decreasing_by list_nth_mut_loop_loop_decreases ls i
-
-/- [loops::list_nth_mut_loop] -/
-def list_nth_mut_loop_fwd (T : Type) (ls : list_t T) (i : U32) : Result T :=
-  list_nth_mut_loop_loop_fwd T ls i
-
-/- [loops::list_nth_mut_loop] -/
-def list_nth_mut_loop_loop_back
-  (T : Type) (ls : list_t T) (i : U32) (ret0 : T) : (Result (list_t T)) :=
-  match h: ls with
-  | list_t.Cons x tl =>
-    if h: i = (U32.ofInt 0 (by intlit))
-    then Result.ret (list_t.Cons ret0 tl)
-    else
-      do
-        let i0 ← i - (U32.ofInt 1 (by intlit))
-        let tl0 ← list_nth_mut_loop_loop_back T tl i0 ret0
-        Result.ret (list_t.Cons x tl0)
-  | list_t.Nil => Result.fail Error.panic
-termination_by list_nth_mut_loop_loop_back ls i ret0 =>
-  list_nth_mut_loop_loop_terminates T ls i
-decreasing_by list_nth_mut_loop_loop_decreases ls i
-
-/- [loops::list_nth_mut_loop] -/
-def list_nth_mut_loop_back
-  (T : Type) (ls : list_t T) (i : U32) (ret0 : T) : Result (list_t T) :=
-  list_nth_mut_loop_loop_back T ls i ret0
-
-/- [loops::list_nth_shared_loop] -/
-def list_nth_shared_loop_loop_fwd
-  (T : Type) (ls : list_t T) (i : U32) : (Result T) :=
-  match h: ls with
-  | list_t.Cons x tl =>
-    if h: i = (U32.ofInt 0 (by intlit))
-    then Result.ret x
-    else
-      do
-        let i0 ← i - (U32.ofInt 1 (by intlit))
-        list_nth_shared_loop_loop_fwd T tl i0
-  | list_t.Nil => Result.fail Error.panic
-termination_by list_nth_shared_loop_loop_fwd ls i =>
-  list_nth_shared_loop_loop_terminates T ls i
-decreasing_by list_nth_shared_loop_loop_decreases ls i
-
-/- [loops::list_nth_shared_loop] -/
-def list_nth_shared_loop_fwd (T : Type) (ls : list_t T) (i : U32) : Result T :=
-  list_nth_shared_loop_loop_fwd T ls i
-
-/- [loops::get_elem_mut] -/
-def get_elem_mut_loop_fwd (x : Usize) (ls : list_t Usize) : (Result Usize) :=
-  match h: ls with
-  | list_t.Cons y tl =>
-    if h: y = x
-    then Result.ret y
-    else get_elem_mut_loop_fwd x tl
-  | list_t.Nil => Result.fail Error.panic
-termination_by get_elem_mut_loop_fwd x ls => get_elem_mut_loop_terminates x ls
-decreasing_by get_elem_mut_loop_decreases x ls
-
-/- [loops::get_elem_mut] -/
-def get_elem_mut_fwd (slots : Vec (list_t Usize)) (x : Usize) : Result Usize :=
-  do
-    let l ←
-      vec_index_mut_fwd (list_t Usize) slots (Usize.ofInt 0 (by intlit))
-    get_elem_mut_loop_fwd x l
-
-/- [loops::get_elem_mut] -/
-def get_elem_mut_loop_back
-  (x : Usize) (ls : list_t Usize) (ret0 : Usize) : (Result (list_t Usize)) :=
-  match h: ls with
-  | list_t.Cons y tl =>
-    if h: y = x
-    then Result.ret (list_t.Cons ret0 tl)
-    else
-      do
-        let tl0 ← get_elem_mut_loop_back x tl ret0
-        Result.ret (list_t.Cons y tl0)
-  | list_t.Nil => Result.fail Error.panic
-termination_by get_elem_mut_loop_back x ls ret0 =>
-  get_elem_mut_loop_terminates x ls
-decreasing_by get_elem_mut_loop_decreases x ls
-
-/- [loops::get_elem_mut] -/
-def get_elem_mut_back
-  (slots : Vec (list_t Usize)) (x : Usize) (ret0 : Usize) :
-  Result (Vec (list_t Usize))
-  :=
-  do
-    let l ←
-      vec_index_mut_fwd (list_t Usize) slots (Usize.ofInt 0 (by intlit))
-    let l0 ← get_elem_mut_loop_back x l ret0
-    vec_index_mut_back (list_t Usize) slots (Usize.ofInt 0 (by intlit)) l0
-
-/- [loops::get_elem_shared] -/
-def get_elem_shared_loop_fwd
-  (x : Usize) (ls : list_t Usize) : (Result Usize) :=
-  match h: ls with
-  | list_t.Cons y tl =>
-    if h: y = x
-    then Result.ret y
-    else get_elem_shared_loop_fwd x tl
-  | list_t.Nil => Result.fail Error.panic
-termination_by get_elem_shared_loop_fwd x ls =>
-  get_elem_shared_loop_terminates x ls
-decreasing_by get_elem_shared_loop_decreases x ls
-
-/- [loops::get_elem_shared] -/
-def get_elem_shared_fwd
-  (slots : Vec (list_t Usize)) (x : Usize) : Result Usize :=
-  do
-    let l ← vec_index_fwd (list_t Usize) slots (Usize.ofInt 0 (by intlit))
-    get_elem_shared_loop_fwd x l
-
-/- [loops::id_mut] -/
-def id_mut_fwd (T : Type) (ls : list_t T) : Result (list_t T) :=
-  Result.ret ls
-
-/- [loops::id_mut] -/
-def id_mut_back
-  (T : Type) (ls : list_t T) (ret0 : list_t T) : Result (list_t T) :=
-  Result.ret ret0
-
-/- [loops::id_shared] -/
-def id_shared_fwd (T : Type) (ls : list_t T) : Result (list_t T) :=
-  Result.ret ls
-
-/- [loops::list_nth_mut_loop_with_id] -/
-def list_nth_mut_loop_with_id_loop_fwd
-  (T : Type) (i : U32) (ls : list_t T) : (Result T) :=
-  match h: ls with
-  | list_t.Cons x tl =>
-    if h: i = (U32.ofInt 0 (by intlit))
-    then Result.ret x
-    else
-      do
-        let i0 ← i - (U32.ofInt 1 (by intlit))
-        list_nth_mut_loop_with_id_loop_fwd T i0 tl
-  | list_t.Nil => Result.fail Error.panic
-termination_by list_nth_mut_loop_with_id_loop_fwd i ls =>
-  list_nth_mut_loop_with_id_loop_terminates T i ls
-decreasing_by list_nth_mut_loop_with_id_loop_decreases i ls
-
-/- [loops::list_nth_mut_loop_with_id] -/
-def list_nth_mut_loop_with_id_fwd
-  (T : Type) (ls : list_t T) (i : U32) : Result T :=
-  do
-    let ls0 ← id_mut_fwd T ls
-    list_nth_mut_loop_with_id_loop_fwd T i ls0
-
-/- [loops::list_nth_mut_loop_with_id] -/
-def list_nth_mut_loop_with_id_loop_back
-  (T : Type) (i : U32) (ls : list_t T) (ret0 : T) : (Result (list_t T)) :=
-  match h: ls with
-  | list_t.Cons x tl =>
-    if h: i = (U32.ofInt 0 (by intlit))
-    then Result.ret (list_t.Cons ret0 tl)
-    else
-      do
-        let i0 ← i - (U32.ofInt 1 (by intlit))
-        let tl0 ← list_nth_mut_loop_with_id_loop_back T i0 tl ret0
-        Result.ret (list_t.Cons x tl0)
-  | list_t.Nil => Result.fail Error.panic
-termination_by list_nth_mut_loop_with_id_loop_back i ls ret0 =>
-  list_nth_mut_loop_with_id_loop_terminates T i ls
-decreasing_by list_nth_mut_loop_with_id_loop_decreases i ls
-
-/- [loops::list_nth_mut_loop_with_id] -/
-def list_nth_mut_loop_with_id_back
-  (T : Type) (ls : list_t T) (i : U32) (ret0 : T) : Result (list_t T) :=
-  do
-    let ls0 ← id_mut_fwd T ls
-    let l ← list_nth_mut_loop_with_id_loop_back T i ls0 ret0
-    id_mut_back T ls l
-
-/- [loops::list_nth_shared_loop_with_id] -/
-def list_nth_shared_loop_with_id_loop_fwd
-  (T : Type) (i : U32) (ls : list_t T) : (Result T) :=
-  match h: ls with
-  | list_t.Cons x tl =>
-    if h: i = (U32.ofInt 0 (by intlit))
-    then Result.ret x
-    else
-      do
-        let i0 ← i - (U32.ofInt 1 (by intlit))
-        list_nth_shared_loop_with_id_loop_fwd T i0 tl
-  | list_t.Nil => Result.fail Error.panic
-termination_by list_nth_shared_loop_with_id_loop_fwd i ls =>
-  list_nth_shared_loop_with_id_loop_terminates T i ls
-decreasing_by list_nth_shared_loop_with_id_loop_decreases i ls
-
-/- [loops::list_nth_shared_loop_with_id] -/
-def list_nth_shared_loop_with_id_fwd
-  (T : Type) (ls : list_t T) (i : U32) : Result T :=
-  do
-    let ls0 ← id_shared_fwd T ls
-    list_nth_shared_loop_with_id_loop_fwd T i ls0
-
-/- [loops::list_nth_mut_loop_pair] -/
-def list_nth_mut_loop_pair_loop_fwd
-  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : (Result (T × T)) :=
-  match h: ls0 with
-  | list_t.Cons x0 tl0 =>
-    match h: ls1 with
-    | list_t.Cons x1 tl1 =>
-      if h: i = (U32.ofInt 0 (by intlit))
-      then Result.ret (x0, x1)
-      else
-        do
-          let i0 ← i - (U32.ofInt 1 (by intlit))
-          list_nth_mut_loop_pair_loop_fwd T tl0 tl1 i0
-    | list_t.Nil => Result.fail Error.panic
-  | list_t.Nil => Result.fail Error.panic
-termination_by list_nth_mut_loop_pair_loop_fwd ls0 ls1 i =>
-  list_nth_mut_loop_pair_loop_terminates T ls0 ls1 i
-decreasing_by list_nth_mut_loop_pair_loop_decreases ls0 ls1 i
-
-/- [loops::list_nth_mut_loop_pair] -/
-def list_nth_mut_loop_pair_fwd
-  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : Result (T × T) :=
-  list_nth_mut_loop_pair_loop_fwd T ls0 ls1 i
-
-/- [loops::list_nth_mut_loop_pair] -/
-def list_nth_mut_loop_pair_loop_back'a
-  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) (ret0 : T) :
-  (Result (list_t T))
-  :=
-  match h: ls0 with
-  | list_t.Cons x0 tl0 =>
-    match h: ls1 with
-    | list_t.Cons x1 tl1 =>
-      if h: i = (U32.ofInt 0 (by intlit))
-      then Result.ret (list_t.Cons ret0 tl0)
-      else
-        do
-          let i0 ← i - (U32.ofInt 1 (by intlit))
-          let tl00 ← list_nth_mut_loop_pair_loop_back'a T tl0 tl1 i0 ret0
-          Result.ret (list_t.Cons x0 tl00)
-    | list_t.Nil => Result.fail Error.panic
-  | list_t.Nil => Result.fail Error.panic
-termination_by list_nth_mut_loop_pair_loop_back'a ls0 ls1 i ret0 =>
-  list_nth_mut_loop_pair_loop_terminates T ls0 ls1 i
-decreasing_by list_nth_mut_loop_pair_loop_decreases ls0 ls1 i
-
-/- [loops::list_nth_mut_loop_pair] -/
-def list_nth_mut_loop_pair_back'a
-  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) (ret0 : T) :
-  Result (list_t T)
-  :=
-  list_nth_mut_loop_pair_loop_back'a T ls0 ls1 i ret0
-
-/- [loops::list_nth_mut_loop_pair] -/
-def list_nth_mut_loop_pair_loop_back'b
-  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) (ret0 : T) :
-  (Result (list_t T))
-  :=
-  match h: ls0 with
-  | list_t.Cons x0 tl0 =>
-    match h: ls1 with
-    | list_t.Cons x1 tl1 =>
-      if h: i = (U32.ofInt 0 (by intlit))
-      then Result.ret (list_t.Cons ret0 tl1)
-      else
-        do
-          let i0 ← i - (U32.ofInt 1 (by intlit))
-          let tl10 ← list_nth_mut_loop_pair_loop_back'b T tl0 tl1 i0 ret0
-          Result.ret (list_t.Cons x1 tl10)
-    | list_t.Nil => Result.fail Error.panic
-  | list_t.Nil => Result.fail Error.panic
-termination_by list_nth_mut_loop_pair_loop_back'b ls0 ls1 i ret0 =>
-  list_nth_mut_loop_pair_loop_terminates T ls0 ls1 i
-decreasing_by list_nth_mut_loop_pair_loop_decreases ls0 ls1 i
-
-/- [loops::list_nth_mut_loop_pair] -/
-def list_nth_mut_loop_pair_back'b
-  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) (ret0 : T) :
-  Result (list_t T)
-  :=
-  list_nth_mut_loop_pair_loop_back'b T ls0 ls1 i ret0
-
-/- [loops::list_nth_shared_loop_pair] -/
-def list_nth_shared_loop_pair_loop_fwd
-  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : (Result (T × T)) :=
-  match h: ls0 with
-  | list_t.Cons x0 tl0 =>
-    match h: ls1 with
-    | list_t.Cons x1 tl1 =>
-      if h: i = (U32.ofInt 0 (by intlit))
-      then Result.ret (x0, x1)
-      else
-        do
-          let i0 ← i - (U32.ofInt 1 (by intlit))
-          list_nth_shared_loop_pair_loop_fwd T tl0 tl1 i0
-    | list_t.Nil => Result.fail Error.panic
-  | list_t.Nil => Result.fail Error.panic
-termination_by list_nth_shared_loop_pair_loop_fwd ls0 ls1 i =>
-  list_nth_shared_loop_pair_loop_terminates T ls0 ls1 i
-decreasing_by list_nth_shared_loop_pair_loop_decreases ls0 ls1 i
-
-/- [loops::list_nth_shared_loop_pair] -/
-def list_nth_shared_loop_pair_fwd
-  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : Result (T × T) :=
-  list_nth_shared_loop_pair_loop_fwd T ls0 ls1 i
-
-/- [loops::list_nth_mut_loop_pair_merge] -/
-def list_nth_mut_loop_pair_merge_loop_fwd
-  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : (Result (T × T)) :=
-  match h: ls0 with
-  | list_t.Cons x0 tl0 =>
-    match h: ls1 with
-    | list_t.Cons x1 tl1 =>
-      if h: i = (U32.ofInt 0 (by intlit))
-      then Result.ret (x0, x1)
-      else
-        do
-          let i0 ← i - (U32.ofInt 1 (by intlit))
-          list_nth_mut_loop_pair_merge_loop_fwd T tl0 tl1 i0
-    | list_t.Nil => Result.fail Error.panic
-  | list_t.Nil => Result.fail Error.panic
-termination_by list_nth_mut_loop_pair_merge_loop_fwd ls0 ls1 i =>
-  list_nth_mut_loop_pair_merge_loop_terminates T ls0 ls1 i
-decreasing_by list_nth_mut_loop_pair_merge_loop_decreases ls0 ls1 i
-
-/- [loops::list_nth_mut_loop_pair_merge] -/
-def list_nth_mut_loop_pair_merge_fwd
-  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : Result (T × T) :=
-  list_nth_mut_loop_pair_merge_loop_fwd T ls0 ls1 i
-
-/- [loops::list_nth_mut_loop_pair_merge] -/
-def list_nth_mut_loop_pair_merge_loop_back
-  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) (ret0 : (T × T)) :
-  (Result ((list_t T) × (list_t T)))
-  :=
-  match h: ls0 with
-  | list_t.Cons x0 tl0 =>
-    match h: ls1 with
-    | list_t.Cons x1 tl1 =>
-      if h: i = (U32.ofInt 0 (by intlit))
-      then
-        let (t, t0) := ret0
-        Result.ret (list_t.Cons t tl0, list_t.Cons t0 tl1)
-      else
-        do
-          let i0 ← i - (U32.ofInt 1 (by intlit))
-          let (tl00, tl10) ←
-            list_nth_mut_loop_pair_merge_loop_back T tl0 tl1 i0 ret0
-          Result.ret (list_t.Cons x0 tl00, list_t.Cons x1 tl10)
-    | list_t.Nil => Result.fail Error.panic
-  | list_t.Nil => Result.fail Error.panic
-termination_by list_nth_mut_loop_pair_merge_loop_back ls0 ls1 i ret0 =>
-  list_nth_mut_loop_pair_merge_loop_terminates T ls0 ls1 i
-decreasing_by list_nth_mut_loop_pair_merge_loop_decreases ls0 ls1 i
-
-/- [loops::list_nth_mut_loop_pair_merge] -/
-def list_nth_mut_loop_pair_merge_back
-  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) (ret0 : (T × T)) :
-  Result ((list_t T) × (list_t T))
-  :=
-  list_nth_mut_loop_pair_merge_loop_back T ls0 ls1 i ret0
-
-/- [loops::list_nth_shared_loop_pair_merge] -/
-def list_nth_shared_loop_pair_merge_loop_fwd
-  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : (Result (T × T)) :=
-  match h: ls0 with
-  | list_t.Cons x0 tl0 =>
-    match h: ls1 with
-    | list_t.Cons x1 tl1 =>
-      if h: i = (U32.ofInt 0 (by intlit))
-      then Result.ret (x0, x1)
-      else
-        do
-          let i0 ← i - (U32.ofInt 1 (by intlit))
-          list_nth_shared_loop_pair_merge_loop_fwd T tl0 tl1 i0
-    | list_t.Nil => Result.fail Error.panic
-  | list_t.Nil => Result.fail Error.panic
-termination_by list_nth_shared_loop_pair_merge_loop_fwd ls0 ls1 i =>
-  list_nth_shared_loop_pair_merge_loop_terminates T ls0 ls1 i
-decreasing_by list_nth_shared_loop_pair_merge_loop_decreases ls0 ls1 i
-
-/- [loops::list_nth_shared_loop_pair_merge] -/
-def list_nth_shared_loop_pair_merge_fwd
-  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : Result (T × T) :=
-  list_nth_shared_loop_pair_merge_loop_fwd T ls0 ls1 i
-
-/- [loops::list_nth_mut_shared_loop_pair] -/
-def list_nth_mut_shared_loop_pair_loop_fwd
-  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : (Result (T × T)) :=
-  match h: ls0 with
-  | list_t.Cons x0 tl0 =>
-    match h: ls1 with
-    | list_t.Cons x1 tl1 =>
-      if h: i = (U32.ofInt 0 (by intlit))
-      then Result.ret (x0, x1)
-      else
-        do
-          let i0 ← i - (U32.ofInt 1 (by intlit))
-          list_nth_mut_shared_loop_pair_loop_fwd T tl0 tl1 i0
-    | list_t.Nil => Result.fail Error.panic
-  | list_t.Nil => Result.fail Error.panic
-termination_by list_nth_mut_shared_loop_pair_loop_fwd ls0 ls1 i =>
-  list_nth_mut_shared_loop_pair_loop_terminates T ls0 ls1 i
-decreasing_by list_nth_mut_shared_loop_pair_loop_decreases ls0 ls1 i
-
-/- [loops::list_nth_mut_shared_loop_pair] -/
-def list_nth_mut_shared_loop_pair_fwd
-  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : Result (T × T) :=
-  list_nth_mut_shared_loop_pair_loop_fwd T ls0 ls1 i
-
-/- [loops::list_nth_mut_shared_loop_pair] -/
-def list_nth_mut_shared_loop_pair_loop_back
-  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) (ret0 : T) :
-  (Result (list_t T))
-  :=
-  match h: ls0 with
-  | list_t.Cons x0 tl0 =>
-    match h: ls1 with
-    | list_t.Cons x1 tl1 =>
-      if h: i = (U32.ofInt 0 (by intlit))
-      then Result.ret (list_t.Cons ret0 tl0)
-      else
-        do
-          let i0 ← i - (U32.ofInt 1 (by intlit))
-          let tl00 ←
-            list_nth_mut_shared_loop_pair_loop_back T tl0 tl1 i0 ret0
-          Result.ret (list_t.Cons x0 tl00)
-    | list_t.Nil => Result.fail Error.panic
-  | list_t.Nil => Result.fail Error.panic
-termination_by list_nth_mut_shared_loop_pair_loop_back ls0 ls1 i ret0 =>
-  list_nth_mut_shared_loop_pair_loop_terminates T ls0 ls1 i
-decreasing_by list_nth_mut_shared_loop_pair_loop_decreases ls0 ls1 i
-
-/- [loops::list_nth_mut_shared_loop_pair] -/
-def list_nth_mut_shared_loop_pair_back
-  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) (ret0 : T) :
-  Result (list_t T)
-  :=
-  list_nth_mut_shared_loop_pair_loop_back T ls0 ls1 i ret0
-
-/- [loops::list_nth_mut_shared_loop_pair_merge] -/
-def list_nth_mut_shared_loop_pair_merge_loop_fwd
-  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : (Result (T × T)) :=
-  match h: ls0 with
-  | list_t.Cons x0 tl0 =>
-    match h: ls1 with
-    | list_t.Cons x1 tl1 =>
-      if h: i = (U32.ofInt 0 (by intlit))
-      then Result.ret (x0, x1)
-      else
-        do
-          let i0 ← i - (U32.ofInt 1 (by intlit))
-          list_nth_mut_shared_loop_pair_merge_loop_fwd T tl0 tl1 i0
-    | list_t.Nil => Result.fail Error.panic
-  | list_t.Nil => Result.fail Error.panic
-termination_by list_nth_mut_shared_loop_pair_merge_loop_fwd ls0 ls1 i =>
-  list_nth_mut_shared_loop_pair_merge_loop_terminates T ls0 ls1 i
-decreasing_by list_nth_mut_shared_loop_pair_merge_loop_decreases ls0 ls1 i
-
-/- [loops::list_nth_mut_shared_loop_pair_merge] -/
-def list_nth_mut_shared_loop_pair_merge_fwd
-  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : Result (T × T) :=
-  list_nth_mut_shared_loop_pair_merge_loop_fwd T ls0 ls1 i
-
-/- [loops::list_nth_mut_shared_loop_pair_merge] -/
-def list_nth_mut_shared_loop_pair_merge_loop_back
-  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) (ret0 : T) :
-  (Result (list_t T))
-  :=
-  match h: ls0 with
-  | list_t.Cons x0 tl0 =>
-    match h: ls1 with
-    | list_t.Cons x1 tl1 =>
-      if h: i = (U32.ofInt 0 (by intlit))
-      then Result.ret (list_t.Cons ret0 tl0)
-      else
-        do
-          let i0 ← i - (U32.ofInt 1 (by intlit))
-          let tl00 ←
-            list_nth_mut_shared_loop_pair_merge_loop_back T tl0 tl1 i0 ret0
-          Result.ret (list_t.Cons x0 tl00)
-    | list_t.Nil => Result.fail Error.panic
-  | list_t.Nil => Result.fail Error.panic
-termination_by list_nth_mut_shared_loop_pair_merge_loop_back ls0 ls1 i ret0 =>
-  list_nth_mut_shared_loop_pair_merge_loop_terminates T ls0 ls1 i
-decreasing_by list_nth_mut_shared_loop_pair_merge_loop_decreases ls0 ls1 i
-
-/- [loops::list_nth_mut_shared_loop_pair_merge] -/
-def list_nth_mut_shared_loop_pair_merge_back
-  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) (ret0 : T) :
-  Result (list_t T)
-  :=
-  list_nth_mut_shared_loop_pair_merge_loop_back T ls0 ls1 i ret0
-
-/- [loops::list_nth_shared_mut_loop_pair] -/
-def list_nth_shared_mut_loop_pair_loop_fwd
-  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : (Result (T × T)) :=
-  match h: ls0 with
-  | list_t.Cons x0 tl0 =>
-    match h: ls1 with
-    | list_t.Cons x1 tl1 =>
-      if h: i = (U32.ofInt 0 (by intlit))
-      then Result.ret (x0, x1)
-      else
-        do
-          let i0 ← i - (U32.ofInt 1 (by intlit))
-          list_nth_shared_mut_loop_pair_loop_fwd T tl0 tl1 i0
-    | list_t.Nil => Result.fail Error.panic
-  | list_t.Nil => Result.fail Error.panic
-termination_by list_nth_shared_mut_loop_pair_loop_fwd ls0 ls1 i =>
-  list_nth_shared_mut_loop_pair_loop_terminates T ls0 ls1 i
-decreasing_by list_nth_shared_mut_loop_pair_loop_decreases ls0 ls1 i
-
-/- [loops::list_nth_shared_mut_loop_pair] -/
-def list_nth_shared_mut_loop_pair_fwd
-  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : Result (T × T) :=
-  list_nth_shared_mut_loop_pair_loop_fwd T ls0 ls1 i
-
-/- [loops::list_nth_shared_mut_loop_pair] -/
-def list_nth_shared_mut_loop_pair_loop_back
-  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) (ret0 : T) :
-  (Result (list_t T))
-  :=
-  match h: ls0 with
-  | list_t.Cons x0 tl0 =>
-    match h: ls1 with
-    | list_t.Cons x1 tl1 =>
-      if h: i = (U32.ofInt 0 (by intlit))
-      then Result.ret (list_t.Cons ret0 tl1)
-      else
-        do
-          let i0 ← i - (U32.ofInt 1 (by intlit))
-          let tl10 ←
-            list_nth_shared_mut_loop_pair_loop_back T tl0 tl1 i0 ret0
-          Result.ret (list_t.Cons x1 tl10)
-    | list_t.Nil => Result.fail Error.panic
-  | list_t.Nil => Result.fail Error.panic
-termination_by list_nth_shared_mut_loop_pair_loop_back ls0 ls1 i ret0 =>
-  list_nth_shared_mut_loop_pair_loop_terminates T ls0 ls1 i
-decreasing_by list_nth_shared_mut_loop_pair_loop_decreases ls0 ls1 i
-
-/- [loops::list_nth_shared_mut_loop_pair] -/
-def list_nth_shared_mut_loop_pair_back
-  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) (ret0 : T) :
-  Result (list_t T)
-  :=
-  list_nth_shared_mut_loop_pair_loop_back T ls0 ls1 i ret0
-
-/- [loops::list_nth_shared_mut_loop_pair_merge] -/
-def list_nth_shared_mut_loop_pair_merge_loop_fwd
-  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : (Result (T × T)) :=
-  match h: ls0 with
-  | list_t.Cons x0 tl0 =>
-    match h: ls1 with
-    | list_t.Cons x1 tl1 =>
-      if h: i = (U32.ofInt 0 (by intlit))
-      then Result.ret (x0, x1)
-      else
-        do
-          let i0 ← i - (U32.ofInt 1 (by intlit))
-          list_nth_shared_mut_loop_pair_merge_loop_fwd T tl0 tl1 i0
-    | list_t.Nil => Result.fail Error.panic
-  | list_t.Nil => Result.fail Error.panic
-termination_by list_nth_shared_mut_loop_pair_merge_loop_fwd ls0 ls1 i =>
-  list_nth_shared_mut_loop_pair_merge_loop_terminates T ls0 ls1 i
-decreasing_by list_nth_shared_mut_loop_pair_merge_loop_decreases ls0 ls1 i
-
-/- [loops::list_nth_shared_mut_loop_pair_merge] -/
-def list_nth_shared_mut_loop_pair_merge_fwd
-  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : Result (T × T) :=
-  list_nth_shared_mut_loop_pair_merge_loop_fwd T ls0 ls1 i
-
-/- [loops::list_nth_shared_mut_loop_pair_merge] -/
-def list_nth_shared_mut_loop_pair_merge_loop_back
-  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) (ret0 : T) :
-  (Result (list_t T))
-  :=
-  match h: ls0 with
-  | list_t.Cons x0 tl0 =>
-    match h: ls1 with
-    | list_t.Cons x1 tl1 =>
-      if h: i = (U32.ofInt 0 (by intlit))
-      then Result.ret (list_t.Cons ret0 tl1)
-      else
-        do
-          let i0 ← i - (U32.ofInt 1 (by intlit))
-          let tl10 ←
-            list_nth_shared_mut_loop_pair_merge_loop_back T tl0 tl1 i0 ret0
-          Result.ret (list_t.Cons x1 tl10)
-    | list_t.Nil => Result.fail Error.panic
-  | list_t.Nil => Result.fail Error.panic
-termination_by list_nth_shared_mut_loop_pair_merge_loop_back ls0 ls1 i ret0 =>
-  list_nth_shared_mut_loop_pair_merge_loop_terminates T ls0 ls1 i
-decreasing_by list_nth_shared_mut_loop_pair_merge_loop_decreases ls0 ls1 i
-
-/- [loops::list_nth_shared_mut_loop_pair_merge] -/
-def list_nth_shared_mut_loop_pair_merge_back
-  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) (ret0 : T) :
-  Result (list_t T)
-  :=
-  list_nth_shared_mut_loop_pair_merge_loop_back T ls0 ls1 i ret0
-
diff --git a/tests/lean/misc-loops/Loops/Types.lean b/tests/lean/misc-loops/Loops/Types.lean
deleted file mode 100644
index ca43f4c8..00000000
--- a/tests/lean/misc-loops/Loops/Types.lean
+++ /dev/null
@@ -1,9 +0,0 @@
--- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
--- [loops]: type definitions
-import Base.Primitives
-
-/- [loops::List] -/
-inductive list_t (T : Type) :=
-| Cons : T -> list_t T -> list_t T
-| Nil : list_t T
-
diff --git a/tests/lean/misc-loops/lake-manifest.json b/tests/lean/misc-loops/lake-manifest.json
deleted file mode 100644
index 57b071ca..00000000
--- a/tests/lean/misc-loops/lake-manifest.json
+++ /dev/null
@@ -1,27 +0,0 @@
-{"version": 4,
- "packagesDir": "./lake-packages",
- "packages":
- [{"git":
-   {"url": "https://github.com/leanprover-community/mathlib4.git",
-    "subDir?": null,
-    "rev": "4037792ead804d7bfa8868e2c4684d4223c15ece",
-    "name": "mathlib",
-    "inputRev?": null}},
-  {"git":
-   {"url": "https://github.com/gebner/quote4",
-    "subDir?": null,
-    "rev": "2412c4fdf4a8b689f4467618e5e7b371ae5014aa",
-    "name": "Qq",
-    "inputRev?": "master"}},
-  {"git":
-   {"url": "https://github.com/JLimperg/aesop",
-    "subDir?": null,
-    "rev": "7fe9ecd9339b0e1796e89d243b776849c305c690",
-    "name": "aesop",
-    "inputRev?": "master"}},
-  {"git":
-   {"url": "https://github.com/leanprover/std4",
-    "subDir?": null,
-    "rev": "24897887905b3a1254b244369f5dd2cf6174b0ee",
-    "name": "std",
-    "inputRev?": "main"}}]}
diff --git a/tests/lean/misc-loops/lakefile.lean b/tests/lean/misc-loops/lakefile.lean
deleted file mode 100644
index 097c0a7d..00000000
--- a/tests/lean/misc-loops/lakefile.lean
+++ /dev/null
@@ -1,12 +0,0 @@
-import Lake
-open Lake DSL
-
-require mathlib from git
-  "https://github.com/leanprover-community/mathlib4.git"
-
-package «loops» {}
-
-lean_lib «Base» {}
-
-@[default_target]
-lean_lib «Loops» {}
diff --git a/tests/lean/misc-loops/lean-toolchain b/tests/lean/misc-loops/lean-toolchain
deleted file mode 100644
index bbf57f10..00000000
--- a/tests/lean/misc-loops/lean-toolchain
+++ /dev/null
@@ -1 +0,0 @@
-leanprover/lean4:nightly-2023-01-21
diff --git a/tests/lean/misc-no_nested_borrows/Base/Primitives.lean b/tests/lean/misc-no_nested_borrows/Base/Primitives.lean
deleted file mode 100644
index 4a66a453..00000000
--- a/tests/lean/misc-no_nested_borrows/Base/Primitives.lean
+++ /dev/null
@@ -1,583 +0,0 @@
-import Lean
-import Lean.Meta.Tactic.Simp
-import Init.Data.List.Basic
-import Mathlib.Tactic.RunCmd
-
---------------------
--- ASSERT COMMAND --
---------------------
-
-open Lean Elab Command Term Meta
-
-syntax (name := assert) "#assert" term: command
-
-@[command_elab assert]
-unsafe
-def assertImpl : CommandElab := fun (_stx: Syntax) => do
-  runTermElabM (fun _ => do
-    let r ← evalTerm Bool (mkConst ``Bool) _stx[1]
-    if not r then
-      logInfo "Assertion failed for: "
-      logInfo _stx[1]
-      logError "Expression reduced to false"
-    pure ())
-
-#eval 2 == 2
-#assert (2 == 2)
-
--------------
--- PRELUDE --
--------------
-
--- Results & monadic combinators
-
-inductive Error where
-   | assertionFailure: Error
-   | integerOverflow: Error
-   | divisionByZero: Error
-   | arrayOutOfBounds: Error
-   | maximumSizeExceeded: Error
-   | panic: Error
-deriving Repr, BEq
-
-open Error
-
-inductive Result (α : Type u) where
-  | ret (v: α): Result α
-  | fail (e: Error): Result α
-deriving Repr, BEq
-
-open Result
-
-instance Result_Inhabited (α : Type u) : Inhabited (Result α) :=
-  Inhabited.mk (fail panic)
-
-/- HELPERS -/
-
-def ret? {α: Type} (r: Result α): Bool :=
-  match r with
-  | Result.ret _ => true
-  | Result.fail _ => false
-
-def massert (b:Bool) : Result Unit :=
-  if b then .ret () else fail assertionFailure
-
-def eval_global {α: Type} (x: Result α) (_: ret? x): α :=
-  match x with
-  | Result.fail _ => by contradiction
-  | Result.ret x => x
-
-/- DO-DSL SUPPORT -/
-
-def bind (x: Result α) (f: α -> Result β) : Result β :=
-  match x with
-  | ret v  => f v 
-  | fail v => fail v
-
--- Allows using Result in do-blocks
-instance : Bind Result where
-  bind := bind
-
--- Allows using return x in do-blocks
-instance : Pure Result where
-  pure := fun x => ret x
-
-/- CUSTOM-DSL SUPPORT -/
-
--- Let-binding the Result of a monadic operation is oftentimes not sufficient,
--- because we may need a hypothesis for equational reasoning in the scope. We
--- rely on subtype, and a custom let-binding operator, in effect recreating our
--- own variant of the do-dsl
-
-def Result.attach {α: Type} (o : Result α): Result { x : α // o = ret x } :=
-  match o with
-  | .ret x => .ret ⟨x, rfl⟩
-  | .fail e => .fail e
-
-macro "let" e:term " ⟵ " f:term : doElem =>
-  `(doElem| let ⟨$e, h⟩ ← Result.attach $f)
-
--- TODO: any way to factorize both definitions?
-macro "let" e:term " <-- " f:term : doElem =>
-  `(doElem| let ⟨$e, h⟩ ← Result.attach $f)
-
--- We call the hypothesis `h`, in effect making it unavailable to the user
--- (because too much shadowing). But in practice, once can use the French single
--- quote notation (input with f< and f>), where `‹ h ›` finds a suitable
--- hypothesis in the context, this is equivalent to `have x: h := by assumption in x`
-#eval do
-  let y <-- .ret (0: Nat)
-  let _: y = 0 := by cases ‹ ret 0 = ret y › ; decide
-  let r: { x: Nat // x = 0 } := ⟨ y, by assumption ⟩
-  .ret r
-
-----------------------
--- MACHINE INTEGERS --
-----------------------
-
--- We redefine our machine integers types.
-
--- For Isize/Usize, we reuse `getNumBits` from `USize`. You cannot reduce `getNumBits`
--- using the simplifier, meaning that proofs do not depend on the compile-time value of
--- USize.size. (Lean assumes 32 or 64-bit platforms, and Rust doesn't really support, at
--- least officially, 16-bit microcontrollers, so this seems like a fine design decision
--- for now.)
-
--- Note from Chris Bailey: "If there's more than one salient property of your
--- definition then the subtyping strategy might get messy, and the property part
--- of a subtype is less discoverable by the simplifier or tactics like
--- library_search." So, we will not add refinements on the return values of the
--- operations defined on Primitives, but will rather rely on custom lemmas to
--- invert on possible return values of the primitive operations.
-
--- Machine integer constants, done via `ofNatCore`, which requires a proof that
--- the `Nat` fits within the desired integer type. We provide a custom tactic.
-
-open System.Platform.getNumBits
-
--- TODO: is there a way of only importing System.Platform.getNumBits?
---
-@[simp] def size_num_bits : Nat := (System.Platform.getNumBits ()).val
-
--- Remark: Lean seems to use < for the comparisons with the upper bounds by convention.
--- We keep the F* convention for now.
-@[simp] def Isize.min : Int := - (HPow.hPow 2 (size_num_bits - 1))
-@[simp] def Isize.max : Int := (HPow.hPow 2 (size_num_bits - 1)) - 1
-@[simp] def I8.min    : Int := - (HPow.hPow 2 7)
-@[simp] def I8.max    : Int := HPow.hPow 2 7 - 1
-@[simp] def I16.min   : Int := - (HPow.hPow 2 15)
-@[simp] def I16.max   : Int := HPow.hPow 2 15 - 1
-@[simp] def I32.min   : Int := -(HPow.hPow 2 31)
-@[simp] def I32.max   : Int := HPow.hPow 2 31 - 1
-@[simp] def I64.min   : Int := -(HPow.hPow 2 63)
-@[simp] def I64.max   : Int := HPow.hPow 2 63 - 1
-@[simp] def I128.min  : Int := -(HPow.hPow 2 127)
-@[simp] def I128.max  : Int := HPow.hPow 2 127 - 1
-@[simp] def Usize.min : Int := 0
-@[simp] def Usize.max : Int := HPow.hPow 2 size_num_bits - 1
-@[simp] def U8.min    : Int := 0
-@[simp] def U8.max    : Int := HPow.hPow 2 8 - 1
-@[simp] def U16.min   : Int := 0
-@[simp] def U16.max   : Int := HPow.hPow 2 16 - 1
-@[simp] def U32.min   : Int := 0
-@[simp] def U32.max   : Int := HPow.hPow 2 32 - 1
-@[simp] def U64.min   : Int := 0
-@[simp] def U64.max   : Int := HPow.hPow 2 64 - 1
-@[simp] def U128.min  : Int := 0
-@[simp] def U128.max  : Int := HPow.hPow 2 128 - 1
-
-#assert (I8.min   == -128)
-#assert (I8.max   == 127)
-#assert (I16.min  == -32768)
-#assert (I16.max  == 32767)
-#assert (I32.min  == -2147483648)
-#assert (I32.max  == 2147483647)
-#assert (I64.min  == -9223372036854775808)
-#assert (I64.max  == 9223372036854775807)
-#assert (I128.min == -170141183460469231731687303715884105728)
-#assert (I128.max == 170141183460469231731687303715884105727)
-#assert (U8.min   == 0)
-#assert (U8.max   == 255)
-#assert (U16.min  == 0)
-#assert (U16.max  == 65535)
-#assert (U32.min  == 0)
-#assert (U32.max  == 4294967295)
-#assert (U64.min  == 0)
-#assert (U64.max  == 18446744073709551615)
-#assert (U128.min == 0)
-#assert (U128.max == 340282366920938463463374607431768211455)
-
-inductive ScalarTy :=
-| Isize
-| I8
-| I16
-| I32
-| I64
-| I128
-| Usize
-| U8
-| U16
-| U32
-| U64
-| U128
-
-def Scalar.min (ty : ScalarTy) : Int :=
-  match ty with
-  | .Isize => Isize.min
-  | .I8    => I8.min
-  | .I16   => I16.min
-  | .I32   => I32.min
-  | .I64   => I64.min
-  | .I128  => I128.min
-  | .Usize => Usize.min
-  | .U8    => U8.min
-  | .U16   => U16.min
-  | .U32   => U32.min
-  | .U64   => U64.min
-  | .U128  => U128.min
-
-def Scalar.max (ty : ScalarTy) : Int :=
-  match ty with
-  | .Isize => Isize.max
-  | .I8    => I8.max
-  | .I16   => I16.max
-  | .I32   => I32.max
-  | .I64   => I64.max
-  | .I128  => I128.max
-  | .Usize => Usize.max
-  | .U8    => U8.max
-  | .U16   => U16.max
-  | .U32   => U32.max
-  | .U64   => U64.max
-  | .U128  => U128.max
-
--- "Conservative" bounds
--- We use those because we can't compare to the isize bounds (which can't
--- reduce at compile-time). Whenever we perform an arithmetic operation like
--- addition we need to check that the result is in bounds: we first compare
--- to the conservative bounds, which reduce, then compare to the real bounds.
--- This is useful for the various #asserts that we want to reduce at
--- type-checking time.
-def Scalar.cMin (ty : ScalarTy) : Int :=
-  match ty with
-  | .Isize => I32.min
-  | _ => Scalar.min ty
-
-def Scalar.cMax (ty : ScalarTy) : Int :=
-  match ty with
-  | .Isize => I32.max
-  | .Usize => U32.max
-  | _ => Scalar.max ty
-
-theorem Scalar.cMin_bound ty : Scalar.min ty <= Scalar.cMin ty := by sorry
-theorem Scalar.cMax_bound ty : Scalar.min ty <= Scalar.cMin ty := by sorry
-
-structure Scalar (ty : ScalarTy) where
-  val : Int
-  hmin : Scalar.min ty <= val
-  hmax : val <= Scalar.max ty
-
-theorem Scalar.bound_suffices (ty : ScalarTy) (x : Int) :
-  Scalar.cMin ty <= x && x <= Scalar.cMax ty ->
-  (decide (Scalar.min ty ≤ x) && decide (x ≤ Scalar.max ty)) = true
-  := by sorry
-
-def Scalar.ofIntCore {ty : ScalarTy} (x : Int)
-  (hmin : Scalar.min ty <= x) (hmax : x <= Scalar.max ty) : Scalar ty :=
-  { val := x, hmin := hmin, hmax := hmax }
-
-def Scalar.ofInt {ty : ScalarTy} (x : Int)
-  (h : Scalar.min ty <= x && x <= Scalar.max ty) : Scalar ty :=
-  let hmin: Scalar.min ty <= x := by sorry
-  let hmax: x <= Scalar.max ty := by sorry
-  Scalar.ofIntCore x hmin hmax
-
--- Further thoughts: look at what has been done here:
--- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/Fin/Basic.lean
--- and
--- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/UInt.lean
--- which both contain a fair amount of reasoning already!
-def Scalar.tryMk (ty : ScalarTy) (x : Int) : Result (Scalar ty) :=
-  -- TODO: write this with only one if then else
-  if hmin_cons: Scalar.cMin ty <= x || Scalar.min ty <= x then
-    if hmax_cons: x <= Scalar.cMax ty || x <= Scalar.max ty then
-      let hmin: Scalar.min ty <= x := by sorry
-      let hmax: x <= Scalar.max ty := by sorry
-      return Scalar.ofIntCore x hmin hmax
-    else fail integerOverflow
-  else fail integerOverflow
-
-def Scalar.neg {ty : ScalarTy} (x : Scalar ty) : Result (Scalar ty) := Scalar.tryMk ty (- x.val)
-
-def Scalar.div {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
-  if y.val != 0 then Scalar.tryMk ty (x.val / y.val) else fail divisionByZero
-
--- Checking that the % operation in Lean computes the same as the remainder operation in Rust
-#assert 1 % 2 = (1:Int)
-#assert (-1) % 2 = -1
-#assert 1 % (-2) = 1
-#assert (-1) % (-2) = -1
-
-def Scalar.rem {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
-  if y.val != 0 then Scalar.tryMk ty (x.val % y.val) else fail divisionByZero
-
-def Scalar.add {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
-  Scalar.tryMk ty (x.val + y.val)
-
-def Scalar.sub {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
-  Scalar.tryMk ty (x.val - y.val)
-
-def Scalar.mul {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
-  Scalar.tryMk ty (x.val * y.val)
-
--- TODO: instances of +, -, * etc. for scalars
-
--- Cast an integer from a [src_ty] to a [tgt_ty]
--- TODO: check the semantics of casts in Rust
-def Scalar.cast {src_ty : ScalarTy} (tgt_ty : ScalarTy) (x : Scalar src_ty) : Result (Scalar tgt_ty) :=
-  Scalar.tryMk tgt_ty x.val
-
--- The scalar types
--- We declare the definitions as reducible so that Lean can unfold them (useful
--- for type class resolution for instance).
-@[reducible] def Isize := Scalar .Isize
-@[reducible] def I8    := Scalar .I8
-@[reducible] def I16   := Scalar .I16
-@[reducible] def I32   := Scalar .I32
-@[reducible] def I64   := Scalar .I64
-@[reducible] def I128  := Scalar .I128
-@[reducible] def Usize := Scalar .Usize
-@[reducible] def U8    := Scalar .U8
-@[reducible] def U16   := Scalar .U16
-@[reducible] def U32   := Scalar .U32
-@[reducible] def U64   := Scalar .U64
-@[reducible] def U128  := Scalar .U128
-
--- TODO: below: not sure this is the best way.
--- Should we rather overload operations like +, -, etc.?
--- Also, it is possible to automate the generation of those definitions
--- with macros (but would it be a good idea? It would be less easy to
--- read the file, which is not supposed to change a lot)
-
--- Negation
-
-/--
-Remark: there is no heterogeneous negation in the Lean prelude: we thus introduce
-one here.
-
-The notation typeclass for heterogeneous addition.
-This enables the notation `- a : β` where `a : α`.
--/
-class HNeg (α : Type u) (β : outParam (Type v)) where
-  /-- `- a` computes the negation of `a`.
-  The meaning of this notation is type-dependent. -/
-  hNeg : α → β
-
-prefix:75  "-"   => HNeg.hNeg
-
-instance : HNeg Isize (Result Isize) where hNeg x := Scalar.neg x
-instance : HNeg I8 (Result I8) where hNeg x := Scalar.neg x
-instance : HNeg I16 (Result I16) where hNeg x := Scalar.neg x
-instance : HNeg I32 (Result I32) where hNeg x := Scalar.neg x
-instance : HNeg I64 (Result I64) where hNeg x := Scalar.neg x
-instance : HNeg I128 (Result I128) where hNeg x := Scalar.neg x
-
--- Addition
-instance {ty} : HAdd (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
-  hAdd x y := Scalar.add x y
-
--- Substraction
-instance {ty} : HSub (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
-  hSub x y := Scalar.sub x y
-
--- Multiplication
-instance {ty} : HMul (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
-  hMul x y := Scalar.mul x y
-
--- Division
-instance {ty} : HDiv (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
-  hDiv x y := Scalar.div x y
-
--- Remainder
-instance {ty} : HMod (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
-  hMod x y := Scalar.rem x y
-
--- ofIntCore
--- TODO: typeclass?
-def Isize.ofIntCore := @Scalar.ofIntCore .Isize
-def I8.ofIntCore    := @Scalar.ofIntCore .I8
-def I16.ofIntCore   := @Scalar.ofIntCore .I16
-def I32.ofIntCore   := @Scalar.ofIntCore .I32
-def I64.ofIntCore   := @Scalar.ofIntCore .I64
-def I128.ofIntCore  := @Scalar.ofIntCore .I128
-def Usize.ofIntCore := @Scalar.ofIntCore .Usize
-def U8.ofIntCore    := @Scalar.ofIntCore .U8
-def U16.ofIntCore   := @Scalar.ofIntCore .U16
-def U32.ofIntCore   := @Scalar.ofIntCore .U32
-def U64.ofIntCore   := @Scalar.ofIntCore .U64
-def U128.ofIntCore  := @Scalar.ofIntCore .U128
-
---  ofInt
--- TODO: typeclass?
-def Isize.ofInt := @Scalar.ofInt .Isize
-def I8.ofInt    := @Scalar.ofInt .I8
-def I16.ofInt   := @Scalar.ofInt .I16
-def I32.ofInt   := @Scalar.ofInt .I32
-def I64.ofInt   := @Scalar.ofInt .I64
-def I128.ofInt  := @Scalar.ofInt .I128
-def Usize.ofInt := @Scalar.ofInt .Usize
-def U8.ofInt    := @Scalar.ofInt .U8
-def U16.ofInt   := @Scalar.ofInt .U16
-def U32.ofInt   := @Scalar.ofInt .U32
-def U64.ofInt   := @Scalar.ofInt .U64
-def U128.ofInt  := @Scalar.ofInt .U128
-
--- Comparisons
-instance {ty} : LT (Scalar ty) where
-  lt a b := LT.lt a.val b.val
-
-instance {ty} : LE (Scalar ty) where le a b := LE.le a.val b.val
-
-instance Scalar.decLt {ty} (a b : Scalar ty) : Decidable (LT.lt a b) := Int.decLt ..
-instance Scalar.decLe {ty} (a b : Scalar ty) : Decidable (LE.le a b) := Int.decLe ..
-
-theorem Scalar.eq_of_val_eq {ty} : ∀ {i j : Scalar ty}, Eq i.val j.val → Eq i j
-  | ⟨_, _, _⟩, ⟨_, _, _⟩, rfl => rfl
-
-theorem Scalar.val_eq_of_eq {ty} {i j : Scalar ty} (h : Eq i j) : Eq i.val j.val :=
-  h ▸ rfl
-
-theorem Scalar.ne_of_val_ne {ty} {i j : Scalar ty} (h : Not (Eq i.val j.val)) : Not (Eq i j) :=
-  fun h' => absurd (val_eq_of_eq h') h
-
-instance (ty : ScalarTy) : DecidableEq (Scalar ty) :=
-  fun i j =>
-    match decEq i.val j.val with
-    | isTrue h  => isTrue (Scalar.eq_of_val_eq h)
-    | isFalse h => isFalse (Scalar.ne_of_val_ne h)
-
-def Scalar.toInt {ty} (n : Scalar ty) : Int := n.val
-
--- Tactic to prove that integers are in bounds
-syntax "intlit" : tactic
-
-macro_rules
-  | `(tactic| intlit) => `(tactic| apply Scalar.bound_suffices ; decide)
-
--- -- We now define a type class that subsumes the various machine integer types, so
--- -- as to write a concise definition for scalar_cast, rather than exhaustively
--- -- enumerating all of the possible pairs. We remark that Rust has sane semantics
--- -- and fails if a cast operation would involve a truncation or modulo.
-
--- class MachineInteger (t: Type) where
---   size: Nat
---   val: t -> Fin size
---   ofNatCore: (n:Nat) -> LT.lt n size -> t
-
--- set_option hygiene false in
--- run_cmd
---   for typeName in [`UInt8, `UInt16, `UInt32, `UInt64, `USize].map Lean.mkIdent do
---   Lean.Elab.Command.elabCommand (← `(
---     namespace $typeName
---     instance: MachineInteger $typeName where
---       size := size
---       val := val
---       ofNatCore := ofNatCore
---     end $typeName
---   ))
-
--- -- Aeneas only instantiates the destination type (`src` is implicit). We rely on
--- -- Lean to infer `src`.
-
--- def scalar_cast { src: Type } (dst: Type) [ MachineInteger src ] [ MachineInteger dst ] (x: src): Result dst :=
---   if h: MachineInteger.val x < MachineInteger.size dst then
---     .ret (MachineInteger.ofNatCore (MachineInteger.val x).val h)
---   else
---     .fail integerOverflow
-
--------------
--- VECTORS --
--------------
-
-def Vec (α : Type u) := { l : List α // List.length l <= Usize.max }
-
-def vec_new (α : Type u): Vec α := ⟨ [], by sorry ⟩
-
-def vec_len (α : Type u) (v : Vec α) : Usize :=
-  let ⟨ v, l ⟩ := v
-  Usize.ofIntCore (List.length v) (by sorry) l
- 
-def vec_push_fwd (α : Type u) (_ : Vec α) (_ : α) : Unit := ()
-
-def vec_push_back (α : Type u) (v : Vec α) (x : α) : Result (Vec α)
-  :=
-  if h : List.length v.val <= U32.max || List.length v.val <= Usize.max then
-    return ⟨ List.concat v.val x, by sorry ⟩
-  else
-    fail maximumSizeExceeded
-
-def vec_insert_fwd (α : Type u) (v: Vec α) (i: Usize) (_: α): Result Unit :=
-  if i.val < List.length v.val then
-    .ret ()
-  else
-    .fail arrayOutOfBounds
-
-def vec_insert_back (α : Type u) (v: Vec α) (i: Usize) (x: α): Result (Vec α) :=
-  if i.val < List.length v.val then
-    -- TODO: maybe we should redefine a list library which uses integers
-    -- (instead of natural numbers)
-    let i : Nat :=
-      match i.val with
-      | .ofNat n => n
-      | .negSucc n => by sorry -- TODO: we can't get here
-    let isLt: i < USize.size := by sorry
-    let i : Fin USize.size := { val := i, isLt := isLt }
-    .ret ⟨ List.set v.val i.val x, by
-      have h: List.length v.val <= Usize.max := v.property
-      rewrite [ List.length_set v.val i.val x ]
-      assumption
-    ⟩
-  else
-    .fail arrayOutOfBounds
-
-def vec_index_fwd (α : Type u) (v: Vec α) (i: Usize): Result α :=
-  if i.val < List.length v.val then
-    let i : Nat :=
-      match i.val with
-      | .ofNat n => n
-      | .negSucc n => by sorry -- TODO: we can't get here
-    let isLt: i < USize.size := by sorry
-    let i : Fin USize.size := { val := i, isLt := isLt }
-    let h: i < List.length v.val := by sorry
-    .ret (List.get v.val ⟨i.val, h⟩)
-  else
-    .fail arrayOutOfBounds
-
-def vec_index_back (α : Type u) (v: Vec α) (i: Usize) (_: α): Result Unit :=
-  if i.val < List.length v.val then
-    .ret ()
-  else
-    .fail arrayOutOfBounds
-
-def vec_index_mut_fwd (α : Type u) (v: Vec α) (i: Usize): Result α :=
-  if i.val < List.length v.val then
-    let i : Nat :=
-      match i.val with
-      | .ofNat n => n
-      | .negSucc n => by sorry -- TODO: we can't get here
-    let isLt: i < USize.size := by sorry
-    let i : Fin USize.size := { val := i, isLt := isLt }
-    let h: i < List.length v.val := by sorry
-    .ret (List.get v.val ⟨i.val, h⟩)
-  else
-    .fail arrayOutOfBounds
-
-def vec_index_mut_back (α : Type u) (v: Vec α) (i: Usize) (x: α): Result (Vec α) :=
-  if i.val < List.length v.val then
-    let i : Nat :=
-      match i.val with
-      | .ofNat n => n
-      | .negSucc n => by sorry -- TODO: we can't get here
-    let isLt: i < USize.size := by sorry
-    let i : Fin USize.size := { val := i, isLt := isLt }
-    .ret ⟨ List.set v.val i.val x, by
-      have h: List.length v.val <= Usize.max := v.property
-      rewrite [ List.length_set v.val i.val x ]
-      assumption
-    ⟩
-  else
-    .fail arrayOutOfBounds
-
-----------
--- MISC --
-----------
-
-def mem_replace_fwd (a : Type) (x : a) (_ : a) : a :=
-  x
-
-def mem_replace_back (a : Type) (_ : a) (y : a) : a :=
-  y
-
-/-- Aeneas-translated function -- useful to reduce non-recursive definitions.
- Use with `simp [ aeneas ]` -/
-register_simp_attr aeneas
diff --git a/tests/lean/misc-no_nested_borrows/NoNestedBorrows.lean b/tests/lean/misc-no_nested_borrows/NoNestedBorrows.lean
deleted file mode 100644
index 12c7d8f7..00000000
--- a/tests/lean/misc-no_nested_borrows/NoNestedBorrows.lean
+++ /dev/null
@@ -1,538 +0,0 @@
--- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
--- [no_nested_borrows]
-import Base.Primitives
-
-/- [no_nested_borrows::Pair] -/
-structure pair_t (T1 T2 : Type) where
-  pair_x : T1
-  pair_y : T2
-
-/- [no_nested_borrows::List] -/
-inductive list_t (T : Type) :=
-| Cons : T -> list_t T -> list_t T
-| Nil : list_t T
-
-/- [no_nested_borrows::One] -/
-inductive one_t (T1 : Type) :=
-| One : T1 -> one_t T1
-
-/- [no_nested_borrows::EmptyEnum] -/
-inductive empty_enum_t :=
-| Empty : empty_enum_t
-
-/- [no_nested_borrows::Enum] -/
-inductive enum_t :=
-| Variant1 : enum_t
-| Variant2 : enum_t
-
-/- [no_nested_borrows::EmptyStruct] -/
-structure empty_struct_t where
-
-/- [no_nested_borrows::Sum] -/
-inductive sum_t (T1 T2 : Type) :=
-| Left : T1 -> sum_t T1 T2
-| Right : T2 -> sum_t T1 T2
-
-/- [no_nested_borrows::neg_test] -/
-def neg_test_fwd (x : I32) : Result I32 :=
-  - x
-
-/- [no_nested_borrows::add_test] -/
-def add_test_fwd (x : U32) (y : U32) : Result U32 :=
-  x + y
-
-/- [no_nested_borrows::subs_test] -/
-def subs_test_fwd (x : U32) (y : U32) : Result U32 :=
-  x - y
-
-/- [no_nested_borrows::div_test] -/
-def div_test_fwd (x : U32) (y : U32) : Result U32 :=
-  x / y
-
-/- [no_nested_borrows::div_test1] -/
-def div_test1_fwd (x : U32) : Result U32 :=
-  x / (U32.ofInt 2 (by intlit))
-
-/- [no_nested_borrows::rem_test] -/
-def rem_test_fwd (x : U32) (y : U32) : Result U32 :=
-  x % y
-
-/- [no_nested_borrows::cast_test] -/
-def cast_test_fwd (x : U32) : Result I32 :=
-  Scalar.cast .I32 x
-
-/- [no_nested_borrows::test2] -/
-def test2_fwd : Result Unit :=
-  do
-    let _ ← (U32.ofInt 23 (by intlit)) + (U32.ofInt 44 (by intlit))
-    Result.ret ()
-
-/- Unit test for [no_nested_borrows::test2] -/
-#assert (test2_fwd == .ret ())
-
-/- [no_nested_borrows::get_max] -/
-def get_max_fwd (x : U32) (y : U32) : Result U32 :=
-  if h: x >= y
-  then Result.ret x
-  else Result.ret y
-
-/- [no_nested_borrows::test3] -/
-def test3_fwd : Result Unit :=
-  do
-    let x ← get_max_fwd (U32.ofInt 4 (by intlit)) (U32.ofInt 3 (by intlit))
-    let y ← get_max_fwd (U32.ofInt 10 (by intlit)) (U32.ofInt 11 (by intlit))
-    let z ← x + y
-    if h: not (z = (U32.ofInt 15 (by intlit)))
-    then Result.fail Error.panic
-    else Result.ret ()
-
-/- Unit test for [no_nested_borrows::test3] -/
-#assert (test3_fwd == .ret ())
-
-/- [no_nested_borrows::test_neg1] -/
-def test_neg1_fwd : Result Unit :=
-  do
-    let y ← - (I32.ofInt 3 (by intlit))
-    if h: not (y = (I32.ofInt (-(3:Int)) (by intlit)))
-    then Result.fail Error.panic
-    else Result.ret ()
-
-/- Unit test for [no_nested_borrows::test_neg1] -/
-#assert (test_neg1_fwd == .ret ())
-
-/- [no_nested_borrows::refs_test1] -/
-def refs_test1_fwd : Result Unit :=
-  if h: not ((I32.ofInt 1 (by intlit)) = (I32.ofInt 1 (by intlit)))
-  then Result.fail Error.panic
-  else Result.ret ()
-
-/- Unit test for [no_nested_borrows::refs_test1] -/
-#assert (refs_test1_fwd == .ret ())
-
-/- [no_nested_borrows::refs_test2] -/
-def refs_test2_fwd : Result Unit :=
-  if h: not ((I32.ofInt 2 (by intlit)) = (I32.ofInt 2 (by intlit)))
-  then Result.fail Error.panic
-  else
-    if h: not ((I32.ofInt 0 (by intlit)) = (I32.ofInt 0 (by intlit)))
-    then Result.fail Error.panic
-    else
-      if h: not ((I32.ofInt 2 (by intlit)) = (I32.ofInt 2 (by intlit)))
-      then Result.fail Error.panic
-      else
-        if h: not ((I32.ofInt 2 (by intlit)) = (I32.ofInt 2 (by intlit)))
-        then Result.fail Error.panic
-        else Result.ret ()
-
-/- Unit test for [no_nested_borrows::refs_test2] -/
-#assert (refs_test2_fwd == .ret ())
-
-/- [no_nested_borrows::test_list1] -/
-def test_list1_fwd : Result Unit :=
-  Result.ret ()
-
-/- Unit test for [no_nested_borrows::test_list1] -/
-#assert (test_list1_fwd == .ret ())
-
-/- [no_nested_borrows::test_box1] -/
-def test_box1_fwd : Result Unit :=
-  let b := (I32.ofInt 1 (by intlit))
-  let x := b
-  if h: not (x = (I32.ofInt 1 (by intlit)))
-  then Result.fail Error.panic
-  else Result.ret ()
-
-/- Unit test for [no_nested_borrows::test_box1] -/
-#assert (test_box1_fwd == .ret ())
-
-/- [no_nested_borrows::copy_int] -/
-def copy_int_fwd (x : I32) : Result I32 :=
-  Result.ret x
-
-/- [no_nested_borrows::test_unreachable] -/
-def test_unreachable_fwd (b : Bool) : Result Unit :=
-  if h: b
-  then Result.fail Error.panic
-  else Result.ret ()
-
-/- [no_nested_borrows::test_panic] -/
-def test_panic_fwd (b : Bool) : Result Unit :=
-  if h: b
-  then Result.fail Error.panic
-  else Result.ret ()
-
-/- [no_nested_borrows::test_copy_int] -/
-def test_copy_int_fwd : Result Unit :=
-  do
-    let y ← copy_int_fwd (I32.ofInt 0 (by intlit))
-    if h: not ((I32.ofInt 0 (by intlit)) = y)
-    then Result.fail Error.panic
-    else Result.ret ()
-
-/- Unit test for [no_nested_borrows::test_copy_int] -/
-#assert (test_copy_int_fwd == .ret ())
-
-/- [no_nested_borrows::is_cons] -/
-def is_cons_fwd (T : Type) (l : list_t T) : Result Bool :=
-  match h: l with
-  | list_t.Cons t l0 => Result.ret true
-  | list_t.Nil => Result.ret false
-
-/- [no_nested_borrows::test_is_cons] -/
-def test_is_cons_fwd : Result Unit :=
-  do
-    let l := list_t.Nil
-    let b ← is_cons_fwd I32 (list_t.Cons (I32.ofInt 0 (by intlit)) l)
-    if h: not b
-    then Result.fail Error.panic
-    else Result.ret ()
-
-/- Unit test for [no_nested_borrows::test_is_cons] -/
-#assert (test_is_cons_fwd == .ret ())
-
-/- [no_nested_borrows::split_list] -/
-def split_list_fwd (T : Type) (l : list_t T) : Result (T × (list_t T)) :=
-  match h: l with
-  | list_t.Cons hd tl => Result.ret (hd, tl)
-  | list_t.Nil => Result.fail Error.panic
-
-/- [no_nested_borrows::test_split_list] -/
-def test_split_list_fwd : Result Unit :=
-  do
-    let l := list_t.Nil
-    let p ← split_list_fwd I32 (list_t.Cons (I32.ofInt 0 (by intlit)) l)
-    let (hd, _) := p
-    if h: not (hd = (I32.ofInt 0 (by intlit)))
-    then Result.fail Error.panic
-    else Result.ret ()
-
-/- Unit test for [no_nested_borrows::test_split_list] -/
-#assert (test_split_list_fwd == .ret ())
-
-/- [no_nested_borrows::choose] -/
-def choose_fwd (T : Type) (b : Bool) (x : T) (y : T) : Result T :=
-  if h: b
-  then Result.ret x
-  else Result.ret y
-
-/- [no_nested_borrows::choose] -/
-def choose_back
-  (T : Type) (b : Bool) (x : T) (y : T) (ret0 : T) : Result (T × T) :=
-  if h: b
-  then Result.ret (ret0, y)
-  else Result.ret (x, ret0)
-
-/- [no_nested_borrows::choose_test] -/
-def choose_test_fwd : Result Unit :=
-  do
-    let z ←
-      choose_fwd I32 true (I32.ofInt 0 (by intlit)) (I32.ofInt 0 (by intlit))
-    let z0 ← z + (I32.ofInt 1 (by intlit))
-    if h: not (z0 = (I32.ofInt 1 (by intlit)))
-    then Result.fail Error.panic
-    else
-      do
-        let (x, y) ←
-          choose_back I32 true (I32.ofInt 0 (by intlit))
-            (I32.ofInt 0 (by intlit)) z0
-        if h: not (x = (I32.ofInt 1 (by intlit)))
-        then Result.fail Error.panic
-        else
-          if h: not (y = (I32.ofInt 0 (by intlit)))
-          then Result.fail Error.panic
-          else Result.ret ()
-
-/- Unit test for [no_nested_borrows::choose_test] -/
-#assert (choose_test_fwd == .ret ())
-
-/- [no_nested_borrows::test_char] -/
-def test_char_fwd : Result Char :=
-  Result.ret 'a'
-
-mutual
-
-/- [no_nested_borrows::NodeElem] -/
-inductive node_elem_t (T : Type) :=
-| Cons : tree_t T -> node_elem_t T -> node_elem_t T
-| Nil : node_elem_t T
-
-/- [no_nested_borrows::Tree] -/
-inductive tree_t (T : Type) :=
-| Leaf : T -> tree_t T
-| Node : T -> node_elem_t T -> tree_t T -> tree_t T
-
-end
-
-/- [no_nested_borrows::list_length] -/
-def list_length_fwd (T : Type) (l : list_t T) : Result U32 :=
-  match h: l with
-  | list_t.Cons t l1 =>
-    do
-      let i ← list_length_fwd T l1
-      (U32.ofInt 1 (by intlit)) + i
-  | list_t.Nil => Result.ret (U32.ofInt 0 (by intlit))
-
-/- [no_nested_borrows::list_nth_shared] -/
-def list_nth_shared_fwd (T : Type) (l : list_t T) (i : U32) : Result T :=
-  match h: l with
-  | list_t.Cons x tl =>
-    if h: i = (U32.ofInt 0 (by intlit))
-    then Result.ret x
-    else
-      do
-        let i0 ← i - (U32.ofInt 1 (by intlit))
-        list_nth_shared_fwd T tl i0
-  | list_t.Nil => Result.fail Error.panic
-
-/- [no_nested_borrows::list_nth_mut] -/
-def list_nth_mut_fwd (T : Type) (l : list_t T) (i : U32) : Result T :=
-  match h: l with
-  | list_t.Cons x tl =>
-    if h: i = (U32.ofInt 0 (by intlit))
-    then Result.ret x
-    else do
-           let i0 ← i - (U32.ofInt 1 (by intlit))
-           list_nth_mut_fwd T tl i0
-  | list_t.Nil => Result.fail Error.panic
-
-/- [no_nested_borrows::list_nth_mut] -/
-def list_nth_mut_back
-  (T : Type) (l : list_t T) (i : U32) (ret0 : T) : Result (list_t T) :=
-  match h: l with
-  | list_t.Cons x tl =>
-    if h: i = (U32.ofInt 0 (by intlit))
-    then Result.ret (list_t.Cons ret0 tl)
-    else
-      do
-        let i0 ← i - (U32.ofInt 1 (by intlit))
-        let tl0 ← list_nth_mut_back T tl i0 ret0
-        Result.ret (list_t.Cons x tl0)
-  | list_t.Nil => Result.fail Error.panic
-
-/- [no_nested_borrows::list_rev_aux] -/
-def list_rev_aux_fwd
-  (T : Type) (li : list_t T) (lo : list_t T) : Result (list_t T) :=
-  match h: li with
-  | list_t.Cons hd tl => list_rev_aux_fwd T tl (list_t.Cons hd lo)
-  | list_t.Nil => Result.ret lo
-
-/- [no_nested_borrows::list_rev] -/
-def list_rev_fwd_back (T : Type) (l : list_t T) : Result (list_t T) :=
-  let li := mem_replace_fwd (list_t T) l list_t.Nil
-  list_rev_aux_fwd T li list_t.Nil
-
-/- [no_nested_borrows::test_list_functions] -/
-def test_list_functions_fwd : Result Unit :=
-  do
-    let l := list_t.Nil
-    let l0 := list_t.Cons (I32.ofInt 2 (by intlit)) l
-    let l1 := list_t.Cons (I32.ofInt 1 (by intlit)) l0
-    let i ← list_length_fwd I32 (list_t.Cons (I32.ofInt 0 (by intlit)) l1)
-    if h: not (i = (U32.ofInt 3 (by intlit)))
-    then Result.fail Error.panic
-    else
-      do
-        let i0 ←
-          list_nth_shared_fwd I32 (list_t.Cons (I32.ofInt 0 (by intlit)) l1)
-            (U32.ofInt 0 (by intlit))
-        if h: not (i0 = (I32.ofInt 0 (by intlit)))
-        then Result.fail Error.panic
-        else
-          do
-            let i1 ←
-              list_nth_shared_fwd I32 (list_t.Cons (I32.ofInt 0 (by intlit))
-                l1) (U32.ofInt 1 (by intlit))
-            if h: not (i1 = (I32.ofInt 1 (by intlit)))
-            then Result.fail Error.panic
-            else
-              do
-                let i2 ←
-                  list_nth_shared_fwd I32 (list_t.Cons
-                    (I32.ofInt 0 (by intlit)) l1) (U32.ofInt 2 (by intlit))
-                if h: not (i2 = (I32.ofInt 2 (by intlit)))
-                then Result.fail Error.panic
-                else
-                  do
-                    let ls ←
-                      list_nth_mut_back I32 (list_t.Cons
-                        (I32.ofInt 0 (by intlit)) l1) (U32.ofInt 1 (by intlit))
-                        (I32.ofInt 3 (by intlit))
-                    let i3 ←
-                      list_nth_shared_fwd I32 ls (U32.ofInt 0 (by intlit))
-                    if h: not (i3 = (I32.ofInt 0 (by intlit)))
-                    then Result.fail Error.panic
-                    else
-                      do
-                        let i4 ←
-                          list_nth_shared_fwd I32 ls (U32.ofInt 1 (by intlit))
-                        if h: not (i4 = (I32.ofInt 3 (by intlit)))
-                        then Result.fail Error.panic
-                        else
-                          do
-                            let i5 ←
-                              list_nth_shared_fwd I32 ls
-                                (U32.ofInt 2 (by intlit))
-                            if h: not (i5 = (I32.ofInt 2 (by intlit)))
-                            then Result.fail Error.panic
-                            else Result.ret ()
-
-/- Unit test for [no_nested_borrows::test_list_functions] -/
-#assert (test_list_functions_fwd == .ret ())
-
-/- [no_nested_borrows::id_mut_pair1] -/
-def id_mut_pair1_fwd (T1 T2 : Type) (x : T1) (y : T2) : Result (T1 × T2) :=
-  Result.ret (x, y)
-
-/- [no_nested_borrows::id_mut_pair1] -/
-def id_mut_pair1_back
-  (T1 T2 : Type) (x : T1) (y : T2) (ret0 : (T1 × T2)) : Result (T1 × T2) :=
-  let (t, t0) := ret0
-  Result.ret (t, t0)
-
-/- [no_nested_borrows::id_mut_pair2] -/
-def id_mut_pair2_fwd (T1 T2 : Type) (p : (T1 × T2)) : Result (T1 × T2) :=
-  let (t, t0) := p
-  Result.ret (t, t0)
-
-/- [no_nested_borrows::id_mut_pair2] -/
-def id_mut_pair2_back
-  (T1 T2 : Type) (p : (T1 × T2)) (ret0 : (T1 × T2)) : Result (T1 × T2) :=
-  let (t, t0) := ret0
-  Result.ret (t, t0)
-
-/- [no_nested_borrows::id_mut_pair3] -/
-def id_mut_pair3_fwd (T1 T2 : Type) (x : T1) (y : T2) : Result (T1 × T2) :=
-  Result.ret (x, y)
-
-/- [no_nested_borrows::id_mut_pair3] -/
-def id_mut_pair3_back'a
-  (T1 T2 : Type) (x : T1) (y : T2) (ret0 : T1) : Result T1 :=
-  Result.ret ret0
-
-/- [no_nested_borrows::id_mut_pair3] -/
-def id_mut_pair3_back'b
-  (T1 T2 : Type) (x : T1) (y : T2) (ret0 : T2) : Result T2 :=
-  Result.ret ret0
-
-/- [no_nested_borrows::id_mut_pair4] -/
-def id_mut_pair4_fwd (T1 T2 : Type) (p : (T1 × T2)) : Result (T1 × T2) :=
-  let (t, t0) := p
-  Result.ret (t, t0)
-
-/- [no_nested_borrows::id_mut_pair4] -/
-def id_mut_pair4_back'a
-  (T1 T2 : Type) (p : (T1 × T2)) (ret0 : T1) : Result T1 :=
-  Result.ret ret0
-
-/- [no_nested_borrows::id_mut_pair4] -/
-def id_mut_pair4_back'b
-  (T1 T2 : Type) (p : (T1 × T2)) (ret0 : T2) : Result T2 :=
-  Result.ret ret0
-
-/- [no_nested_borrows::StructWithTuple] -/
-structure struct_with_tuple_t (T1 T2 : Type) where
-  struct_with_tuple_p : (T1 × T2)
-
-/- [no_nested_borrows::new_tuple1] -/
-def new_tuple1_fwd : Result (struct_with_tuple_t U32 U32) :=
-  Result.ret
-  {
-    struct_with_tuple_p :=
-      ((U32.ofInt 1 (by intlit)), (U32.ofInt 2 (by intlit)))
-  }
-
-/- [no_nested_borrows::new_tuple2] -/
-def new_tuple2_fwd : Result (struct_with_tuple_t I16 I16) :=
-  Result.ret
-  {
-    struct_with_tuple_p :=
-      ((I16.ofInt 1 (by intlit)), (I16.ofInt 2 (by intlit)))
-  }
-
-/- [no_nested_borrows::new_tuple3] -/
-def new_tuple3_fwd : Result (struct_with_tuple_t U64 I64) :=
-  Result.ret
-  {
-    struct_with_tuple_p :=
-      ((U64.ofInt 1 (by intlit)), (I64.ofInt 2 (by intlit)))
-  }
-
-/- [no_nested_borrows::StructWithPair] -/
-structure struct_with_pair_t (T1 T2 : Type) where
-  struct_with_pair_p : pair_t T1 T2
-
-/- [no_nested_borrows::new_pair1] -/
-def new_pair1_fwd : Result (struct_with_pair_t U32 U32) :=
-  Result.ret
-  {
-    struct_with_pair_p :=
-      {
-        pair_x := (U32.ofInt 1 (by intlit)),
-        pair_y := (U32.ofInt 2 (by intlit))
-      }
-  }
-
-/- [no_nested_borrows::test_constants] -/
-def test_constants_fwd : Result Unit :=
-  do
-    let swt ← new_tuple1_fwd
-    let (i, _) := swt.struct_with_tuple_p
-    if h: not (i = (U32.ofInt 1 (by intlit)))
-    then Result.fail Error.panic
-    else
-      do
-        let swt0 ← new_tuple2_fwd
-        let (i0, _) := swt0.struct_with_tuple_p
-        if h: not (i0 = (I16.ofInt 1 (by intlit)))
-        then Result.fail Error.panic
-        else
-          do
-            let swt1 ← new_tuple3_fwd
-            let (i1, _) := swt1.struct_with_tuple_p
-            if h: not (i1 = (U64.ofInt 1 (by intlit)))
-            then Result.fail Error.panic
-            else
-              do
-                let swp ← new_pair1_fwd
-                if h: not (swp.struct_with_pair_p.pair_x =
-                  (U32.ofInt 1 (by intlit)))
-                then Result.fail Error.panic
-                else Result.ret ()
-
-/- Unit test for [no_nested_borrows::test_constants] -/
-#assert (test_constants_fwd == .ret ())
-
-/- [no_nested_borrows::test_weird_borrows1] -/
-def test_weird_borrows1_fwd : Result Unit :=
-  Result.ret ()
-
-/- Unit test for [no_nested_borrows::test_weird_borrows1] -/
-#assert (test_weird_borrows1_fwd == .ret ())
-
-/- [no_nested_borrows::test_mem_replace] -/
-def test_mem_replace_fwd_back (px : U32) : Result U32 :=
-  let y := mem_replace_fwd U32 px (U32.ofInt 1 (by intlit))
-  if h: not (y = (U32.ofInt 0 (by intlit)))
-  then Result.fail Error.panic
-  else Result.ret (U32.ofInt 2 (by intlit))
-
-/- [no_nested_borrows::test_shared_borrow_bool1] -/
-def test_shared_borrow_bool1_fwd (b : Bool) : Result U32 :=
-  if h: b
-  then Result.ret (U32.ofInt 0 (by intlit))
-  else Result.ret (U32.ofInt 1 (by intlit))
-
-/- [no_nested_borrows::test_shared_borrow_bool2] -/
-def test_shared_borrow_bool2_fwd : Result U32 :=
-  Result.ret (U32.ofInt 0 (by intlit))
-
-/- [no_nested_borrows::test_shared_borrow_enum1] -/
-def test_shared_borrow_enum1_fwd (l : list_t U32) : Result U32 :=
-  match h: l with
-  | list_t.Cons i l0 => Result.ret (U32.ofInt 1 (by intlit))
-  | list_t.Nil => Result.ret (U32.ofInt 0 (by intlit))
-
-/- [no_nested_borrows::test_shared_borrow_enum2] -/
-def test_shared_borrow_enum2_fwd : Result U32 :=
-  Result.ret (U32.ofInt 0 (by intlit))
-
diff --git a/tests/lean/misc-no_nested_borrows/lake-manifest.json b/tests/lean/misc-no_nested_borrows/lake-manifest.json
deleted file mode 100644
index 57b071ca..00000000
--- a/tests/lean/misc-no_nested_borrows/lake-manifest.json
+++ /dev/null
@@ -1,27 +0,0 @@
-{"version": 4,
- "packagesDir": "./lake-packages",
- "packages":
- [{"git":
-   {"url": "https://github.com/leanprover-community/mathlib4.git",
-    "subDir?": null,
-    "rev": "4037792ead804d7bfa8868e2c4684d4223c15ece",
-    "name": "mathlib",
-    "inputRev?": null}},
-  {"git":
-   {"url": "https://github.com/gebner/quote4",
-    "subDir?": null,
-    "rev": "2412c4fdf4a8b689f4467618e5e7b371ae5014aa",
-    "name": "Qq",
-    "inputRev?": "master"}},
-  {"git":
-   {"url": "https://github.com/JLimperg/aesop",
-    "subDir?": null,
-    "rev": "7fe9ecd9339b0e1796e89d243b776849c305c690",
-    "name": "aesop",
-    "inputRev?": "master"}},
-  {"git":
-   {"url": "https://github.com/leanprover/std4",
-    "subDir?": null,
-    "rev": "24897887905b3a1254b244369f5dd2cf6174b0ee",
-    "name": "std",
-    "inputRev?": "main"}}]}
diff --git a/tests/lean/misc-no_nested_borrows/lakefile.lean b/tests/lean/misc-no_nested_borrows/lakefile.lean
deleted file mode 100644
index 58619110..00000000
--- a/tests/lean/misc-no_nested_borrows/lakefile.lean
+++ /dev/null
@@ -1,12 +0,0 @@
-import Lake
-open Lake DSL
-
-require mathlib from git
-  "https://github.com/leanprover-community/mathlib4.git"
-
-package «no_nested_borrows» {}
-
-lean_lib «Base» {}
-
-@[default_target]
-lean_lib «NoNestedBorrows» {}
diff --git a/tests/lean/misc-no_nested_borrows/lean-toolchain b/tests/lean/misc-no_nested_borrows/lean-toolchain
deleted file mode 100644
index bbf57f10..00000000
--- a/tests/lean/misc-no_nested_borrows/lean-toolchain
+++ /dev/null
@@ -1 +0,0 @@
-leanprover/lean4:nightly-2023-01-21
diff --git a/tests/lean/misc-paper/Base/Primitives.lean b/tests/lean/misc-paper/Base/Primitives.lean
deleted file mode 100644
index 4a66a453..00000000
--- a/tests/lean/misc-paper/Base/Primitives.lean
+++ /dev/null
@@ -1,583 +0,0 @@
-import Lean
-import Lean.Meta.Tactic.Simp
-import Init.Data.List.Basic
-import Mathlib.Tactic.RunCmd
-
---------------------
--- ASSERT COMMAND --
---------------------
-
-open Lean Elab Command Term Meta
-
-syntax (name := assert) "#assert" term: command
-
-@[command_elab assert]
-unsafe
-def assertImpl : CommandElab := fun (_stx: Syntax) => do
-  runTermElabM (fun _ => do
-    let r ← evalTerm Bool (mkConst ``Bool) _stx[1]
-    if not r then
-      logInfo "Assertion failed for: "
-      logInfo _stx[1]
-      logError "Expression reduced to false"
-    pure ())
-
-#eval 2 == 2
-#assert (2 == 2)
-
--------------
--- PRELUDE --
--------------
-
--- Results & monadic combinators
-
-inductive Error where
-   | assertionFailure: Error
-   | integerOverflow: Error
-   | divisionByZero: Error
-   | arrayOutOfBounds: Error
-   | maximumSizeExceeded: Error
-   | panic: Error
-deriving Repr, BEq
-
-open Error
-
-inductive Result (α : Type u) where
-  | ret (v: α): Result α
-  | fail (e: Error): Result α
-deriving Repr, BEq
-
-open Result
-
-instance Result_Inhabited (α : Type u) : Inhabited (Result α) :=
-  Inhabited.mk (fail panic)
-
-/- HELPERS -/
-
-def ret? {α: Type} (r: Result α): Bool :=
-  match r with
-  | Result.ret _ => true
-  | Result.fail _ => false
-
-def massert (b:Bool) : Result Unit :=
-  if b then .ret () else fail assertionFailure
-
-def eval_global {α: Type} (x: Result α) (_: ret? x): α :=
-  match x with
-  | Result.fail _ => by contradiction
-  | Result.ret x => x
-
-/- DO-DSL SUPPORT -/
-
-def bind (x: Result α) (f: α -> Result β) : Result β :=
-  match x with
-  | ret v  => f v 
-  | fail v => fail v
-
--- Allows using Result in do-blocks
-instance : Bind Result where
-  bind := bind
-
--- Allows using return x in do-blocks
-instance : Pure Result where
-  pure := fun x => ret x
-
-/- CUSTOM-DSL SUPPORT -/
-
--- Let-binding the Result of a monadic operation is oftentimes not sufficient,
--- because we may need a hypothesis for equational reasoning in the scope. We
--- rely on subtype, and a custom let-binding operator, in effect recreating our
--- own variant of the do-dsl
-
-def Result.attach {α: Type} (o : Result α): Result { x : α // o = ret x } :=
-  match o with
-  | .ret x => .ret ⟨x, rfl⟩
-  | .fail e => .fail e
-
-macro "let" e:term " ⟵ " f:term : doElem =>
-  `(doElem| let ⟨$e, h⟩ ← Result.attach $f)
-
--- TODO: any way to factorize both definitions?
-macro "let" e:term " <-- " f:term : doElem =>
-  `(doElem| let ⟨$e, h⟩ ← Result.attach $f)
-
--- We call the hypothesis `h`, in effect making it unavailable to the user
--- (because too much shadowing). But in practice, once can use the French single
--- quote notation (input with f< and f>), where `‹ h ›` finds a suitable
--- hypothesis in the context, this is equivalent to `have x: h := by assumption in x`
-#eval do
-  let y <-- .ret (0: Nat)
-  let _: y = 0 := by cases ‹ ret 0 = ret y › ; decide
-  let r: { x: Nat // x = 0 } := ⟨ y, by assumption ⟩
-  .ret r
-
-----------------------
--- MACHINE INTEGERS --
-----------------------
-
--- We redefine our machine integers types.
-
--- For Isize/Usize, we reuse `getNumBits` from `USize`. You cannot reduce `getNumBits`
--- using the simplifier, meaning that proofs do not depend on the compile-time value of
--- USize.size. (Lean assumes 32 or 64-bit platforms, and Rust doesn't really support, at
--- least officially, 16-bit microcontrollers, so this seems like a fine design decision
--- for now.)
-
--- Note from Chris Bailey: "If there's more than one salient property of your
--- definition then the subtyping strategy might get messy, and the property part
--- of a subtype is less discoverable by the simplifier or tactics like
--- library_search." So, we will not add refinements on the return values of the
--- operations defined on Primitives, but will rather rely on custom lemmas to
--- invert on possible return values of the primitive operations.
-
--- Machine integer constants, done via `ofNatCore`, which requires a proof that
--- the `Nat` fits within the desired integer type. We provide a custom tactic.
-
-open System.Platform.getNumBits
-
--- TODO: is there a way of only importing System.Platform.getNumBits?
---
-@[simp] def size_num_bits : Nat := (System.Platform.getNumBits ()).val
-
--- Remark: Lean seems to use < for the comparisons with the upper bounds by convention.
--- We keep the F* convention for now.
-@[simp] def Isize.min : Int := - (HPow.hPow 2 (size_num_bits - 1))
-@[simp] def Isize.max : Int := (HPow.hPow 2 (size_num_bits - 1)) - 1
-@[simp] def I8.min    : Int := - (HPow.hPow 2 7)
-@[simp] def I8.max    : Int := HPow.hPow 2 7 - 1
-@[simp] def I16.min   : Int := - (HPow.hPow 2 15)
-@[simp] def I16.max   : Int := HPow.hPow 2 15 - 1
-@[simp] def I32.min   : Int := -(HPow.hPow 2 31)
-@[simp] def I32.max   : Int := HPow.hPow 2 31 - 1
-@[simp] def I64.min   : Int := -(HPow.hPow 2 63)
-@[simp] def I64.max   : Int := HPow.hPow 2 63 - 1
-@[simp] def I128.min  : Int := -(HPow.hPow 2 127)
-@[simp] def I128.max  : Int := HPow.hPow 2 127 - 1
-@[simp] def Usize.min : Int := 0
-@[simp] def Usize.max : Int := HPow.hPow 2 size_num_bits - 1
-@[simp] def U8.min    : Int := 0
-@[simp] def U8.max    : Int := HPow.hPow 2 8 - 1
-@[simp] def U16.min   : Int := 0
-@[simp] def U16.max   : Int := HPow.hPow 2 16 - 1
-@[simp] def U32.min   : Int := 0
-@[simp] def U32.max   : Int := HPow.hPow 2 32 - 1
-@[simp] def U64.min   : Int := 0
-@[simp] def U64.max   : Int := HPow.hPow 2 64 - 1
-@[simp] def U128.min  : Int := 0
-@[simp] def U128.max  : Int := HPow.hPow 2 128 - 1
-
-#assert (I8.min   == -128)
-#assert (I8.max   == 127)
-#assert (I16.min  == -32768)
-#assert (I16.max  == 32767)
-#assert (I32.min  == -2147483648)
-#assert (I32.max  == 2147483647)
-#assert (I64.min  == -9223372036854775808)
-#assert (I64.max  == 9223372036854775807)
-#assert (I128.min == -170141183460469231731687303715884105728)
-#assert (I128.max == 170141183460469231731687303715884105727)
-#assert (U8.min   == 0)
-#assert (U8.max   == 255)
-#assert (U16.min  == 0)
-#assert (U16.max  == 65535)
-#assert (U32.min  == 0)
-#assert (U32.max  == 4294967295)
-#assert (U64.min  == 0)
-#assert (U64.max  == 18446744073709551615)
-#assert (U128.min == 0)
-#assert (U128.max == 340282366920938463463374607431768211455)
-
-inductive ScalarTy :=
-| Isize
-| I8
-| I16
-| I32
-| I64
-| I128
-| Usize
-| U8
-| U16
-| U32
-| U64
-| U128
-
-def Scalar.min (ty : ScalarTy) : Int :=
-  match ty with
-  | .Isize => Isize.min
-  | .I8    => I8.min
-  | .I16   => I16.min
-  | .I32   => I32.min
-  | .I64   => I64.min
-  | .I128  => I128.min
-  | .Usize => Usize.min
-  | .U8    => U8.min
-  | .U16   => U16.min
-  | .U32   => U32.min
-  | .U64   => U64.min
-  | .U128  => U128.min
-
-def Scalar.max (ty : ScalarTy) : Int :=
-  match ty with
-  | .Isize => Isize.max
-  | .I8    => I8.max
-  | .I16   => I16.max
-  | .I32   => I32.max
-  | .I64   => I64.max
-  | .I128  => I128.max
-  | .Usize => Usize.max
-  | .U8    => U8.max
-  | .U16   => U16.max
-  | .U32   => U32.max
-  | .U64   => U64.max
-  | .U128  => U128.max
-
--- "Conservative" bounds
--- We use those because we can't compare to the isize bounds (which can't
--- reduce at compile-time). Whenever we perform an arithmetic operation like
--- addition we need to check that the result is in bounds: we first compare
--- to the conservative bounds, which reduce, then compare to the real bounds.
--- This is useful for the various #asserts that we want to reduce at
--- type-checking time.
-def Scalar.cMin (ty : ScalarTy) : Int :=
-  match ty with
-  | .Isize => I32.min
-  | _ => Scalar.min ty
-
-def Scalar.cMax (ty : ScalarTy) : Int :=
-  match ty with
-  | .Isize => I32.max
-  | .Usize => U32.max
-  | _ => Scalar.max ty
-
-theorem Scalar.cMin_bound ty : Scalar.min ty <= Scalar.cMin ty := by sorry
-theorem Scalar.cMax_bound ty : Scalar.min ty <= Scalar.cMin ty := by sorry
-
-structure Scalar (ty : ScalarTy) where
-  val : Int
-  hmin : Scalar.min ty <= val
-  hmax : val <= Scalar.max ty
-
-theorem Scalar.bound_suffices (ty : ScalarTy) (x : Int) :
-  Scalar.cMin ty <= x && x <= Scalar.cMax ty ->
-  (decide (Scalar.min ty ≤ x) && decide (x ≤ Scalar.max ty)) = true
-  := by sorry
-
-def Scalar.ofIntCore {ty : ScalarTy} (x : Int)
-  (hmin : Scalar.min ty <= x) (hmax : x <= Scalar.max ty) : Scalar ty :=
-  { val := x, hmin := hmin, hmax := hmax }
-
-def Scalar.ofInt {ty : ScalarTy} (x : Int)
-  (h : Scalar.min ty <= x && x <= Scalar.max ty) : Scalar ty :=
-  let hmin: Scalar.min ty <= x := by sorry
-  let hmax: x <= Scalar.max ty := by sorry
-  Scalar.ofIntCore x hmin hmax
-
--- Further thoughts: look at what has been done here:
--- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/Fin/Basic.lean
--- and
--- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/UInt.lean
--- which both contain a fair amount of reasoning already!
-def Scalar.tryMk (ty : ScalarTy) (x : Int) : Result (Scalar ty) :=
-  -- TODO: write this with only one if then else
-  if hmin_cons: Scalar.cMin ty <= x || Scalar.min ty <= x then
-    if hmax_cons: x <= Scalar.cMax ty || x <= Scalar.max ty then
-      let hmin: Scalar.min ty <= x := by sorry
-      let hmax: x <= Scalar.max ty := by sorry
-      return Scalar.ofIntCore x hmin hmax
-    else fail integerOverflow
-  else fail integerOverflow
-
-def Scalar.neg {ty : ScalarTy} (x : Scalar ty) : Result (Scalar ty) := Scalar.tryMk ty (- x.val)
-
-def Scalar.div {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
-  if y.val != 0 then Scalar.tryMk ty (x.val / y.val) else fail divisionByZero
-
--- Checking that the % operation in Lean computes the same as the remainder operation in Rust
-#assert 1 % 2 = (1:Int)
-#assert (-1) % 2 = -1
-#assert 1 % (-2) = 1
-#assert (-1) % (-2) = -1
-
-def Scalar.rem {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
-  if y.val != 0 then Scalar.tryMk ty (x.val % y.val) else fail divisionByZero
-
-def Scalar.add {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
-  Scalar.tryMk ty (x.val + y.val)
-
-def Scalar.sub {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
-  Scalar.tryMk ty (x.val - y.val)
-
-def Scalar.mul {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
-  Scalar.tryMk ty (x.val * y.val)
-
--- TODO: instances of +, -, * etc. for scalars
-
--- Cast an integer from a [src_ty] to a [tgt_ty]
--- TODO: check the semantics of casts in Rust
-def Scalar.cast {src_ty : ScalarTy} (tgt_ty : ScalarTy) (x : Scalar src_ty) : Result (Scalar tgt_ty) :=
-  Scalar.tryMk tgt_ty x.val
-
--- The scalar types
--- We declare the definitions as reducible so that Lean can unfold them (useful
--- for type class resolution for instance).
-@[reducible] def Isize := Scalar .Isize
-@[reducible] def I8    := Scalar .I8
-@[reducible] def I16   := Scalar .I16
-@[reducible] def I32   := Scalar .I32
-@[reducible] def I64   := Scalar .I64
-@[reducible] def I128  := Scalar .I128
-@[reducible] def Usize := Scalar .Usize
-@[reducible] def U8    := Scalar .U8
-@[reducible] def U16   := Scalar .U16
-@[reducible] def U32   := Scalar .U32
-@[reducible] def U64   := Scalar .U64
-@[reducible] def U128  := Scalar .U128
-
--- TODO: below: not sure this is the best way.
--- Should we rather overload operations like +, -, etc.?
--- Also, it is possible to automate the generation of those definitions
--- with macros (but would it be a good idea? It would be less easy to
--- read the file, which is not supposed to change a lot)
-
--- Negation
-
-/--
-Remark: there is no heterogeneous negation in the Lean prelude: we thus introduce
-one here.
-
-The notation typeclass for heterogeneous addition.
-This enables the notation `- a : β` where `a : α`.
--/
-class HNeg (α : Type u) (β : outParam (Type v)) where
-  /-- `- a` computes the negation of `a`.
-  The meaning of this notation is type-dependent. -/
-  hNeg : α → β
-
-prefix:75  "-"   => HNeg.hNeg
-
-instance : HNeg Isize (Result Isize) where hNeg x := Scalar.neg x
-instance : HNeg I8 (Result I8) where hNeg x := Scalar.neg x
-instance : HNeg I16 (Result I16) where hNeg x := Scalar.neg x
-instance : HNeg I32 (Result I32) where hNeg x := Scalar.neg x
-instance : HNeg I64 (Result I64) where hNeg x := Scalar.neg x
-instance : HNeg I128 (Result I128) where hNeg x := Scalar.neg x
-
--- Addition
-instance {ty} : HAdd (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
-  hAdd x y := Scalar.add x y
-
--- Substraction
-instance {ty} : HSub (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
-  hSub x y := Scalar.sub x y
-
--- Multiplication
-instance {ty} : HMul (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
-  hMul x y := Scalar.mul x y
-
--- Division
-instance {ty} : HDiv (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
-  hDiv x y := Scalar.div x y
-
--- Remainder
-instance {ty} : HMod (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
-  hMod x y := Scalar.rem x y
-
--- ofIntCore
--- TODO: typeclass?
-def Isize.ofIntCore := @Scalar.ofIntCore .Isize
-def I8.ofIntCore    := @Scalar.ofIntCore .I8
-def I16.ofIntCore   := @Scalar.ofIntCore .I16
-def I32.ofIntCore   := @Scalar.ofIntCore .I32
-def I64.ofIntCore   := @Scalar.ofIntCore .I64
-def I128.ofIntCore  := @Scalar.ofIntCore .I128
-def Usize.ofIntCore := @Scalar.ofIntCore .Usize
-def U8.ofIntCore    := @Scalar.ofIntCore .U8
-def U16.ofIntCore   := @Scalar.ofIntCore .U16
-def U32.ofIntCore   := @Scalar.ofIntCore .U32
-def U64.ofIntCore   := @Scalar.ofIntCore .U64
-def U128.ofIntCore  := @Scalar.ofIntCore .U128
-
---  ofInt
--- TODO: typeclass?
-def Isize.ofInt := @Scalar.ofInt .Isize
-def I8.ofInt    := @Scalar.ofInt .I8
-def I16.ofInt   := @Scalar.ofInt .I16
-def I32.ofInt   := @Scalar.ofInt .I32
-def I64.ofInt   := @Scalar.ofInt .I64
-def I128.ofInt  := @Scalar.ofInt .I128
-def Usize.ofInt := @Scalar.ofInt .Usize
-def U8.ofInt    := @Scalar.ofInt .U8
-def U16.ofInt   := @Scalar.ofInt .U16
-def U32.ofInt   := @Scalar.ofInt .U32
-def U64.ofInt   := @Scalar.ofInt .U64
-def U128.ofInt  := @Scalar.ofInt .U128
-
--- Comparisons
-instance {ty} : LT (Scalar ty) where
-  lt a b := LT.lt a.val b.val
-
-instance {ty} : LE (Scalar ty) where le a b := LE.le a.val b.val
-
-instance Scalar.decLt {ty} (a b : Scalar ty) : Decidable (LT.lt a b) := Int.decLt ..
-instance Scalar.decLe {ty} (a b : Scalar ty) : Decidable (LE.le a b) := Int.decLe ..
-
-theorem Scalar.eq_of_val_eq {ty} : ∀ {i j : Scalar ty}, Eq i.val j.val → Eq i j
-  | ⟨_, _, _⟩, ⟨_, _, _⟩, rfl => rfl
-
-theorem Scalar.val_eq_of_eq {ty} {i j : Scalar ty} (h : Eq i j) : Eq i.val j.val :=
-  h ▸ rfl
-
-theorem Scalar.ne_of_val_ne {ty} {i j : Scalar ty} (h : Not (Eq i.val j.val)) : Not (Eq i j) :=
-  fun h' => absurd (val_eq_of_eq h') h
-
-instance (ty : ScalarTy) : DecidableEq (Scalar ty) :=
-  fun i j =>
-    match decEq i.val j.val with
-    | isTrue h  => isTrue (Scalar.eq_of_val_eq h)
-    | isFalse h => isFalse (Scalar.ne_of_val_ne h)
-
-def Scalar.toInt {ty} (n : Scalar ty) : Int := n.val
-
--- Tactic to prove that integers are in bounds
-syntax "intlit" : tactic
-
-macro_rules
-  | `(tactic| intlit) => `(tactic| apply Scalar.bound_suffices ; decide)
-
--- -- We now define a type class that subsumes the various machine integer types, so
--- -- as to write a concise definition for scalar_cast, rather than exhaustively
--- -- enumerating all of the possible pairs. We remark that Rust has sane semantics
--- -- and fails if a cast operation would involve a truncation or modulo.
-
--- class MachineInteger (t: Type) where
---   size: Nat
---   val: t -> Fin size
---   ofNatCore: (n:Nat) -> LT.lt n size -> t
-
--- set_option hygiene false in
--- run_cmd
---   for typeName in [`UInt8, `UInt16, `UInt32, `UInt64, `USize].map Lean.mkIdent do
---   Lean.Elab.Command.elabCommand (← `(
---     namespace $typeName
---     instance: MachineInteger $typeName where
---       size := size
---       val := val
---       ofNatCore := ofNatCore
---     end $typeName
---   ))
-
--- -- Aeneas only instantiates the destination type (`src` is implicit). We rely on
--- -- Lean to infer `src`.
-
--- def scalar_cast { src: Type } (dst: Type) [ MachineInteger src ] [ MachineInteger dst ] (x: src): Result dst :=
---   if h: MachineInteger.val x < MachineInteger.size dst then
---     .ret (MachineInteger.ofNatCore (MachineInteger.val x).val h)
---   else
---     .fail integerOverflow
-
--------------
--- VECTORS --
--------------
-
-def Vec (α : Type u) := { l : List α // List.length l <= Usize.max }
-
-def vec_new (α : Type u): Vec α := ⟨ [], by sorry ⟩
-
-def vec_len (α : Type u) (v : Vec α) : Usize :=
-  let ⟨ v, l ⟩ := v
-  Usize.ofIntCore (List.length v) (by sorry) l
- 
-def vec_push_fwd (α : Type u) (_ : Vec α) (_ : α) : Unit := ()
-
-def vec_push_back (α : Type u) (v : Vec α) (x : α) : Result (Vec α)
-  :=
-  if h : List.length v.val <= U32.max || List.length v.val <= Usize.max then
-    return ⟨ List.concat v.val x, by sorry ⟩
-  else
-    fail maximumSizeExceeded
-
-def vec_insert_fwd (α : Type u) (v: Vec α) (i: Usize) (_: α): Result Unit :=
-  if i.val < List.length v.val then
-    .ret ()
-  else
-    .fail arrayOutOfBounds
-
-def vec_insert_back (α : Type u) (v: Vec α) (i: Usize) (x: α): Result (Vec α) :=
-  if i.val < List.length v.val then
-    -- TODO: maybe we should redefine a list library which uses integers
-    -- (instead of natural numbers)
-    let i : Nat :=
-      match i.val with
-      | .ofNat n => n
-      | .negSucc n => by sorry -- TODO: we can't get here
-    let isLt: i < USize.size := by sorry
-    let i : Fin USize.size := { val := i, isLt := isLt }
-    .ret ⟨ List.set v.val i.val x, by
-      have h: List.length v.val <= Usize.max := v.property
-      rewrite [ List.length_set v.val i.val x ]
-      assumption
-    ⟩
-  else
-    .fail arrayOutOfBounds
-
-def vec_index_fwd (α : Type u) (v: Vec α) (i: Usize): Result α :=
-  if i.val < List.length v.val then
-    let i : Nat :=
-      match i.val with
-      | .ofNat n => n
-      | .negSucc n => by sorry -- TODO: we can't get here
-    let isLt: i < USize.size := by sorry
-    let i : Fin USize.size := { val := i, isLt := isLt }
-    let h: i < List.length v.val := by sorry
-    .ret (List.get v.val ⟨i.val, h⟩)
-  else
-    .fail arrayOutOfBounds
-
-def vec_index_back (α : Type u) (v: Vec α) (i: Usize) (_: α): Result Unit :=
-  if i.val < List.length v.val then
-    .ret ()
-  else
-    .fail arrayOutOfBounds
-
-def vec_index_mut_fwd (α : Type u) (v: Vec α) (i: Usize): Result α :=
-  if i.val < List.length v.val then
-    let i : Nat :=
-      match i.val with
-      | .ofNat n => n
-      | .negSucc n => by sorry -- TODO: we can't get here
-    let isLt: i < USize.size := by sorry
-    let i : Fin USize.size := { val := i, isLt := isLt }
-    let h: i < List.length v.val := by sorry
-    .ret (List.get v.val ⟨i.val, h⟩)
-  else
-    .fail arrayOutOfBounds
-
-def vec_index_mut_back (α : Type u) (v: Vec α) (i: Usize) (x: α): Result (Vec α) :=
-  if i.val < List.length v.val then
-    let i : Nat :=
-      match i.val with
-      | .ofNat n => n
-      | .negSucc n => by sorry -- TODO: we can't get here
-    let isLt: i < USize.size := by sorry
-    let i : Fin USize.size := { val := i, isLt := isLt }
-    .ret ⟨ List.set v.val i.val x, by
-      have h: List.length v.val <= Usize.max := v.property
-      rewrite [ List.length_set v.val i.val x ]
-      assumption
-    ⟩
-  else
-    .fail arrayOutOfBounds
-
-----------
--- MISC --
-----------
-
-def mem_replace_fwd (a : Type) (x : a) (_ : a) : a :=
-  x
-
-def mem_replace_back (a : Type) (_ : a) (y : a) : a :=
-  y
-
-/-- Aeneas-translated function -- useful to reduce non-recursive definitions.
- Use with `simp [ aeneas ]` -/
-register_simp_attr aeneas
diff --git a/tests/lean/misc-paper/Paper.lean b/tests/lean/misc-paper/Paper.lean
deleted file mode 100644
index 0b16fb8e..00000000
--- a/tests/lean/misc-paper/Paper.lean
+++ /dev/null
@@ -1,123 +0,0 @@
--- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
--- [paper]
-import Base.Primitives
-
-/- [paper::ref_incr] -/
-def ref_incr_fwd_back (x : I32) : Result I32 :=
-  x + (I32.ofInt 1 (by intlit))
-
-/- [paper::test_incr] -/
-def test_incr_fwd : Result Unit :=
-  do
-    let x ← ref_incr_fwd_back (I32.ofInt 0 (by intlit))
-    if h: not (x = (I32.ofInt 1 (by intlit)))
-    then Result.fail Error.panic
-    else Result.ret ()
-
-/- Unit test for [paper::test_incr] -/
-#assert (test_incr_fwd == .ret ())
-
-/- [paper::choose] -/
-def choose_fwd (T : Type) (b : Bool) (x : T) (y : T) : Result T :=
-  if h: b
-  then Result.ret x
-  else Result.ret y
-
-/- [paper::choose] -/
-def choose_back
-  (T : Type) (b : Bool) (x : T) (y : T) (ret0 : T) : Result (T × T) :=
-  if h: b
-  then Result.ret (ret0, y)
-  else Result.ret (x, ret0)
-
-/- [paper::test_choose] -/
-def test_choose_fwd : Result Unit :=
-  do
-    let z ←
-      choose_fwd I32 true (I32.ofInt 0 (by intlit)) (I32.ofInt 0 (by intlit))
-    let z0 ← z + (I32.ofInt 1 (by intlit))
-    if h: not (z0 = (I32.ofInt 1 (by intlit)))
-    then Result.fail Error.panic
-    else
-      do
-        let (x, y) ←
-          choose_back I32 true (I32.ofInt 0 (by intlit))
-            (I32.ofInt 0 (by intlit)) z0
-        if h: not (x = (I32.ofInt 1 (by intlit)))
-        then Result.fail Error.panic
-        else
-          if h: not (y = (I32.ofInt 0 (by intlit)))
-          then Result.fail Error.panic
-          else Result.ret ()
-
-/- Unit test for [paper::test_choose] -/
-#assert (test_choose_fwd == .ret ())
-
-/- [paper::List] -/
-inductive list_t (T : Type) :=
-| Cons : T -> list_t T -> list_t T
-| Nil : list_t T
-
-/- [paper::list_nth_mut] -/
-def list_nth_mut_fwd (T : Type) (l : list_t T) (i : U32) : Result T :=
-  match h: l with
-  | list_t.Cons x tl =>
-    if h: i = (U32.ofInt 0 (by intlit))
-    then Result.ret x
-    else do
-           let i0 ← i - (U32.ofInt 1 (by intlit))
-           list_nth_mut_fwd T tl i0
-  | list_t.Nil => Result.fail Error.panic
-
-/- [paper::list_nth_mut] -/
-def list_nth_mut_back
-  (T : Type) (l : list_t T) (i : U32) (ret0 : T) : Result (list_t T) :=
-  match h: l with
-  | list_t.Cons x tl =>
-    if h: i = (U32.ofInt 0 (by intlit))
-    then Result.ret (list_t.Cons ret0 tl)
-    else
-      do
-        let i0 ← i - (U32.ofInt 1 (by intlit))
-        let tl0 ← list_nth_mut_back T tl i0 ret0
-        Result.ret (list_t.Cons x tl0)
-  | list_t.Nil => Result.fail Error.panic
-
-/- [paper::sum] -/
-def sum_fwd (l : list_t I32) : Result I32 :=
-  match h: l with
-  | list_t.Cons x tl => do
-                          let i ← sum_fwd tl
-                          x + i
-  | list_t.Nil => Result.ret (I32.ofInt 0 (by intlit))
-
-/- [paper::test_nth] -/
-def test_nth_fwd : Result Unit :=
-  do
-    let l := list_t.Nil
-    let l0 := list_t.Cons (I32.ofInt 3 (by intlit)) l
-    let l1 := list_t.Cons (I32.ofInt 2 (by intlit)) l0
-    let x ←
-      list_nth_mut_fwd I32 (list_t.Cons (I32.ofInt 1 (by intlit)) l1)
-        (U32.ofInt 2 (by intlit))
-    let x0 ← x + (I32.ofInt 1 (by intlit))
-    let l2 ←
-      list_nth_mut_back I32 (list_t.Cons (I32.ofInt 1 (by intlit)) l1)
-        (U32.ofInt 2 (by intlit)) x0
-    let i ← sum_fwd l2
-    if h: not (i = (I32.ofInt 7 (by intlit)))
-    then Result.fail Error.panic
-    else Result.ret ()
-
-/- Unit test for [paper::test_nth] -/
-#assert (test_nth_fwd == .ret ())
-
-/- [paper::call_choose] -/
-def call_choose_fwd (p : (U32 × U32)) : Result U32 :=
-  do
-    let (px, py) := p
-    let pz ← choose_fwd U32 true px py
-    let pz0 ← pz + (U32.ofInt 1 (by intlit))
-    let (px0, _) ← choose_back U32 true px py pz0
-    Result.ret px0
-
diff --git a/tests/lean/misc-paper/lake-manifest.json b/tests/lean/misc-paper/lake-manifest.json
deleted file mode 100644
index 57b071ca..00000000
--- a/tests/lean/misc-paper/lake-manifest.json
+++ /dev/null
@@ -1,27 +0,0 @@
-{"version": 4,
- "packagesDir": "./lake-packages",
- "packages":
- [{"git":
-   {"url": "https://github.com/leanprover-community/mathlib4.git",
-    "subDir?": null,
-    "rev": "4037792ead804d7bfa8868e2c4684d4223c15ece",
-    "name": "mathlib",
-    "inputRev?": null}},
-  {"git":
-   {"url": "https://github.com/gebner/quote4",
-    "subDir?": null,
-    "rev": "2412c4fdf4a8b689f4467618e5e7b371ae5014aa",
-    "name": "Qq",
-    "inputRev?": "master"}},
-  {"git":
-   {"url": "https://github.com/JLimperg/aesop",
-    "subDir?": null,
-    "rev": "7fe9ecd9339b0e1796e89d243b776849c305c690",
-    "name": "aesop",
-    "inputRev?": "master"}},
-  {"git":
-   {"url": "https://github.com/leanprover/std4",
-    "subDir?": null,
-    "rev": "24897887905b3a1254b244369f5dd2cf6174b0ee",
-    "name": "std",
-    "inputRev?": "main"}}]}
diff --git a/tests/lean/misc-paper/lakefile.lean b/tests/lean/misc-paper/lakefile.lean
deleted file mode 100644
index 75d7208e..00000000
--- a/tests/lean/misc-paper/lakefile.lean
+++ /dev/null
@@ -1,12 +0,0 @@
-import Lake
-open Lake DSL
-
-require mathlib from git
-  "https://github.com/leanprover-community/mathlib4.git"
-
-package «paper» {}
-
-lean_lib «Base» {}
-
-@[default_target]
-lean_lib «Paper» {}
diff --git a/tests/lean/misc-paper/lean-toolchain b/tests/lean/misc-paper/lean-toolchain
deleted file mode 100644
index bbf57f10..00000000
--- a/tests/lean/misc-paper/lean-toolchain
+++ /dev/null
@@ -1 +0,0 @@
-leanprover/lean4:nightly-2023-01-21
diff --git a/tests/lean/misc-polonius_list/Base/Primitives.lean b/tests/lean/misc-polonius_list/Base/Primitives.lean
deleted file mode 100644
index 4a66a453..00000000
--- a/tests/lean/misc-polonius_list/Base/Primitives.lean
+++ /dev/null
@@ -1,583 +0,0 @@
-import Lean
-import Lean.Meta.Tactic.Simp
-import Init.Data.List.Basic
-import Mathlib.Tactic.RunCmd
-
---------------------
--- ASSERT COMMAND --
---------------------
-
-open Lean Elab Command Term Meta
-
-syntax (name := assert) "#assert" term: command
-
-@[command_elab assert]
-unsafe
-def assertImpl : CommandElab := fun (_stx: Syntax) => do
-  runTermElabM (fun _ => do
-    let r ← evalTerm Bool (mkConst ``Bool) _stx[1]
-    if not r then
-      logInfo "Assertion failed for: "
-      logInfo _stx[1]
-      logError "Expression reduced to false"
-    pure ())
-
-#eval 2 == 2
-#assert (2 == 2)
-
--------------
--- PRELUDE --
--------------
-
--- Results & monadic combinators
-
-inductive Error where
-   | assertionFailure: Error
-   | integerOverflow: Error
-   | divisionByZero: Error
-   | arrayOutOfBounds: Error
-   | maximumSizeExceeded: Error
-   | panic: Error
-deriving Repr, BEq
-
-open Error
-
-inductive Result (α : Type u) where
-  | ret (v: α): Result α
-  | fail (e: Error): Result α
-deriving Repr, BEq
-
-open Result
-
-instance Result_Inhabited (α : Type u) : Inhabited (Result α) :=
-  Inhabited.mk (fail panic)
-
-/- HELPERS -/
-
-def ret? {α: Type} (r: Result α): Bool :=
-  match r with
-  | Result.ret _ => true
-  | Result.fail _ => false
-
-def massert (b:Bool) : Result Unit :=
-  if b then .ret () else fail assertionFailure
-
-def eval_global {α: Type} (x: Result α) (_: ret? x): α :=
-  match x with
-  | Result.fail _ => by contradiction
-  | Result.ret x => x
-
-/- DO-DSL SUPPORT -/
-
-def bind (x: Result α) (f: α -> Result β) : Result β :=
-  match x with
-  | ret v  => f v 
-  | fail v => fail v
-
--- Allows using Result in do-blocks
-instance : Bind Result where
-  bind := bind
-
--- Allows using return x in do-blocks
-instance : Pure Result where
-  pure := fun x => ret x
-
-/- CUSTOM-DSL SUPPORT -/
-
--- Let-binding the Result of a monadic operation is oftentimes not sufficient,
--- because we may need a hypothesis for equational reasoning in the scope. We
--- rely on subtype, and a custom let-binding operator, in effect recreating our
--- own variant of the do-dsl
-
-def Result.attach {α: Type} (o : Result α): Result { x : α // o = ret x } :=
-  match o with
-  | .ret x => .ret ⟨x, rfl⟩
-  | .fail e => .fail e
-
-macro "let" e:term " ⟵ " f:term : doElem =>
-  `(doElem| let ⟨$e, h⟩ ← Result.attach $f)
-
--- TODO: any way to factorize both definitions?
-macro "let" e:term " <-- " f:term : doElem =>
-  `(doElem| let ⟨$e, h⟩ ← Result.attach $f)
-
--- We call the hypothesis `h`, in effect making it unavailable to the user
--- (because too much shadowing). But in practice, once can use the French single
--- quote notation (input with f< and f>), where `‹ h ›` finds a suitable
--- hypothesis in the context, this is equivalent to `have x: h := by assumption in x`
-#eval do
-  let y <-- .ret (0: Nat)
-  let _: y = 0 := by cases ‹ ret 0 = ret y › ; decide
-  let r: { x: Nat // x = 0 } := ⟨ y, by assumption ⟩
-  .ret r
-
-----------------------
--- MACHINE INTEGERS --
-----------------------
-
--- We redefine our machine integers types.
-
--- For Isize/Usize, we reuse `getNumBits` from `USize`. You cannot reduce `getNumBits`
--- using the simplifier, meaning that proofs do not depend on the compile-time value of
--- USize.size. (Lean assumes 32 or 64-bit platforms, and Rust doesn't really support, at
--- least officially, 16-bit microcontrollers, so this seems like a fine design decision
--- for now.)
-
--- Note from Chris Bailey: "If there's more than one salient property of your
--- definition then the subtyping strategy might get messy, and the property part
--- of a subtype is less discoverable by the simplifier or tactics like
--- library_search." So, we will not add refinements on the return values of the
--- operations defined on Primitives, but will rather rely on custom lemmas to
--- invert on possible return values of the primitive operations.
-
--- Machine integer constants, done via `ofNatCore`, which requires a proof that
--- the `Nat` fits within the desired integer type. We provide a custom tactic.
-
-open System.Platform.getNumBits
-
--- TODO: is there a way of only importing System.Platform.getNumBits?
---
-@[simp] def size_num_bits : Nat := (System.Platform.getNumBits ()).val
-
--- Remark: Lean seems to use < for the comparisons with the upper bounds by convention.
--- We keep the F* convention for now.
-@[simp] def Isize.min : Int := - (HPow.hPow 2 (size_num_bits - 1))
-@[simp] def Isize.max : Int := (HPow.hPow 2 (size_num_bits - 1)) - 1
-@[simp] def I8.min    : Int := - (HPow.hPow 2 7)
-@[simp] def I8.max    : Int := HPow.hPow 2 7 - 1
-@[simp] def I16.min   : Int := - (HPow.hPow 2 15)
-@[simp] def I16.max   : Int := HPow.hPow 2 15 - 1
-@[simp] def I32.min   : Int := -(HPow.hPow 2 31)
-@[simp] def I32.max   : Int := HPow.hPow 2 31 - 1
-@[simp] def I64.min   : Int := -(HPow.hPow 2 63)
-@[simp] def I64.max   : Int := HPow.hPow 2 63 - 1
-@[simp] def I128.min  : Int := -(HPow.hPow 2 127)
-@[simp] def I128.max  : Int := HPow.hPow 2 127 - 1
-@[simp] def Usize.min : Int := 0
-@[simp] def Usize.max : Int := HPow.hPow 2 size_num_bits - 1
-@[simp] def U8.min    : Int := 0
-@[simp] def U8.max    : Int := HPow.hPow 2 8 - 1
-@[simp] def U16.min   : Int := 0
-@[simp] def U16.max   : Int := HPow.hPow 2 16 - 1
-@[simp] def U32.min   : Int := 0
-@[simp] def U32.max   : Int := HPow.hPow 2 32 - 1
-@[simp] def U64.min   : Int := 0
-@[simp] def U64.max   : Int := HPow.hPow 2 64 - 1
-@[simp] def U128.min  : Int := 0
-@[simp] def U128.max  : Int := HPow.hPow 2 128 - 1
-
-#assert (I8.min   == -128)
-#assert (I8.max   == 127)
-#assert (I16.min  == -32768)
-#assert (I16.max  == 32767)
-#assert (I32.min  == -2147483648)
-#assert (I32.max  == 2147483647)
-#assert (I64.min  == -9223372036854775808)
-#assert (I64.max  == 9223372036854775807)
-#assert (I128.min == -170141183460469231731687303715884105728)
-#assert (I128.max == 170141183460469231731687303715884105727)
-#assert (U8.min   == 0)
-#assert (U8.max   == 255)
-#assert (U16.min  == 0)
-#assert (U16.max  == 65535)
-#assert (U32.min  == 0)
-#assert (U32.max  == 4294967295)
-#assert (U64.min  == 0)
-#assert (U64.max  == 18446744073709551615)
-#assert (U128.min == 0)
-#assert (U128.max == 340282366920938463463374607431768211455)
-
-inductive ScalarTy :=
-| Isize
-| I8
-| I16
-| I32
-| I64
-| I128
-| Usize
-| U8
-| U16
-| U32
-| U64
-| U128
-
-def Scalar.min (ty : ScalarTy) : Int :=
-  match ty with
-  | .Isize => Isize.min
-  | .I8    => I8.min
-  | .I16   => I16.min
-  | .I32   => I32.min
-  | .I64   => I64.min
-  | .I128  => I128.min
-  | .Usize => Usize.min
-  | .U8    => U8.min
-  | .U16   => U16.min
-  | .U32   => U32.min
-  | .U64   => U64.min
-  | .U128  => U128.min
-
-def Scalar.max (ty : ScalarTy) : Int :=
-  match ty with
-  | .Isize => Isize.max
-  | .I8    => I8.max
-  | .I16   => I16.max
-  | .I32   => I32.max
-  | .I64   => I64.max
-  | .I128  => I128.max
-  | .Usize => Usize.max
-  | .U8    => U8.max
-  | .U16   => U16.max
-  | .U32   => U32.max
-  | .U64   => U64.max
-  | .U128  => U128.max
-
--- "Conservative" bounds
--- We use those because we can't compare to the isize bounds (which can't
--- reduce at compile-time). Whenever we perform an arithmetic operation like
--- addition we need to check that the result is in bounds: we first compare
--- to the conservative bounds, which reduce, then compare to the real bounds.
--- This is useful for the various #asserts that we want to reduce at
--- type-checking time.
-def Scalar.cMin (ty : ScalarTy) : Int :=
-  match ty with
-  | .Isize => I32.min
-  | _ => Scalar.min ty
-
-def Scalar.cMax (ty : ScalarTy) : Int :=
-  match ty with
-  | .Isize => I32.max
-  | .Usize => U32.max
-  | _ => Scalar.max ty
-
-theorem Scalar.cMin_bound ty : Scalar.min ty <= Scalar.cMin ty := by sorry
-theorem Scalar.cMax_bound ty : Scalar.min ty <= Scalar.cMin ty := by sorry
-
-structure Scalar (ty : ScalarTy) where
-  val : Int
-  hmin : Scalar.min ty <= val
-  hmax : val <= Scalar.max ty
-
-theorem Scalar.bound_suffices (ty : ScalarTy) (x : Int) :
-  Scalar.cMin ty <= x && x <= Scalar.cMax ty ->
-  (decide (Scalar.min ty ≤ x) && decide (x ≤ Scalar.max ty)) = true
-  := by sorry
-
-def Scalar.ofIntCore {ty : ScalarTy} (x : Int)
-  (hmin : Scalar.min ty <= x) (hmax : x <= Scalar.max ty) : Scalar ty :=
-  { val := x, hmin := hmin, hmax := hmax }
-
-def Scalar.ofInt {ty : ScalarTy} (x : Int)
-  (h : Scalar.min ty <= x && x <= Scalar.max ty) : Scalar ty :=
-  let hmin: Scalar.min ty <= x := by sorry
-  let hmax: x <= Scalar.max ty := by sorry
-  Scalar.ofIntCore x hmin hmax
-
--- Further thoughts: look at what has been done here:
--- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/Fin/Basic.lean
--- and
--- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/UInt.lean
--- which both contain a fair amount of reasoning already!
-def Scalar.tryMk (ty : ScalarTy) (x : Int) : Result (Scalar ty) :=
-  -- TODO: write this with only one if then else
-  if hmin_cons: Scalar.cMin ty <= x || Scalar.min ty <= x then
-    if hmax_cons: x <= Scalar.cMax ty || x <= Scalar.max ty then
-      let hmin: Scalar.min ty <= x := by sorry
-      let hmax: x <= Scalar.max ty := by sorry
-      return Scalar.ofIntCore x hmin hmax
-    else fail integerOverflow
-  else fail integerOverflow
-
-def Scalar.neg {ty : ScalarTy} (x : Scalar ty) : Result (Scalar ty) := Scalar.tryMk ty (- x.val)
-
-def Scalar.div {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
-  if y.val != 0 then Scalar.tryMk ty (x.val / y.val) else fail divisionByZero
-
--- Checking that the % operation in Lean computes the same as the remainder operation in Rust
-#assert 1 % 2 = (1:Int)
-#assert (-1) % 2 = -1
-#assert 1 % (-2) = 1
-#assert (-1) % (-2) = -1
-
-def Scalar.rem {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
-  if y.val != 0 then Scalar.tryMk ty (x.val % y.val) else fail divisionByZero
-
-def Scalar.add {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
-  Scalar.tryMk ty (x.val + y.val)
-
-def Scalar.sub {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
-  Scalar.tryMk ty (x.val - y.val)
-
-def Scalar.mul {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
-  Scalar.tryMk ty (x.val * y.val)
-
--- TODO: instances of +, -, * etc. for scalars
-
--- Cast an integer from a [src_ty] to a [tgt_ty]
--- TODO: check the semantics of casts in Rust
-def Scalar.cast {src_ty : ScalarTy} (tgt_ty : ScalarTy) (x : Scalar src_ty) : Result (Scalar tgt_ty) :=
-  Scalar.tryMk tgt_ty x.val
-
--- The scalar types
--- We declare the definitions as reducible so that Lean can unfold them (useful
--- for type class resolution for instance).
-@[reducible] def Isize := Scalar .Isize
-@[reducible] def I8    := Scalar .I8
-@[reducible] def I16   := Scalar .I16
-@[reducible] def I32   := Scalar .I32
-@[reducible] def I64   := Scalar .I64
-@[reducible] def I128  := Scalar .I128
-@[reducible] def Usize := Scalar .Usize
-@[reducible] def U8    := Scalar .U8
-@[reducible] def U16   := Scalar .U16
-@[reducible] def U32   := Scalar .U32
-@[reducible] def U64   := Scalar .U64
-@[reducible] def U128  := Scalar .U128
-
--- TODO: below: not sure this is the best way.
--- Should we rather overload operations like +, -, etc.?
--- Also, it is possible to automate the generation of those definitions
--- with macros (but would it be a good idea? It would be less easy to
--- read the file, which is not supposed to change a lot)
-
--- Negation
-
-/--
-Remark: there is no heterogeneous negation in the Lean prelude: we thus introduce
-one here.
-
-The notation typeclass for heterogeneous addition.
-This enables the notation `- a : β` where `a : α`.
--/
-class HNeg (α : Type u) (β : outParam (Type v)) where
-  /-- `- a` computes the negation of `a`.
-  The meaning of this notation is type-dependent. -/
-  hNeg : α → β
-
-prefix:75  "-"   => HNeg.hNeg
-
-instance : HNeg Isize (Result Isize) where hNeg x := Scalar.neg x
-instance : HNeg I8 (Result I8) where hNeg x := Scalar.neg x
-instance : HNeg I16 (Result I16) where hNeg x := Scalar.neg x
-instance : HNeg I32 (Result I32) where hNeg x := Scalar.neg x
-instance : HNeg I64 (Result I64) where hNeg x := Scalar.neg x
-instance : HNeg I128 (Result I128) where hNeg x := Scalar.neg x
-
--- Addition
-instance {ty} : HAdd (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
-  hAdd x y := Scalar.add x y
-
--- Substraction
-instance {ty} : HSub (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
-  hSub x y := Scalar.sub x y
-
--- Multiplication
-instance {ty} : HMul (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
-  hMul x y := Scalar.mul x y
-
--- Division
-instance {ty} : HDiv (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
-  hDiv x y := Scalar.div x y
-
--- Remainder
-instance {ty} : HMod (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
-  hMod x y := Scalar.rem x y
-
--- ofIntCore
--- TODO: typeclass?
-def Isize.ofIntCore := @Scalar.ofIntCore .Isize
-def I8.ofIntCore    := @Scalar.ofIntCore .I8
-def I16.ofIntCore   := @Scalar.ofIntCore .I16
-def I32.ofIntCore   := @Scalar.ofIntCore .I32
-def I64.ofIntCore   := @Scalar.ofIntCore .I64
-def I128.ofIntCore  := @Scalar.ofIntCore .I128
-def Usize.ofIntCore := @Scalar.ofIntCore .Usize
-def U8.ofIntCore    := @Scalar.ofIntCore .U8
-def U16.ofIntCore   := @Scalar.ofIntCore .U16
-def U32.ofIntCore   := @Scalar.ofIntCore .U32
-def U64.ofIntCore   := @Scalar.ofIntCore .U64
-def U128.ofIntCore  := @Scalar.ofIntCore .U128
-
---  ofInt
--- TODO: typeclass?
-def Isize.ofInt := @Scalar.ofInt .Isize
-def I8.ofInt    := @Scalar.ofInt .I8
-def I16.ofInt   := @Scalar.ofInt .I16
-def I32.ofInt   := @Scalar.ofInt .I32
-def I64.ofInt   := @Scalar.ofInt .I64
-def I128.ofInt  := @Scalar.ofInt .I128
-def Usize.ofInt := @Scalar.ofInt .Usize
-def U8.ofInt    := @Scalar.ofInt .U8
-def U16.ofInt   := @Scalar.ofInt .U16
-def U32.ofInt   := @Scalar.ofInt .U32
-def U64.ofInt   := @Scalar.ofInt .U64
-def U128.ofInt  := @Scalar.ofInt .U128
-
--- Comparisons
-instance {ty} : LT (Scalar ty) where
-  lt a b := LT.lt a.val b.val
-
-instance {ty} : LE (Scalar ty) where le a b := LE.le a.val b.val
-
-instance Scalar.decLt {ty} (a b : Scalar ty) : Decidable (LT.lt a b) := Int.decLt ..
-instance Scalar.decLe {ty} (a b : Scalar ty) : Decidable (LE.le a b) := Int.decLe ..
-
-theorem Scalar.eq_of_val_eq {ty} : ∀ {i j : Scalar ty}, Eq i.val j.val → Eq i j
-  | ⟨_, _, _⟩, ⟨_, _, _⟩, rfl => rfl
-
-theorem Scalar.val_eq_of_eq {ty} {i j : Scalar ty} (h : Eq i j) : Eq i.val j.val :=
-  h ▸ rfl
-
-theorem Scalar.ne_of_val_ne {ty} {i j : Scalar ty} (h : Not (Eq i.val j.val)) : Not (Eq i j) :=
-  fun h' => absurd (val_eq_of_eq h') h
-
-instance (ty : ScalarTy) : DecidableEq (Scalar ty) :=
-  fun i j =>
-    match decEq i.val j.val with
-    | isTrue h  => isTrue (Scalar.eq_of_val_eq h)
-    | isFalse h => isFalse (Scalar.ne_of_val_ne h)
-
-def Scalar.toInt {ty} (n : Scalar ty) : Int := n.val
-
--- Tactic to prove that integers are in bounds
-syntax "intlit" : tactic
-
-macro_rules
-  | `(tactic| intlit) => `(tactic| apply Scalar.bound_suffices ; decide)
-
--- -- We now define a type class that subsumes the various machine integer types, so
--- -- as to write a concise definition for scalar_cast, rather than exhaustively
--- -- enumerating all of the possible pairs. We remark that Rust has sane semantics
--- -- and fails if a cast operation would involve a truncation or modulo.
-
--- class MachineInteger (t: Type) where
---   size: Nat
---   val: t -> Fin size
---   ofNatCore: (n:Nat) -> LT.lt n size -> t
-
--- set_option hygiene false in
--- run_cmd
---   for typeName in [`UInt8, `UInt16, `UInt32, `UInt64, `USize].map Lean.mkIdent do
---   Lean.Elab.Command.elabCommand (← `(
---     namespace $typeName
---     instance: MachineInteger $typeName where
---       size := size
---       val := val
---       ofNatCore := ofNatCore
---     end $typeName
---   ))
-
--- -- Aeneas only instantiates the destination type (`src` is implicit). We rely on
--- -- Lean to infer `src`.
-
--- def scalar_cast { src: Type } (dst: Type) [ MachineInteger src ] [ MachineInteger dst ] (x: src): Result dst :=
---   if h: MachineInteger.val x < MachineInteger.size dst then
---     .ret (MachineInteger.ofNatCore (MachineInteger.val x).val h)
---   else
---     .fail integerOverflow
-
--------------
--- VECTORS --
--------------
-
-def Vec (α : Type u) := { l : List α // List.length l <= Usize.max }
-
-def vec_new (α : Type u): Vec α := ⟨ [], by sorry ⟩
-
-def vec_len (α : Type u) (v : Vec α) : Usize :=
-  let ⟨ v, l ⟩ := v
-  Usize.ofIntCore (List.length v) (by sorry) l
- 
-def vec_push_fwd (α : Type u) (_ : Vec α) (_ : α) : Unit := ()
-
-def vec_push_back (α : Type u) (v : Vec α) (x : α) : Result (Vec α)
-  :=
-  if h : List.length v.val <= U32.max || List.length v.val <= Usize.max then
-    return ⟨ List.concat v.val x, by sorry ⟩
-  else
-    fail maximumSizeExceeded
-
-def vec_insert_fwd (α : Type u) (v: Vec α) (i: Usize) (_: α): Result Unit :=
-  if i.val < List.length v.val then
-    .ret ()
-  else
-    .fail arrayOutOfBounds
-
-def vec_insert_back (α : Type u) (v: Vec α) (i: Usize) (x: α): Result (Vec α) :=
-  if i.val < List.length v.val then
-    -- TODO: maybe we should redefine a list library which uses integers
-    -- (instead of natural numbers)
-    let i : Nat :=
-      match i.val with
-      | .ofNat n => n
-      | .negSucc n => by sorry -- TODO: we can't get here
-    let isLt: i < USize.size := by sorry
-    let i : Fin USize.size := { val := i, isLt := isLt }
-    .ret ⟨ List.set v.val i.val x, by
-      have h: List.length v.val <= Usize.max := v.property
-      rewrite [ List.length_set v.val i.val x ]
-      assumption
-    ⟩
-  else
-    .fail arrayOutOfBounds
-
-def vec_index_fwd (α : Type u) (v: Vec α) (i: Usize): Result α :=
-  if i.val < List.length v.val then
-    let i : Nat :=
-      match i.val with
-      | .ofNat n => n
-      | .negSucc n => by sorry -- TODO: we can't get here
-    let isLt: i < USize.size := by sorry
-    let i : Fin USize.size := { val := i, isLt := isLt }
-    let h: i < List.length v.val := by sorry
-    .ret (List.get v.val ⟨i.val, h⟩)
-  else
-    .fail arrayOutOfBounds
-
-def vec_index_back (α : Type u) (v: Vec α) (i: Usize) (_: α): Result Unit :=
-  if i.val < List.length v.val then
-    .ret ()
-  else
-    .fail arrayOutOfBounds
-
-def vec_index_mut_fwd (α : Type u) (v: Vec α) (i: Usize): Result α :=
-  if i.val < List.length v.val then
-    let i : Nat :=
-      match i.val with
-      | .ofNat n => n
-      | .negSucc n => by sorry -- TODO: we can't get here
-    let isLt: i < USize.size := by sorry
-    let i : Fin USize.size := { val := i, isLt := isLt }
-    let h: i < List.length v.val := by sorry
-    .ret (List.get v.val ⟨i.val, h⟩)
-  else
-    .fail arrayOutOfBounds
-
-def vec_index_mut_back (α : Type u) (v: Vec α) (i: Usize) (x: α): Result (Vec α) :=
-  if i.val < List.length v.val then
-    let i : Nat :=
-      match i.val with
-      | .ofNat n => n
-      | .negSucc n => by sorry -- TODO: we can't get here
-    let isLt: i < USize.size := by sorry
-    let i : Fin USize.size := { val := i, isLt := isLt }
-    .ret ⟨ List.set v.val i.val x, by
-      have h: List.length v.val <= Usize.max := v.property
-      rewrite [ List.length_set v.val i.val x ]
-      assumption
-    ⟩
-  else
-    .fail arrayOutOfBounds
-
-----------
--- MISC --
-----------
-
-def mem_replace_fwd (a : Type) (x : a) (_ : a) : a :=
-  x
-
-def mem_replace_back (a : Type) (_ : a) (y : a) : a :=
-  y
-
-/-- Aeneas-translated function -- useful to reduce non-recursive definitions.
- Use with `simp [ aeneas ]` -/
-register_simp_attr aeneas
diff --git a/tests/lean/misc-polonius_list/PoloniusList.lean b/tests/lean/misc-polonius_list/PoloniusList.lean
deleted file mode 100644
index 79696996..00000000
--- a/tests/lean/misc-polonius_list/PoloniusList.lean
+++ /dev/null
@@ -1,31 +0,0 @@
--- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
--- [polonius_list]
-import Base.Primitives
-
-/- [polonius_list::List] -/
-inductive list_t (T : Type) :=
-| Cons : T -> list_t T -> list_t T
-| Nil : list_t T
-
-/- [polonius_list::get_list_at_x] -/
-def get_list_at_x_fwd (ls : list_t U32) (x : U32) : Result (list_t U32) :=
-  match h: ls with
-  | list_t.Cons hd tl =>
-    if h: hd = x
-    then Result.ret (list_t.Cons hd tl)
-    else get_list_at_x_fwd tl x
-  | list_t.Nil => Result.ret list_t.Nil
-
-/- [polonius_list::get_list_at_x] -/
-def get_list_at_x_back
-  (ls : list_t U32) (x : U32) (ret0 : list_t U32) : Result (list_t U32) :=
-  match h: ls with
-  | list_t.Cons hd tl =>
-    if h: hd = x
-    then Result.ret ret0
-    else
-      do
-        let tl0 ← get_list_at_x_back tl x ret0
-        Result.ret (list_t.Cons hd tl0)
-  | list_t.Nil => Result.ret ret0
-
diff --git a/tests/lean/misc-polonius_list/lake-manifest.json b/tests/lean/misc-polonius_list/lake-manifest.json
deleted file mode 100644
index 57b071ca..00000000
--- a/tests/lean/misc-polonius_list/lake-manifest.json
+++ /dev/null
@@ -1,27 +0,0 @@
-{"version": 4,
- "packagesDir": "./lake-packages",
- "packages":
- [{"git":
-   {"url": "https://github.com/leanprover-community/mathlib4.git",
-    "subDir?": null,
-    "rev": "4037792ead804d7bfa8868e2c4684d4223c15ece",
-    "name": "mathlib",
-    "inputRev?": null}},
-  {"git":
-   {"url": "https://github.com/gebner/quote4",
-    "subDir?": null,
-    "rev": "2412c4fdf4a8b689f4467618e5e7b371ae5014aa",
-    "name": "Qq",
-    "inputRev?": "master"}},
-  {"git":
-   {"url": "https://github.com/JLimperg/aesop",
-    "subDir?": null,
-    "rev": "7fe9ecd9339b0e1796e89d243b776849c305c690",
-    "name": "aesop",
-    "inputRev?": "master"}},
-  {"git":
-   {"url": "https://github.com/leanprover/std4",
-    "subDir?": null,
-    "rev": "24897887905b3a1254b244369f5dd2cf6174b0ee",
-    "name": "std",
-    "inputRev?": "main"}}]}
diff --git a/tests/lean/misc-polonius_list/lakefile.lean b/tests/lean/misc-polonius_list/lakefile.lean
deleted file mode 100644
index e89d4259..00000000
--- a/tests/lean/misc-polonius_list/lakefile.lean
+++ /dev/null
@@ -1,12 +0,0 @@
-import Lake
-open Lake DSL
-
-require mathlib from git
-  "https://github.com/leanprover-community/mathlib4.git"
-
-package «polonius_list» {}
-
-lean_lib «Base» {}
-
-@[default_target]
-lean_lib «PoloniusList» {}
diff --git a/tests/lean/misc-polonius_list/lean-toolchain b/tests/lean/misc-polonius_list/lean-toolchain
deleted file mode 100644
index bbf57f10..00000000
--- a/tests/lean/misc-polonius_list/lean-toolchain
+++ /dev/null
@@ -1 +0,0 @@
-leanprover/lean4:nightly-2023-01-21