Merge branch 'main' into son_fixes2

45 files changed, 7140 insertions, 2922 deletions

diff --git a/tests/coq/array/Array.v b/tests/coq/array/Array.v
new file mode 100644
index 00000000..1f2cc0e0
--- /dev/null
+++ b/tests/coq/array/Array.v
@@ -0,0 +1,544 @@
+(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
+(** [array] *)
+Require Import Primitives.
+Import Primitives.
+Require Import Coq.ZArith.ZArith.
+Require Import List.
+Import ListNotations.
+Local Open Scope Primitives_scope.
+Module Array.
+
+(** [array::AB]
+    Source: 'src/array.rs', lines 3:0-3:11 *)
+Inductive AB_t := | AB_A : AB_t | AB_B : AB_t.
+
+(** [array::incr]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ())
+    Source: 'src/array.rs', lines 8:0-8:24 *)
+Definition incr (x : u32) : result u32 :=
+  u32_add x 1%u32.
+
+(** [array::array_to_shared_slice_]: forward function
+    Source: 'src/array.rs', lines 16:0-16:53 *)
+Definition array_to_shared_slice_
+  (T : Type) (s : array T 32%usize) : result (slice T) :=
+  array_to_slice T 32%usize s
+.
+
+(** [array::array_to_mut_slice_]: forward function
+    Source: 'src/array.rs', lines 21:0-21:58 *)
+Definition array_to_mut_slice_
+  (T : Type) (s : array T 32%usize) : result (slice T) :=
+  array_to_slice T 32%usize s
+.
+
+(** [array::array_to_mut_slice_]: backward function 0
+    Source: 'src/array.rs', lines 21:0-21:58 *)
+Definition array_to_mut_slice__back
+  (T : Type) (s : array T 32%usize) (ret : slice T) :
+  result (array T 32%usize)
+  :=
+  array_from_slice T 32%usize s ret
+.
+
+(** [array::array_len]: forward function
+    Source: 'src/array.rs', lines 25:0-25:40 *)
+Definition array_len (T : Type) (s : array T 32%usize) : result usize :=
+  s0 <- array_to_slice T 32%usize s; let i := slice_len T s0 in Return i
+.
+
+(** [array::shared_array_len]: forward function
+    Source: 'src/array.rs', lines 29:0-29:48 *)
+Definition shared_array_len (T : Type) (s : array T 32%usize) : result usize :=
+  s0 <- array_to_slice T 32%usize s; let i := slice_len T s0 in Return i
+.
+
+(** [array::shared_slice_len]: forward function
+    Source: 'src/array.rs', lines 33:0-33:44 *)
+Definition shared_slice_len (T : Type) (s : slice T) : result usize :=
+  let i := slice_len T s in Return i
+.
+
+(** [array::index_array_shared]: forward function
+    Source: 'src/array.rs', lines 37:0-37:57 *)
+Definition index_array_shared
+  (T : Type) (s : array T 32%usize) (i : usize) : result T :=
+  array_index_usize T 32%usize s i
+.
+
+(** [array::index_array_u32]: forward function
+    Source: 'src/array.rs', lines 44:0-44:53 *)
+Definition index_array_u32 (s : array u32 32%usize) (i : usize) : result u32 :=
+  array_index_usize u32 32%usize s i
+.
+
+(** [array::index_array_copy]: forward function
+    Source: 'src/array.rs', lines 48:0-48:45 *)
+Definition index_array_copy (x : array u32 32%usize) : result u32 :=
+  array_index_usize u32 32%usize x 0%usize
+.
+
+(** [array::index_mut_array]: forward function
+    Source: 'src/array.rs', lines 52:0-52:62 *)
+Definition index_mut_array
+  (T : Type) (s : array T 32%usize) (i : usize) : result T :=
+  array_index_usize T 32%usize s i
+.
+
+(** [array::index_mut_array]: backward function 0
+    Source: 'src/array.rs', lines 52:0-52:62 *)
+Definition index_mut_array_back
+  (T : Type) (s : array T 32%usize) (i : usize) (ret : T) :
+  result (array T 32%usize)
+  :=
+  array_update_usize T 32%usize s i ret
+.
+
+(** [array::index_slice]: forward function
+    Source: 'src/array.rs', lines 56:0-56:46 *)
+Definition index_slice (T : Type) (s : slice T) (i : usize) : result T :=
+  slice_index_usize T s i
+.
+
+(** [array::index_mut_slice]: forward function
+    Source: 'src/array.rs', lines 60:0-60:58 *)
+Definition index_mut_slice (T : Type) (s : slice T) (i : usize) : result T :=
+  slice_index_usize T s i
+.
+
+(** [array::index_mut_slice]: backward function 0
+    Source: 'src/array.rs', lines 60:0-60:58 *)
+Definition index_mut_slice_back
+  (T : Type) (s : slice T) (i : usize) (ret : T) : result (slice T) :=
+  slice_update_usize T s i ret
+.
+
+(** [array::slice_subslice_shared_]: forward function
+    Source: 'src/array.rs', lines 64:0-64:70 *)
+Definition slice_subslice_shared_
+  (x : slice u32) (y : usize) (z : usize) : result (slice u32) :=
+  core_slice_index_Slice_index u32 (core_ops_range_Range usize)
+    (core_slice_index_SliceIndexRangeUsizeSliceTInst u32) x
+    {| core_ops_range_Range_start := y; core_ops_range_Range_end_ := z |}
+.
+
+(** [array::slice_subslice_mut_]: forward function
+    Source: 'src/array.rs', lines 68:0-68:75 *)
+Definition slice_subslice_mut_
+  (x : slice u32) (y : usize) (z : usize) : result (slice u32) :=
+  core_slice_index_Slice_index_mut u32 (core_ops_range_Range usize)
+    (core_slice_index_SliceIndexRangeUsizeSliceTInst u32) x
+    {| core_ops_range_Range_start := y; core_ops_range_Range_end_ := z |}
+.
+
+(** [array::slice_subslice_mut_]: backward function 0
+    Source: 'src/array.rs', lines 68:0-68:75 *)
+Definition slice_subslice_mut__back
+  (x : slice u32) (y : usize) (z : usize) (ret : slice u32) :
+  result (slice u32)
+  :=
+  core_slice_index_Slice_index_mut_back u32 (core_ops_range_Range usize)
+    (core_slice_index_SliceIndexRangeUsizeSliceTInst u32) x
+    {| core_ops_range_Range_start := y; core_ops_range_Range_end_ := z |} ret
+.
+
+(** [array::array_to_slice_shared_]: forward function
+    Source: 'src/array.rs', lines 72:0-72:54 *)
+Definition array_to_slice_shared_
+  (x : array u32 32%usize) : result (slice u32) :=
+  array_to_slice u32 32%usize x
+.
+
+(** [array::array_to_slice_mut_]: forward function
+    Source: 'src/array.rs', lines 76:0-76:59 *)
+Definition array_to_slice_mut_ (x : array u32 32%usize) : result (slice u32) :=
+  array_to_slice u32 32%usize x
+.
+
+(** [array::array_to_slice_mut_]: backward function 0
+    Source: 'src/array.rs', lines 76:0-76:59 *)
+Definition array_to_slice_mut__back
+  (x : array u32 32%usize) (ret : slice u32) : result (array u32 32%usize) :=
+  array_from_slice u32 32%usize x ret
+.
+
+(** [array::array_subslice_shared_]: forward function
+    Source: 'src/array.rs', lines 80:0-80:74 *)
+Definition array_subslice_shared_
+  (x : array u32 32%usize) (y : usize) (z : usize) : result (slice u32) :=
+  core_array_Array_index u32 (core_ops_range_Range usize) 32%usize
+    (core_ops_index_IndexSliceTIInst u32 (core_ops_range_Range usize)
+    (core_slice_index_SliceIndexRangeUsizeSliceTInst u32)) x
+    {| core_ops_range_Range_start := y; core_ops_range_Range_end_ := z |}
+.
+
+(** [array::array_subslice_mut_]: forward function
+    Source: 'src/array.rs', lines 84:0-84:79 *)
+Definition array_subslice_mut_
+  (x : array u32 32%usize) (y : usize) (z : usize) : result (slice u32) :=
+  core_array_Array_index_mut u32 (core_ops_range_Range usize) 32%usize
+    (core_ops_index_IndexMutSliceTIInst u32 (core_ops_range_Range usize)
+    (core_slice_index_SliceIndexRangeUsizeSliceTInst u32)) x
+    {| core_ops_range_Range_start := y; core_ops_range_Range_end_ := z |}
+.
+
+(** [array::array_subslice_mut_]: backward function 0
+    Source: 'src/array.rs', lines 84:0-84:79 *)
+Definition array_subslice_mut__back
+  (x : array u32 32%usize) (y : usize) (z : usize) (ret : slice u32) :
+  result (array u32 32%usize)
+  :=
+  core_array_Array_index_mut_back u32 (core_ops_range_Range usize) 32%usize
+    (core_ops_index_IndexMutSliceTIInst u32 (core_ops_range_Range usize)
+    (core_slice_index_SliceIndexRangeUsizeSliceTInst u32)) x
+    {| core_ops_range_Range_start := y; core_ops_range_Range_end_ := z |} ret
+.
+
+(** [array::index_slice_0]: forward function
+    Source: 'src/array.rs', lines 88:0-88:38 *)
+Definition index_slice_0 (T : Type) (s : slice T) : result T :=
+  slice_index_usize T s 0%usize
+.
+
+(** [array::index_array_0]: forward function
+    Source: 'src/array.rs', lines 92:0-92:42 *)
+Definition index_array_0 (T : Type) (s : array T 32%usize) : result T :=
+  array_index_usize T 32%usize s 0%usize
+.
+
+(** [array::index_index_array]: forward function
+    Source: 'src/array.rs', lines 103:0-103:71 *)
+Definition index_index_array
+  (s : array (array u32 32%usize) 32%usize) (i : usize) (j : usize) :
+  result u32
+  :=
+  a <- array_index_usize (array u32 32%usize) 32%usize s i;
+  array_index_usize u32 32%usize a j
+.
+
+(** [array::update_update_array]: forward function
+    Source: 'src/array.rs', lines 114:0-114:70 *)
+Definition update_update_array
+  (s : array (array u32 32%usize) 32%usize) (i : usize) (j : usize) :
+  result unit
+  :=
+  a <- array_index_usize (array u32 32%usize) 32%usize s i;
+  a0 <- array_update_usize u32 32%usize a j 0%u32;
+  _ <- array_update_usize (array u32 32%usize) 32%usize s i a0;
+  Return tt
+.
+
+(** [array::array_local_deep_copy]: forward function
+    Source: 'src/array.rs', lines 118:0-118:43 *)
+Definition array_local_deep_copy (x : array u32 32%usize) : result unit :=
+  Return tt
+.
+
+(** [array::take_array]: forward function
+    Source: 'src/array.rs', lines 122:0-122:30 *)
+Definition take_array (a : array u32 2%usize) : result unit :=
+  Return tt.
+
+(** [array::take_array_borrow]: forward function
+    Source: 'src/array.rs', lines 123:0-123:38 *)
+Definition take_array_borrow (a : array u32 2%usize) : result unit :=
+  Return tt
+.
+
+(** [array::take_slice]: forward function
+    Source: 'src/array.rs', lines 124:0-124:28 *)
+Definition take_slice (s : slice u32) : result unit :=
+  Return tt.
+
+(** [array::take_mut_slice]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ())
+    Source: 'src/array.rs', lines 125:0-125:36 *)
+Definition take_mut_slice (s : slice u32) : result (slice u32) :=
+  Return s.
+
+(** [array::const_array]: forward function
+    Source: 'src/array.rs', lines 127:0-127:32 *)
+Definition const_array : result (array u32 2%usize) :=
+  Return (mk_array u32 2%usize [ 0%u32; 0%u32 ])
+.
+
+(** [array::const_slice]: forward function
+    Source: 'src/array.rs', lines 131:0-131:20 *)
+Definition const_slice : result unit :=
+  _ <- array_to_slice u32 2%usize (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
+  Return tt
+.
+
+(** [array::take_all]: forward function
+    Source: 'src/array.rs', lines 141:0-141:17 *)
+Definition take_all : result unit :=
+  _ <- take_array (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
+  _ <- take_array_borrow (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
+  s <- array_to_slice u32 2%usize (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
+  _ <- take_slice s;
+  s0 <- array_to_slice u32 2%usize (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
+  s1 <- take_mut_slice s0;
+  _ <- array_from_slice u32 2%usize (mk_array u32 2%usize [ 0%u32; 0%u32 ]) s1;
+  Return tt
+.
+
+(** [array::index_array]: forward function
+    Source: 'src/array.rs', lines 155:0-155:38 *)
+Definition index_array (x : array u32 2%usize) : result u32 :=
+  array_index_usize u32 2%usize x 0%usize
+.
+
+(** [array::index_array_borrow]: forward function
+    Source: 'src/array.rs', lines 158:0-158:46 *)
+Definition index_array_borrow (x : array u32 2%usize) : result u32 :=
+  array_index_usize u32 2%usize x 0%usize
+.
+
+(** [array::index_slice_u32_0]: forward function
+    Source: 'src/array.rs', lines 162:0-162:42 *)
+Definition index_slice_u32_0 (x : slice u32) : result u32 :=
+  slice_index_usize u32 x 0%usize
+.
+
+(** [array::index_mut_slice_u32_0]: forward function
+    Source: 'src/array.rs', lines 166:0-166:50 *)
+Definition index_mut_slice_u32_0 (x : slice u32) : result u32 :=
+  slice_index_usize u32 x 0%usize
+.
+
+(** [array::index_mut_slice_u32_0]: backward function 0
+    Source: 'src/array.rs', lines 166:0-166:50 *)
+Definition index_mut_slice_u32_0_back (x : slice u32) : result (slice u32) :=
+  _ <- slice_index_usize u32 x 0%usize; Return x
+.
+
+(** [array::index_all]: forward function
+    Source: 'src/array.rs', lines 170:0-170:25 *)
+Definition index_all : result u32 :=
+  i <- index_array (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
+  i0 <- index_array (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
+  i1 <- u32_add i i0;
+  i2 <- index_array_borrow (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
+  i3 <- u32_add i1 i2;
+  s <- array_to_slice u32 2%usize (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
+  i4 <- index_slice_u32_0 s;
+  i5 <- u32_add i3 i4;
+  s0 <- array_to_slice u32 2%usize (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
+  i6 <- index_mut_slice_u32_0 s0;
+  i7 <- u32_add i5 i6;
+  s1 <- index_mut_slice_u32_0_back s0;
+  _ <- array_from_slice u32 2%usize (mk_array u32 2%usize [ 0%u32; 0%u32 ]) s1;
+  Return i7
+.
+
+(** [array::update_array]: forward function
+    Source: 'src/array.rs', lines 184:0-184:36 *)
+Definition update_array (x : array u32 2%usize) : result unit :=
+  _ <- array_update_usize u32 2%usize x 0%usize 1%u32; Return tt
+.
+
+(** [array::update_array_mut_borrow]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ())
+    Source: 'src/array.rs', lines 187:0-187:48 *)
+Definition update_array_mut_borrow
+  (x : array u32 2%usize) : result (array u32 2%usize) :=
+  array_update_usize u32 2%usize x 0%usize 1%u32
+.
+
+(** [array::update_mut_slice]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ())
+    Source: 'src/array.rs', lines 190:0-190:38 *)
+Definition update_mut_slice (x : slice u32) : result (slice u32) :=
+  slice_update_usize u32 x 0%usize 1%u32
+.
+
+(** [array::update_all]: forward function
+    Source: 'src/array.rs', lines 194:0-194:19 *)
+Definition update_all : result unit :=
+  _ <- update_array (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
+  x <- update_array_mut_borrow (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
+  s <- array_to_slice u32 2%usize x;
+  s0 <- update_mut_slice s;
+  _ <- array_from_slice u32 2%usize x s0;
+  Return tt
+.
+
+(** [array::range_all]: forward function
+    Source: 'src/array.rs', lines 205:0-205:18 *)
+Definition range_all : result unit :=
+  s <-
+    core_array_Array_index_mut u32 (core_ops_range_Range usize) 4%usize
+      (core_ops_index_IndexMutSliceTIInst u32 (core_ops_range_Range usize)
+      (core_slice_index_SliceIndexRangeUsizeSliceTInst u32))
+      (mk_array u32 4%usize [ 0%u32; 0%u32; 0%u32; 0%u32 ])
+      {|
+        core_ops_range_Range_start := 1%usize;
+        core_ops_range_Range_end_ := 3%usize
+      |};
+  s0 <- update_mut_slice s;
+  _ <-
+    core_array_Array_index_mut_back u32 (core_ops_range_Range usize) 4%usize
+      (core_ops_index_IndexMutSliceTIInst u32 (core_ops_range_Range usize)
+      (core_slice_index_SliceIndexRangeUsizeSliceTInst u32))
+      (mk_array u32 4%usize [ 0%u32; 0%u32; 0%u32; 0%u32 ])
+      {|
+        core_ops_range_Range_start := 1%usize;
+        core_ops_range_Range_end_ := 3%usize
+      |} s0;
+  Return tt
+.
+
+(** [array::deref_array_borrow]: forward function
+    Source: 'src/array.rs', lines 214:0-214:46 *)
+Definition deref_array_borrow (x : array u32 2%usize) : result u32 :=
+  array_index_usize u32 2%usize x 0%usize
+.
+
+(** [array::deref_array_mut_borrow]: forward function
+    Source: 'src/array.rs', lines 219:0-219:54 *)
+Definition deref_array_mut_borrow (x : array u32 2%usize) : result u32 :=
+  array_index_usize u32 2%usize x 0%usize
+.
+
+(** [array::deref_array_mut_borrow]: backward function 0
+    Source: 'src/array.rs', lines 219:0-219:54 *)
+Definition deref_array_mut_borrow_back
+  (x : array u32 2%usize) : result (array u32 2%usize) :=
+  _ <- array_index_usize u32 2%usize x 0%usize; Return x
+.
+
+(** [array::take_array_t]: forward function
+    Source: 'src/array.rs', lines 227:0-227:31 *)
+Definition take_array_t (a : array AB_t 2%usize) : result unit :=
+  Return tt.
+
+(** [array::non_copyable_array]: forward function
+    Source: 'src/array.rs', lines 229:0-229:27 *)
+Definition non_copyable_array : result unit :=
+  _ <- take_array_t (mk_array AB_t 2%usize [ AB_A; AB_B ]); Return tt
+.
+
+(** [array::sum]: loop 0: forward function
+    Source: 'src/array.rs', lines 242:0-250:1 *)
+Fixpoint sum_loop
+  (n : nat) (s : slice u32) (sum0 : u32) (i : usize) : result u32 :=
+  match n with
+  | O => Fail_ OutOfFuel
+  | S n0 =>
+    let i0 := slice_len u32 s in
+    if i s< i0
+    then (
+      i1 <- slice_index_usize u32 s i;
+      sum1 <- u32_add sum0 i1;
+      i2 <- usize_add i 1%usize;
+      sum_loop n0 s sum1 i2)
+    else Return sum0
+  end
+.
+
+(** [array::sum]: forward function
+    Source: 'src/array.rs', lines 242:0-242:28 *)
+Definition sum (n : nat) (s : slice u32) : result u32 :=
+  sum_loop n s 0%u32 0%usize
+.
+
+(** [array::sum2]: loop 0: forward function
+    Source: 'src/array.rs', lines 252:0-261:1 *)
+Fixpoint sum2_loop
+  (n : nat) (s : slice u32) (s2 : slice u32) (sum0 : u32) (i : usize) :
+  result u32
+  :=
+  match n with
+  | O => Fail_ OutOfFuel
+  | S n0 =>
+    let i0 := slice_len u32 s in
+    if i s< i0
+    then (
+      i1 <- slice_index_usize u32 s i;
+      i2 <- slice_index_usize u32 s2 i;
+      i3 <- u32_add i1 i2;
+      sum1 <- u32_add sum0 i3;
+      i4 <- usize_add i 1%usize;
+      sum2_loop n0 s s2 sum1 i4)
+    else Return sum0
+  end
+.
+
+(** [array::sum2]: forward function
+    Source: 'src/array.rs', lines 252:0-252:41 *)
+Definition sum2 (n : nat) (s : slice u32) (s2 : slice u32) : result u32 :=
+  let i := slice_len u32 s in
+  let i0 := slice_len u32 s2 in
+  if negb (i s= i0) then Fail_ Failure else sum2_loop n s s2 0%u32 0%usize
+.
+
+(** [array::f0]: forward function
+    Source: 'src/array.rs', lines 263:0-263:11 *)
+Definition f0 : result unit :=
+  s <- array_to_slice u32 2%usize (mk_array u32 2%usize [ 1%u32; 2%u32 ]);
+  s0 <- slice_update_usize u32 s 0%usize 1%u32;
+  _ <- array_from_slice u32 2%usize (mk_array u32 2%usize [ 1%u32; 2%u32 ]) s0;
+  Return tt
+.
+
+(** [array::f1]: forward function
+    Source: 'src/array.rs', lines 268:0-268:11 *)
+Definition f1 : result unit :=
+  _ <-
+    array_update_usize u32 2%usize (mk_array u32 2%usize [ 1%u32; 2%u32 ])
+      0%usize 1%u32;
+  Return tt
+.
+
+(** [array::f2]: forward function
+    Source: 'src/array.rs', lines 273:0-273:17 *)
+Definition f2 (i : u32) : result unit :=
+  Return tt.
+
+(** [array::f4]: forward function
+    Source: 'src/array.rs', lines 282:0-282:54 *)
+Definition f4
+  (x : array u32 32%usize) (y : usize) (z : usize) : result (slice u32) :=
+  core_array_Array_index u32 (core_ops_range_Range usize) 32%usize
+    (core_ops_index_IndexSliceTIInst u32 (core_ops_range_Range usize)
+    (core_slice_index_SliceIndexRangeUsizeSliceTInst u32)) x
+    {| core_ops_range_Range_start := y; core_ops_range_Range_end_ := z |}
+.
+
+(** [array::f3]: forward function
+    Source: 'src/array.rs', lines 275:0-275:18 *)
+Definition f3 (n : nat) : result u32 :=
+  i <-
+    array_index_usize u32 2%usize (mk_array u32 2%usize [ 1%u32; 2%u32 ])
+      0%usize;
+  _ <- f2 i;
+  let b := array_repeat u32 32%usize 0%u32 in
+  s <- array_to_slice u32 2%usize (mk_array u32 2%usize [ 1%u32; 2%u32 ]);
+  s0 <- f4 b 16%usize 18%usize;
+  sum2 n s s0
+.
+
+(** [array::SZ]
+    Source: 'src/array.rs', lines 286:0-286:19 *)
+Definition sz_body : result usize := Return 32%usize.
+Definition sz_c : usize := sz_body%global.
+
+(** [array::f5]: forward function
+    Source: 'src/array.rs', lines 289:0-289:31 *)
+Definition f5 (x : array u32 32%usize) : result u32 :=
+  array_index_usize u32 32%usize x 0%usize
+.
+
+(** [array::ite]: forward function
+    Source: 'src/array.rs', lines 294:0-294:12 *)
+Definition ite : result unit :=
+  s <- array_to_slice u32 2%usize (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
+  s0 <- array_to_slice u32 2%usize (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
+  s1 <- index_mut_slice_u32_0_back s0;
+  _ <- array_from_slice u32 2%usize (mk_array u32 2%usize [ 0%u32; 0%u32 ]) s1;
+  s2 <- index_mut_slice_u32_0_back s;
+  _ <- array_from_slice u32 2%usize (mk_array u32 2%usize [ 0%u32; 0%u32 ]) s2;
+  Return tt
+.
+
+End Array.
diff --git a/tests/coq/array/Array_Funs.v b/tests/coq/array/Array_Funs.v
deleted file mode 100644
index 6d791873..00000000
--- a/tests/coq/array/Array_Funs.v
+++ /dev/null
@@ -1,467 +0,0 @@
-(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
-(** [array]: function definitions *)
-Require Import Primitives.
-Import Primitives.
-Require Import Coq.ZArith.ZArith.
-Require Import List.
-Import ListNotations.
-Local Open Scope Primitives_scope.
-Require Export Array_Types.
-Import Array_Types.
-Module Array_Funs.
-
-(** [array::array_to_shared_slice_]: forward function *)
-Definition array_to_shared_slice__fwd
-  (T : Type) (s : array T 32%usize) : result (slice T) :=
-  array_to_slice_shared T 32%usize s
-.
-
-(** [array::array_to_mut_slice_]: forward function *)
-Definition array_to_mut_slice__fwd
-  (T : Type) (s : array T 32%usize) : result (slice T) :=
-  array_to_slice_mut_fwd T 32%usize s
-.
-
-(** [array::array_to_mut_slice_]: backward function 0 *)
-Definition array_to_mut_slice__back
-  (T : Type) (s : array T 32%usize) (ret : slice T) :
-  result (array T 32%usize)
-  :=
-  array_to_slice_mut_back T 32%usize s ret
-.
-
-(** [array::array_len]: forward function *)
-Definition array_len_fwd (T : Type) (s : array T 32%usize) : result usize :=
-  s0 <- array_to_slice_shared T 32%usize s; let i := slice_len T s0 in Return i
-.
-
-(** [array::shared_array_len]: forward function *)
-Definition shared_array_len_fwd
-  (T : Type) (s : array T 32%usize) : result usize :=
-  s0 <- array_to_slice_shared T 32%usize s; let i := slice_len T s0 in Return i
-.
-
-(** [array::shared_slice_len]: forward function *)
-Definition shared_slice_len_fwd (T : Type) (s : slice T) : result usize :=
-  let i := slice_len T s in Return i
-.
-
-(** [array::index_array_shared]: forward function *)
-Definition index_array_shared_fwd
-  (T : Type) (s : array T 32%usize) (i : usize) : result T :=
-  array_index_shared T 32%usize s i
-.
-
-(** [array::index_array_u32]: forward function *)
-Definition index_array_u32_fwd
-  (s : array u32 32%usize) (i : usize) : result u32 :=
-  array_index_shared u32 32%usize s i
-.
-
-(** [array::index_array_generic]: forward function *)
-Definition index_array_generic_fwd
-  (N : usize) (s : array u32 N) (i : usize) : result u32 :=
-  array_index_shared u32 N s i
-.
-
-(** [array::index_array_generic_call]: forward function *)
-Definition index_array_generic_call_fwd
-  (N : usize) (s : array u32 N) (i : usize) : result u32 :=
-  index_array_generic_fwd N s i
-.
-
-(** [array::index_array_copy]: forward function *)
-Definition index_array_copy_fwd (x : array u32 32%usize) : result u32 :=
-  array_index_shared u32 32%usize x 0%usize
-.
-
-(** [array::index_mut_array]: forward function *)
-Definition index_mut_array_fwd
-  (T : Type) (s : array T 32%usize) (i : usize) : result T :=
-  array_index_mut_fwd T 32%usize s i
-.
-
-(** [array::index_mut_array]: backward function 0 *)
-Definition index_mut_array_back
-  (T : Type) (s : array T 32%usize) (i : usize) (ret : T) :
-  result (array T 32%usize)
-  :=
-  array_index_mut_back T 32%usize s i ret
-.
-
-(** [array::index_slice]: forward function *)
-Definition index_slice_fwd (T : Type) (s : slice T) (i : usize) : result T :=
-  slice_index_shared T s i
-.
-
-(** [array::index_mut_slice]: forward function *)
-Definition index_mut_slice_fwd
-  (T : Type) (s : slice T) (i : usize) : result T :=
-  slice_index_mut_fwd T s i
-.
-
-(** [array::index_mut_slice]: backward function 0 *)
-Definition index_mut_slice_back
-  (T : Type) (s : slice T) (i : usize) (ret : T) : result (slice T) :=
-  slice_index_mut_back T s i ret
-.
-
-(** [array::slice_subslice_shared_]: forward function *)
-Definition slice_subslice_shared__fwd
-  (x : slice u32) (y : usize) (z : usize) : result (slice u32) :=
-  slice_subslice_shared u32 x (mk_range y z)
-.
-
-(** [array::slice_subslice_mut_]: forward function *)
-Definition slice_subslice_mut__fwd
-  (x : slice u32) (y : usize) (z : usize) : result (slice u32) :=
-  slice_subslice_mut_fwd u32 x (mk_range y z)
-.
-
-(** [array::slice_subslice_mut_]: backward function 0 *)
-Definition slice_subslice_mut__back
-  (x : slice u32) (y : usize) (z : usize) (ret : slice u32) :
-  result (slice u32)
-  :=
-  slice_subslice_mut_back u32 x (mk_range y z) ret
-.
-
-(** [array::array_to_slice_shared_]: forward function *)
-Definition array_to_slice_shared__fwd
-  (x : array u32 32%usize) : result (slice u32) :=
-  array_to_slice_shared u32 32%usize x
-.
-
-(** [array::array_to_slice_mut_]: forward function *)
-Definition array_to_slice_mut__fwd
-  (x : array u32 32%usize) : result (slice u32) :=
-  array_to_slice_mut_fwd u32 32%usize x
-.
-
-(** [array::array_to_slice_mut_]: backward function 0 *)
-Definition array_to_slice_mut__back
-  (x : array u32 32%usize) (ret : slice u32) : result (array u32 32%usize) :=
-  array_to_slice_mut_back u32 32%usize x ret
-.
-
-(** [array::array_subslice_shared_]: forward function *)
-Definition array_subslice_shared__fwd
-  (x : array u32 32%usize) (y : usize) (z : usize) : result (slice u32) :=
-  array_subslice_shared u32 32%usize x (mk_range y z)
-.
-
-(** [array::array_subslice_mut_]: forward function *)
-Definition array_subslice_mut__fwd
-  (x : array u32 32%usize) (y : usize) (z : usize) : result (slice u32) :=
-  array_subslice_mut_fwd u32 32%usize x (mk_range y z)
-.
-
-(** [array::array_subslice_mut_]: backward function 0 *)
-Definition array_subslice_mut__back
-  (x : array u32 32%usize) (y : usize) (z : usize) (ret : slice u32) :
-  result (array u32 32%usize)
-  :=
-  array_subslice_mut_back u32 32%usize x (mk_range y z) ret
-.
-
-(** [array::index_slice_0]: forward function *)
-Definition index_slice_0_fwd (T : Type) (s : slice T) : result T :=
-  slice_index_shared T s 0%usize
-.
-
-(** [array::index_array_0]: forward function *)
-Definition index_array_0_fwd (T : Type) (s : array T 32%usize) : result T :=
-  array_index_shared T 32%usize s 0%usize
-.
-
-(** [array::index_index_array]: forward function *)
-Definition index_index_array_fwd
-  (s : array (array u32 32%usize) 32%usize) (i : usize) (j : usize) :
-  result u32
-  :=
-  a <- array_index_shared (array u32 32%usize) 32%usize s i;
-  array_index_shared u32 32%usize a j
-.
-
-(** [array::update_update_array]: forward function *)
-Definition update_update_array_fwd
-  (s : array (array u32 32%usize) 32%usize) (i : usize) (j : usize) :
-  result unit
-  :=
-  a <- array_index_mut_fwd (array u32 32%usize) 32%usize s i;
-  a0 <- array_index_mut_back u32 32%usize a j 0%u32;
-  _ <- array_index_mut_back (array u32 32%usize) 32%usize s i a0;
-  Return tt
-.
-
-(** [array::array_local_deep_copy]: forward function *)
-Definition array_local_deep_copy_fwd (x : array u32 32%usize) : result unit :=
-  Return tt
-.
-
-(** [array::take_array]: forward function *)
-Definition take_array_fwd (a : array u32 2%usize) : result unit :=
-  Return tt.
-
-(** [array::take_array_borrow]: forward function *)
-Definition take_array_borrow_fwd (a : array u32 2%usize) : result unit :=
-  Return tt
-.
-
-(** [array::take_slice]: forward function *)
-Definition take_slice_fwd (s : slice u32) : result unit :=
-  Return tt.
-
-(** [array::take_mut_slice]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ()) *)
-Definition take_mut_slice_fwd_back (s : slice u32) : result (slice u32) :=
-  Return s
-.
-
-(** [array::take_all]: forward function *)
-Definition take_all_fwd : result unit :=
-  _ <- take_array_fwd (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
-  _ <- take_array_borrow_fwd (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
-  s <-
-    array_to_slice_shared u32 2%usize (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
-  _ <- take_slice_fwd s;
-  s0 <-
-    array_to_slice_mut_fwd u32 2%usize (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
-  s1 <- take_mut_slice_fwd_back s0;
-  _ <-
-    array_to_slice_mut_back u32 2%usize (mk_array u32 2%usize [ 0%u32; 0%u32 ])
-      s1;
-  Return tt
-.
-
-(** [array::index_array]: forward function *)
-Definition index_array_fwd (x : array u32 2%usize) : result u32 :=
-  array_index_shared u32 2%usize x 0%usize
-.
-
-(** [array::index_array_borrow]: forward function *)
-Definition index_array_borrow_fwd (x : array u32 2%usize) : result u32 :=
-  array_index_shared u32 2%usize x 0%usize
-.
-
-(** [array::index_slice_u32_0]: forward function *)
-Definition index_slice_u32_0_fwd (x : slice u32) : result u32 :=
-  slice_index_shared u32 x 0%usize
-.
-
-(** [array::index_mut_slice_u32_0]: forward function *)
-Definition index_mut_slice_u32_0_fwd (x : slice u32) : result u32 :=
-  slice_index_shared u32 x 0%usize
-.
-
-(** [array::index_mut_slice_u32_0]: backward function 0 *)
-Definition index_mut_slice_u32_0_back (x : slice u32) : result (slice u32) :=
-  _ <- slice_index_shared u32 x 0%usize; Return x
-.
-
-(** [array::index_all]: forward function *)
-Definition index_all_fwd : result u32 :=
-  i <- index_array_fwd (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
-  i0 <- index_array_fwd (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
-  i1 <- u32_add i i0;
-  i2 <- index_array_borrow_fwd (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
-  i3 <- u32_add i1 i2;
-  s <-
-    array_to_slice_shared u32 2%usize (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
-  i4 <- index_slice_u32_0_fwd s;
-  i5 <- u32_add i3 i4;
-  s0 <-
-    array_to_slice_mut_fwd u32 2%usize (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
-  i6 <- index_mut_slice_u32_0_fwd s0;
-  i7 <- u32_add i5 i6;
-  s1 <- index_mut_slice_u32_0_back s0;
-  _ <-
-    array_to_slice_mut_back u32 2%usize (mk_array u32 2%usize [ 0%u32; 0%u32 ])
-      s1;
-  Return i7
-.
-
-(** [array::update_array]: forward function *)
-Definition update_array_fwd (x : array u32 2%usize) : result unit :=
-  _ <- array_index_mut_back u32 2%usize x 0%usize 1%u32; Return tt
-.
-
-(** [array::update_array_mut_borrow]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ()) *)
-Definition update_array_mut_borrow_fwd_back
-  (x : array u32 2%usize) : result (array u32 2%usize) :=
-  array_index_mut_back u32 2%usize x 0%usize 1%u32
-.
-
-(** [array::update_mut_slice]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ()) *)
-Definition update_mut_slice_fwd_back (x : slice u32) : result (slice u32) :=
-  slice_index_mut_back u32 x 0%usize 1%u32
-.
-
-(** [array::update_all]: forward function *)
-Definition update_all_fwd : result unit :=
-  _ <- update_array_fwd (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
-  x <-
-    update_array_mut_borrow_fwd_back (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
-  s <- array_to_slice_mut_fwd u32 2%usize x;
-  s0 <- update_mut_slice_fwd_back s;
-  _ <- array_to_slice_mut_back u32 2%usize x s0;
-  Return tt
-.
-
-(** [array::range_all]: forward function *)
-Definition range_all_fwd : result unit :=
-  s <-
-    array_subslice_mut_fwd u32 4%usize
-      (mk_array u32 4%usize [ 0%u32; 0%u32; 0%u32; 0%u32 ]) (mk_range 1%usize
-      3%usize);
-  s0 <- update_mut_slice_fwd_back s;
-  _ <-
-    array_subslice_mut_back u32 4%usize
-      (mk_array u32 4%usize [ 0%u32; 0%u32; 0%u32; 0%u32 ]) (mk_range 1%usize
-      3%usize) s0;
-  Return tt
-.
-
-(** [array::deref_array_borrow]: forward function *)
-Definition deref_array_borrow_fwd (x : array u32 2%usize) : result u32 :=
-  array_index_shared u32 2%usize x 0%usize
-.
-
-(** [array::deref_array_mut_borrow]: forward function *)
-Definition deref_array_mut_borrow_fwd (x : array u32 2%usize) : result u32 :=
-  array_index_shared u32 2%usize x 0%usize
-.
-
-(** [array::deref_array_mut_borrow]: backward function 0 *)
-Definition deref_array_mut_borrow_back
-  (x : array u32 2%usize) : result (array u32 2%usize) :=
-  _ <- array_index_shared u32 2%usize x 0%usize; Return x
-.
-
-(** [array::take_array_t]: forward function *)
-Definition take_array_t_fwd (a : array T_t 2%usize) : result unit :=
-  Return tt.
-
-(** [array::non_copyable_array]: forward function *)
-Definition non_copyable_array_fwd : result unit :=
-  _ <- take_array_t_fwd (mk_array T_t 2%usize [ TA; TB ]); Return tt
-.
-
-(** [array::sum]: loop 0: forward function *)
-Fixpoint sum_loop_fwd
-  (n : nat) (s : slice u32) (sum : u32) (i : usize) : result u32 :=
-  match n with
-  | O => Fail_ OutOfFuel
-  | S n0 =>
-    let i0 := slice_len u32 s in
-    if i s< i0
-    then (
-      i1 <- slice_index_shared u32 s i;
-      sum0 <- u32_add sum i1;
-      i2 <- usize_add i 1%usize;
-      sum_loop_fwd n0 s sum0 i2)
-    else Return sum
-  end
-.
-
-(** [array::sum]: forward function *)
-Definition sum_fwd (n : nat) (s : slice u32) : result u32 :=
-  sum_loop_fwd n s 0%u32 0%usize
-.
-
-(** [array::sum2]: loop 0: forward function *)
-Fixpoint sum2_loop_fwd
-  (n : nat) (s : slice u32) (s2 : slice u32) (sum : u32) (i : usize) :
-  result u32
-  :=
-  match n with
-  | O => Fail_ OutOfFuel
-  | S n0 =>
-    let i0 := slice_len u32 s in
-    if i s< i0
-    then (
-      i1 <- slice_index_shared u32 s i;
-      i2 <- slice_index_shared u32 s2 i;
-      i3 <- u32_add i1 i2;
-      sum0 <- u32_add sum i3;
-      i4 <- usize_add i 1%usize;
-      sum2_loop_fwd n0 s s2 sum0 i4)
-    else Return sum
-  end
-.
-
-(** [array::sum2]: forward function *)
-Definition sum2_fwd (n : nat) (s : slice u32) (s2 : slice u32) : result u32 :=
-  let i := slice_len u32 s in
-  let i0 := slice_len u32 s2 in
-  if negb (i s= i0) then Fail_ Failure else sum2_loop_fwd n s s2 0%u32 0%usize
-.
-
-(** [array::f0]: forward function *)
-Definition f0_fwd : result unit :=
-  s <-
-    array_to_slice_mut_fwd u32 2%usize (mk_array u32 2%usize [ 1%u32; 2%u32 ]);
-  s0 <- slice_index_mut_back u32 s 0%usize 1%u32;
-  _ <-
-    array_to_slice_mut_back u32 2%usize (mk_array u32 2%usize [ 1%u32; 2%u32 ])
-      s0;
-  Return tt
-.
-
-(** [array::f1]: forward function *)
-Definition f1_fwd : result unit :=
-  _ <-
-    array_index_mut_back u32 2%usize (mk_array u32 2%usize [ 1%u32; 2%u32 ])
-      0%usize 1%u32;
-  Return tt
-.
-
-(** [array::f2]: forward function *)
-Definition f2_fwd (i : u32) : result unit :=
-  Return tt.
-
-(** [array::f4]: forward function *)
-Definition f4_fwd
-  (x : array u32 32%usize) (y : usize) (z : usize) : result (slice u32) :=
-  array_subslice_shared u32 32%usize x (mk_range y z)
-.
-
-(** [array::f3]: forward function *)
-Definition f3_fwd (n : nat) : result u32 :=
-  i <-
-    array_index_shared u32 2%usize (mk_array u32 2%usize [ 1%u32; 2%u32 ])
-      0%usize;
-  _ <- f2_fwd i;
-  s <-
-    array_to_slice_shared u32 2%usize (mk_array u32 2%usize [ 1%u32; 2%u32 ]);
-  s0 <-
-    f4_fwd
-      (mk_array u32 32%usize [
-        0%u32; 0%u32; 0%u32; 0%u32; 0%u32; 0%u32; 0%u32; 0%u32; 0%u32; 0%u32;
-        0%u32; 0%u32; 0%u32; 0%u32; 0%u32; 0%u32; 0%u32; 0%u32; 0%u32; 0%u32;
-        0%u32; 0%u32; 0%u32; 0%u32; 0%u32; 0%u32; 0%u32; 0%u32; 0%u32; 0%u32;
-        0%u32; 0%u32
-        ]) 16%usize 18%usize;
-  sum2_fwd n s s0
-.
-
-(** [array::ite]: forward function *)
-Definition ite_fwd : result unit :=
-  s <-
-    array_to_slice_mut_fwd u32 2%usize (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
-  s0 <-
-    array_to_slice_mut_fwd u32 2%usize (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
-  s1 <- index_mut_slice_u32_0_back s0;
-  _ <-
-    array_to_slice_mut_back u32 2%usize (mk_array u32 2%usize [ 0%u32; 0%u32 ])
-      s1;
-  s2 <- index_mut_slice_u32_0_back s;
-  _ <-
-    array_to_slice_mut_back u32 2%usize (mk_array u32 2%usize [ 0%u32; 0%u32 ])
-      s2;
-  Return tt
-.
-
-End Array_Funs .
diff --git a/tests/coq/array/Array_Types.v b/tests/coq/array/Array_Types.v
deleted file mode 100644
index 7be6dc9b..00000000
--- a/tests/coq/array/Array_Types.v
+++ /dev/null
@@ -1,14 +0,0 @@
-(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
-(** [array]: type definitions *)
-Require Import Primitives.
-Import Primitives.
-Require Import Coq.ZArith.ZArith.
-Require Import List.
-Import ListNotations.
-Local Open Scope Primitives_scope.
-Module Array_Types.
-
-(** [array::T] *)
-Inductive T_t := | TA : T_t | TB : T_t.
-
-End Array_Types .
diff --git a/tests/coq/array/Primitives.v b/tests/coq/array/Primitives.v
index 71a2d9c3..99ffe070 100644
--- a/tests/coq/array/Primitives.v
+++ b/tests/coq/array/Primitives.v
@@ -63,13 +63,15 @@ Check (if true then Return (1 + 2) else Fail_ Failure)%global = 3.
 
 (*** Misc *)
 
-
 Definition string := Coq.Strings.String.string.
 Definition char := Coq.Strings.Ascii.ascii.
 Definition char_of_byte := Coq.Strings.Ascii.ascii_of_byte.
 
-Definition mem_replace_fwd (a : Type) (x : a) (y : a) : a := x .
-Definition mem_replace_back (a : Type) (x : a) (y : a) : a := y .
+Definition core_mem_replace (a : Type) (x : a) (y : a) : a := x .
+Definition core_mem_replace_back (a : Type) (x : a) (y : a) : a := y .
+
+Record mut_raw_ptr (T : Type) := { mut_raw_ptr_v : T }.
+Record const_raw_ptr (T : Type) := { const_raw_ptr_v : T }.
 
 (*** Scalars *)
 
@@ -253,6 +255,12 @@ Definition scalar_rem {ty} (x y: scalar ty) : result (scalar ty) := mk_scalar ty
   
 Definition scalar_neg {ty} (x: scalar ty) : result (scalar ty) := mk_scalar ty (-(to_Z x)).
 
+Axiom scalar_xor : forall ty, scalar ty -> scalar ty -> scalar ty. (* TODO *)
+Axiom scalar_or : forall ty, scalar ty -> scalar ty -> scalar ty. (* TODO *)
+Axiom scalar_and : forall ty, scalar ty -> scalar ty -> scalar ty. (* TODO *)
+Axiom scalar_shl : forall ty0 ty1, scalar ty0 -> scalar ty1 -> result (scalar ty0). (* TODO *)
+Axiom scalar_shr : forall ty0 ty1, scalar ty0 -> scalar ty1 -> result (scalar ty0). (* TODO *)
+
 (** Cast an integer from a [src_ty] to a [tgt_ty] *)
 (* TODO: check the semantics of casts in Rust *)
 Definition scalar_cast (src_ty tgt_ty : scalar_ty) (x : scalar src_ty) : result (scalar tgt_ty) :=
@@ -370,6 +378,76 @@ Definition u32_mul   := @scalar_mul U32.
 Definition u64_mul   := @scalar_mul U64.
 Definition u128_mul  := @scalar_mul U128.
 
+(** Xor *)
+Definition u8_xor := @scalar_xor U8.
+Definition u16_xor := @scalar_xor U16.
+Definition u32_xor := @scalar_xor U32.
+Definition u64_xor := @scalar_xor U64.
+Definition u128_xor := @scalar_xor U128.
+Definition usize_xor := @scalar_xor Usize.
+Definition i8_xor := @scalar_xor I8.
+Definition i16_xor := @scalar_xor I16.
+Definition i32_xor := @scalar_xor I32.
+Definition i64_xor := @scalar_xor I64.
+Definition i128_xor := @scalar_xor I128.
+Definition isize_xor := @scalar_xor Isize.
+
+(** Or *)
+Definition u8_or := @scalar_or U8.
+Definition u16_or := @scalar_or U16.
+Definition u32_or := @scalar_or U32.
+Definition u64_or := @scalar_or U64.
+Definition u128_or := @scalar_or U128.
+Definition usize_or := @scalar_or Usize.
+Definition i8_or := @scalar_or I8.
+Definition i16_or := @scalar_or I16.
+Definition i32_or := @scalar_or I32.
+Definition i64_or := @scalar_or I64.
+Definition i128_or := @scalar_or I128.
+Definition isize_or := @scalar_or Isize.
+
+(** And *)
+Definition u8_and := @scalar_and U8.
+Definition u16_and := @scalar_and U16.
+Definition u32_and := @scalar_and U32.
+Definition u64_and := @scalar_and U64.
+Definition u128_and := @scalar_and U128.
+Definition usize_and := @scalar_and Usize.
+Definition i8_and := @scalar_and I8.
+Definition i16_and := @scalar_and I16.
+Definition i32_and := @scalar_and I32.
+Definition i64_and := @scalar_and I64.
+Definition i128_and := @scalar_and I128.
+Definition isize_and := @scalar_and Isize.
+
+(** Shift left *)
+Definition u8_shl {ty} := @scalar_shl U8 ty.
+Definition u16_shl {ty} := @scalar_shl U16 ty.
+Definition u32_shl {ty} := @scalar_shl U32 ty.
+Definition u64_shl {ty} := @scalar_shl U64 ty.
+Definition u128_shl {ty} := @scalar_shl U128 ty.
+Definition usize_shl {ty} := @scalar_shl Usize ty.
+Definition i8_shl {ty} := @scalar_shl I8 ty.
+Definition i16_shl {ty} := @scalar_shl I16 ty.
+Definition i32_shl {ty} := @scalar_shl I32 ty.
+Definition i64_shl {ty} := @scalar_shl I64 ty.
+Definition i128_shl {ty} := @scalar_shl I128 ty.
+Definition isize_shl {ty} := @scalar_shl Isize ty.
+
+(** Shift right *)
+Definition u8_shr {ty} := @scalar_shr U8 ty.
+Definition u16_shr {ty} := @scalar_shr U16 ty.
+Definition u32_shr {ty} := @scalar_shr U32 ty.
+Definition u64_shr {ty} := @scalar_shr U64 ty.
+Definition u128_shr {ty} := @scalar_shr U128 ty.
+Definition usize_shr {ty} := @scalar_shr Usize ty.
+Definition i8_shr {ty} := @scalar_shr I8 ty.
+Definition i16_shr {ty} := @scalar_shr I16 ty.
+Definition i32_shr {ty} := @scalar_shr I32 ty.
+Definition i64_shr {ty} := @scalar_shr I64 ty.
+Definition i128_shr {ty} := @scalar_shr I128 ty.
+Definition isize_shr {ty} := @scalar_shr Isize ty.
+
 (** Small utility *)
 Definition usize_to_nat (x: usize) : nat := Z.to_nat (to_Z x).
 
@@ -394,12 +472,89 @@ Notation "x s< y" := (scalar_ltb x y)  (at level 80) : Primitives_scope.
 Notation "x s>= y" := (scalar_geb x y)  (at level 80) : Primitives_scope.
 Notation "x s> y" := (scalar_gtb x y)  (at level 80) : Primitives_scope.
 
-(*** Range *)
-Record range (T : Type) := mk_range {
-  start: T;
-  end_: T;
+(** Constants *)
+Definition core_u8_max    := u8_max %u32.
+Definition core_u16_max   := u16_max %u32.
+Definition core_u32_max   := u32_max %u32.
+Definition core_u64_max   := u64_max %u64.
+Definition core_u128_max  := u64_max %u128.
+Axiom core_usize_max : usize. (** TODO *)
+Definition core_i8_max    := i8_max %i32.
+Definition core_i16_max   := i16_max %i32.
+Definition core_i32_max   := i32_max %i32.
+Definition core_i64_max   := i64_max %i64.
+Definition core_i128_max  := i64_max %i128.
+Axiom core_isize_max : isize. (** TODO *)
+
+(*** core::ops *)
+
+(* Trait declaration: [core::ops::index::Index] *)
+Record core_ops_index_Index (Self Idx : Type) := mk_core_ops_index_Index {
+  core_ops_index_Index_Output : Type;
+  core_ops_index_Index_index : Self -> Idx -> result core_ops_index_Index_Output;
+}.
+Arguments mk_core_ops_index_Index {_ _}.
+Arguments core_ops_index_Index_Output {_ _}.
+Arguments core_ops_index_Index_index {_ _}.
+
+(* Trait declaration: [core::ops::index::IndexMut] *)
+Record core_ops_index_IndexMut (Self Idx : Type) := mk_core_ops_index_IndexMut {
+  core_ops_index_IndexMut_indexInst : core_ops_index_Index Self Idx;
+  core_ops_index_IndexMut_index_mut : Self -> Idx -> result core_ops_index_IndexMut_indexInst.(core_ops_index_Index_Output);
+  core_ops_index_IndexMut_index_mut_back : Self -> Idx -> core_ops_index_IndexMut_indexInst.(core_ops_index_Index_Output) -> result Self;
+}.
+Arguments mk_core_ops_index_IndexMut {_ _}.
+Arguments core_ops_index_IndexMut_indexInst {_ _}.
+Arguments core_ops_index_IndexMut_index_mut {_ _}.
+Arguments core_ops_index_IndexMut_index_mut_back {_ _}.
+
+(* Trait declaration [core::ops::deref::Deref] *)
+Record core_ops_deref_Deref (Self : Type) := mk_core_ops_deref_Deref {
+  core_ops_deref_Deref_target : Type;
+  core_ops_deref_Deref_deref : Self -> result core_ops_deref_Deref_target;
 }.
-Arguments mk_range {_}.
+Arguments mk_core_ops_deref_Deref {_}.
+Arguments core_ops_deref_Deref_target {_}.
+Arguments core_ops_deref_Deref_deref {_}.
+
+(* Trait declaration [core::ops::deref::DerefMut] *)
+Record core_ops_deref_DerefMut (Self : Type) := mk_core_ops_deref_DerefMut {
+  core_ops_deref_DerefMut_derefInst : core_ops_deref_Deref Self;
+  core_ops_deref_DerefMut_deref_mut : Self -> result core_ops_deref_DerefMut_derefInst.(core_ops_deref_Deref_target);
+  core_ops_deref_DerefMut_deref_mut_back : Self -> core_ops_deref_DerefMut_derefInst.(core_ops_deref_Deref_target) -> result Self;
+}.
+Arguments mk_core_ops_deref_DerefMut {_}.
+Arguments core_ops_deref_DerefMut_derefInst {_}.
+Arguments core_ops_deref_DerefMut_deref_mut {_}.
+Arguments core_ops_deref_DerefMut_deref_mut_back {_}.
+
+Record core_ops_range_Range (T : Type) := mk_core_ops_range_Range {
+  core_ops_range_Range_start : T;
+  core_ops_range_Range_end_ : T;
+}.
+Arguments mk_core_ops_range_Range {_}.
+Arguments core_ops_range_Range_start {_}.
+Arguments core_ops_range_Range_end_ {_}.
+
+(*** [alloc] *)
+
+Definition alloc_boxed_Box_deref (T : Type) (x : T) : result T := Return x.
+Definition alloc_boxed_Box_deref_mut (T : Type) (x : T) : result T := Return x.
+Definition alloc_boxed_Box_deref_mut_back (T : Type) (_ : T) (x : T) : result T := Return x.
+
+(* Trait instance *)
+Definition alloc_boxed_Box_coreopsDerefInst (Self : Type) : core_ops_deref_Deref Self := {|
+  core_ops_deref_Deref_target := Self;
+  core_ops_deref_Deref_deref := alloc_boxed_Box_deref Self;
+|}.
+
+(* Trait instance *)
+Definition alloc_boxed_Box_coreopsDerefMutInst (Self : Type) : core_ops_deref_DerefMut Self := {|
+  core_ops_deref_DerefMut_derefInst := alloc_boxed_Box_coreopsDerefInst Self;
+  core_ops_deref_DerefMut_deref_mut := alloc_boxed_Box_deref_mut Self;
+  core_ops_deref_DerefMut_deref_mut_back := alloc_boxed_Box_deref_mut_back Self;
+|}.
+
 
 (*** Arrays *)
 Definition array T (n : usize) := { l: list T | Z.of_nat (length l) = to_Z n}.
@@ -419,51 +574,50 @@ Qed.
 (* TODO: finish the definitions *)
 Axiom mk_array : forall (T : Type) (n : usize) (l : list T), array T n.
 
-Axiom array_index_shared : forall (T : Type) (n : usize) (x : array T n) (i : usize), result T.
-Axiom array_index_mut_fwd : forall (T : Type) (n : usize) (x : array T n) (i : usize), result T.
-Axiom array_index_mut_back : forall (T : Type) (n : usize) (x : array T n) (i : usize) (nx : T), result (array T n).
+(* For initialization *)
+Axiom array_repeat : forall (T : Type) (n : usize) (x : T), array T n.
+
+Axiom array_index_usize : forall (T : Type) (n : usize) (x : array T n) (i : usize), result T.
+Axiom array_update_usize : forall (T : Type) (n : usize) (x : array T n) (i : usize) (nx : T), result (array T n).
 
 (*** Slice *)
 Definition slice T := { l: list T | Z.of_nat (length l) <= usize_max}.
 
 Axiom slice_len : forall (T : Type) (s : slice T), usize.
-Axiom slice_index_shared : forall (T : Type) (x : slice T) (i : usize), result T.
-Axiom slice_index_mut_fwd : forall (T : Type) (x : slice T) (i : usize), result T.
-Axiom slice_index_mut_back : forall (T : Type) (x : slice T) (i : usize) (nx : T), result (slice T).
+Axiom slice_index_usize : forall (T : Type) (x : slice T) (i : usize), result T.
+Axiom slice_update_usize : forall (T : Type) (x : slice T) (i : usize) (nx : T), result (slice T).
 
 (*** Subslices *)
 
-Axiom array_to_slice_shared : forall (T : Type) (n : usize) (x : array T n), result (slice T).
-Axiom array_to_slice_mut_fwd : forall (T : Type) (n : usize) (x : array T n), result (slice T).
-Axiom array_to_slice_mut_back : forall (T : Type) (n : usize) (x : array T n) (s : slice T), result (array T n).
+Axiom array_to_slice : forall (T : Type) (n : usize) (x : array T n), result (slice T).
+Axiom array_from_slice : forall (T : Type) (n : usize) (x : array T n) (s : slice T), result (array T n).
 
-Axiom array_subslice_shared: forall (T : Type) (n : usize) (x : array T n) (r : range usize), result (slice T).
-Axiom array_subslice_mut_fwd: forall (T : Type) (n : usize) (x : array T n) (r : range usize), result (slice T).
-Axiom array_subslice_mut_back: forall (T : Type) (n : usize) (x : array T n) (r : range usize) (ns : slice T), result (array T n).
-Axiom slice_subslice_shared: forall (T : Type) (x : slice T) (r : range usize), result (slice T).
-Axiom slice_subslice_mut_fwd: forall (T : Type) (x : slice T) (r : range usize), result (slice T).
-Axiom slice_subslice_mut_back: forall (T : Type) (x : slice T) (r : range usize) (ns : slice T), result (slice T).
+Axiom array_subslice: forall (T : Type) (n : usize) (x : array T n) (r : core_ops_range_Range usize), result (slice T).
+Axiom array_update_subslice: forall (T : Type) (n : usize) (x : array T n) (r : core_ops_range_Range usize) (ns : slice T), result (array T n).
+
+Axiom slice_subslice: forall (T : Type) (x : slice T) (r : core_ops_range_Range usize), result (slice T).
+Axiom slice_update_subslice: forall (T : Type) (x : slice T) (r : core_ops_range_Range usize) (ns : slice T), result (slice T).
 
 (*** Vectors *)
 
-Definition vec T := { l: list T | Z.of_nat (length l) <= usize_max }.
+Definition alloc_vec_Vec T := { l: list T | Z.of_nat (length l) <= usize_max }.
 
-Definition vec_to_list {T: Type} (v: vec T) : list T := proj1_sig v.
+Definition alloc_vec_Vec_to_list {T: Type} (v: alloc_vec_Vec T) : list T := proj1_sig v.
 
-Definition vec_length {T: Type} (v: vec T) : Z := Z.of_nat (length (vec_to_list v)).
+Definition alloc_vec_Vec_length {T: Type} (v: alloc_vec_Vec T) : Z := Z.of_nat (length (alloc_vec_Vec_to_list v)).
 
-Definition vec_new (T: Type) : vec T := (exist _ [] le_0_usize_max).
+Definition alloc_vec_Vec_new (T: Type) : alloc_vec_Vec T := (exist _ [] le_0_usize_max).
 
-Lemma vec_len_in_usize {T} (v: vec T) : usize_min <= vec_length v <= usize_max.
+Lemma alloc_vec_Vec_len_in_usize {T} (v: alloc_vec_Vec T) : usize_min <= alloc_vec_Vec_length v <= usize_max.
 Proof.
-  unfold vec_length, usize_min.
+  unfold alloc_vec_Vec_length, usize_min.
   split.
   - lia.
   - apply (proj2_sig v).
 Qed.
 
-Definition vec_len (T: Type) (v: vec T) : usize :=
-  exist _ (vec_length v) (vec_len_in_usize v).
+Definition alloc_vec_Vec_len (T: Type) (v: alloc_vec_Vec T) : usize :=
+  exist _ (alloc_vec_Vec_length v) (alloc_vec_Vec_len_in_usize v).
 
 Fixpoint list_update {A} (l: list A) (n: nat) (a: A)
   : list A :=
@@ -474,50 +628,279 @@ Fixpoint list_update {A} (l: list A) (n: nat) (a: A)
     | S m => x :: (list_update t m a)
 end end.
 
-Definition vec_bind {A B} (v: vec A) (f: list A -> result (list B)) : result (vec B) :=
-  l <- f (vec_to_list v) ;
+Definition alloc_vec_Vec_bind {A B} (v: alloc_vec_Vec A) (f: list A -> result (list B)) : result (alloc_vec_Vec B) :=
+  l <- f (alloc_vec_Vec_to_list v) ;
   match sumbool_of_bool (scalar_le_max Usize (Z.of_nat (length l))) with
   | left H => Return (exist _ l (scalar_le_max_valid _ _ H))
   | right _ => Fail_ Failure
   end.
 
 (* The **forward** function shouldn't be used *)
-Definition vec_push_fwd (T: Type) (v: vec T) (x: T) : unit := tt.
+Definition alloc_vec_Vec_push_fwd (T: Type) (v: alloc_vec_Vec T) (x: T) : unit := tt.
 
-Definition vec_push_back (T: Type) (v: vec T) (x: T) : result (vec T) :=
-  vec_bind v (fun l => Return (l ++ [x])).
+Definition alloc_vec_Vec_push (T: Type) (v: alloc_vec_Vec T) (x: T) : result (alloc_vec_Vec T) :=
+  alloc_vec_Vec_bind v (fun l => Return (l ++ [x])).
 
 (* The **forward** function shouldn't be used *)
-Definition vec_insert_fwd (T: Type) (v: vec T) (i: usize) (x: T) : result unit :=
-  if to_Z i <? vec_length v then Return tt else Fail_ Failure.
+Definition alloc_vec_Vec_insert_fwd (T: Type) (v: alloc_vec_Vec T) (i: usize) (x: T) : result unit :=
+  if to_Z i <? alloc_vec_Vec_length v then Return tt else Fail_ Failure.
 
-Definition vec_insert_back (T: Type) (v: vec T) (i: usize) (x: T) : result (vec T) :=
-  vec_bind v (fun l =>
+Definition alloc_vec_Vec_insert (T: Type) (v: alloc_vec_Vec T) (i: usize) (x: T) : result (alloc_vec_Vec T) :=
+  alloc_vec_Vec_bind v (fun l =>
     if to_Z i <? Z.of_nat (length l)
     then Return (list_update l (usize_to_nat i) x)
     else Fail_ Failure).
 
-(* The **backward** function shouldn't be used *)
-Definition vec_index_fwd (T: Type) (v: vec T) (i: usize) : result T :=
-  match nth_error (vec_to_list v) (usize_to_nat i) with
-  | Some n => Return n
-  | None   => Fail_ Failure
-  end.
-
-Definition vec_index_back (T: Type) (v: vec T) (i: usize) (x: T) : result unit :=
-  if to_Z i <? vec_length v then Return tt else Fail_ Failure.
-
-(* The **backward** function shouldn't be used *)
-Definition vec_index_mut_fwd (T: Type) (v: vec T) (i: usize) : result T :=
-  match nth_error (vec_to_list v) (usize_to_nat i) with
-  | Some n => Return n
-  | None   => Fail_ Failure
+(* Helper *)
+Axiom alloc_vec_Vec_index_usize : forall {T : Type} (v : alloc_vec_Vec T) (i : usize), result T.
+
+(* Helper *)
+Axiom alloc_vec_Vec_update_usize : forall {T : Type} (v : alloc_vec_Vec T) (i : usize) (x : T), result (alloc_vec_Vec T).
+
+(* Trait declaration: [core::slice::index::private_slice_index::Sealed] *)
+Definition core_slice_index_private_slice_index_Sealed (self : Type) := unit.
+
+(* Trait declaration: [core::slice::index::SliceIndex] *)
+Record core_slice_index_SliceIndex (Self T : Type) := mk_core_slice_index_SliceIndex {
+  core_slice_index_SliceIndex_sealedInst : core_slice_index_private_slice_index_Sealed Self;
+  core_slice_index_SliceIndex_Output : Type;
+  core_slice_index_SliceIndex_get : Self -> T -> result (option core_slice_index_SliceIndex_Output);
+  core_slice_index_SliceIndex_get_mut : Self -> T -> result (option core_slice_index_SliceIndex_Output);
+  core_slice_index_SliceIndex_get_mut_back : Self -> T -> option core_slice_index_SliceIndex_Output -> result T;
+  core_slice_index_SliceIndex_get_unchecked : Self -> const_raw_ptr T -> result (const_raw_ptr core_slice_index_SliceIndex_Output);
+  core_slice_index_SliceIndex_get_unchecked_mut : Self -> mut_raw_ptr T -> result (mut_raw_ptr core_slice_index_SliceIndex_Output);
+  core_slice_index_SliceIndex_index : Self -> T -> result core_slice_index_SliceIndex_Output;
+  core_slice_index_SliceIndex_index_mut : Self -> T -> result core_slice_index_SliceIndex_Output;
+  core_slice_index_SliceIndex_index_mut_back : Self -> T -> core_slice_index_SliceIndex_Output -> result T;
+}.
+Arguments mk_core_slice_index_SliceIndex {_ _}.
+Arguments core_slice_index_SliceIndex_sealedInst {_ _}.
+Arguments core_slice_index_SliceIndex_Output {_ _}.
+Arguments core_slice_index_SliceIndex_get {_ _}.
+Arguments core_slice_index_SliceIndex_get_mut {_ _}.
+Arguments core_slice_index_SliceIndex_get_mut_back {_ _}.
+Arguments core_slice_index_SliceIndex_get_unchecked {_ _}.
+Arguments core_slice_index_SliceIndex_get_unchecked_mut {_ _}.
+Arguments core_slice_index_SliceIndex_index {_ _}.
+Arguments core_slice_index_SliceIndex_index_mut {_ _}.
+Arguments core_slice_index_SliceIndex_index_mut_back {_ _}.
+
+(* [core::slice::index::[T]::index]: forward function *)
+Definition core_slice_index_Slice_index
+  (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T))
+  (s : slice T) (i : Idx) : result inst.(core_slice_index_SliceIndex_Output) :=
+  x <- inst.(core_slice_index_SliceIndex_get) i s;
+  match x with
+  | None => Fail_ Failure
+  | Some x => Return x
   end.
 
-Definition vec_index_mut_back (T: Type) (v: vec T) (i: usize) (x: T) : result (vec T) :=
-  vec_bind v (fun l =>
-    if to_Z i <? Z.of_nat (length l)
-    then Return (list_update l (usize_to_nat i) x)
-    else Fail_ Failure).
+(* [core::slice::index::Range:::get]: forward function *)
+Axiom core_slice_index_RangeUsize_get : forall (T : Type) (i : core_ops_range_Range usize) (s : slice T), result (option (slice T)).
+
+(* [core::slice::index::Range::get_mut]: forward function *)
+Axiom core_slice_index_RangeUsize_get_mut :
+  forall (T : Type), core_ops_range_Range usize -> slice T -> result (option (slice T)).
+
+(* [core::slice::index::Range::get_mut]: backward function 0 *)
+Axiom core_slice_index_RangeUsize_get_mut_back :
+  forall (T : Type), core_ops_range_Range usize -> slice T -> option (slice T) -> result (slice T).
+
+(* [core::slice::index::Range::get_unchecked]: forward function *)
+Definition core_slice_index_RangeUsize_get_unchecked
+  (T : Type) :
+  core_ops_range_Range usize -> const_raw_ptr (slice T) -> result (const_raw_ptr (slice T)) :=
+  (* Don't know what the model should be - for now we always fail to make
+     sure code which uses it fails *)
+  fun _ _ => Fail_ Failure.
+
+(* [core::slice::index::Range::get_unchecked_mut]: forward function *)
+Definition core_slice_index_RangeUsize_get_unchecked_mut
+  (T : Type) :
+  core_ops_range_Range usize -> mut_raw_ptr (slice T) -> result (mut_raw_ptr (slice T)) :=
+  (* Don't know what the model should be - for now we always fail to make
+    sure code which uses it fails *)
+  fun _ _ => Fail_ Failure.
+
+(* [core::slice::index::Range::index]: forward function *)
+Axiom core_slice_index_RangeUsize_index :
+  forall (T : Type), core_ops_range_Range usize -> slice T -> result (slice T).
+
+(* [core::slice::index::Range::index_mut]: forward function *)
+Axiom core_slice_index_RangeUsize_index_mut :
+  forall (T : Type), core_ops_range_Range usize -> slice T -> result (slice T).
+
+(* [core::slice::index::Range::index_mut]: backward function 0 *)
+Axiom core_slice_index_RangeUsize_index_mut_back :
+  forall (T : Type), core_ops_range_Range usize -> slice T -> slice T -> result (slice T).
+
+(* [core::slice::index::[T]::index_mut]: forward function *)
+Axiom core_slice_index_Slice_index_mut :
+  forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T)),
+  slice T -> Idx -> result inst.(core_slice_index_SliceIndex_Output).
+
+(* [core::slice::index::[T]::index_mut]: backward function 0 *)
+Axiom core_slice_index_Slice_index_mut_back :
+  forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T)),
+  slice T -> Idx -> inst.(core_slice_index_SliceIndex_Output) -> result (slice T).
+
+(* [core::array::[T; N]::index]: forward function *)
+Axiom core_array_Array_index :
+  forall (T Idx : Type) (N : usize) (inst : core_ops_index_Index (slice T) Idx)
+  (a : array T N) (i : Idx), result inst.(core_ops_index_Index_Output).
+
+(* [core::array::[T; N]::index_mut]: forward function *)
+Axiom core_array_Array_index_mut :
+  forall (T Idx : Type) (N : usize) (inst : core_ops_index_IndexMut (slice T) Idx)
+  (a : array T N) (i : Idx), result inst.(core_ops_index_IndexMut_indexInst).(core_ops_index_Index_Output).
+
+(* [core::array::[T; N]::index_mut]: backward function 0 *)
+Axiom core_array_Array_index_mut_back :
+  forall (T Idx : Type) (N : usize) (inst : core_ops_index_IndexMut (slice T) Idx)
+  (a : array T N) (i : Idx) (x : inst.(core_ops_index_IndexMut_indexInst).(core_ops_index_Index_Output)), result (array T N).
+
+(* Trait implementation: [core::slice::index::private_slice_index::Range] *)
+Definition core_slice_index_private_slice_index_SealedRangeUsizeInst
+  : core_slice_index_private_slice_index_Sealed (core_ops_range_Range usize) := tt.
+
+(* Trait implementation: [core::slice::index::Range] *)
+Definition core_slice_index_SliceIndexRangeUsizeSliceTInst (T : Type) :
+  core_slice_index_SliceIndex (core_ops_range_Range usize) (slice T) := {|
+  core_slice_index_SliceIndex_sealedInst := core_slice_index_private_slice_index_SealedRangeUsizeInst;
+  core_slice_index_SliceIndex_Output := slice T;
+  core_slice_index_SliceIndex_get := core_slice_index_RangeUsize_get T;
+  core_slice_index_SliceIndex_get_mut := core_slice_index_RangeUsize_get_mut T;
+  core_slice_index_SliceIndex_get_mut_back := core_slice_index_RangeUsize_get_mut_back T;
+  core_slice_index_SliceIndex_get_unchecked := core_slice_index_RangeUsize_get_unchecked T;
+  core_slice_index_SliceIndex_get_unchecked_mut := core_slice_index_RangeUsize_get_unchecked_mut T;
+  core_slice_index_SliceIndex_index := core_slice_index_RangeUsize_index T;
+  core_slice_index_SliceIndex_index_mut := core_slice_index_RangeUsize_index_mut T;
+  core_slice_index_SliceIndex_index_mut_back := core_slice_index_RangeUsize_index_mut_back T;
+|}.
+
+(* Trait implementation: [core::slice::index::[T]] *)
+Definition core_ops_index_IndexSliceTIInst (T Idx : Type)
+  (inst : core_slice_index_SliceIndex Idx (slice T)) :
+  core_ops_index_Index (slice T) Idx := {|
+  core_ops_index_Index_Output := inst.(core_slice_index_SliceIndex_Output);
+  core_ops_index_Index_index := core_slice_index_Slice_index T Idx inst;
+|}.
+
+(* Trait implementation: [core::slice::index::[T]] *)
+Definition core_ops_index_IndexMutSliceTIInst (T Idx : Type)
+  (inst : core_slice_index_SliceIndex Idx (slice T)) :
+  core_ops_index_IndexMut (slice T) Idx := {|
+  core_ops_index_IndexMut_indexInst := core_ops_index_IndexSliceTIInst T Idx inst;
+  core_ops_index_IndexMut_index_mut := core_slice_index_Slice_index_mut T Idx inst;
+  core_ops_index_IndexMut_index_mut_back := core_slice_index_Slice_index_mut_back T Idx inst;
+|}.
+
+(* Trait implementation: [core::array::[T; N]] *)
+Definition core_ops_index_IndexArrayInst (T Idx : Type) (N : usize)
+  (inst : core_ops_index_Index (slice T) Idx) :
+  core_ops_index_Index (array T N) Idx := {|
+  core_ops_index_Index_Output := inst.(core_ops_index_Index_Output);
+  core_ops_index_Index_index := core_array_Array_index T Idx N inst;
+|}.
+
+(* Trait implementation: [core::array::[T; N]] *)
+Definition core_ops_index_IndexMutArrayInst (T Idx : Type) (N : usize)
+  (inst : core_ops_index_IndexMut (slice T) Idx) :
+  core_ops_index_IndexMut (array T N) Idx := {|
+  core_ops_index_IndexMut_indexInst := core_ops_index_IndexArrayInst T Idx N inst.(core_ops_index_IndexMut_indexInst);
+  core_ops_index_IndexMut_index_mut := core_array_Array_index_mut T Idx N inst;
+  core_ops_index_IndexMut_index_mut_back := core_array_Array_index_mut_back T Idx N inst;
+|}.
+
+(* [core::slice::index::usize::get]: forward function *)
+Axiom core_slice_index_usize_get : forall (T : Type), usize -> slice T -> result (option T).
+
+(* [core::slice::index::usize::get_mut]: forward function *)
+Axiom core_slice_index_usize_get_mut : forall (T : Type), usize -> slice T -> result (option T).
+
+(* [core::slice::index::usize::get_mut]: backward function 0 *)
+Axiom core_slice_index_usize_get_mut_back :
+  forall (T : Type), usize -> slice T -> option T -> result (slice T).
+
+(* [core::slice::index::usize::get_unchecked]: forward function *)
+Axiom core_slice_index_usize_get_unchecked :
+  forall (T : Type), usize -> const_raw_ptr (slice T) -> result (const_raw_ptr T).
+
+(* [core::slice::index::usize::get_unchecked_mut]: forward function *)
+Axiom core_slice_index_usize_get_unchecked_mut :
+  forall (T : Type), usize -> mut_raw_ptr (slice T) -> result (mut_raw_ptr T).
+
+(* [core::slice::index::usize::index]: forward function *)
+Axiom core_slice_index_usize_index : forall (T : Type), usize -> slice T -> result T.
+
+(* [core::slice::index::usize::index_mut]: forward function *)
+Axiom core_slice_index_usize_index_mut : forall (T : Type), usize -> slice T -> result T.
+
+(* [core::slice::index::usize::index_mut]: backward function 0 *)
+Axiom core_slice_index_usize_index_mut_back :
+  forall (T : Type), usize -> slice T -> T -> result (slice T).
+
+(* Trait implementation: [core::slice::index::private_slice_index::usize] *)
+Definition core_slice_index_private_slice_index_SealedUsizeInst
+  : core_slice_index_private_slice_index_Sealed usize := tt.
+
+(* Trait implementation: [core::slice::index::usize] *)
+Definition core_slice_index_SliceIndexUsizeSliceTInst (T : Type) :
+  core_slice_index_SliceIndex usize (slice T) := {|
+  core_slice_index_SliceIndex_sealedInst := core_slice_index_private_slice_index_SealedUsizeInst;
+  core_slice_index_SliceIndex_Output := T;
+  core_slice_index_SliceIndex_get := core_slice_index_usize_get T;
+  core_slice_index_SliceIndex_get_mut := core_slice_index_usize_get_mut T;
+  core_slice_index_SliceIndex_get_mut_back := core_slice_index_usize_get_mut_back T;
+  core_slice_index_SliceIndex_get_unchecked := core_slice_index_usize_get_unchecked T;
+  core_slice_index_SliceIndex_get_unchecked_mut := core_slice_index_usize_get_unchecked_mut T;
+  core_slice_index_SliceIndex_index := core_slice_index_usize_index T;
+  core_slice_index_SliceIndex_index_mut := core_slice_index_usize_index_mut T;
+  core_slice_index_SliceIndex_index_mut_back := core_slice_index_usize_index_mut_back T;
+|}.
+
+(* [alloc::vec::Vec::index]: forward function *)
+Axiom alloc_vec_Vec_index : forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T))
+  (Self : alloc_vec_Vec T) (i : Idx), result inst.(core_slice_index_SliceIndex_Output).
+
+(* [alloc::vec::Vec::index_mut]: forward function *)
+Axiom alloc_vec_Vec_index_mut : forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T))
+  (Self : alloc_vec_Vec T) (i : Idx), result inst.(core_slice_index_SliceIndex_Output).
+
+(* [alloc::vec::Vec::index_mut]: backward function 0 *)
+Axiom alloc_vec_Vec_index_mut_back :
+  forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T))
+  (Self : alloc_vec_Vec T) (i : Idx) (x : inst.(core_slice_index_SliceIndex_Output)), result (alloc_vec_Vec T).
+
+(* Trait implementation: [alloc::vec::Vec] *)
+Definition alloc_vec_Vec_coreopsindexIndexInst (T Idx : Type)
+  (inst : core_slice_index_SliceIndex Idx (slice T)) :
+  core_ops_index_Index (alloc_vec_Vec T) Idx := {|
+  core_ops_index_Index_Output := inst.(core_slice_index_SliceIndex_Output);
+  core_ops_index_Index_index := alloc_vec_Vec_index T Idx inst;
+|}.
+
+(* Trait implementation: [alloc::vec::Vec] *)
+Definition alloc_vec_Vec_coreopsindexIndexMutInst (T Idx : Type)
+  (inst : core_slice_index_SliceIndex Idx (slice T)) :
+  core_ops_index_IndexMut (alloc_vec_Vec T) Idx := {|
+  core_ops_index_IndexMut_indexInst := alloc_vec_Vec_coreopsindexIndexInst T Idx inst;
+  core_ops_index_IndexMut_index_mut := alloc_vec_Vec_index_mut T Idx inst;
+  core_ops_index_IndexMut_index_mut_back := alloc_vec_Vec_index_mut_back T Idx inst;
+|}.
+
+(*** Theorems *)
+
+Axiom alloc_vec_Vec_index_eq : forall {a : Type} (v : alloc_vec_Vec a) (i : usize) (x : a),
+  alloc_vec_Vec_index a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i =
+    alloc_vec_Vec_index_usize v i.
+
+Axiom alloc_vec_Vec_index_mut_eq : forall {a : Type} (v : alloc_vec_Vec a) (i : usize) (x : a),
+  alloc_vec_Vec_index_mut a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i =
+    alloc_vec_Vec_index_usize v i.
+
+Axiom alloc_vec_Vec_index_mut_back_eq : forall {a : Type} (v : alloc_vec_Vec a) (i : usize) (x : a),
+  alloc_vec_Vec_index_mut_back a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i x =
+    alloc_vec_Vec_update_usize v i x.
 
 End Primitives.
diff --git a/tests/coq/array/_CoqProject b/tests/coq/array/_CoqProject
index f33cefe6..87d8fc3d 100644
--- a/tests/coq/array/_CoqProject
+++ b/tests/coq/array/_CoqProject
@@ -3,6 +3,5 @@
 -arg -w
 -arg all
 
-Array_Funs.v
 Primitives.v
-Array_Types.v
+Array.v
diff --git a/tests/coq/betree/BetreeMain_Funs.v b/tests/coq/betree/BetreeMain_Funs.v
index 1e457433..a5dd4230 100644
--- a/tests/coq/betree/BetreeMain_Funs.v
+++ b/tests/coq/betree/BetreeMain_Funs.v
@@ -6,1193 +6,1228 @@ Require Import Coq.ZArith.ZArith.
 Require Import List.
 Import ListNotations.
 Local Open Scope Primitives_scope.
-Require Export BetreeMain_Types.
-Import BetreeMain_Types.
-Require Export BetreeMain_Opaque.
-Import BetreeMain_Opaque.
+Require Import BetreeMain_Types.
+Include BetreeMain_Types.
+Require Import BetreeMain_FunsExternal.
+Include BetreeMain_FunsExternal.
 Module BetreeMain_Funs.
 
-(** [betree_main::betree::load_internal_node]: forward function *)
-Definition betree_load_internal_node_fwd
+(** [betree_main::betree::load_internal_node]: forward function
+    Source: 'src/betree.rs', lines 36:0-36:52 *)
+Definition betree_load_internal_node
   (id : u64) (st : state) :
-  result (state * (Betree_list_t (u64 * Betree_message_t)))
+  result (state * (betree_List_t (u64 * betree_Message_t)))
   :=
-  betree_utils_load_internal_node_fwd id st
+  betree_utils_load_internal_node id st
 .
 
-(** [betree_main::betree::store_internal_node]: forward function *)
-Definition betree_store_internal_node_fwd
-  (id : u64) (content : Betree_list_t (u64 * Betree_message_t)) (st : state) :
+(** [betree_main::betree::store_internal_node]: forward function
+    Source: 'src/betree.rs', lines 41:0-41:60 *)
+Definition betree_store_internal_node
+  (id : u64) (content : betree_List_t (u64 * betree_Message_t)) (st : state) :
   result (state * unit)
   :=
-  p <- betree_utils_store_internal_node_fwd id content st;
+  p <- betree_utils_store_internal_node id content st;
   let (st0, _) := p in
   Return (st0, tt)
 .
 
-(** [betree_main::betree::load_leaf_node]: forward function *)
-Definition betree_load_leaf_node_fwd
-  (id : u64) (st : state) : result (state * (Betree_list_t (u64 * u64))) :=
-  betree_utils_load_leaf_node_fwd id st
+(** [betree_main::betree::load_leaf_node]: forward function
+    Source: 'src/betree.rs', lines 46:0-46:44 *)
+Definition betree_load_leaf_node
+  (id : u64) (st : state) : result (state * (betree_List_t (u64 * u64))) :=
+  betree_utils_load_leaf_node id st
 .
 
-(** [betree_main::betree::store_leaf_node]: forward function *)
-Definition betree_store_leaf_node_fwd
-  (id : u64) (content : Betree_list_t (u64 * u64)) (st : state) :
+(** [betree_main::betree::store_leaf_node]: forward function
+    Source: 'src/betree.rs', lines 51:0-51:52 *)
+Definition betree_store_leaf_node
+  (id : u64) (content : betree_List_t (u64 * u64)) (st : state) :
   result (state * unit)
   :=
-  p <- betree_utils_store_leaf_node_fwd id content st;
+  p <- betree_utils_store_leaf_node id content st;
   let (st0, _) := p in
   Return (st0, tt)
 .
 
-(** [betree_main::betree::fresh_node_id]: forward function *)
-Definition betree_fresh_node_id_fwd (counter : u64) : result u64 :=
+(** [betree_main::betree::fresh_node_id]: forward function
+    Source: 'src/betree.rs', lines 55:0-55:48 *)
+Definition betree_fresh_node_id (counter : u64) : result u64 :=
   _ <- u64_add counter 1%u64; Return counter
 .
 
-(** [betree_main::betree::fresh_node_id]: backward function 0 *)
+(** [betree_main::betree::fresh_node_id]: backward function 0
+    Source: 'src/betree.rs', lines 55:0-55:48 *)
 Definition betree_fresh_node_id_back (counter : u64) : result u64 :=
   u64_add counter 1%u64
 .
 
-(** [betree_main::betree::NodeIdCounter::{0}::new]: forward function *)
-Definition betree_node_id_counter_new_fwd : result Betree_node_id_counter_t :=
-  Return {| Betree_node_id_counter_next_node_id := 0%u64 |}
+(** [betree_main::betree::{betree_main::betree::NodeIdCounter}::new]: forward function
+    Source: 'src/betree.rs', lines 206:4-206:20 *)
+Definition betree_NodeIdCounter_new : result betree_NodeIdCounter_t :=
+  Return {| betree_NodeIdCounter_next_node_id := 0%u64 |}
 .
 
-(** [betree_main::betree::NodeIdCounter::{0}::fresh_id]: forward function *)
-Definition betree_node_id_counter_fresh_id_fwd
-  (self : Betree_node_id_counter_t) : result u64 :=
-  _ <- u64_add self.(Betree_node_id_counter_next_node_id) 1%u64;
-  Return self.(Betree_node_id_counter_next_node_id)
+(** [betree_main::betree::{betree_main::betree::NodeIdCounter}::fresh_id]: forward function
+    Source: 'src/betree.rs', lines 210:4-210:36 *)
+Definition betree_NodeIdCounter_fresh_id
+  (self : betree_NodeIdCounter_t) : result u64 :=
+  _ <- u64_add self.(betree_NodeIdCounter_next_node_id) 1%u64;
+  Return self.(betree_NodeIdCounter_next_node_id)
 .
 
-(** [betree_main::betree::NodeIdCounter::{0}::fresh_id]: backward function 0 *)
-Definition betree_node_id_counter_fresh_id_back
-  (self : Betree_node_id_counter_t) : result Betree_node_id_counter_t :=
-  i <- u64_add self.(Betree_node_id_counter_next_node_id) 1%u64;
-  Return {| Betree_node_id_counter_next_node_id := i |}
+(** [betree_main::betree::{betree_main::betree::NodeIdCounter}::fresh_id]: backward function 0
+    Source: 'src/betree.rs', lines 210:4-210:36 *)
+Definition betree_NodeIdCounter_fresh_id_back
+  (self : betree_NodeIdCounter_t) : result betree_NodeIdCounter_t :=
+  i <- u64_add self.(betree_NodeIdCounter_next_node_id) 1%u64;
+  Return {| betree_NodeIdCounter_next_node_id := i |}
 .
 
-(** [core::num::u64::{9}::MAX] *)
-Definition core_num_u64_max_body : result u64 :=
-  Return 18446744073709551615%u64
-.
-Definition core_num_u64_max_c : u64 := core_num_u64_max_body%global.
-
-(** [betree_main::betree::upsert_update]: forward function *)
-Definition betree_upsert_update_fwd
-  (prev : option u64) (st : Betree_upsert_fun_state_t) : result u64 :=
+(** [betree_main::betree::upsert_update]: forward function
+    Source: 'src/betree.rs', lines 234:0-234:70 *)
+Definition betree_upsert_update
+  (prev : option u64) (st : betree_UpsertFunState_t) : result u64 :=
   match prev with
   | None =>
     match st with
-    | BetreeUpsertFunStateAdd v => Return v
-    | BetreeUpsertFunStateSub i => Return 0%u64
+    | Betree_UpsertFunState_Add v => Return v
+    | Betree_UpsertFunState_Sub i => Return 0%u64
     end
   | Some prev0 =>
     match st with
-    | BetreeUpsertFunStateAdd v =>
-      margin <- u64_sub core_num_u64_max_c prev0;
-      if margin s>= v then u64_add prev0 v else Return core_num_u64_max_c
-    | BetreeUpsertFunStateSub v =>
+    | Betree_UpsertFunState_Add v =>
+      margin <- u64_sub core_u64_max prev0;
+      if margin s>= v then u64_add prev0 v else Return core_u64_max
+    | Betree_UpsertFunState_Sub v =>
       if prev0 s>= v then u64_sub prev0 v else Return 0%u64
     end
   end
 .
 
-(** [betree_main::betree::List::{1}::len]: forward function *)
-Fixpoint betree_list_len_fwd
-  (T : Type) (n : nat) (self : Betree_list_t T) : result u64 :=
+(** [betree_main::betree::{betree_main::betree::List<T>#1}::len]: forward function
+    Source: 'src/betree.rs', lines 276:4-276:24 *)
+Fixpoint betree_List_len
+  (T : Type) (n : nat) (self : betree_List_t T) : result u64 :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
     match self with
-    | BetreeListCons t tl => i <- betree_list_len_fwd T n0 tl; u64_add 1%u64 i
-    | BetreeListNil => Return 0%u64
+    | Betree_List_Cons t tl => i <- betree_List_len T n0 tl; u64_add 1%u64 i
+    | Betree_List_Nil => Return 0%u64
     end
   end
 .
 
-(** [betree_main::betree::List::{1}::split_at]: forward function *)
-Fixpoint betree_list_split_at_fwd
-  (T : Type) (n : nat) (self : Betree_list_t T) (n0 : u64) :
-  result ((Betree_list_t T) * (Betree_list_t T))
+(** [betree_main::betree::{betree_main::betree::List<T>#1}::split_at]: forward function
+    Source: 'src/betree.rs', lines 284:4-284:51 *)
+Fixpoint betree_List_split_at
+  (T : Type) (n : nat) (self : betree_List_t T) (n0 : u64) :
+  result ((betree_List_t T) * (betree_List_t T))
   :=
   match n with
   | O => Fail_ OutOfFuel
   | S n1 =>
     if n0 s= 0%u64
-    then Return (BetreeListNil, self)
+    then Return (Betree_List_Nil, self)
     else
       match self with
-      | BetreeListCons hd tl =>
+      | Betree_List_Cons hd tl =>
         i <- u64_sub n0 1%u64;
-        p <- betree_list_split_at_fwd T n1 tl i;
+        p <- betree_List_split_at T n1 tl i;
         let (ls0, ls1) := p in
         let l := ls0 in
-        Return (BetreeListCons hd l, ls1)
-      | BetreeListNil => Fail_ Failure
+        Return (Betree_List_Cons hd l, ls1)
+      | Betree_List_Nil => Fail_ Failure
       end
   end
 .
 
-(** [betree_main::betree::List::{1}::push_front]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ()) *)
-Definition betree_list_push_front_fwd_back
-  (T : Type) (self : Betree_list_t T) (x : T) : result (Betree_list_t T) :=
-  let tl := mem_replace_fwd (Betree_list_t T) self BetreeListNil in
+(** [betree_main::betree::{betree_main::betree::List<T>#1}::push_front]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ())
+    Source: 'src/betree.rs', lines 299:4-299:34 *)
+Definition betree_List_push_front
+  (T : Type) (self : betree_List_t T) (x : T) : result (betree_List_t T) :=
+  let tl := core_mem_replace (betree_List_t T) self Betree_List_Nil in
   let l := tl in
-  Return (BetreeListCons x l)
+  Return (Betree_List_Cons x l)
 .
 
-(** [betree_main::betree::List::{1}::pop_front]: forward function *)
-Definition betree_list_pop_front_fwd
-  (T : Type) (self : Betree_list_t T) : result T :=
-  let ls := mem_replace_fwd (Betree_list_t T) self BetreeListNil in
+(** [betree_main::betree::{betree_main::betree::List<T>#1}::pop_front]: forward function
+    Source: 'src/betree.rs', lines 306:4-306:32 *)
+Definition betree_List_pop_front
+  (T : Type) (self : betree_List_t T) : result T :=
+  let ls := core_mem_replace (betree_List_t T) self Betree_List_Nil in
   match ls with
-  | BetreeListCons x tl => Return x
-  | BetreeListNil => Fail_ Failure
+  | Betree_List_Cons x tl => Return x
+  | Betree_List_Nil => Fail_ Failure
   end
 .
 
-(** [betree_main::betree::List::{1}::pop_front]: backward function 0 *)
-Definition betree_list_pop_front_back
-  (T : Type) (self : Betree_list_t T) : result (Betree_list_t T) :=
-  let ls := mem_replace_fwd (Betree_list_t T) self BetreeListNil in
+(** [betree_main::betree::{betree_main::betree::List<T>#1}::pop_front]: backward function 0
+    Source: 'src/betree.rs', lines 306:4-306:32 *)
+Definition betree_List_pop_front_back
+  (T : Type) (self : betree_List_t T) : result (betree_List_t T) :=
+  let ls := core_mem_replace (betree_List_t T) self Betree_List_Nil in
   match ls with
-  | BetreeListCons x tl => Return tl
-  | BetreeListNil => Fail_ Failure
+  | Betree_List_Cons x tl => Return tl
+  | Betree_List_Nil => Fail_ Failure
   end
 .
 
-(** [betree_main::betree::List::{1}::hd]: forward function *)
-Definition betree_list_hd_fwd (T : Type) (self : Betree_list_t T) : result T :=
+(** [betree_main::betree::{betree_main::betree::List<T>#1}::hd]: forward function
+    Source: 'src/betree.rs', lines 318:4-318:22 *)
+Definition betree_List_hd (T : Type) (self : betree_List_t T) : result T :=
   match self with
-  | BetreeListCons hd l => Return hd
-  | BetreeListNil => Fail_ Failure
+  | Betree_List_Cons hd l => Return hd
+  | Betree_List_Nil => Fail_ Failure
   end
 .
 
-(** [betree_main::betree::List::{2}::head_has_key]: forward function *)
-Definition betree_list_head_has_key_fwd
-  (T : Type) (self : Betree_list_t (u64 * T)) (key : u64) : result bool :=
+(** [betree_main::betree::{betree_main::betree::List<(u64, T)>#2}::head_has_key]: forward function
+    Source: 'src/betree.rs', lines 327:4-327:44 *)
+Definition betree_ListTupleU64T_head_has_key
+  (T : Type) (self : betree_List_t (u64 * T)) (key : u64) : result bool :=
   match self with
-  | BetreeListCons hd l => let (i, _) := hd in Return (i s= key)
-  | BetreeListNil => Return false
+  | Betree_List_Cons hd l => let (i, _) := hd in Return (i s= key)
+  | Betree_List_Nil => Return false
   end
 .
 
-(** [betree_main::betree::List::{2}::partition_at_pivot]: forward function *)
-Fixpoint betree_list_partition_at_pivot_fwd
-  (T : Type) (n : nat) (self : Betree_list_t (u64 * T)) (pivot : u64) :
-  result ((Betree_list_t (u64 * T)) * (Betree_list_t (u64 * T)))
+(** [betree_main::betree::{betree_main::betree::List<(u64, T)>#2}::partition_at_pivot]: forward function
+    Source: 'src/betree.rs', lines 339:4-339:73 *)
+Fixpoint betree_ListTupleU64T_partition_at_pivot
+  (T : Type) (n : nat) (self : betree_List_t (u64 * T)) (pivot : u64) :
+  result ((betree_List_t (u64 * T)) * (betree_List_t (u64 * T)))
   :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
     match self with
-    | BetreeListCons hd tl =>
+    | Betree_List_Cons hd tl =>
       let (i, t) := hd in
       if i s>= pivot
-      then Return (BetreeListNil, BetreeListCons (i, t) tl)
+      then Return (Betree_List_Nil, Betree_List_Cons (i, t) tl)
       else (
-        p <- betree_list_partition_at_pivot_fwd T n0 tl pivot;
+        p <- betree_ListTupleU64T_partition_at_pivot T n0 tl pivot;
         let (ls0, ls1) := p in
         let l := ls0 in
-        Return (BetreeListCons (i, t) l, ls1))
-    | BetreeListNil => Return (BetreeListNil, BetreeListNil)
+        Return (Betree_List_Cons (i, t) l, ls1))
+    | Betree_List_Nil => Return (Betree_List_Nil, Betree_List_Nil)
     end
   end
 .
 
-(** [betree_main::betree::Leaf::{3}::split]: forward function *)
-Definition betree_leaf_split_fwd
-  (n : nat) (self : Betree_leaf_t) (content : Betree_list_t (u64 * u64))
-  (params : Betree_params_t) (node_id_cnt : Betree_node_id_counter_t)
+(** [betree_main::betree::{betree_main::betree::Leaf#3}::split]: forward function
+    Source: 'src/betree.rs', lines 359:4-364:17 *)
+Definition betree_Leaf_split
+  (n : nat) (self : betree_Leaf_t) (content : betree_List_t (u64 * u64))
+  (params : betree_Params_t) (node_id_cnt : betree_NodeIdCounter_t)
   (st : state) :
-  result (state * Betree_internal_t)
+  result (state * betree_Internal_t)
   :=
   p <-
-    betree_list_split_at_fwd (u64 * u64) n content
-      params.(Betree_params_split_size);
+    betree_List_split_at (u64 * u64) n content
+      params.(betree_Params_split_size);
   let (content0, content1) := p in
-  p0 <- betree_list_hd_fwd (u64 * u64) content1;
+  p0 <- betree_List_hd (u64 * u64) content1;
   let (pivot, _) := p0 in
-  id0 <- betree_node_id_counter_fresh_id_fwd node_id_cnt;
-  node_id_cnt0 <- betree_node_id_counter_fresh_id_back node_id_cnt;
-  id1 <- betree_node_id_counter_fresh_id_fwd node_id_cnt0;
-  p1 <- betree_store_leaf_node_fwd id0 content0 st;
+  id0 <- betree_NodeIdCounter_fresh_id node_id_cnt;
+  node_id_cnt0 <- betree_NodeIdCounter_fresh_id_back node_id_cnt;
+  id1 <- betree_NodeIdCounter_fresh_id node_id_cnt0;
+  p1 <- betree_store_leaf_node id0 content0 st;
   let (st0, _) := p1 in
-  p2 <- betree_store_leaf_node_fwd id1 content1 st0;
+  p2 <- betree_store_leaf_node id1 content1 st0;
   let (st1, _) := p2 in
-  let n0 := BetreeNodeLeaf
+  let n0 := Betree_Node_Leaf
     {|
-      Betree_leaf_id := id0;
-      Betree_leaf_size := params.(Betree_params_split_size)
+      betree_Leaf_id := id0;
+      betree_Leaf_size := params.(betree_Params_split_size)
     |} in
-  let n1 := BetreeNodeLeaf
+  let n1 := Betree_Node_Leaf
     {|
-      Betree_leaf_id := id1;
-      Betree_leaf_size := params.(Betree_params_split_size)
+      betree_Leaf_id := id1;
+      betree_Leaf_size := params.(betree_Params_split_size)
     |} in
-  Return (st1, mkBetree_internal_t self.(Betree_leaf_id) pivot n0 n1)
+  Return (st1, mkbetree_Internal_t self.(betree_Leaf_id) pivot n0 n1)
 .
 
-(** [betree_main::betree::Leaf::{3}::split]: backward function 2 *)
-Definition betree_leaf_split_back
-  (n : nat) (self : Betree_leaf_t) (content : Betree_list_t (u64 * u64))
-  (params : Betree_params_t) (node_id_cnt : Betree_node_id_counter_t)
+(** [betree_main::betree::{betree_main::betree::Leaf#3}::split]: backward function 2
+    Source: 'src/betree.rs', lines 359:4-364:17 *)
+Definition betree_Leaf_split_back
+  (n : nat) (self : betree_Leaf_t) (content : betree_List_t (u64 * u64))
+  (params : betree_Params_t) (node_id_cnt : betree_NodeIdCounter_t)
   (st : state) :
-  result Betree_node_id_counter_t
+  result betree_NodeIdCounter_t
   :=
   p <-
-    betree_list_split_at_fwd (u64 * u64) n content
-      params.(Betree_params_split_size);
+    betree_List_split_at (u64 * u64) n content
+      params.(betree_Params_split_size);
   let (content0, content1) := p in
-  _ <- betree_list_hd_fwd (u64 * u64) content1;
-  id0 <- betree_node_id_counter_fresh_id_fwd node_id_cnt;
-  node_id_cnt0 <- betree_node_id_counter_fresh_id_back node_id_cnt;
-  id1 <- betree_node_id_counter_fresh_id_fwd node_id_cnt0;
-  p0 <- betree_store_leaf_node_fwd id0 content0 st;
+  _ <- betree_List_hd (u64 * u64) content1;
+  id0 <- betree_NodeIdCounter_fresh_id node_id_cnt;
+  node_id_cnt0 <- betree_NodeIdCounter_fresh_id_back node_id_cnt;
+  id1 <- betree_NodeIdCounter_fresh_id node_id_cnt0;
+  p0 <- betree_store_leaf_node id0 content0 st;
   let (st0, _) := p0 in
-  _ <- betree_store_leaf_node_fwd id1 content1 st0;
-  betree_node_id_counter_fresh_id_back node_id_cnt0
+  _ <- betree_store_leaf_node id1 content1 st0;
+  betree_NodeIdCounter_fresh_id_back node_id_cnt0
 .
 
-(** [betree_main::betree::Node::{5}::lookup_first_message_for_key]: forward function *)
-Fixpoint betree_node_lookup_first_message_for_key_fwd
-  (n : nat) (key : u64) (msgs : Betree_list_t (u64 * Betree_message_t)) :
-  result (Betree_list_t (u64 * Betree_message_t))
+(** [betree_main::betree::{betree_main::betree::Node#5}::lookup_first_message_for_key]: forward function
+    Source: 'src/betree.rs', lines 789:4-792:34 *)
+Fixpoint betree_Node_lookup_first_message_for_key
+  (n : nat) (key : u64) (msgs : betree_List_t (u64 * betree_Message_t)) :
+  result (betree_List_t (u64 * betree_Message_t))
   :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
     match msgs with
-    | BetreeListCons x next_msgs =>
+    | Betree_List_Cons x next_msgs =>
       let (i, m) := x in
       if i s>= key
-      then Return (BetreeListCons (i, m) next_msgs)
-      else betree_node_lookup_first_message_for_key_fwd n0 key next_msgs
-    | BetreeListNil => Return BetreeListNil
+      then Return (Betree_List_Cons (i, m) next_msgs)
+      else betree_Node_lookup_first_message_for_key n0 key next_msgs
+    | Betree_List_Nil => Return Betree_List_Nil
     end
   end
 .
 
-(** [betree_main::betree::Node::{5}::lookup_first_message_for_key]: backward function 0 *)
-Fixpoint betree_node_lookup_first_message_for_key_back
-  (n : nat) (key : u64) (msgs : Betree_list_t (u64 * Betree_message_t))
-  (ret : Betree_list_t (u64 * Betree_message_t)) :
-  result (Betree_list_t (u64 * Betree_message_t))
+(** [betree_main::betree::{betree_main::betree::Node#5}::lookup_first_message_for_key]: backward function 0
+    Source: 'src/betree.rs', lines 789:4-792:34 *)
+Fixpoint betree_Node_lookup_first_message_for_key_back
+  (n : nat) (key : u64) (msgs : betree_List_t (u64 * betree_Message_t))
+  (ret : betree_List_t (u64 * betree_Message_t)) :
+  result (betree_List_t (u64 * betree_Message_t))
   :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
     match msgs with
-    | BetreeListCons x next_msgs =>
+    | Betree_List_Cons x next_msgs =>
       let (i, m) := x in
       if i s>= key
       then Return ret
       else (
         next_msgs0 <-
-          betree_node_lookup_first_message_for_key_back n0 key next_msgs ret;
-        Return (BetreeListCons (i, m) next_msgs0))
-    | BetreeListNil => Return ret
+          betree_Node_lookup_first_message_for_key_back n0 key next_msgs ret;
+        Return (Betree_List_Cons (i, m) next_msgs0))
+    | Betree_List_Nil => Return ret
+    end
+  end
+.
+
+(** [betree_main::betree::{betree_main::betree::Node#5}::lookup_in_bindings]: forward function
+    Source: 'src/betree.rs', lines 636:4-636:80 *)
+Fixpoint betree_Node_lookup_in_bindings
+  (n : nat) (key : u64) (bindings : betree_List_t (u64 * u64)) :
+  result (option u64)
+  :=
+  match n with
+  | O => Fail_ OutOfFuel
+  | S n0 =>
+    match bindings with
+    | Betree_List_Cons hd tl =>
+      let (i, i0) := hd in
+      if i s= key
+      then Return (Some i0)
+      else
+        if i s> key
+        then Return None
+        else betree_Node_lookup_in_bindings n0 key tl
+    | Betree_List_Nil => Return None
     end
   end
 .
 
-(** [betree_main::betree::Node::{5}::apply_upserts]: forward function *)
-Fixpoint betree_node_apply_upserts_fwd
-  (n : nat) (msgs : Betree_list_t (u64 * Betree_message_t)) (prev : option u64)
+(** [betree_main::betree::{betree_main::betree::Node#5}::apply_upserts]: forward function
+    Source: 'src/betree.rs', lines 819:4-819:90 *)
+Fixpoint betree_Node_apply_upserts
+  (n : nat) (msgs : betree_List_t (u64 * betree_Message_t)) (prev : option u64)
   (key : u64) (st : state) :
   result (state * u64)
   :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
-    b <- betree_list_head_has_key_fwd Betree_message_t msgs key;
+    b <- betree_ListTupleU64T_head_has_key betree_Message_t msgs key;
     if b
     then (
-      msg <- betree_list_pop_front_fwd (u64 * Betree_message_t) msgs;
+      msg <- betree_List_pop_front (u64 * betree_Message_t) msgs;
       let (_, m) := msg in
       match m with
-      | BetreeMessageInsert i => Fail_ Failure
-      | BetreeMessageDelete => Fail_ Failure
-      | BetreeMessageUpsert s =>
-        v <- betree_upsert_update_fwd prev s;
-        msgs0 <- betree_list_pop_front_back (u64 * Betree_message_t) msgs;
-        betree_node_apply_upserts_fwd n0 msgs0 (Some v) key st
+      | Betree_Message_Insert i => Fail_ Failure
+      | Betree_Message_Delete => Fail_ Failure
+      | Betree_Message_Upsert s =>
+        v <- betree_upsert_update prev s;
+        msgs0 <- betree_List_pop_front_back (u64 * betree_Message_t) msgs;
+        betree_Node_apply_upserts n0 msgs0 (Some v) key st
       end)
     else (
-      p <- core_option_option_unwrap_fwd u64 prev st;
+      p <- core_option_Option_unwrap u64 prev st;
       let (st0, v) := p in
       _ <-
-        betree_list_push_front_fwd_back (u64 * Betree_message_t) msgs (key,
-          BetreeMessageInsert v);
+        betree_List_push_front (u64 * betree_Message_t) msgs (key,
+          Betree_Message_Insert v);
       Return (st0, v))
   end
 .
 
-(** [betree_main::betree::Node::{5}::apply_upserts]: backward function 0 *)
-Fixpoint betree_node_apply_upserts_back
-  (n : nat) (msgs : Betree_list_t (u64 * Betree_message_t)) (prev : option u64)
+(** [betree_main::betree::{betree_main::betree::Node#5}::apply_upserts]: backward function 0
+    Source: 'src/betree.rs', lines 819:4-819:90 *)
+Fixpoint betree_Node_apply_upserts_back
+  (n : nat) (msgs : betree_List_t (u64 * betree_Message_t)) (prev : option u64)
   (key : u64) (st : state) :
-  result (Betree_list_t (u64 * Betree_message_t))
+  result (betree_List_t (u64 * betree_Message_t))
   :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
-    b <- betree_list_head_has_key_fwd Betree_message_t msgs key;
+    b <- betree_ListTupleU64T_head_has_key betree_Message_t msgs key;
     if b
     then (
-      msg <- betree_list_pop_front_fwd (u64 * Betree_message_t) msgs;
+      msg <- betree_List_pop_front (u64 * betree_Message_t) msgs;
       let (_, m) := msg in
       match m with
-      | BetreeMessageInsert i => Fail_ Failure
-      | BetreeMessageDelete => Fail_ Failure
-      | BetreeMessageUpsert s =>
-        v <- betree_upsert_update_fwd prev s;
-        msgs0 <- betree_list_pop_front_back (u64 * Betree_message_t) msgs;
-        betree_node_apply_upserts_back n0 msgs0 (Some v) key st
+      | Betree_Message_Insert i => Fail_ Failure
+      | Betree_Message_Delete => Fail_ Failure
+      | Betree_Message_Upsert s =>
+        v <- betree_upsert_update prev s;
+        msgs0 <- betree_List_pop_front_back (u64 * betree_Message_t) msgs;
+        betree_Node_apply_upserts_back n0 msgs0 (Some v) key st
       end)
     else (
-      p <- core_option_option_unwrap_fwd u64 prev st;
+      p <- core_option_Option_unwrap u64 prev st;
       let (_, v) := p in
-      betree_list_push_front_fwd_back (u64 * Betree_message_t) msgs (key,
-        BetreeMessageInsert v))
+      betree_List_push_front (u64 * betree_Message_t) msgs (key,
+        Betree_Message_Insert v))
   end
 .
 
-(** [betree_main::betree::Node::{5}::lookup_in_bindings]: forward function *)
-Fixpoint betree_node_lookup_in_bindings_fwd
-  (n : nat) (key : u64) (bindings : Betree_list_t (u64 * u64)) :
-  result (option u64)
-  :=
-  match n with
-  | O => Fail_ OutOfFuel
-  | S n0 =>
-    match bindings with
-    | BetreeListCons hd tl =>
-      let (i, i0) := hd in
-      if i s= key
-      then Return (Some i0)
-      else
-        if i s> key
-        then Return None
-        else betree_node_lookup_in_bindings_fwd n0 key tl
-    | BetreeListNil => Return None
-    end
-  end
-.
-
-(** [betree_main::betree::Internal::{4}::lookup_in_children]: forward function *)
-Fixpoint betree_internal_lookup_in_children_fwd
-  (n : nat) (self : Betree_internal_t) (key : u64) (st : state) :
+(** [betree_main::betree::{betree_main::betree::Internal#4}::lookup_in_children]: forward function
+    Source: 'src/betree.rs', lines 395:4-395:63 *)
+Fixpoint betree_Internal_lookup_in_children
+  (n : nat) (self : betree_Internal_t) (key : u64) (st : state) :
   result (state * (option u64))
   :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
-    if key s< self.(Betree_internal_pivot)
-    then betree_node_lookup_fwd n0 self.(Betree_internal_left) key st
-    else betree_node_lookup_fwd n0 self.(Betree_internal_right) key st
+    if key s< self.(betree_Internal_pivot)
+    then betree_Node_lookup n0 self.(betree_Internal_left) key st
+    else betree_Node_lookup n0 self.(betree_Internal_right) key st
   end
 
-(** [betree_main::betree::Internal::{4}::lookup_in_children]: backward function 0 *)
-with betree_internal_lookup_in_children_back
-  (n : nat) (self : Betree_internal_t) (key : u64) (st : state) :
-  result Betree_internal_t
+(** [betree_main::betree::{betree_main::betree::Internal#4}::lookup_in_children]: backward function 0
+    Source: 'src/betree.rs', lines 395:4-395:63 *)
+with betree_Internal_lookup_in_children_back
+  (n : nat) (self : betree_Internal_t) (key : u64) (st : state) :
+  result betree_Internal_t
   :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
-    if key s< self.(Betree_internal_pivot)
+    if key s< self.(betree_Internal_pivot)
     then (
-      n1 <- betree_node_lookup_back n0 self.(Betree_internal_left) key st;
-      Return (mkBetree_internal_t self.(Betree_internal_id)
-        self.(Betree_internal_pivot) n1 self.(Betree_internal_right)))
+      n1 <- betree_Node_lookup_back n0 self.(betree_Internal_left) key st;
+      Return (mkbetree_Internal_t self.(betree_Internal_id)
+        self.(betree_Internal_pivot) n1 self.(betree_Internal_right)))
     else (
-      n1 <- betree_node_lookup_back n0 self.(Betree_internal_right) key st;
-      Return (mkBetree_internal_t self.(Betree_internal_id)
-        self.(Betree_internal_pivot) self.(Betree_internal_left) n1))
+      n1 <- betree_Node_lookup_back n0 self.(betree_Internal_right) key st;
+      Return (mkbetree_Internal_t self.(betree_Internal_id)
+        self.(betree_Internal_pivot) self.(betree_Internal_left) n1))
   end
 
-(** [betree_main::betree::Node::{5}::lookup]: forward function *)
-with betree_node_lookup_fwd
-  (n : nat) (self : Betree_node_t) (key : u64) (st : state) :
+(** [betree_main::betree::{betree_main::betree::Node#5}::lookup]: forward function
+    Source: 'src/betree.rs', lines 709:4-709:58 *)
+with betree_Node_lookup
+  (n : nat) (self : betree_Node_t) (key : u64) (st : state) :
   result (state * (option u64))
   :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
     match self with
-    | BetreeNodeInternal node =>
-      p <- betree_load_internal_node_fwd node.(Betree_internal_id) st;
+    | Betree_Node_Internal node =>
+      p <- betree_load_internal_node node.(betree_Internal_id) st;
       let (st0, msgs) := p in
-      pending <- betree_node_lookup_first_message_for_key_fwd n0 key msgs;
+      pending <- betree_Node_lookup_first_message_for_key n0 key msgs;
       match pending with
-      | BetreeListCons p0 l =>
+      | Betree_List_Cons p0 l =>
         let (k, msg) := p0 in
         if k s<> key
         then (
-          p1 <- betree_internal_lookup_in_children_fwd n0 node key st0;
-          let (st1, opt) := p1 in
+          p1 <- betree_Internal_lookup_in_children n0 node key st0;
+          let (st1, o) := p1 in
           _ <-
-            betree_node_lookup_first_message_for_key_back n0 key msgs
-              (BetreeListCons (k, msg) l);
-          Return (st1, opt))
+            betree_Node_lookup_first_message_for_key_back n0 key msgs
+              (Betree_List_Cons (k, msg) l);
+          Return (st1, o))
         else
           match msg with
-          | BetreeMessageInsert v =>
+          | Betree_Message_Insert v =>
             _ <-
-              betree_node_lookup_first_message_for_key_back n0 key msgs
-                (BetreeListCons (k, BetreeMessageInsert v) l);
+              betree_Node_lookup_first_message_for_key_back n0 key msgs
+                (Betree_List_Cons (k, Betree_Message_Insert v) l);
             Return (st0, Some v)
-          | BetreeMessageDelete =>
+          | Betree_Message_Delete =>
             _ <-
-              betree_node_lookup_first_message_for_key_back n0 key msgs
-                (BetreeListCons (k, BetreeMessageDelete) l);
+              betree_Node_lookup_first_message_for_key_back n0 key msgs
+                (Betree_List_Cons (k, Betree_Message_Delete) l);
             Return (st0, None)
-          | BetreeMessageUpsert ufs =>
-            p1 <- betree_internal_lookup_in_children_fwd n0 node key st0;
+          | Betree_Message_Upsert ufs =>
+            p1 <- betree_Internal_lookup_in_children n0 node key st0;
             let (st1, v) := p1 in
             p2 <-
-              betree_node_apply_upserts_fwd n0 (BetreeListCons (k,
-                BetreeMessageUpsert ufs) l) v key st1;
+              betree_Node_apply_upserts n0 (Betree_List_Cons (k,
+                Betree_Message_Upsert ufs) l) v key st1;
             let (st2, v0) := p2 in
-            node0 <- betree_internal_lookup_in_children_back n0 node key st0;
+            node0 <- betree_Internal_lookup_in_children_back n0 node key st0;
             pending0 <-
-              betree_node_apply_upserts_back n0 (BetreeListCons (k,
-                BetreeMessageUpsert ufs) l) v key st1;
+              betree_Node_apply_upserts_back n0 (Betree_List_Cons (k,
+                Betree_Message_Upsert ufs) l) v key st1;
             msgs0 <-
-              betree_node_lookup_first_message_for_key_back n0 key msgs
+              betree_Node_lookup_first_message_for_key_back n0 key msgs
                 pending0;
             p3 <-
-              betree_store_internal_node_fwd node0.(Betree_internal_id) msgs0
-                st2;
+              betree_store_internal_node node0.(betree_Internal_id) msgs0 st2;
             let (st3, _) := p3 in
             Return (st3, Some v0)
           end
-      | BetreeListNil =>
-        p0 <- betree_internal_lookup_in_children_fwd n0 node key st0;
-        let (st1, opt) := p0 in
+      | Betree_List_Nil =>
+        p0 <- betree_Internal_lookup_in_children n0 node key st0;
+        let (st1, o) := p0 in
         _ <-
-          betree_node_lookup_first_message_for_key_back n0 key msgs
-            BetreeListNil;
-        Return (st1, opt)
+          betree_Node_lookup_first_message_for_key_back n0 key msgs
+            Betree_List_Nil;
+        Return (st1, o)
       end
-    | BetreeNodeLeaf node =>
-      p <- betree_load_leaf_node_fwd node.(Betree_leaf_id) st;
+    | Betree_Node_Leaf node =>
+      p <- betree_load_leaf_node node.(betree_Leaf_id) st;
       let (st0, bindings) := p in
-      opt <- betree_node_lookup_in_bindings_fwd n0 key bindings;
-      Return (st0, opt)
+      o <- betree_Node_lookup_in_bindings n0 key bindings;
+      Return (st0, o)
     end
   end
 
-(** [betree_main::betree::Node::{5}::lookup]: backward function 0 *)
-with betree_node_lookup_back
-  (n : nat) (self : Betree_node_t) (key : u64) (st : state) :
-  result Betree_node_t
+(** [betree_main::betree::{betree_main::betree::Node#5}::lookup]: backward function 0
+    Source: 'src/betree.rs', lines 709:4-709:58 *)
+with betree_Node_lookup_back
+  (n : nat) (self : betree_Node_t) (key : u64) (st : state) :
+  result betree_Node_t
   :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
     match self with
-    | BetreeNodeInternal node =>
-      p <- betree_load_internal_node_fwd node.(Betree_internal_id) st;
+    | Betree_Node_Internal node =>
+      p <- betree_load_internal_node node.(betree_Internal_id) st;
       let (st0, msgs) := p in
-      pending <- betree_node_lookup_first_message_for_key_fwd n0 key msgs;
+      pending <- betree_Node_lookup_first_message_for_key n0 key msgs;
       match pending with
-      | BetreeListCons p0 l =>
+      | Betree_List_Cons p0 l =>
         let (k, msg) := p0 in
         if k s<> key
         then (
           _ <-
-            betree_node_lookup_first_message_for_key_back n0 key msgs
-              (BetreeListCons (k, msg) l);
-          node0 <- betree_internal_lookup_in_children_back n0 node key st0;
-          Return (BetreeNodeInternal node0))
+            betree_Node_lookup_first_message_for_key_back n0 key msgs
+              (Betree_List_Cons (k, msg) l);
+          node0 <- betree_Internal_lookup_in_children_back n0 node key st0;
+          Return (Betree_Node_Internal node0))
         else
           match msg with
-          | BetreeMessageInsert v =>
+          | Betree_Message_Insert v =>
             _ <-
-              betree_node_lookup_first_message_for_key_back n0 key msgs
-                (BetreeListCons (k, BetreeMessageInsert v) l);
-            Return (BetreeNodeInternal node)
-          | BetreeMessageDelete =>
+              betree_Node_lookup_first_message_for_key_back n0 key msgs
+                (Betree_List_Cons (k, Betree_Message_Insert v) l);
+            Return (Betree_Node_Internal node)
+          | Betree_Message_Delete =>
             _ <-
-              betree_node_lookup_first_message_for_key_back n0 key msgs
-                (BetreeListCons (k, BetreeMessageDelete) l);
-            Return (BetreeNodeInternal node)
-          | BetreeMessageUpsert ufs =>
-            p1 <- betree_internal_lookup_in_children_fwd n0 node key st0;
+              betree_Node_lookup_first_message_for_key_back n0 key msgs
+                (Betree_List_Cons (k, Betree_Message_Delete) l);
+            Return (Betree_Node_Internal node)
+          | Betree_Message_Upsert ufs =>
+            p1 <- betree_Internal_lookup_in_children n0 node key st0;
             let (st1, v) := p1 in
             p2 <-
-              betree_node_apply_upserts_fwd n0 (BetreeListCons (k,
-                BetreeMessageUpsert ufs) l) v key st1;
+              betree_Node_apply_upserts n0 (Betree_List_Cons (k,
+                Betree_Message_Upsert ufs) l) v key st1;
             let (st2, _) := p2 in
-            node0 <- betree_internal_lookup_in_children_back n0 node key st0;
+            node0 <- betree_Internal_lookup_in_children_back n0 node key st0;
             pending0 <-
-              betree_node_apply_upserts_back n0 (BetreeListCons (k,
-                BetreeMessageUpsert ufs) l) v key st1;
+              betree_Node_apply_upserts_back n0 (Betree_List_Cons (k,
+                Betree_Message_Upsert ufs) l) v key st1;
             msgs0 <-
-              betree_node_lookup_first_message_for_key_back n0 key msgs
+              betree_Node_lookup_first_message_for_key_back n0 key msgs
                 pending0;
             _ <-
-              betree_store_internal_node_fwd node0.(Betree_internal_id) msgs0
-                st2;
-            Return (BetreeNodeInternal node0)
+              betree_store_internal_node node0.(betree_Internal_id) msgs0 st2;
+            Return (Betree_Node_Internal node0)
           end
-      | BetreeListNil =>
+      | Betree_List_Nil =>
         _ <-
-          betree_node_lookup_first_message_for_key_back n0 key msgs
-            BetreeListNil;
-        node0 <- betree_internal_lookup_in_children_back n0 node key st0;
-        Return (BetreeNodeInternal node0)
+          betree_Node_lookup_first_message_for_key_back n0 key msgs
+            Betree_List_Nil;
+        node0 <- betree_Internal_lookup_in_children_back n0 node key st0;
+        Return (Betree_Node_Internal node0)
       end
-    | BetreeNodeLeaf node =>
-      p <- betree_load_leaf_node_fwd node.(Betree_leaf_id) st;
+    | Betree_Node_Leaf node =>
+      p <- betree_load_leaf_node node.(betree_Leaf_id) st;
       let (_, bindings) := p in
-      _ <- betree_node_lookup_in_bindings_fwd n0 key bindings;
-      Return (BetreeNodeLeaf node)
+      _ <- betree_Node_lookup_in_bindings n0 key bindings;
+      Return (Betree_Node_Leaf node)
     end
   end
 .
 
-(** [betree_main::betree::Node::{5}::filter_messages_for_key]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ()) *)
-Fixpoint betree_node_filter_messages_for_key_fwd_back
-  (n : nat) (key : u64) (msgs : Betree_list_t (u64 * Betree_message_t)) :
-  result (Betree_list_t (u64 * Betree_message_t))
+(** [betree_main::betree::{betree_main::betree::Node#5}::filter_messages_for_key]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ())
+    Source: 'src/betree.rs', lines 674:4-674:77 *)
+Fixpoint betree_Node_filter_messages_for_key
+  (n : nat) (key : u64) (msgs : betree_List_t (u64 * betree_Message_t)) :
+  result (betree_List_t (u64 * betree_Message_t))
   :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
     match msgs with
-    | BetreeListCons p l =>
+    | Betree_List_Cons p l =>
       let (k, m) := p in
       if k s= key
       then (
         msgs0 <-
-          betree_list_pop_front_back (u64 * Betree_message_t) (BetreeListCons
+          betree_List_pop_front_back (u64 * betree_Message_t) (Betree_List_Cons
             (k, m) l);
-        betree_node_filter_messages_for_key_fwd_back n0 key msgs0)
-      else Return (BetreeListCons (k, m) l)
-    | BetreeListNil => Return BetreeListNil
+        betree_Node_filter_messages_for_key n0 key msgs0)
+      else Return (Betree_List_Cons (k, m) l)
+    | Betree_List_Nil => Return Betree_List_Nil
     end
   end
 .
 
-(** [betree_main::betree::Node::{5}::lookup_first_message_after_key]: forward function *)
-Fixpoint betree_node_lookup_first_message_after_key_fwd
-  (n : nat) (key : u64) (msgs : Betree_list_t (u64 * Betree_message_t)) :
-  result (Betree_list_t (u64 * Betree_message_t))
+(** [betree_main::betree::{betree_main::betree::Node#5}::lookup_first_message_after_key]: forward function
+    Source: 'src/betree.rs', lines 689:4-692:34 *)
+Fixpoint betree_Node_lookup_first_message_after_key
+  (n : nat) (key : u64) (msgs : betree_List_t (u64 * betree_Message_t)) :
+  result (betree_List_t (u64 * betree_Message_t))
   :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
     match msgs with
-    | BetreeListCons p next_msgs =>
+    | Betree_List_Cons p next_msgs =>
       let (k, m) := p in
       if k s= key
-      then betree_node_lookup_first_message_after_key_fwd n0 key next_msgs
-      else Return (BetreeListCons (k, m) next_msgs)
-    | BetreeListNil => Return BetreeListNil
+      then betree_Node_lookup_first_message_after_key n0 key next_msgs
+      else Return (Betree_List_Cons (k, m) next_msgs)
+    | Betree_List_Nil => Return Betree_List_Nil
     end
   end
 .
 
-(** [betree_main::betree::Node::{5}::lookup_first_message_after_key]: backward function 0 *)
-Fixpoint betree_node_lookup_first_message_after_key_back
-  (n : nat) (key : u64) (msgs : Betree_list_t (u64 * Betree_message_t))
-  (ret : Betree_list_t (u64 * Betree_message_t)) :
-  result (Betree_list_t (u64 * Betree_message_t))
+(** [betree_main::betree::{betree_main::betree::Node#5}::lookup_first_message_after_key]: backward function 0
+    Source: 'src/betree.rs', lines 689:4-692:34 *)
+Fixpoint betree_Node_lookup_first_message_after_key_back
+  (n : nat) (key : u64) (msgs : betree_List_t (u64 * betree_Message_t))
+  (ret : betree_List_t (u64 * betree_Message_t)) :
+  result (betree_List_t (u64 * betree_Message_t))
   :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
     match msgs with
-    | BetreeListCons p next_msgs =>
+    | Betree_List_Cons p next_msgs =>
       let (k, m) := p in
       if k s= key
       then (
         next_msgs0 <-
-          betree_node_lookup_first_message_after_key_back n0 key next_msgs ret;
-        Return (BetreeListCons (k, m) next_msgs0))
+          betree_Node_lookup_first_message_after_key_back n0 key next_msgs ret;
+        Return (Betree_List_Cons (k, m) next_msgs0))
       else Return ret
-    | BetreeListNil => Return ret
+    | Betree_List_Nil => Return ret
     end
   end
 .
 
-(** [betree_main::betree::Node::{5}::apply_to_internal]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ()) *)
-Definition betree_node_apply_to_internal_fwd_back
-  (n : nat) (msgs : Betree_list_t (u64 * Betree_message_t)) (key : u64)
-  (new_msg : Betree_message_t) :
-  result (Betree_list_t (u64 * Betree_message_t))
+(** [betree_main::betree::{betree_main::betree::Node#5}::apply_to_internal]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ())
+    Source: 'src/betree.rs', lines 521:4-521:89 *)
+Definition betree_Node_apply_to_internal
+  (n : nat) (msgs : betree_List_t (u64 * betree_Message_t)) (key : u64)
+  (new_msg : betree_Message_t) :
+  result (betree_List_t (u64 * betree_Message_t))
   :=
-  msgs0 <- betree_node_lookup_first_message_for_key_fwd n key msgs;
-  b <- betree_list_head_has_key_fwd Betree_message_t msgs0 key;
+  msgs0 <- betree_Node_lookup_first_message_for_key n key msgs;
+  b <- betree_ListTupleU64T_head_has_key betree_Message_t msgs0 key;
   if b
   then
     match new_msg with
-    | BetreeMessageInsert i =>
-      msgs1 <- betree_node_filter_messages_for_key_fwd_back n key msgs0;
+    | Betree_Message_Insert i =>
+      msgs1 <- betree_Node_filter_messages_for_key n key msgs0;
       msgs2 <-
-        betree_list_push_front_fwd_back (u64 * Betree_message_t) msgs1 (key,
-          BetreeMessageInsert i);
-      betree_node_lookup_first_message_for_key_back n key msgs msgs2
-    | BetreeMessageDelete =>
-      msgs1 <- betree_node_filter_messages_for_key_fwd_back n key msgs0;
+        betree_List_push_front (u64 * betree_Message_t) msgs1 (key,
+          Betree_Message_Insert i);
+      betree_Node_lookup_first_message_for_key_back n key msgs msgs2
+    | Betree_Message_Delete =>
+      msgs1 <- betree_Node_filter_messages_for_key n key msgs0;
       msgs2 <-
-        betree_list_push_front_fwd_back (u64 * Betree_message_t) msgs1 (key,
-          BetreeMessageDelete);
-      betree_node_lookup_first_message_for_key_back n key msgs msgs2
-    | BetreeMessageUpsert s =>
-      p <- betree_list_hd_fwd (u64 * Betree_message_t) msgs0;
+        betree_List_push_front (u64 * betree_Message_t) msgs1 (key,
+          Betree_Message_Delete);
+      betree_Node_lookup_first_message_for_key_back n key msgs msgs2
+    | Betree_Message_Upsert s =>
+      p <- betree_List_hd (u64 * betree_Message_t) msgs0;
       let (_, m) := p in
       match m with
-      | BetreeMessageInsert prev =>
-        v <- betree_upsert_update_fwd (Some prev) s;
-        msgs1 <- betree_list_pop_front_back (u64 * Betree_message_t) msgs0;
+      | Betree_Message_Insert prev =>
+        v <- betree_upsert_update (Some prev) s;
+        msgs1 <- betree_List_pop_front_back (u64 * betree_Message_t) msgs0;
         msgs2 <-
-          betree_list_push_front_fwd_back (u64 * Betree_message_t) msgs1 (key,
-            BetreeMessageInsert v);
-        betree_node_lookup_first_message_for_key_back n key msgs msgs2
-      | BetreeMessageDelete =>
-        v <- betree_upsert_update_fwd None s;
-        msgs1 <- betree_list_pop_front_back (u64 * Betree_message_t) msgs0;
+          betree_List_push_front (u64 * betree_Message_t) msgs1 (key,
+            Betree_Message_Insert v);
+        betree_Node_lookup_first_message_for_key_back n key msgs msgs2
+      | Betree_Message_Delete =>
+        v <- betree_upsert_update None s;
+        msgs1 <- betree_List_pop_front_back (u64 * betree_Message_t) msgs0;
         msgs2 <-
-          betree_list_push_front_fwd_back (u64 * Betree_message_t) msgs1 (key,
-            BetreeMessageInsert v);
-        betree_node_lookup_first_message_for_key_back n key msgs msgs2
-      | BetreeMessageUpsert ufs =>
-        msgs1 <- betree_node_lookup_first_message_after_key_fwd n key msgs0;
+          betree_List_push_front (u64 * betree_Message_t) msgs1 (key,
+            Betree_Message_Insert v);
+        betree_Node_lookup_first_message_for_key_back n key msgs msgs2
+      | Betree_Message_Upsert ufs =>
+        msgs1 <- betree_Node_lookup_first_message_after_key n key msgs0;
         msgs2 <-
-          betree_list_push_front_fwd_back (u64 * Betree_message_t) msgs1 (key,
-            BetreeMessageUpsert s);
+          betree_List_push_front (u64 * betree_Message_t) msgs1 (key,
+            Betree_Message_Upsert s);
         msgs3 <-
-          betree_node_lookup_first_message_after_key_back n key msgs0 msgs2;
-        betree_node_lookup_first_message_for_key_back n key msgs msgs3
+          betree_Node_lookup_first_message_after_key_back n key msgs0 msgs2;
+        betree_Node_lookup_first_message_for_key_back n key msgs msgs3
       end
     end
   else (
     msgs1 <-
-      betree_list_push_front_fwd_back (u64 * Betree_message_t) msgs0 (key,
-        new_msg);
-    betree_node_lookup_first_message_for_key_back n key msgs msgs1)
+      betree_List_push_front (u64 * betree_Message_t) msgs0 (key, new_msg);
+    betree_Node_lookup_first_message_for_key_back n key msgs msgs1)
 .
 
-(** [betree_main::betree::Node::{5}::apply_messages_to_internal]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ()) *)
-Fixpoint betree_node_apply_messages_to_internal_fwd_back
-  (n : nat) (msgs : Betree_list_t (u64 * Betree_message_t))
-  (new_msgs : Betree_list_t (u64 * Betree_message_t)) :
-  result (Betree_list_t (u64 * Betree_message_t))
+(** [betree_main::betree::{betree_main::betree::Node#5}::apply_messages_to_internal]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ())
+    Source: 'src/betree.rs', lines 502:4-505:5 *)
+Fixpoint betree_Node_apply_messages_to_internal
+  (n : nat) (msgs : betree_List_t (u64 * betree_Message_t))
+  (new_msgs : betree_List_t (u64 * betree_Message_t)) :
+  result (betree_List_t (u64 * betree_Message_t))
   :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
     match new_msgs with
-    | BetreeListCons new_msg new_msgs_tl =>
+    | Betree_List_Cons new_msg new_msgs_tl =>
       let (i, m) := new_msg in
-      msgs0 <- betree_node_apply_to_internal_fwd_back n0 msgs i m;
-      betree_node_apply_messages_to_internal_fwd_back n0 msgs0 new_msgs_tl
-    | BetreeListNil => Return msgs
+      msgs0 <- betree_Node_apply_to_internal n0 msgs i m;
+      betree_Node_apply_messages_to_internal n0 msgs0 new_msgs_tl
+    | Betree_List_Nil => Return msgs
     end
   end
 .
 
-(** [betree_main::betree::Node::{5}::lookup_mut_in_bindings]: forward function *)
-Fixpoint betree_node_lookup_mut_in_bindings_fwd
-  (n : nat) (key : u64) (bindings : Betree_list_t (u64 * u64)) :
-  result (Betree_list_t (u64 * u64))
+(** [betree_main::betree::{betree_main::betree::Node#5}::lookup_mut_in_bindings]: forward function
+    Source: 'src/betree.rs', lines 653:4-656:32 *)
+Fixpoint betree_Node_lookup_mut_in_bindings
+  (n : nat) (key : u64) (bindings : betree_List_t (u64 * u64)) :
+  result (betree_List_t (u64 * u64))
   :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
     match bindings with
-    | BetreeListCons hd tl =>
+    | Betree_List_Cons hd tl =>
       let (i, i0) := hd in
       if i s>= key
-      then Return (BetreeListCons (i, i0) tl)
-      else betree_node_lookup_mut_in_bindings_fwd n0 key tl
-    | BetreeListNil => Return BetreeListNil
+      then Return (Betree_List_Cons (i, i0) tl)
+      else betree_Node_lookup_mut_in_bindings n0 key tl
+    | Betree_List_Nil => Return Betree_List_Nil
     end
   end
 .
 
-(** [betree_main::betree::Node::{5}::lookup_mut_in_bindings]: backward function 0 *)
-Fixpoint betree_node_lookup_mut_in_bindings_back
-  (n : nat) (key : u64) (bindings : Betree_list_t (u64 * u64))
-  (ret : Betree_list_t (u64 * u64)) :
-  result (Betree_list_t (u64 * u64))
+(** [betree_main::betree::{betree_main::betree::Node#5}::lookup_mut_in_bindings]: backward function 0
+    Source: 'src/betree.rs', lines 653:4-656:32 *)
+Fixpoint betree_Node_lookup_mut_in_bindings_back
+  (n : nat) (key : u64) (bindings : betree_List_t (u64 * u64))
+  (ret : betree_List_t (u64 * u64)) :
+  result (betree_List_t (u64 * u64))
   :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
     match bindings with
-    | BetreeListCons hd tl =>
+    | Betree_List_Cons hd tl =>
       let (i, i0) := hd in
       if i s>= key
       then Return ret
       else (
-        tl0 <- betree_node_lookup_mut_in_bindings_back n0 key tl ret;
-        Return (BetreeListCons (i, i0) tl0))
-    | BetreeListNil => Return ret
+        tl0 <- betree_Node_lookup_mut_in_bindings_back n0 key tl ret;
+        Return (Betree_List_Cons (i, i0) tl0))
+    | Betree_List_Nil => Return ret
     end
   end
 .
 
-(** [betree_main::betree::Node::{5}::apply_to_leaf]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ()) *)
-Definition betree_node_apply_to_leaf_fwd_back
-  (n : nat) (bindings : Betree_list_t (u64 * u64)) (key : u64)
-  (new_msg : Betree_message_t) :
-  result (Betree_list_t (u64 * u64))
+(** [betree_main::betree::{betree_main::betree::Node#5}::apply_to_leaf]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ())
+    Source: 'src/betree.rs', lines 460:4-460:87 *)
+Definition betree_Node_apply_to_leaf
+  (n : nat) (bindings : betree_List_t (u64 * u64)) (key : u64)
+  (new_msg : betree_Message_t) :
+  result (betree_List_t (u64 * u64))
   :=
-  bindings0 <- betree_node_lookup_mut_in_bindings_fwd n key bindings;
-  b <- betree_list_head_has_key_fwd u64 bindings0 key;
+  bindings0 <- betree_Node_lookup_mut_in_bindings n key bindings;
+  b <- betree_ListTupleU64T_head_has_key u64 bindings0 key;
   if b
   then (
-    hd <- betree_list_pop_front_fwd (u64 * u64) bindings0;
+    hd <- betree_List_pop_front (u64 * u64) bindings0;
     match new_msg with
-    | BetreeMessageInsert v =>
-      bindings1 <- betree_list_pop_front_back (u64 * u64) bindings0;
-      bindings2 <-
-        betree_list_push_front_fwd_back (u64 * u64) bindings1 (key, v);
-      betree_node_lookup_mut_in_bindings_back n key bindings bindings2
-    | BetreeMessageDelete =>
-      bindings1 <- betree_list_pop_front_back (u64 * u64) bindings0;
-      betree_node_lookup_mut_in_bindings_back n key bindings bindings1
-    | BetreeMessageUpsert s =>
+    | Betree_Message_Insert v =>
+      bindings1 <- betree_List_pop_front_back (u64 * u64) bindings0;
+      bindings2 <- betree_List_push_front (u64 * u64) bindings1 (key, v);
+      betree_Node_lookup_mut_in_bindings_back n key bindings bindings2
+    | Betree_Message_Delete =>
+      bindings1 <- betree_List_pop_front_back (u64 * u64) bindings0;
+      betree_Node_lookup_mut_in_bindings_back n key bindings bindings1
+    | Betree_Message_Upsert s =>
       let (_, i) := hd in
-      v <- betree_upsert_update_fwd (Some i) s;
-      bindings1 <- betree_list_pop_front_back (u64 * u64) bindings0;
-      bindings2 <-
-        betree_list_push_front_fwd_back (u64 * u64) bindings1 (key, v);
-      betree_node_lookup_mut_in_bindings_back n key bindings bindings2
+      v <- betree_upsert_update (Some i) s;
+      bindings1 <- betree_List_pop_front_back (u64 * u64) bindings0;
+      bindings2 <- betree_List_push_front (u64 * u64) bindings1 (key, v);
+      betree_Node_lookup_mut_in_bindings_back n key bindings bindings2
     end)
   else
     match new_msg with
-    | BetreeMessageInsert v =>
-      bindings1 <-
-        betree_list_push_front_fwd_back (u64 * u64) bindings0 (key, v);
-      betree_node_lookup_mut_in_bindings_back n key bindings bindings1
-    | BetreeMessageDelete =>
-      betree_node_lookup_mut_in_bindings_back n key bindings bindings0
-    | BetreeMessageUpsert s =>
-      v <- betree_upsert_update_fwd None s;
-      bindings1 <-
-        betree_list_push_front_fwd_back (u64 * u64) bindings0 (key, v);
-      betree_node_lookup_mut_in_bindings_back n key bindings bindings1
+    | Betree_Message_Insert v =>
+      bindings1 <- betree_List_push_front (u64 * u64) bindings0 (key, v);
+      betree_Node_lookup_mut_in_bindings_back n key bindings bindings1
+    | Betree_Message_Delete =>
+      betree_Node_lookup_mut_in_bindings_back n key bindings bindings0
+    | Betree_Message_Upsert s =>
+      v <- betree_upsert_update None s;
+      bindings1 <- betree_List_push_front (u64 * u64) bindings0 (key, v);
+      betree_Node_lookup_mut_in_bindings_back n key bindings bindings1
     end
 .
 
-(** [betree_main::betree::Node::{5}::apply_messages_to_leaf]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ()) *)
-Fixpoint betree_node_apply_messages_to_leaf_fwd_back
-  (n : nat) (bindings : Betree_list_t (u64 * u64))
-  (new_msgs : Betree_list_t (u64 * Betree_message_t)) :
-  result (Betree_list_t (u64 * u64))
+(** [betree_main::betree::{betree_main::betree::Node#5}::apply_messages_to_leaf]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ())
+    Source: 'src/betree.rs', lines 444:4-447:5 *)
+Fixpoint betree_Node_apply_messages_to_leaf
+  (n : nat) (bindings : betree_List_t (u64 * u64))
+  (new_msgs : betree_List_t (u64 * betree_Message_t)) :
+  result (betree_List_t (u64 * u64))
   :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
     match new_msgs with
-    | BetreeListCons new_msg new_msgs_tl =>
+    | Betree_List_Cons new_msg new_msgs_tl =>
       let (i, m) := new_msg in
-      bindings0 <- betree_node_apply_to_leaf_fwd_back n0 bindings i m;
-      betree_node_apply_messages_to_leaf_fwd_back n0 bindings0 new_msgs_tl
-    | BetreeListNil => Return bindings
+      bindings0 <- betree_Node_apply_to_leaf n0 bindings i m;
+      betree_Node_apply_messages_to_leaf n0 bindings0 new_msgs_tl
+    | Betree_List_Nil => Return bindings
     end
   end
 .
 
-(** [betree_main::betree::Internal::{4}::flush]: forward function *)
-Fixpoint betree_internal_flush_fwd
-  (n : nat) (self : Betree_internal_t) (params : Betree_params_t)
-  (node_id_cnt : Betree_node_id_counter_t)
-  (content : Betree_list_t (u64 * Betree_message_t)) (st : state) :
-  result (state * (Betree_list_t (u64 * Betree_message_t)))
+(** [betree_main::betree::{betree_main::betree::Internal#4}::flush]: forward function
+    Source: 'src/betree.rs', lines 410:4-415:26 *)
+Fixpoint betree_Internal_flush
+  (n : nat) (self : betree_Internal_t) (params : betree_Params_t)
+  (node_id_cnt : betree_NodeIdCounter_t)
+  (content : betree_List_t (u64 * betree_Message_t)) (st : state) :
+  result (state * (betree_List_t (u64 * betree_Message_t)))
   :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
     p <-
-      betree_list_partition_at_pivot_fwd Betree_message_t n0 content
-        self.(Betree_internal_pivot);
+      betree_ListTupleU64T_partition_at_pivot betree_Message_t n0 content
+        self.(betree_Internal_pivot);
     let (msgs_left, msgs_right) := p in
-    len_left <- betree_list_len_fwd (u64 * Betree_message_t) n0 msgs_left;
-    if len_left s>= params.(Betree_params_min_flush_size)
+    len_left <- betree_List_len (u64 * betree_Message_t) n0 msgs_left;
+    if len_left s>= params.(betree_Params_min_flush_size)
     then (
       p0 <-
-        betree_node_apply_messages_fwd n0 self.(Betree_internal_left) params
+        betree_Node_apply_messages n0 self.(betree_Internal_left) params
           node_id_cnt msgs_left st;
       let (st0, _) := p0 in
       p1 <-
-        betree_node_apply_messages_back n0 self.(Betree_internal_left) params
+        betree_Node_apply_messages_back n0 self.(betree_Internal_left) params
           node_id_cnt msgs_left st;
       let (_, node_id_cnt0) := p1 in
-      len_right <- betree_list_len_fwd (u64 * Betree_message_t) n0 msgs_right;
-      if len_right s>= params.(Betree_params_min_flush_size)
+      len_right <- betree_List_len (u64 * betree_Message_t) n0 msgs_right;
+      if len_right s>= params.(betree_Params_min_flush_size)
       then (
         p2 <-
-          betree_node_apply_messages_fwd n0 self.(Betree_internal_right) params
+          betree_Node_apply_messages n0 self.(betree_Internal_right) params
             node_id_cnt0 msgs_right st0;
         let (st1, _) := p2 in
         _ <-
-          betree_node_apply_messages_back n0 self.(Betree_internal_right)
+          betree_Node_apply_messages_back n0 self.(betree_Internal_right)
             params node_id_cnt0 msgs_right st0;
-        Return (st1, BetreeListNil))
+        Return (st1, Betree_List_Nil))
       else Return (st0, msgs_right))
     else (
       p0 <-
-        betree_node_apply_messages_fwd n0 self.(Betree_internal_right) params
+        betree_Node_apply_messages n0 self.(betree_Internal_right) params
           node_id_cnt msgs_right st;
       let (st0, _) := p0 in
       _ <-
-        betree_node_apply_messages_back n0 self.(Betree_internal_right) params
+        betree_Node_apply_messages_back n0 self.(betree_Internal_right) params
           node_id_cnt msgs_right st;
       Return (st0, msgs_left))
   end
 
-(** [betree_main::betree::Internal::{4}::flush]: backward function 0 *)
-with betree_internal_flush_back
-  (n : nat) (self : Betree_internal_t) (params : Betree_params_t)
-  (node_id_cnt : Betree_node_id_counter_t)
-  (content : Betree_list_t (u64 * Betree_message_t)) (st : state) :
-  result (Betree_internal_t * Betree_node_id_counter_t)
+(** [betree_main::betree::{betree_main::betree::Internal#4}::flush]: backward function 0
+    Source: 'src/betree.rs', lines 410:4-415:26 *)
+with betree_Internal_flush_back
+  (n : nat) (self : betree_Internal_t) (params : betree_Params_t)
+  (node_id_cnt : betree_NodeIdCounter_t)
+  (content : betree_List_t (u64 * betree_Message_t)) (st : state) :
+  result (betree_Internal_t * betree_NodeIdCounter_t)
   :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
     p <-
-      betree_list_partition_at_pivot_fwd Betree_message_t n0 content
-        self.(Betree_internal_pivot);
+      betree_ListTupleU64T_partition_at_pivot betree_Message_t n0 content
+        self.(betree_Internal_pivot);
     let (msgs_left, msgs_right) := p in
-    len_left <- betree_list_len_fwd (u64 * Betree_message_t) n0 msgs_left;
-    if len_left s>= params.(Betree_params_min_flush_size)
+    len_left <- betree_List_len (u64 * betree_Message_t) n0 msgs_left;
+    if len_left s>= params.(betree_Params_min_flush_size)
     then (
       p0 <-
-        betree_node_apply_messages_fwd n0 self.(Betree_internal_left) params
+        betree_Node_apply_messages n0 self.(betree_Internal_left) params
           node_id_cnt msgs_left st;
       let (st0, _) := p0 in
       p1 <-
-        betree_node_apply_messages_back n0 self.(Betree_internal_left) params
+        betree_Node_apply_messages_back n0 self.(betree_Internal_left) params
           node_id_cnt msgs_left st;
       let (n1, node_id_cnt0) := p1 in
-      len_right <- betree_list_len_fwd (u64 * Betree_message_t) n0 msgs_right;
-      if len_right s>= params.(Betree_params_min_flush_size)
+      len_right <- betree_List_len (u64 * betree_Message_t) n0 msgs_right;
+      if len_right s>= params.(betree_Params_min_flush_size)
       then (
         p2 <-
-          betree_node_apply_messages_back n0 self.(Betree_internal_right)
+          betree_Node_apply_messages_back n0 self.(betree_Internal_right)
             params node_id_cnt0 msgs_right st0;
         let (n2, node_id_cnt1) := p2 in
-        Return (mkBetree_internal_t self.(Betree_internal_id)
-          self.(Betree_internal_pivot) n1 n2, node_id_cnt1))
+        Return (mkbetree_Internal_t self.(betree_Internal_id)
+          self.(betree_Internal_pivot) n1 n2, node_id_cnt1))
       else
-        Return (mkBetree_internal_t self.(Betree_internal_id)
-          self.(Betree_internal_pivot) n1 self.(Betree_internal_right),
+        Return (mkbetree_Internal_t self.(betree_Internal_id)
+          self.(betree_Internal_pivot) n1 self.(betree_Internal_right),
           node_id_cnt0))
     else (
       p0 <-
-        betree_node_apply_messages_back n0 self.(Betree_internal_right) params
+        betree_Node_apply_messages_back n0 self.(betree_Internal_right) params
           node_id_cnt msgs_right st;
       let (n1, node_id_cnt0) := p0 in
-      Return (mkBetree_internal_t self.(Betree_internal_id)
-        self.(Betree_internal_pivot) self.(Betree_internal_left) n1,
+      Return (mkbetree_Internal_t self.(betree_Internal_id)
+        self.(betree_Internal_pivot) self.(betree_Internal_left) n1,
         node_id_cnt0))
   end
 
-(** [betree_main::betree::Node::{5}::apply_messages]: forward function *)
-with betree_node_apply_messages_fwd
-  (n : nat) (self : Betree_node_t) (params : Betree_params_t)
-  (node_id_cnt : Betree_node_id_counter_t)
-  (msgs : Betree_list_t (u64 * Betree_message_t)) (st : state) :
+(** [betree_main::betree::{betree_main::betree::Node#5}::apply_messages]: forward function
+    Source: 'src/betree.rs', lines 588:4-593:5 *)
+with betree_Node_apply_messages
+  (n : nat) (self : betree_Node_t) (params : betree_Params_t)
+  (node_id_cnt : betree_NodeIdCounter_t)
+  (msgs : betree_List_t (u64 * betree_Message_t)) (st : state) :
   result (state * unit)
   :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
     match self with
-    | BetreeNodeInternal node =>
-      p <- betree_load_internal_node_fwd node.(Betree_internal_id) st;
+    | Betree_Node_Internal node =>
+      p <- betree_load_internal_node node.(betree_Internal_id) st;
       let (st0, content) := p in
-      content0 <-
-        betree_node_apply_messages_to_internal_fwd_back n0 content msgs;
-      num_msgs <- betree_list_len_fwd (u64 * Betree_message_t) n0 content0;
-      if num_msgs s>= params.(Betree_params_min_flush_size)
+      content0 <- betree_Node_apply_messages_to_internal n0 content msgs;
+      num_msgs <- betree_List_len (u64 * betree_Message_t) n0 content0;
+      if num_msgs s>= params.(betree_Params_min_flush_size)
       then (
-        p0 <-
-          betree_internal_flush_fwd n0 node params node_id_cnt content0 st0;
+        p0 <- betree_Internal_flush n0 node params node_id_cnt content0 st0;
         let (st1, content1) := p0 in
         p1 <-
-          betree_internal_flush_back n0 node params node_id_cnt content0 st0;
+          betree_Internal_flush_back n0 node params node_id_cnt content0 st0;
         let (node0, _) := p1 in
         p2 <-
-          betree_store_internal_node_fwd node0.(Betree_internal_id) content1
-            st1;
+          betree_store_internal_node node0.(betree_Internal_id) content1 st1;
         let (st2, _) := p2 in
         Return (st2, tt))
       else (
         p0 <-
-          betree_store_internal_node_fwd node.(Betree_internal_id) content0 st0;
+          betree_store_internal_node node.(betree_Internal_id) content0 st0;
         let (st1, _) := p0 in
         Return (st1, tt))
-    | BetreeNodeLeaf node =>
-      p <- betree_load_leaf_node_fwd node.(Betree_leaf_id) st;
+    | Betree_Node_Leaf node =>
+      p <- betree_load_leaf_node node.(betree_Leaf_id) st;
       let (st0, content) := p in
-      content0 <- betree_node_apply_messages_to_leaf_fwd_back n0 content msgs;
-      len <- betree_list_len_fwd (u64 * u64) n0 content0;
-      i <- u64_mul 2%u64 params.(Betree_params_split_size);
+      content0 <- betree_Node_apply_messages_to_leaf n0 content msgs;
+      len <- betree_List_len (u64 * u64) n0 content0;
+      i <- u64_mul 2%u64 params.(betree_Params_split_size);
       if len s>= i
       then (
-        p0 <- betree_leaf_split_fwd n0 node content0 params node_id_cnt st0;
+        p0 <- betree_Leaf_split n0 node content0 params node_id_cnt st0;
         let (st1, _) := p0 in
-        p1 <-
-          betree_store_leaf_node_fwd node.(Betree_leaf_id) BetreeListNil st1;
+        p1 <- betree_store_leaf_node node.(betree_Leaf_id) Betree_List_Nil st1;
         let (st2, _) := p1 in
         Return (st2, tt))
       else (
-        p0 <- betree_store_leaf_node_fwd node.(Betree_leaf_id) content0 st0;
+        p0 <- betree_store_leaf_node node.(betree_Leaf_id) content0 st0;
         let (st1, _) := p0 in
         Return (st1, tt))
     end
   end
 
-(** [betree_main::betree::Node::{5}::apply_messages]: backward function 0 *)
-with betree_node_apply_messages_back
-  (n : nat) (self : Betree_node_t) (params : Betree_params_t)
-  (node_id_cnt : Betree_node_id_counter_t)
-  (msgs : Betree_list_t (u64 * Betree_message_t)) (st : state) :
-  result (Betree_node_t * Betree_node_id_counter_t)
+(** [betree_main::betree::{betree_main::betree::Node#5}::apply_messages]: backward function 0
+    Source: 'src/betree.rs', lines 588:4-593:5 *)
+with betree_Node_apply_messages_back
+  (n : nat) (self : betree_Node_t) (params : betree_Params_t)
+  (node_id_cnt : betree_NodeIdCounter_t)
+  (msgs : betree_List_t (u64 * betree_Message_t)) (st : state) :
+  result (betree_Node_t * betree_NodeIdCounter_t)
   :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
     match self with
-    | BetreeNodeInternal node =>
-      p <- betree_load_internal_node_fwd node.(Betree_internal_id) st;
+    | Betree_Node_Internal node =>
+      p <- betree_load_internal_node node.(betree_Internal_id) st;
       let (st0, content) := p in
-      content0 <-
-        betree_node_apply_messages_to_internal_fwd_back n0 content msgs;
-      num_msgs <- betree_list_len_fwd (u64 * Betree_message_t) n0 content0;
-      if num_msgs s>= params.(Betree_params_min_flush_size)
+      content0 <- betree_Node_apply_messages_to_internal n0 content msgs;
+      num_msgs <- betree_List_len (u64 * betree_Message_t) n0 content0;
+      if num_msgs s>= params.(betree_Params_min_flush_size)
       then (
-        p0 <-
-          betree_internal_flush_fwd n0 node params node_id_cnt content0 st0;
+        p0 <- betree_Internal_flush n0 node params node_id_cnt content0 st0;
         let (st1, content1) := p0 in
         p1 <-
-          betree_internal_flush_back n0 node params node_id_cnt content0 st0;
+          betree_Internal_flush_back n0 node params node_id_cnt content0 st0;
         let (node0, node_id_cnt0) := p1 in
         _ <-
-          betree_store_internal_node_fwd node0.(Betree_internal_id) content1
-            st1;
-        Return (BetreeNodeInternal node0, node_id_cnt0))
+          betree_store_internal_node node0.(betree_Internal_id) content1 st1;
+        Return (Betree_Node_Internal node0, node_id_cnt0))
       else (
-        _ <-
-          betree_store_internal_node_fwd node.(Betree_internal_id) content0 st0;
-        Return (BetreeNodeInternal node, node_id_cnt))
-    | BetreeNodeLeaf node =>
-      p <- betree_load_leaf_node_fwd node.(Betree_leaf_id) st;
+        _ <- betree_store_internal_node node.(betree_Internal_id) content0 st0;
+        Return (Betree_Node_Internal node, node_id_cnt))
+    | Betree_Node_Leaf node =>
+      p <- betree_load_leaf_node node.(betree_Leaf_id) st;
       let (st0, content) := p in
-      content0 <- betree_node_apply_messages_to_leaf_fwd_back n0 content msgs;
-      len <- betree_list_len_fwd (u64 * u64) n0 content0;
-      i <- u64_mul 2%u64 params.(Betree_params_split_size);
+      content0 <- betree_Node_apply_messages_to_leaf n0 content msgs;
+      len <- betree_List_len (u64 * u64) n0 content0;
+      i <- u64_mul 2%u64 params.(betree_Params_split_size);
       if len s>= i
       then (
-        p0 <- betree_leaf_split_fwd n0 node content0 params node_id_cnt st0;
+        p0 <- betree_Leaf_split n0 node content0 params node_id_cnt st0;
         let (st1, new_node) := p0 in
-        _ <-
-          betree_store_leaf_node_fwd node.(Betree_leaf_id) BetreeListNil st1;
+        _ <- betree_store_leaf_node node.(betree_Leaf_id) Betree_List_Nil st1;
         node_id_cnt0 <-
-          betree_leaf_split_back n0 node content0 params node_id_cnt st0;
-        Return (BetreeNodeInternal new_node, node_id_cnt0))
+          betree_Leaf_split_back n0 node content0 params node_id_cnt st0;
+        Return (Betree_Node_Internal new_node, node_id_cnt0))
       else (
-        _ <- betree_store_leaf_node_fwd node.(Betree_leaf_id) content0 st0;
-        Return (BetreeNodeLeaf
-          {| Betree_leaf_id := node.(Betree_leaf_id); Betree_leaf_size := len
+        _ <- betree_store_leaf_node node.(betree_Leaf_id) content0 st0;
+        Return (Betree_Node_Leaf
+          {| betree_Leaf_id := node.(betree_Leaf_id); betree_Leaf_size := len
           |}, node_id_cnt))
     end
   end
 .
 
-(** [betree_main::betree::Node::{5}::apply]: forward function *)
-Definition betree_node_apply_fwd
-  (n : nat) (self : Betree_node_t) (params : Betree_params_t)
-  (node_id_cnt : Betree_node_id_counter_t) (key : u64)
-  (new_msg : Betree_message_t) (st : state) :
+(** [betree_main::betree::{betree_main::betree::Node#5}::apply]: forward function
+    Source: 'src/betree.rs', lines 576:4-582:5 *)
+Definition betree_Node_apply
+  (n : nat) (self : betree_Node_t) (params : betree_Params_t)
+  (node_id_cnt : betree_NodeIdCounter_t) (key : u64)
+  (new_msg : betree_Message_t) (st : state) :
   result (state * unit)
   :=
-  let l := BetreeListNil in
+  let l := Betree_List_Nil in
   p <-
-    betree_node_apply_messages_fwd n self params node_id_cnt (BetreeListCons
+    betree_Node_apply_messages n self params node_id_cnt (Betree_List_Cons
       (key, new_msg) l) st;
   let (st0, _) := p in
   _ <-
-    betree_node_apply_messages_back n self params node_id_cnt (BetreeListCons
+    betree_Node_apply_messages_back n self params node_id_cnt (Betree_List_Cons
       (key, new_msg) l) st;
   Return (st0, tt)
 .
 
-(** [betree_main::betree::Node::{5}::apply]: backward function 0 *)
-Definition betree_node_apply_back
-  (n : nat) (self : Betree_node_t) (params : Betree_params_t)
-  (node_id_cnt : Betree_node_id_counter_t) (key : u64)
-  (new_msg : Betree_message_t) (st : state) :
-  result (Betree_node_t * Betree_node_id_counter_t)
+(** [betree_main::betree::{betree_main::betree::Node#5}::apply]: backward function 0
+    Source: 'src/betree.rs', lines 576:4-582:5 *)
+Definition betree_Node_apply_back
+  (n : nat) (self : betree_Node_t) (params : betree_Params_t)
+  (node_id_cnt : betree_NodeIdCounter_t) (key : u64)
+  (new_msg : betree_Message_t) (st : state) :
+  result (betree_Node_t * betree_NodeIdCounter_t)
   :=
-  let l := BetreeListNil in
-  betree_node_apply_messages_back n self params node_id_cnt (BetreeListCons
+  let l := Betree_List_Nil in
+  betree_Node_apply_messages_back n self params node_id_cnt (Betree_List_Cons
     (key, new_msg) l) st
 .
 
-(** [betree_main::betree::BeTree::{6}::new]: forward function *)
-Definition betree_be_tree_new_fwd
+(** [betree_main::betree::{betree_main::betree::BeTree#6}::new]: forward function
+    Source: 'src/betree.rs', lines 849:4-849:60 *)
+Definition betree_BeTree_new
   (min_flush_size : u64) (split_size : u64) (st : state) :
-  result (state * Betree_be_tree_t)
+  result (state * betree_BeTree_t)
   :=
-  node_id_cnt <- betree_node_id_counter_new_fwd;
-  id <- betree_node_id_counter_fresh_id_fwd node_id_cnt;
-  p <- betree_store_leaf_node_fwd id BetreeListNil st;
+  node_id_cnt <- betree_NodeIdCounter_new;
+  id <- betree_NodeIdCounter_fresh_id node_id_cnt;
+  p <- betree_store_leaf_node id Betree_List_Nil st;
   let (st0, _) := p in
-  node_id_cnt0 <- betree_node_id_counter_fresh_id_back node_id_cnt;
+  node_id_cnt0 <- betree_NodeIdCounter_fresh_id_back node_id_cnt;
   Return (st0,
     {|
-      Betree_be_tree_params :=
+      betree_BeTree_params :=
         {|
-          Betree_params_min_flush_size := min_flush_size;
-          Betree_params_split_size := split_size
+          betree_Params_min_flush_size := min_flush_size;
+          betree_Params_split_size := split_size
         |};
-      Betree_be_tree_node_id_cnt := node_id_cnt0;
-      Betree_be_tree_root :=
-        (BetreeNodeLeaf {| Betree_leaf_id := id; Betree_leaf_size := 0%u64 |})
+      betree_BeTree_node_id_cnt := node_id_cnt0;
+      betree_BeTree_root :=
+        (Betree_Node_Leaf
+          {| betree_Leaf_id := id; betree_Leaf_size := 0%u64 |})
     |})
 .
 
-(** [betree_main::betree::BeTree::{6}::apply]: forward function *)
-Definition betree_be_tree_apply_fwd
-  (n : nat) (self : Betree_be_tree_t) (key : u64) (msg : Betree_message_t)
+(** [betree_main::betree::{betree_main::betree::BeTree#6}::apply]: forward function
+    Source: 'src/betree.rs', lines 868:4-868:47 *)
+Definition betree_BeTree_apply
+  (n : nat) (self : betree_BeTree_t) (key : u64) (msg : betree_Message_t)
   (st : state) :
   result (state * unit)
   :=
   p <-
-    betree_node_apply_fwd n self.(Betree_be_tree_root)
-      self.(Betree_be_tree_params) self.(Betree_be_tree_node_id_cnt) key msg st;
+    betree_Node_apply n self.(betree_BeTree_root) self.(betree_BeTree_params)
+      self.(betree_BeTree_node_id_cnt) key msg st;
   let (st0, _) := p in
   _ <-
-    betree_node_apply_back n self.(Betree_be_tree_root)
-      self.(Betree_be_tree_params) self.(Betree_be_tree_node_id_cnt) key msg st;
+    betree_Node_apply_back n self.(betree_BeTree_root)
+      self.(betree_BeTree_params) self.(betree_BeTree_node_id_cnt) key msg st;
   Return (st0, tt)
 .
 
-(** [betree_main::betree::BeTree::{6}::apply]: backward function 0 *)
-Definition betree_be_tree_apply_back
-  (n : nat) (self : Betree_be_tree_t) (key : u64) (msg : Betree_message_t)
+(** [betree_main::betree::{betree_main::betree::BeTree#6}::apply]: backward function 0
+    Source: 'src/betree.rs', lines 868:4-868:47 *)
+Definition betree_BeTree_apply_back
+  (n : nat) (self : betree_BeTree_t) (key : u64) (msg : betree_Message_t)
   (st : state) :
-  result Betree_be_tree_t
+  result betree_BeTree_t
   :=
   p <-
-    betree_node_apply_back n self.(Betree_be_tree_root)
-      self.(Betree_be_tree_params) self.(Betree_be_tree_node_id_cnt) key msg st;
+    betree_Node_apply_back n self.(betree_BeTree_root)
+      self.(betree_BeTree_params) self.(betree_BeTree_node_id_cnt) key msg st;
   let (n0, nic) := p in
   Return
     {|
-      Betree_be_tree_params := self.(Betree_be_tree_params);
-      Betree_be_tree_node_id_cnt := nic;
-      Betree_be_tree_root := n0
+      betree_BeTree_params := self.(betree_BeTree_params);
+      betree_BeTree_node_id_cnt := nic;
+      betree_BeTree_root := n0
     |}
 .
 
-(** [betree_main::betree::BeTree::{6}::insert]: forward function *)
-Definition betree_be_tree_insert_fwd
-  (n : nat) (self : Betree_be_tree_t) (key : u64) (value : u64) (st : state) :
+(** [betree_main::betree::{betree_main::betree::BeTree#6}::insert]: forward function
+    Source: 'src/betree.rs', lines 874:4-874:52 *)
+Definition betree_BeTree_insert
+  (n : nat) (self : betree_BeTree_t) (key : u64) (value : u64) (st : state) :
   result (state * unit)
   :=
-  p <- betree_be_tree_apply_fwd n self key (BetreeMessageInsert value) st;
+  p <- betree_BeTree_apply n self key (Betree_Message_Insert value) st;
   let (st0, _) := p in
-  _ <- betree_be_tree_apply_back n self key (BetreeMessageInsert value) st;
+  _ <- betree_BeTree_apply_back n self key (Betree_Message_Insert value) st;
   Return (st0, tt)
 .
 
-(** [betree_main::betree::BeTree::{6}::insert]: backward function 0 *)
-Definition betree_be_tree_insert_back
-  (n : nat) (self : Betree_be_tree_t) (key : u64) (value : u64) (st : state) :
-  result Betree_be_tree_t
+(** [betree_main::betree::{betree_main::betree::BeTree#6}::insert]: backward function 0
+    Source: 'src/betree.rs', lines 874:4-874:52 *)
+Definition betree_BeTree_insert_back
+  (n : nat) (self : betree_BeTree_t) (key : u64) (value : u64) (st : state) :
+  result betree_BeTree_t
   :=
-  betree_be_tree_apply_back n self key (BetreeMessageInsert value) st
+  betree_BeTree_apply_back n self key (Betree_Message_Insert value) st
 .
 
-(** [betree_main::betree::BeTree::{6}::delete]: forward function *)
-Definition betree_be_tree_delete_fwd
-  (n : nat) (self : Betree_be_tree_t) (key : u64) (st : state) :
+(** [betree_main::betree::{betree_main::betree::BeTree#6}::delete]: forward function
+    Source: 'src/betree.rs', lines 880:4-880:38 *)
+Definition betree_BeTree_delete
+  (n : nat) (self : betree_BeTree_t) (key : u64) (st : state) :
   result (state * unit)
   :=
-  p <- betree_be_tree_apply_fwd n self key BetreeMessageDelete st;
+  p <- betree_BeTree_apply n self key Betree_Message_Delete st;
   let (st0, _) := p in
-  _ <- betree_be_tree_apply_back n self key BetreeMessageDelete st;
+  _ <- betree_BeTree_apply_back n self key Betree_Message_Delete st;
   Return (st0, tt)
 .
 
-(** [betree_main::betree::BeTree::{6}::delete]: backward function 0 *)
-Definition betree_be_tree_delete_back
-  (n : nat) (self : Betree_be_tree_t) (key : u64) (st : state) :
-  result Betree_be_tree_t
+(** [betree_main::betree::{betree_main::betree::BeTree#6}::delete]: backward function 0
+    Source: 'src/betree.rs', lines 880:4-880:38 *)
+Definition betree_BeTree_delete_back
+  (n : nat) (self : betree_BeTree_t) (key : u64) (st : state) :
+  result betree_BeTree_t
   :=
-  betree_be_tree_apply_back n self key BetreeMessageDelete st
+  betree_BeTree_apply_back n self key Betree_Message_Delete st
 .
 
-(** [betree_main::betree::BeTree::{6}::upsert]: forward function *)
-Definition betree_be_tree_upsert_fwd
-  (n : nat) (self : Betree_be_tree_t) (key : u64)
-  (upd : Betree_upsert_fun_state_t) (st : state) :
+(** [betree_main::betree::{betree_main::betree::BeTree#6}::upsert]: forward function
+    Source: 'src/betree.rs', lines 886:4-886:59 *)
+Definition betree_BeTree_upsert
+  (n : nat) (self : betree_BeTree_t) (key : u64)
+  (upd : betree_UpsertFunState_t) (st : state) :
   result (state * unit)
   :=
-  p <- betree_be_tree_apply_fwd n self key (BetreeMessageUpsert upd) st;
+  p <- betree_BeTree_apply n self key (Betree_Message_Upsert upd) st;
   let (st0, _) := p in
-  _ <- betree_be_tree_apply_back n self key (BetreeMessageUpsert upd) st;
+  _ <- betree_BeTree_apply_back n self key (Betree_Message_Upsert upd) st;
   Return (st0, tt)
 .
 
-(** [betree_main::betree::BeTree::{6}::upsert]: backward function 0 *)
-Definition betree_be_tree_upsert_back
-  (n : nat) (self : Betree_be_tree_t) (key : u64)
-  (upd : Betree_upsert_fun_state_t) (st : state) :
-  result Betree_be_tree_t
+(** [betree_main::betree::{betree_main::betree::BeTree#6}::upsert]: backward function 0
+    Source: 'src/betree.rs', lines 886:4-886:59 *)
+Definition betree_BeTree_upsert_back
+  (n : nat) (self : betree_BeTree_t) (key : u64)
+  (upd : betree_UpsertFunState_t) (st : state) :
+  result betree_BeTree_t
   :=
-  betree_be_tree_apply_back n self key (BetreeMessageUpsert upd) st
+  betree_BeTree_apply_back n self key (Betree_Message_Upsert upd) st
 .
 
-(** [betree_main::betree::BeTree::{6}::lookup]: forward function *)
-Definition betree_be_tree_lookup_fwd
-  (n : nat) (self : Betree_be_tree_t) (key : u64) (st : state) :
+(** [betree_main::betree::{betree_main::betree::BeTree#6}::lookup]: forward function
+    Source: 'src/betree.rs', lines 895:4-895:62 *)
+Definition betree_BeTree_lookup
+  (n : nat) (self : betree_BeTree_t) (key : u64) (st : state) :
   result (state * (option u64))
   :=
-  betree_node_lookup_fwd n self.(Betree_be_tree_root) key st
+  betree_Node_lookup n self.(betree_BeTree_root) key st
 .
 
-(** [betree_main::betree::BeTree::{6}::lookup]: backward function 0 *)
-Definition betree_be_tree_lookup_back
-  (n : nat) (self : Betree_be_tree_t) (key : u64) (st : state) :
-  result Betree_be_tree_t
+(** [betree_main::betree::{betree_main::betree::BeTree#6}::lookup]: backward function 0
+    Source: 'src/betree.rs', lines 895:4-895:62 *)
+Definition betree_BeTree_lookup_back
+  (n : nat) (self : betree_BeTree_t) (key : u64) (st : state) :
+  result betree_BeTree_t
   :=
-  n0 <- betree_node_lookup_back n self.(Betree_be_tree_root) key st;
+  n0 <- betree_Node_lookup_back n self.(betree_BeTree_root) key st;
   Return
     {|
-      Betree_be_tree_params := self.(Betree_be_tree_params);
-      Betree_be_tree_node_id_cnt := self.(Betree_be_tree_node_id_cnt);
-      Betree_be_tree_root := n0
+      betree_BeTree_params := self.(betree_BeTree_params);
+      betree_BeTree_node_id_cnt := self.(betree_BeTree_node_id_cnt);
+      betree_BeTree_root := n0
     |}
 .
 
-(** [betree_main::main]: forward function *)
-Definition main_fwd : result unit :=
+(** [betree_main::main]: forward function
+    Source: 'src/betree_main.rs', lines 5:0-5:9 *)
+Definition main : result unit :=
   Return tt.
 
 (** Unit test for [betree_main::main] *)
-Check (main_fwd )%return.
+Check (main )%return.
 
-End BetreeMain_Funs .
+End BetreeMain_Funs.
diff --git a/tests/coq/betree/BetreeMain_FunsExternal.v b/tests/coq/betree/BetreeMain_FunsExternal.v
new file mode 100644
index 00000000..07dba263
--- /dev/null
+++ b/tests/coq/betree/BetreeMain_FunsExternal.v
@@ -0,0 +1,46 @@
+(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
+(** [betree_main]: external functions.
+-- This is a template file: rename it to "FunsExternal.lean" and fill the holes. *)
+Require Import Primitives.
+Import Primitives.
+Require Import Coq.ZArith.ZArith.
+Require Import List.
+Import ListNotations.
+Local Open Scope Primitives_scope.
+Require Export BetreeMain_Types.
+Import BetreeMain_Types.
+Module BetreeMain_FunsExternal.
+
+(** [betree_main::betree_utils::load_internal_node]: forward function
+    Source: 'src/betree_utils.rs', lines 98:0-98:63 *)
+Axiom betree_utils_load_internal_node
+  : u64 -> state -> result (state * (betree_List_t (u64 * betree_Message_t)))
+.
+
+(** [betree_main::betree_utils::store_internal_node]: forward function
+    Source: 'src/betree_utils.rs', lines 115:0-115:71 *)
+Axiom betree_utils_store_internal_node
+  :
+  u64 -> betree_List_t (u64 * betree_Message_t) -> state -> result (state *
+    unit)
+.
+
+(** [betree_main::betree_utils::load_leaf_node]: forward function
+    Source: 'src/betree_utils.rs', lines 132:0-132:55 *)
+Axiom betree_utils_load_leaf_node
+  : u64 -> state -> result (state * (betree_List_t (u64 * u64)))
+.
+
+(** [betree_main::betree_utils::store_leaf_node]: forward function
+    Source: 'src/betree_utils.rs', lines 145:0-145:63 *)
+Axiom betree_utils_store_leaf_node
+  : u64 -> betree_List_t (u64 * u64) -> state -> result (state * unit)
+.
+
+(** [core::option::{core::option::Option<T>}::unwrap]: forward function
+    Source: '/rustc/d59363ad0b6391b7fc5bbb02c9ccf9300eef3753/library/core/src/option.rs', lines 932:4-932:34 *)
+Axiom core_option_Option_unwrap :
+  forall(T : Type), option T -> state -> result (state * T)
+.
+
+End BetreeMain_FunsExternal.
diff --git a/tests/coq/betree/BetreeMain_FunsExternal_Template.v b/tests/coq/betree/BetreeMain_FunsExternal_Template.v
new file mode 100644
index 00000000..36022a20
--- /dev/null
+++ b/tests/coq/betree/BetreeMain_FunsExternal_Template.v
@@ -0,0 +1,46 @@
+(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
+(** [betree_main]: external functions.
+-- This is a template file: rename it to "FunsExternal.lean" and fill the holes. *)
+Require Import Primitives.
+Import Primitives.
+Require Import Coq.ZArith.ZArith.
+Require Import List.
+Import ListNotations.
+Local Open Scope Primitives_scope.
+Require Import BetreeMain_Types.
+Include BetreeMain_Types.
+Module BetreeMain_FunsExternal_Template.
+
+(** [betree_main::betree_utils::load_internal_node]: forward function
+    Source: 'src/betree_utils.rs', lines 98:0-98:63 *)
+Axiom betree_utils_load_internal_node
+  : u64 -> state -> result (state * (betree_List_t (u64 * betree_Message_t)))
+.
+
+(** [betree_main::betree_utils::store_internal_node]: forward function
+    Source: 'src/betree_utils.rs', lines 115:0-115:71 *)
+Axiom betree_utils_store_internal_node
+  :
+  u64 -> betree_List_t (u64 * betree_Message_t) -> state -> result (state *
+    unit)
+.
+
+(** [betree_main::betree_utils::load_leaf_node]: forward function
+    Source: 'src/betree_utils.rs', lines 132:0-132:55 *)
+Axiom betree_utils_load_leaf_node
+  : u64 -> state -> result (state * (betree_List_t (u64 * u64)))
+.
+
+(** [betree_main::betree_utils::store_leaf_node]: forward function
+    Source: 'src/betree_utils.rs', lines 145:0-145:63 *)
+Axiom betree_utils_store_leaf_node
+  : u64 -> betree_List_t (u64 * u64) -> state -> result (state * unit)
+.
+
+(** [core::option::{core::option::Option<T>}::unwrap]: forward function
+    Source: '/rustc/d59363ad0b6391b7fc5bbb02c9ccf9300eef3753/library/core/src/option.rs', lines 932:4-932:34 *)
+Axiom core_option_Option_unwrap :
+  forall(T : Type), option T -> state -> result (state * T)
+.
+
+End BetreeMain_FunsExternal_Template.
diff --git a/tests/coq/betree/BetreeMain_Opaque.v b/tests/coq/betree/BetreeMain_Opaque.v
deleted file mode 100644
index ecd81b9d..00000000
--- a/tests/coq/betree/BetreeMain_Opaque.v
+++ /dev/null
@@ -1,40 +0,0 @@
-(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
-(** [betree_main]: external function declarations *)
-Require Import Primitives.
-Import Primitives.
-Require Import Coq.ZArith.ZArith.
-Require Import List.
-Import ListNotations.
-Local Open Scope Primitives_scope.
-Require Export BetreeMain_Types.
-Import BetreeMain_Types.
-Module BetreeMain_Opaque.
-
-(** [betree_main::betree_utils::load_internal_node]: forward function *)
-Axiom betree_utils_load_internal_node_fwd
-  : u64 -> state -> result (state * (Betree_list_t (u64 * Betree_message_t)))
-.
-
-(** [betree_main::betree_utils::store_internal_node]: forward function *)
-Axiom betree_utils_store_internal_node_fwd
-  :
-  u64 -> Betree_list_t (u64 * Betree_message_t) -> state -> result (state *
-    unit)
-.
-
-(** [betree_main::betree_utils::load_leaf_node]: forward function *)
-Axiom betree_utils_load_leaf_node_fwd
-  : u64 -> state -> result (state * (Betree_list_t (u64 * u64)))
-.
-
-(** [betree_main::betree_utils::store_leaf_node]: forward function *)
-Axiom betree_utils_store_leaf_node_fwd
-  : u64 -> Betree_list_t (u64 * u64) -> state -> result (state * unit)
-.
-
-(** [core::option::Option::{0}::unwrap]: forward function *)
-Axiom core_option_option_unwrap_fwd :
-  forall(T : Type), option T -> state -> result (state * T)
-.
-
-End BetreeMain_Opaque .
diff --git a/tests/coq/betree/BetreeMain_Types.v b/tests/coq/betree/BetreeMain_Types.v
index 4a4e75aa..22989256 100644
--- a/tests/coq/betree/BetreeMain_Types.v
+++ b/tests/coq/betree/BetreeMain_Types.v
@@ -6,105 +6,113 @@ Require Import Coq.ZArith.ZArith.
 Require Import List.
 Import ListNotations.
 Local Open Scope Primitives_scope.
+Require Import BetreeMain_TypesExternal.
+Include BetreeMain_TypesExternal.
 Module BetreeMain_Types.
 
-(** [betree_main::betree::List] *)
-Inductive Betree_list_t (T : Type) :=
-| BetreeListCons : T -> Betree_list_t T -> Betree_list_t T
-| BetreeListNil : Betree_list_t T
+(** [betree_main::betree::List]
+    Source: 'src/betree.rs', lines 17:0-17:23 *)
+Inductive betree_List_t (T : Type) :=
+| Betree_List_Cons : T -> betree_List_t T -> betree_List_t T
+| Betree_List_Nil : betree_List_t T
 .
 
-Arguments BetreeListCons {T} _ _.
-Arguments BetreeListNil {T}.
+Arguments Betree_List_Cons { _ }.
+Arguments Betree_List_Nil { _ }.
 
-(** [betree_main::betree::UpsertFunState] *)
-Inductive Betree_upsert_fun_state_t :=
-| BetreeUpsertFunStateAdd : u64 -> Betree_upsert_fun_state_t
-| BetreeUpsertFunStateSub : u64 -> Betree_upsert_fun_state_t
+(** [betree_main::betree::UpsertFunState]
+    Source: 'src/betree.rs', lines 63:0-63:23 *)
+Inductive betree_UpsertFunState_t :=
+| Betree_UpsertFunState_Add : u64 -> betree_UpsertFunState_t
+| Betree_UpsertFunState_Sub : u64 -> betree_UpsertFunState_t
 .
 
-(** [betree_main::betree::Message] *)
-Inductive Betree_message_t :=
-| BetreeMessageInsert : u64 -> Betree_message_t
-| BetreeMessageDelete : Betree_message_t
-| BetreeMessageUpsert : Betree_upsert_fun_state_t -> Betree_message_t
+(** [betree_main::betree::Message]
+    Source: 'src/betree.rs', lines 69:0-69:23 *)
+Inductive betree_Message_t :=
+| Betree_Message_Insert : u64 -> betree_Message_t
+| Betree_Message_Delete : betree_Message_t
+| Betree_Message_Upsert : betree_UpsertFunState_t -> betree_Message_t
 .
 
-(** [betree_main::betree::Leaf] *)
-Record Betree_leaf_t :=
-mkBetree_leaf_t {
-  Betree_leaf_id : u64; Betree_leaf_size : u64;
+(** [betree_main::betree::Leaf]
+    Source: 'src/betree.rs', lines 167:0-167:11 *)
+Record betree_Leaf_t :=
+mkbetree_Leaf_t {
+  betree_Leaf_id : u64; betree_Leaf_size : u64;
 }
 .
 
-(** [betree_main::betree::Internal] *)
-Inductive Betree_internal_t :=
-| mkBetree_internal_t :
+(** [betree_main::betree::Internal]
+    Source: 'src/betree.rs', lines 156:0-156:15 *)
+Inductive betree_Internal_t :=
+| mkbetree_Internal_t :
   u64 ->
   u64 ->
-  Betree_node_t ->
-  Betree_node_t ->
-  Betree_internal_t
-
-(** [betree_main::betree::Node] *)
-with Betree_node_t :=
-| BetreeNodeInternal : Betree_internal_t -> Betree_node_t
-| BetreeNodeLeaf : Betree_leaf_t -> Betree_node_t
+  betree_Node_t ->
+  betree_Node_t ->
+  betree_Internal_t
+
+(** [betree_main::betree::Node]
+    Source: 'src/betree.rs', lines 179:0-179:9 *)
+with betree_Node_t :=
+| Betree_Node_Internal : betree_Internal_t -> betree_Node_t
+| Betree_Node_Leaf : betree_Leaf_t -> betree_Node_t
 .
 
-Definition Betree_internal_id (x : Betree_internal_t) :=
-  match x with | mkBetree_internal_t x0 _ _ _ => x0 end
+Definition betree_Internal_id (x : betree_Internal_t) :=
+  match x with | mkbetree_Internal_t x0 _ _ _ => x0 end
 .
 
-Notation "x1 .(Betree_internal_id)" := (Betree_internal_id x1) (at level 9).
+Notation "x1 .(betree_Internal_id)" := (betree_Internal_id x1) (at level 9).
 
-Definition Betree_internal_pivot (x : Betree_internal_t) :=
-  match x with | mkBetree_internal_t _ x0 _ _ => x0 end
+Definition betree_Internal_pivot (x : betree_Internal_t) :=
+  match x with | mkbetree_Internal_t _ x0 _ _ => x0 end
 .
 
-Notation "x1 .(Betree_internal_pivot)" := (Betree_internal_pivot x1)
+Notation "x1 .(betree_Internal_pivot)" := (betree_Internal_pivot x1)
   (at level 9)
 .
 
-Definition Betree_internal_left (x : Betree_internal_t) :=
-  match x with | mkBetree_internal_t _ _ x0 _ => x0 end
+Definition betree_Internal_left (x : betree_Internal_t) :=
+  match x with | mkbetree_Internal_t _ _ x0 _ => x0 end
 .
 
-Notation "x1 .(Betree_internal_left)" := (Betree_internal_left x1) (at level 9)
+Notation "x1 .(betree_Internal_left)" := (betree_Internal_left x1) (at level 9)
 .
 
-Definition Betree_internal_right (x : Betree_internal_t) :=
-  match x with | mkBetree_internal_t _ _ _ x0 => x0 end
+Definition betree_Internal_right (x : betree_Internal_t) :=
+  match x with | mkbetree_Internal_t _ _ _ x0 => x0 end
 .
 
-Notation "x1 .(Betree_internal_right)" := (Betree_internal_right x1)
+Notation "x1 .(betree_Internal_right)" := (betree_Internal_right x1)
   (at level 9)
 .
 
-(** [betree_main::betree::Params] *)
-Record Betree_params_t :=
-mkBetree_params_t {
-  Betree_params_min_flush_size : u64; Betree_params_split_size : u64;
+(** [betree_main::betree::Params]
+    Source: 'src/betree.rs', lines 187:0-187:13 *)
+Record betree_Params_t :=
+mkbetree_Params_t {
+  betree_Params_min_flush_size : u64; betree_Params_split_size : u64;
 }
 .
 
-(** [betree_main::betree::NodeIdCounter] *)
-Record Betree_node_id_counter_t :=
-mkBetree_node_id_counter_t {
-  Betree_node_id_counter_next_node_id : u64;
+(** [betree_main::betree::NodeIdCounter]
+    Source: 'src/betree.rs', lines 201:0-201:20 *)
+Record betree_NodeIdCounter_t :=
+mkbetree_NodeIdCounter_t {
+  betree_NodeIdCounter_next_node_id : u64;
 }
 .
 
-(** [betree_main::betree::BeTree] *)
-Record Betree_be_tree_t :=
-mkBetree_be_tree_t {
-  Betree_be_tree_params : Betree_params_t;
-  Betree_be_tree_node_id_cnt : Betree_node_id_counter_t;
-  Betree_be_tree_root : Betree_node_t;
+(** [betree_main::betree::BeTree]
+    Source: 'src/betree.rs', lines 218:0-218:17 *)
+Record betree_BeTree_t :=
+mkbetree_BeTree_t {
+  betree_BeTree_params : betree_Params_t;
+  betree_BeTree_node_id_cnt : betree_NodeIdCounter_t;
+  betree_BeTree_root : betree_Node_t;
 }
 .
 
-(** The state type used in the state-error monad *)
-Axiom state : Type.
-
-End BetreeMain_Types .
+End BetreeMain_Types.
diff --git a/tests/coq/betree/BetreeMain_TypesExternal.v b/tests/coq/betree/BetreeMain_TypesExternal.v
new file mode 100644
index 00000000..50c4a4f8
--- /dev/null
+++ b/tests/coq/betree/BetreeMain_TypesExternal.v
@@ -0,0 +1,15 @@
+(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
+(** [betree_main]: external types.
+-- This is a template file: rename it to "TypesExternal.lean" and fill the holes. *)
+Require Import Primitives.
+Import Primitives.
+Require Import Coq.ZArith.ZArith.
+Require Import List.
+Import ListNotations.
+Local Open Scope Primitives_scope.
+Module BetreeMain_TypesExternal.
+
+(** The state type used in the state-error monad *)
+Axiom state : Type.
+
+End BetreeMain_TypesExternal.
diff --git a/tests/coq/betree/BetreeMain_TypesExternal_Template.v b/tests/coq/betree/BetreeMain_TypesExternal_Template.v
new file mode 100644
index 00000000..651de2b7
--- /dev/null
+++ b/tests/coq/betree/BetreeMain_TypesExternal_Template.v
@@ -0,0 +1,15 @@
+(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
+(** [betree_main]: external types.
+-- This is a template file: rename it to "TypesExternal.lean" and fill the holes. *)
+Require Import Primitives.
+Import Primitives.
+Require Import Coq.ZArith.ZArith.
+Require Import List.
+Import ListNotations.
+Local Open Scope Primitives_scope.
+Module BetreeMain_TypesExternal_Template.
+
+(** The state type used in the state-error monad *)
+Axiom state : Type.
+
+End BetreeMain_TypesExternal_Template.
diff --git a/tests/coq/betree/Primitives.v b/tests/coq/betree/Primitives.v
index 71a2d9c3..99ffe070 100644
--- a/tests/coq/betree/Primitives.v
+++ b/tests/coq/betree/Primitives.v
@@ -63,13 +63,15 @@ Check (if true then Return (1 + 2) else Fail_ Failure)%global = 3.
 
 (*** Misc *)
 
-
 Definition string := Coq.Strings.String.string.
 Definition char := Coq.Strings.Ascii.ascii.
 Definition char_of_byte := Coq.Strings.Ascii.ascii_of_byte.
 
-Definition mem_replace_fwd (a : Type) (x : a) (y : a) : a := x .
-Definition mem_replace_back (a : Type) (x : a) (y : a) : a := y .
+Definition core_mem_replace (a : Type) (x : a) (y : a) : a := x .
+Definition core_mem_replace_back (a : Type) (x : a) (y : a) : a := y .
+
+Record mut_raw_ptr (T : Type) := { mut_raw_ptr_v : T }.
+Record const_raw_ptr (T : Type) := { const_raw_ptr_v : T }.
 
 (*** Scalars *)
 
@@ -253,6 +255,12 @@ Definition scalar_rem {ty} (x y: scalar ty) : result (scalar ty) := mk_scalar ty
   
 Definition scalar_neg {ty} (x: scalar ty) : result (scalar ty) := mk_scalar ty (-(to_Z x)).
 
+Axiom scalar_xor : forall ty, scalar ty -> scalar ty -> scalar ty. (* TODO *)
+Axiom scalar_or : forall ty, scalar ty -> scalar ty -> scalar ty. (* TODO *)
+Axiom scalar_and : forall ty, scalar ty -> scalar ty -> scalar ty. (* TODO *)
+Axiom scalar_shl : forall ty0 ty1, scalar ty0 -> scalar ty1 -> result (scalar ty0). (* TODO *)
+Axiom scalar_shr : forall ty0 ty1, scalar ty0 -> scalar ty1 -> result (scalar ty0). (* TODO *)
+
 (** Cast an integer from a [src_ty] to a [tgt_ty] *)
 (* TODO: check the semantics of casts in Rust *)
 Definition scalar_cast (src_ty tgt_ty : scalar_ty) (x : scalar src_ty) : result (scalar tgt_ty) :=
@@ -370,6 +378,76 @@ Definition u32_mul   := @scalar_mul U32.
 Definition u64_mul   := @scalar_mul U64.
 Definition u128_mul  := @scalar_mul U128.
 
+(** Xor *)
+Definition u8_xor := @scalar_xor U8.
+Definition u16_xor := @scalar_xor U16.
+Definition u32_xor := @scalar_xor U32.
+Definition u64_xor := @scalar_xor U64.
+Definition u128_xor := @scalar_xor U128.
+Definition usize_xor := @scalar_xor Usize.
+Definition i8_xor := @scalar_xor I8.
+Definition i16_xor := @scalar_xor I16.
+Definition i32_xor := @scalar_xor I32.
+Definition i64_xor := @scalar_xor I64.
+Definition i128_xor := @scalar_xor I128.
+Definition isize_xor := @scalar_xor Isize.
+
+(** Or *)
+Definition u8_or := @scalar_or U8.
+Definition u16_or := @scalar_or U16.
+Definition u32_or := @scalar_or U32.
+Definition u64_or := @scalar_or U64.
+Definition u128_or := @scalar_or U128.
+Definition usize_or := @scalar_or Usize.
+Definition i8_or := @scalar_or I8.
+Definition i16_or := @scalar_or I16.
+Definition i32_or := @scalar_or I32.
+Definition i64_or := @scalar_or I64.
+Definition i128_or := @scalar_or I128.
+Definition isize_or := @scalar_or Isize.
+
+(** And *)
+Definition u8_and := @scalar_and U8.
+Definition u16_and := @scalar_and U16.
+Definition u32_and := @scalar_and U32.
+Definition u64_and := @scalar_and U64.
+Definition u128_and := @scalar_and U128.
+Definition usize_and := @scalar_and Usize.
+Definition i8_and := @scalar_and I8.
+Definition i16_and := @scalar_and I16.
+Definition i32_and := @scalar_and I32.
+Definition i64_and := @scalar_and I64.
+Definition i128_and := @scalar_and I128.
+Definition isize_and := @scalar_and Isize.
+
+(** Shift left *)
+Definition u8_shl {ty} := @scalar_shl U8 ty.
+Definition u16_shl {ty} := @scalar_shl U16 ty.
+Definition u32_shl {ty} := @scalar_shl U32 ty.
+Definition u64_shl {ty} := @scalar_shl U64 ty.
+Definition u128_shl {ty} := @scalar_shl U128 ty.
+Definition usize_shl {ty} := @scalar_shl Usize ty.
+Definition i8_shl {ty} := @scalar_shl I8 ty.
+Definition i16_shl {ty} := @scalar_shl I16 ty.
+Definition i32_shl {ty} := @scalar_shl I32 ty.
+Definition i64_shl {ty} := @scalar_shl I64 ty.
+Definition i128_shl {ty} := @scalar_shl I128 ty.
+Definition isize_shl {ty} := @scalar_shl Isize ty.
+
+(** Shift right *)
+Definition u8_shr {ty} := @scalar_shr U8 ty.
+Definition u16_shr {ty} := @scalar_shr U16 ty.
+Definition u32_shr {ty} := @scalar_shr U32 ty.
+Definition u64_shr {ty} := @scalar_shr U64 ty.
+Definition u128_shr {ty} := @scalar_shr U128 ty.
+Definition usize_shr {ty} := @scalar_shr Usize ty.
+Definition i8_shr {ty} := @scalar_shr I8 ty.
+Definition i16_shr {ty} := @scalar_shr I16 ty.
+Definition i32_shr {ty} := @scalar_shr I32 ty.
+Definition i64_shr {ty} := @scalar_shr I64 ty.
+Definition i128_shr {ty} := @scalar_shr I128 ty.
+Definition isize_shr {ty} := @scalar_shr Isize ty.
+
 (** Small utility *)
 Definition usize_to_nat (x: usize) : nat := Z.to_nat (to_Z x).
 
@@ -394,12 +472,89 @@ Notation "x s< y" := (scalar_ltb x y)  (at level 80) : Primitives_scope.
 Notation "x s>= y" := (scalar_geb x y)  (at level 80) : Primitives_scope.
 Notation "x s> y" := (scalar_gtb x y)  (at level 80) : Primitives_scope.
 
-(*** Range *)
-Record range (T : Type) := mk_range {
-  start: T;
-  end_: T;
+(** Constants *)
+Definition core_u8_max    := u8_max %u32.
+Definition core_u16_max   := u16_max %u32.
+Definition core_u32_max   := u32_max %u32.
+Definition core_u64_max   := u64_max %u64.
+Definition core_u128_max  := u64_max %u128.
+Axiom core_usize_max : usize. (** TODO *)
+Definition core_i8_max    := i8_max %i32.
+Definition core_i16_max   := i16_max %i32.
+Definition core_i32_max   := i32_max %i32.
+Definition core_i64_max   := i64_max %i64.
+Definition core_i128_max  := i64_max %i128.
+Axiom core_isize_max : isize. (** TODO *)
+
+(*** core::ops *)
+
+(* Trait declaration: [core::ops::index::Index] *)
+Record core_ops_index_Index (Self Idx : Type) := mk_core_ops_index_Index {
+  core_ops_index_Index_Output : Type;
+  core_ops_index_Index_index : Self -> Idx -> result core_ops_index_Index_Output;
+}.
+Arguments mk_core_ops_index_Index {_ _}.
+Arguments core_ops_index_Index_Output {_ _}.
+Arguments core_ops_index_Index_index {_ _}.
+
+(* Trait declaration: [core::ops::index::IndexMut] *)
+Record core_ops_index_IndexMut (Self Idx : Type) := mk_core_ops_index_IndexMut {
+  core_ops_index_IndexMut_indexInst : core_ops_index_Index Self Idx;
+  core_ops_index_IndexMut_index_mut : Self -> Idx -> result core_ops_index_IndexMut_indexInst.(core_ops_index_Index_Output);
+  core_ops_index_IndexMut_index_mut_back : Self -> Idx -> core_ops_index_IndexMut_indexInst.(core_ops_index_Index_Output) -> result Self;
+}.
+Arguments mk_core_ops_index_IndexMut {_ _}.
+Arguments core_ops_index_IndexMut_indexInst {_ _}.
+Arguments core_ops_index_IndexMut_index_mut {_ _}.
+Arguments core_ops_index_IndexMut_index_mut_back {_ _}.
+
+(* Trait declaration [core::ops::deref::Deref] *)
+Record core_ops_deref_Deref (Self : Type) := mk_core_ops_deref_Deref {
+  core_ops_deref_Deref_target : Type;
+  core_ops_deref_Deref_deref : Self -> result core_ops_deref_Deref_target;
 }.
-Arguments mk_range {_}.
+Arguments mk_core_ops_deref_Deref {_}.
+Arguments core_ops_deref_Deref_target {_}.
+Arguments core_ops_deref_Deref_deref {_}.
+
+(* Trait declaration [core::ops::deref::DerefMut] *)
+Record core_ops_deref_DerefMut (Self : Type) := mk_core_ops_deref_DerefMut {
+  core_ops_deref_DerefMut_derefInst : core_ops_deref_Deref Self;
+  core_ops_deref_DerefMut_deref_mut : Self -> result core_ops_deref_DerefMut_derefInst.(core_ops_deref_Deref_target);
+  core_ops_deref_DerefMut_deref_mut_back : Self -> core_ops_deref_DerefMut_derefInst.(core_ops_deref_Deref_target) -> result Self;
+}.
+Arguments mk_core_ops_deref_DerefMut {_}.
+Arguments core_ops_deref_DerefMut_derefInst {_}.
+Arguments core_ops_deref_DerefMut_deref_mut {_}.
+Arguments core_ops_deref_DerefMut_deref_mut_back {_}.
+
+Record core_ops_range_Range (T : Type) := mk_core_ops_range_Range {
+  core_ops_range_Range_start : T;
+  core_ops_range_Range_end_ : T;
+}.
+Arguments mk_core_ops_range_Range {_}.
+Arguments core_ops_range_Range_start {_}.
+Arguments core_ops_range_Range_end_ {_}.
+
+(*** [alloc] *)
+
+Definition alloc_boxed_Box_deref (T : Type) (x : T) : result T := Return x.
+Definition alloc_boxed_Box_deref_mut (T : Type) (x : T) : result T := Return x.
+Definition alloc_boxed_Box_deref_mut_back (T : Type) (_ : T) (x : T) : result T := Return x.
+
+(* Trait instance *)
+Definition alloc_boxed_Box_coreopsDerefInst (Self : Type) : core_ops_deref_Deref Self := {|
+  core_ops_deref_Deref_target := Self;
+  core_ops_deref_Deref_deref := alloc_boxed_Box_deref Self;
+|}.
+
+(* Trait instance *)
+Definition alloc_boxed_Box_coreopsDerefMutInst (Self : Type) : core_ops_deref_DerefMut Self := {|
+  core_ops_deref_DerefMut_derefInst := alloc_boxed_Box_coreopsDerefInst Self;
+  core_ops_deref_DerefMut_deref_mut := alloc_boxed_Box_deref_mut Self;
+  core_ops_deref_DerefMut_deref_mut_back := alloc_boxed_Box_deref_mut_back Self;
+|}.
+
 
 (*** Arrays *)
 Definition array T (n : usize) := { l: list T | Z.of_nat (length l) = to_Z n}.
@@ -419,51 +574,50 @@ Qed.
 (* TODO: finish the definitions *)
 Axiom mk_array : forall (T : Type) (n : usize) (l : list T), array T n.
 
-Axiom array_index_shared : forall (T : Type) (n : usize) (x : array T n) (i : usize), result T.
-Axiom array_index_mut_fwd : forall (T : Type) (n : usize) (x : array T n) (i : usize), result T.
-Axiom array_index_mut_back : forall (T : Type) (n : usize) (x : array T n) (i : usize) (nx : T), result (array T n).
+(* For initialization *)
+Axiom array_repeat : forall (T : Type) (n : usize) (x : T), array T n.
+
+Axiom array_index_usize : forall (T : Type) (n : usize) (x : array T n) (i : usize), result T.
+Axiom array_update_usize : forall (T : Type) (n : usize) (x : array T n) (i : usize) (nx : T), result (array T n).
 
 (*** Slice *)
 Definition slice T := { l: list T | Z.of_nat (length l) <= usize_max}.
 
 Axiom slice_len : forall (T : Type) (s : slice T), usize.
-Axiom slice_index_shared : forall (T : Type) (x : slice T) (i : usize), result T.
-Axiom slice_index_mut_fwd : forall (T : Type) (x : slice T) (i : usize), result T.
-Axiom slice_index_mut_back : forall (T : Type) (x : slice T) (i : usize) (nx : T), result (slice T).
+Axiom slice_index_usize : forall (T : Type) (x : slice T) (i : usize), result T.
+Axiom slice_update_usize : forall (T : Type) (x : slice T) (i : usize) (nx : T), result (slice T).
 
 (*** Subslices *)
 
-Axiom array_to_slice_shared : forall (T : Type) (n : usize) (x : array T n), result (slice T).
-Axiom array_to_slice_mut_fwd : forall (T : Type) (n : usize) (x : array T n), result (slice T).
-Axiom array_to_slice_mut_back : forall (T : Type) (n : usize) (x : array T n) (s : slice T), result (array T n).
+Axiom array_to_slice : forall (T : Type) (n : usize) (x : array T n), result (slice T).
+Axiom array_from_slice : forall (T : Type) (n : usize) (x : array T n) (s : slice T), result (array T n).
 
-Axiom array_subslice_shared: forall (T : Type) (n : usize) (x : array T n) (r : range usize), result (slice T).
-Axiom array_subslice_mut_fwd: forall (T : Type) (n : usize) (x : array T n) (r : range usize), result (slice T).
-Axiom array_subslice_mut_back: forall (T : Type) (n : usize) (x : array T n) (r : range usize) (ns : slice T), result (array T n).
-Axiom slice_subslice_shared: forall (T : Type) (x : slice T) (r : range usize), result (slice T).
-Axiom slice_subslice_mut_fwd: forall (T : Type) (x : slice T) (r : range usize), result (slice T).
-Axiom slice_subslice_mut_back: forall (T : Type) (x : slice T) (r : range usize) (ns : slice T), result (slice T).
+Axiom array_subslice: forall (T : Type) (n : usize) (x : array T n) (r : core_ops_range_Range usize), result (slice T).
+Axiom array_update_subslice: forall (T : Type) (n : usize) (x : array T n) (r : core_ops_range_Range usize) (ns : slice T), result (array T n).
+
+Axiom slice_subslice: forall (T : Type) (x : slice T) (r : core_ops_range_Range usize), result (slice T).
+Axiom slice_update_subslice: forall (T : Type) (x : slice T) (r : core_ops_range_Range usize) (ns : slice T), result (slice T).
 
 (*** Vectors *)
 
-Definition vec T := { l: list T | Z.of_nat (length l) <= usize_max }.
+Definition alloc_vec_Vec T := { l: list T | Z.of_nat (length l) <= usize_max }.
 
-Definition vec_to_list {T: Type} (v: vec T) : list T := proj1_sig v.
+Definition alloc_vec_Vec_to_list {T: Type} (v: alloc_vec_Vec T) : list T := proj1_sig v.
 
-Definition vec_length {T: Type} (v: vec T) : Z := Z.of_nat (length (vec_to_list v)).
+Definition alloc_vec_Vec_length {T: Type} (v: alloc_vec_Vec T) : Z := Z.of_nat (length (alloc_vec_Vec_to_list v)).
 
-Definition vec_new (T: Type) : vec T := (exist _ [] le_0_usize_max).
+Definition alloc_vec_Vec_new (T: Type) : alloc_vec_Vec T := (exist _ [] le_0_usize_max).
 
-Lemma vec_len_in_usize {T} (v: vec T) : usize_min <= vec_length v <= usize_max.
+Lemma alloc_vec_Vec_len_in_usize {T} (v: alloc_vec_Vec T) : usize_min <= alloc_vec_Vec_length v <= usize_max.
 Proof.
-  unfold vec_length, usize_min.
+  unfold alloc_vec_Vec_length, usize_min.
   split.
   - lia.
   - apply (proj2_sig v).
 Qed.
 
-Definition vec_len (T: Type) (v: vec T) : usize :=
-  exist _ (vec_length v) (vec_len_in_usize v).
+Definition alloc_vec_Vec_len (T: Type) (v: alloc_vec_Vec T) : usize :=
+  exist _ (alloc_vec_Vec_length v) (alloc_vec_Vec_len_in_usize v).
 
 Fixpoint list_update {A} (l: list A) (n: nat) (a: A)
   : list A :=
@@ -474,50 +628,279 @@ Fixpoint list_update {A} (l: list A) (n: nat) (a: A)
     | S m => x :: (list_update t m a)
 end end.
 
-Definition vec_bind {A B} (v: vec A) (f: list A -> result (list B)) : result (vec B) :=
-  l <- f (vec_to_list v) ;
+Definition alloc_vec_Vec_bind {A B} (v: alloc_vec_Vec A) (f: list A -> result (list B)) : result (alloc_vec_Vec B) :=
+  l <- f (alloc_vec_Vec_to_list v) ;
   match sumbool_of_bool (scalar_le_max Usize (Z.of_nat (length l))) with
   | left H => Return (exist _ l (scalar_le_max_valid _ _ H))
   | right _ => Fail_ Failure
   end.
 
 (* The **forward** function shouldn't be used *)
-Definition vec_push_fwd (T: Type) (v: vec T) (x: T) : unit := tt.
+Definition alloc_vec_Vec_push_fwd (T: Type) (v: alloc_vec_Vec T) (x: T) : unit := tt.
 
-Definition vec_push_back (T: Type) (v: vec T) (x: T) : result (vec T) :=
-  vec_bind v (fun l => Return (l ++ [x])).
+Definition alloc_vec_Vec_push (T: Type) (v: alloc_vec_Vec T) (x: T) : result (alloc_vec_Vec T) :=
+  alloc_vec_Vec_bind v (fun l => Return (l ++ [x])).
 
 (* The **forward** function shouldn't be used *)
-Definition vec_insert_fwd (T: Type) (v: vec T) (i: usize) (x: T) : result unit :=
-  if to_Z i <? vec_length v then Return tt else Fail_ Failure.
+Definition alloc_vec_Vec_insert_fwd (T: Type) (v: alloc_vec_Vec T) (i: usize) (x: T) : result unit :=
+  if to_Z i <? alloc_vec_Vec_length v then Return tt else Fail_ Failure.
 
-Definition vec_insert_back (T: Type) (v: vec T) (i: usize) (x: T) : result (vec T) :=
-  vec_bind v (fun l =>
+Definition alloc_vec_Vec_insert (T: Type) (v: alloc_vec_Vec T) (i: usize) (x: T) : result (alloc_vec_Vec T) :=
+  alloc_vec_Vec_bind v (fun l =>
     if to_Z i <? Z.of_nat (length l)
     then Return (list_update l (usize_to_nat i) x)
     else Fail_ Failure).
 
-(* The **backward** function shouldn't be used *)
-Definition vec_index_fwd (T: Type) (v: vec T) (i: usize) : result T :=
-  match nth_error (vec_to_list v) (usize_to_nat i) with
-  | Some n => Return n
-  | None   => Fail_ Failure
-  end.
-
-Definition vec_index_back (T: Type) (v: vec T) (i: usize) (x: T) : result unit :=
-  if to_Z i <? vec_length v then Return tt else Fail_ Failure.
-
-(* The **backward** function shouldn't be used *)
-Definition vec_index_mut_fwd (T: Type) (v: vec T) (i: usize) : result T :=
-  match nth_error (vec_to_list v) (usize_to_nat i) with
-  | Some n => Return n
-  | None   => Fail_ Failure
+(* Helper *)
+Axiom alloc_vec_Vec_index_usize : forall {T : Type} (v : alloc_vec_Vec T) (i : usize), result T.
+
+(* Helper *)
+Axiom alloc_vec_Vec_update_usize : forall {T : Type} (v : alloc_vec_Vec T) (i : usize) (x : T), result (alloc_vec_Vec T).
+
+(* Trait declaration: [core::slice::index::private_slice_index::Sealed] *)
+Definition core_slice_index_private_slice_index_Sealed (self : Type) := unit.
+
+(* Trait declaration: [core::slice::index::SliceIndex] *)
+Record core_slice_index_SliceIndex (Self T : Type) := mk_core_slice_index_SliceIndex {
+  core_slice_index_SliceIndex_sealedInst : core_slice_index_private_slice_index_Sealed Self;
+  core_slice_index_SliceIndex_Output : Type;
+  core_slice_index_SliceIndex_get : Self -> T -> result (option core_slice_index_SliceIndex_Output);
+  core_slice_index_SliceIndex_get_mut : Self -> T -> result (option core_slice_index_SliceIndex_Output);
+  core_slice_index_SliceIndex_get_mut_back : Self -> T -> option core_slice_index_SliceIndex_Output -> result T;
+  core_slice_index_SliceIndex_get_unchecked : Self -> const_raw_ptr T -> result (const_raw_ptr core_slice_index_SliceIndex_Output);
+  core_slice_index_SliceIndex_get_unchecked_mut : Self -> mut_raw_ptr T -> result (mut_raw_ptr core_slice_index_SliceIndex_Output);
+  core_slice_index_SliceIndex_index : Self -> T -> result core_slice_index_SliceIndex_Output;
+  core_slice_index_SliceIndex_index_mut : Self -> T -> result core_slice_index_SliceIndex_Output;
+  core_slice_index_SliceIndex_index_mut_back : Self -> T -> core_slice_index_SliceIndex_Output -> result T;
+}.
+Arguments mk_core_slice_index_SliceIndex {_ _}.
+Arguments core_slice_index_SliceIndex_sealedInst {_ _}.
+Arguments core_slice_index_SliceIndex_Output {_ _}.
+Arguments core_slice_index_SliceIndex_get {_ _}.
+Arguments core_slice_index_SliceIndex_get_mut {_ _}.
+Arguments core_slice_index_SliceIndex_get_mut_back {_ _}.
+Arguments core_slice_index_SliceIndex_get_unchecked {_ _}.
+Arguments core_slice_index_SliceIndex_get_unchecked_mut {_ _}.
+Arguments core_slice_index_SliceIndex_index {_ _}.
+Arguments core_slice_index_SliceIndex_index_mut {_ _}.
+Arguments core_slice_index_SliceIndex_index_mut_back {_ _}.
+
+(* [core::slice::index::[T]::index]: forward function *)
+Definition core_slice_index_Slice_index
+  (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T))
+  (s : slice T) (i : Idx) : result inst.(core_slice_index_SliceIndex_Output) :=
+  x <- inst.(core_slice_index_SliceIndex_get) i s;
+  match x with
+  | None => Fail_ Failure
+  | Some x => Return x
   end.
 
-Definition vec_index_mut_back (T: Type) (v: vec T) (i: usize) (x: T) : result (vec T) :=
-  vec_bind v (fun l =>
-    if to_Z i <? Z.of_nat (length l)
-    then Return (list_update l (usize_to_nat i) x)
-    else Fail_ Failure).
+(* [core::slice::index::Range:::get]: forward function *)
+Axiom core_slice_index_RangeUsize_get : forall (T : Type) (i : core_ops_range_Range usize) (s : slice T), result (option (slice T)).
+
+(* [core::slice::index::Range::get_mut]: forward function *)
+Axiom core_slice_index_RangeUsize_get_mut :
+  forall (T : Type), core_ops_range_Range usize -> slice T -> result (option (slice T)).
+
+(* [core::slice::index::Range::get_mut]: backward function 0 *)
+Axiom core_slice_index_RangeUsize_get_mut_back :
+  forall (T : Type), core_ops_range_Range usize -> slice T -> option (slice T) -> result (slice T).
+
+(* [core::slice::index::Range::get_unchecked]: forward function *)
+Definition core_slice_index_RangeUsize_get_unchecked
+  (T : Type) :
+  core_ops_range_Range usize -> const_raw_ptr (slice T) -> result (const_raw_ptr (slice T)) :=
+  (* Don't know what the model should be - for now we always fail to make
+     sure code which uses it fails *)
+  fun _ _ => Fail_ Failure.
+
+(* [core::slice::index::Range::get_unchecked_mut]: forward function *)
+Definition core_slice_index_RangeUsize_get_unchecked_mut
+  (T : Type) :
+  core_ops_range_Range usize -> mut_raw_ptr (slice T) -> result (mut_raw_ptr (slice T)) :=
+  (* Don't know what the model should be - for now we always fail to make
+    sure code which uses it fails *)
+  fun _ _ => Fail_ Failure.
+
+(* [core::slice::index::Range::index]: forward function *)
+Axiom core_slice_index_RangeUsize_index :
+  forall (T : Type), core_ops_range_Range usize -> slice T -> result (slice T).
+
+(* [core::slice::index::Range::index_mut]: forward function *)
+Axiom core_slice_index_RangeUsize_index_mut :
+  forall (T : Type), core_ops_range_Range usize -> slice T -> result (slice T).
+
+(* [core::slice::index::Range::index_mut]: backward function 0 *)
+Axiom core_slice_index_RangeUsize_index_mut_back :
+  forall (T : Type), core_ops_range_Range usize -> slice T -> slice T -> result (slice T).
+
+(* [core::slice::index::[T]::index_mut]: forward function *)
+Axiom core_slice_index_Slice_index_mut :
+  forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T)),
+  slice T -> Idx -> result inst.(core_slice_index_SliceIndex_Output).
+
+(* [core::slice::index::[T]::index_mut]: backward function 0 *)
+Axiom core_slice_index_Slice_index_mut_back :
+  forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T)),
+  slice T -> Idx -> inst.(core_slice_index_SliceIndex_Output) -> result (slice T).
+
+(* [core::array::[T; N]::index]: forward function *)
+Axiom core_array_Array_index :
+  forall (T Idx : Type) (N : usize) (inst : core_ops_index_Index (slice T) Idx)
+  (a : array T N) (i : Idx), result inst.(core_ops_index_Index_Output).
+
+(* [core::array::[T; N]::index_mut]: forward function *)
+Axiom core_array_Array_index_mut :
+  forall (T Idx : Type) (N : usize) (inst : core_ops_index_IndexMut (slice T) Idx)
+  (a : array T N) (i : Idx), result inst.(core_ops_index_IndexMut_indexInst).(core_ops_index_Index_Output).
+
+(* [core::array::[T; N]::index_mut]: backward function 0 *)
+Axiom core_array_Array_index_mut_back :
+  forall (T Idx : Type) (N : usize) (inst : core_ops_index_IndexMut (slice T) Idx)
+  (a : array T N) (i : Idx) (x : inst.(core_ops_index_IndexMut_indexInst).(core_ops_index_Index_Output)), result (array T N).
+
+(* Trait implementation: [core::slice::index::private_slice_index::Range] *)
+Definition core_slice_index_private_slice_index_SealedRangeUsizeInst
+  : core_slice_index_private_slice_index_Sealed (core_ops_range_Range usize) := tt.
+
+(* Trait implementation: [core::slice::index::Range] *)
+Definition core_slice_index_SliceIndexRangeUsizeSliceTInst (T : Type) :
+  core_slice_index_SliceIndex (core_ops_range_Range usize) (slice T) := {|
+  core_slice_index_SliceIndex_sealedInst := core_slice_index_private_slice_index_SealedRangeUsizeInst;
+  core_slice_index_SliceIndex_Output := slice T;
+  core_slice_index_SliceIndex_get := core_slice_index_RangeUsize_get T;
+  core_slice_index_SliceIndex_get_mut := core_slice_index_RangeUsize_get_mut T;
+  core_slice_index_SliceIndex_get_mut_back := core_slice_index_RangeUsize_get_mut_back T;
+  core_slice_index_SliceIndex_get_unchecked := core_slice_index_RangeUsize_get_unchecked T;
+  core_slice_index_SliceIndex_get_unchecked_mut := core_slice_index_RangeUsize_get_unchecked_mut T;
+  core_slice_index_SliceIndex_index := core_slice_index_RangeUsize_index T;
+  core_slice_index_SliceIndex_index_mut := core_slice_index_RangeUsize_index_mut T;
+  core_slice_index_SliceIndex_index_mut_back := core_slice_index_RangeUsize_index_mut_back T;
+|}.
+
+(* Trait implementation: [core::slice::index::[T]] *)
+Definition core_ops_index_IndexSliceTIInst (T Idx : Type)
+  (inst : core_slice_index_SliceIndex Idx (slice T)) :
+  core_ops_index_Index (slice T) Idx := {|
+  core_ops_index_Index_Output := inst.(core_slice_index_SliceIndex_Output);
+  core_ops_index_Index_index := core_slice_index_Slice_index T Idx inst;
+|}.
+
+(* Trait implementation: [core::slice::index::[T]] *)
+Definition core_ops_index_IndexMutSliceTIInst (T Idx : Type)
+  (inst : core_slice_index_SliceIndex Idx (slice T)) :
+  core_ops_index_IndexMut (slice T) Idx := {|
+  core_ops_index_IndexMut_indexInst := core_ops_index_IndexSliceTIInst T Idx inst;
+  core_ops_index_IndexMut_index_mut := core_slice_index_Slice_index_mut T Idx inst;
+  core_ops_index_IndexMut_index_mut_back := core_slice_index_Slice_index_mut_back T Idx inst;
+|}.
+
+(* Trait implementation: [core::array::[T; N]] *)
+Definition core_ops_index_IndexArrayInst (T Idx : Type) (N : usize)
+  (inst : core_ops_index_Index (slice T) Idx) :
+  core_ops_index_Index (array T N) Idx := {|
+  core_ops_index_Index_Output := inst.(core_ops_index_Index_Output);
+  core_ops_index_Index_index := core_array_Array_index T Idx N inst;
+|}.
+
+(* Trait implementation: [core::array::[T; N]] *)
+Definition core_ops_index_IndexMutArrayInst (T Idx : Type) (N : usize)
+  (inst : core_ops_index_IndexMut (slice T) Idx) :
+  core_ops_index_IndexMut (array T N) Idx := {|
+  core_ops_index_IndexMut_indexInst := core_ops_index_IndexArrayInst T Idx N inst.(core_ops_index_IndexMut_indexInst);
+  core_ops_index_IndexMut_index_mut := core_array_Array_index_mut T Idx N inst;
+  core_ops_index_IndexMut_index_mut_back := core_array_Array_index_mut_back T Idx N inst;
+|}.
+
+(* [core::slice::index::usize::get]: forward function *)
+Axiom core_slice_index_usize_get : forall (T : Type), usize -> slice T -> result (option T).
+
+(* [core::slice::index::usize::get_mut]: forward function *)
+Axiom core_slice_index_usize_get_mut : forall (T : Type), usize -> slice T -> result (option T).
+
+(* [core::slice::index::usize::get_mut]: backward function 0 *)
+Axiom core_slice_index_usize_get_mut_back :
+  forall (T : Type), usize -> slice T -> option T -> result (slice T).
+
+(* [core::slice::index::usize::get_unchecked]: forward function *)
+Axiom core_slice_index_usize_get_unchecked :
+  forall (T : Type), usize -> const_raw_ptr (slice T) -> result (const_raw_ptr T).
+
+(* [core::slice::index::usize::get_unchecked_mut]: forward function *)
+Axiom core_slice_index_usize_get_unchecked_mut :
+  forall (T : Type), usize -> mut_raw_ptr (slice T) -> result (mut_raw_ptr T).
+
+(* [core::slice::index::usize::index]: forward function *)
+Axiom core_slice_index_usize_index : forall (T : Type), usize -> slice T -> result T.
+
+(* [core::slice::index::usize::index_mut]: forward function *)
+Axiom core_slice_index_usize_index_mut : forall (T : Type), usize -> slice T -> result T.
+
+(* [core::slice::index::usize::index_mut]: backward function 0 *)
+Axiom core_slice_index_usize_index_mut_back :
+  forall (T : Type), usize -> slice T -> T -> result (slice T).
+
+(* Trait implementation: [core::slice::index::private_slice_index::usize] *)
+Definition core_slice_index_private_slice_index_SealedUsizeInst
+  : core_slice_index_private_slice_index_Sealed usize := tt.
+
+(* Trait implementation: [core::slice::index::usize] *)
+Definition core_slice_index_SliceIndexUsizeSliceTInst (T : Type) :
+  core_slice_index_SliceIndex usize (slice T) := {|
+  core_slice_index_SliceIndex_sealedInst := core_slice_index_private_slice_index_SealedUsizeInst;
+  core_slice_index_SliceIndex_Output := T;
+  core_slice_index_SliceIndex_get := core_slice_index_usize_get T;
+  core_slice_index_SliceIndex_get_mut := core_slice_index_usize_get_mut T;
+  core_slice_index_SliceIndex_get_mut_back := core_slice_index_usize_get_mut_back T;
+  core_slice_index_SliceIndex_get_unchecked := core_slice_index_usize_get_unchecked T;
+  core_slice_index_SliceIndex_get_unchecked_mut := core_slice_index_usize_get_unchecked_mut T;
+  core_slice_index_SliceIndex_index := core_slice_index_usize_index T;
+  core_slice_index_SliceIndex_index_mut := core_slice_index_usize_index_mut T;
+  core_slice_index_SliceIndex_index_mut_back := core_slice_index_usize_index_mut_back T;
+|}.
+
+(* [alloc::vec::Vec::index]: forward function *)
+Axiom alloc_vec_Vec_index : forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T))
+  (Self : alloc_vec_Vec T) (i : Idx), result inst.(core_slice_index_SliceIndex_Output).
+
+(* [alloc::vec::Vec::index_mut]: forward function *)
+Axiom alloc_vec_Vec_index_mut : forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T))
+  (Self : alloc_vec_Vec T) (i : Idx), result inst.(core_slice_index_SliceIndex_Output).
+
+(* [alloc::vec::Vec::index_mut]: backward function 0 *)
+Axiom alloc_vec_Vec_index_mut_back :
+  forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T))
+  (Self : alloc_vec_Vec T) (i : Idx) (x : inst.(core_slice_index_SliceIndex_Output)), result (alloc_vec_Vec T).
+
+(* Trait implementation: [alloc::vec::Vec] *)
+Definition alloc_vec_Vec_coreopsindexIndexInst (T Idx : Type)
+  (inst : core_slice_index_SliceIndex Idx (slice T)) :
+  core_ops_index_Index (alloc_vec_Vec T) Idx := {|
+  core_ops_index_Index_Output := inst.(core_slice_index_SliceIndex_Output);
+  core_ops_index_Index_index := alloc_vec_Vec_index T Idx inst;
+|}.
+
+(* Trait implementation: [alloc::vec::Vec] *)
+Definition alloc_vec_Vec_coreopsindexIndexMutInst (T Idx : Type)
+  (inst : core_slice_index_SliceIndex Idx (slice T)) :
+  core_ops_index_IndexMut (alloc_vec_Vec T) Idx := {|
+  core_ops_index_IndexMut_indexInst := alloc_vec_Vec_coreopsindexIndexInst T Idx inst;
+  core_ops_index_IndexMut_index_mut := alloc_vec_Vec_index_mut T Idx inst;
+  core_ops_index_IndexMut_index_mut_back := alloc_vec_Vec_index_mut_back T Idx inst;
+|}.
+
+(*** Theorems *)
+
+Axiom alloc_vec_Vec_index_eq : forall {a : Type} (v : alloc_vec_Vec a) (i : usize) (x : a),
+  alloc_vec_Vec_index a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i =
+    alloc_vec_Vec_index_usize v i.
+
+Axiom alloc_vec_Vec_index_mut_eq : forall {a : Type} (v : alloc_vec_Vec a) (i : usize) (x : a),
+  alloc_vec_Vec_index_mut a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i =
+    alloc_vec_Vec_index_usize v i.
+
+Axiom alloc_vec_Vec_index_mut_back_eq : forall {a : Type} (v : alloc_vec_Vec a) (i : usize) (x : a),
+  alloc_vec_Vec_index_mut_back a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i x =
+    alloc_vec_Vec_update_usize v i x.
 
 End Primitives.
diff --git a/tests/coq/betree/_CoqProject b/tests/coq/betree/_CoqProject
index 42c62421..13e4b9c1 100644
--- a/tests/coq/betree/_CoqProject
+++ b/tests/coq/betree/_CoqProject
@@ -4,6 +4,9 @@
 -arg all
 
 BetreeMain_Types.v
+BetreeMain_TypesExternal_Template.v
 Primitives.v
+BetreeMain_FunsExternal_Template.v
 BetreeMain_Funs.v
-BetreeMain_Opaque.v
+BetreeMain_TypesExternal.v
+BetreeMain_FunsExternal.v
diff --git a/tests/coq/hashmap/Hashmap_Funs.v b/tests/coq/hashmap/Hashmap_Funs.v
index e950ba0b..64de44a6 100644
--- a/tests/coq/hashmap/Hashmap_Funs.v
+++ b/tests/coq/hashmap/Hashmap_Funs.v
@@ -6,103 +6,115 @@ Require Import Coq.ZArith.ZArith.
 Require Import List.
 Import ListNotations.
 Local Open Scope Primitives_scope.
-Require Export Hashmap_Types.
-Import Hashmap_Types.
+Require Import Hashmap_Types.
+Include Hashmap_Types.
 Module Hashmap_Funs.
 
-(** [hashmap::hash_key]: forward function *)
-Definition hash_key_fwd (k : usize) : result usize :=
+(** [hashmap::hash_key]: forward function
+    Source: 'src/hashmap.rs', lines 27:0-27:32 *)
+Definition hash_key (k : usize) : result usize :=
   Return k.
 
-(** [hashmap::HashMap::{0}::allocate_slots]: loop 0: forward function *)
-Fixpoint hash_map_allocate_slots_loop_fwd
-  (T : Type) (n : nat) (slots : vec (List_t T)) (n0 : usize) :
-  result (vec (List_t T))
+(** [hashmap::{hashmap::HashMap<T>}::allocate_slots]: loop 0: forward function
+    Source: 'src/hashmap.rs', lines 50:4-56:5 *)
+Fixpoint hashMap_allocate_slots_loop
+  (T : Type) (n : nat) (slots : alloc_vec_Vec (List_t T)) (n0 : usize) :
+  result (alloc_vec_Vec (List_t T))
   :=
   match n with
   | O => Fail_ OutOfFuel
   | S n1 =>
     if n0 s> 0%usize
     then (
-      slots0 <- vec_push_back (List_t T) slots ListNil;
+      slots0 <- alloc_vec_Vec_push (List_t T) slots List_Nil;
       n2 <- usize_sub n0 1%usize;
-      hash_map_allocate_slots_loop_fwd T n1 slots0 n2)
+      hashMap_allocate_slots_loop T n1 slots0 n2)
     else Return slots
   end
 .
 
-(** [hashmap::HashMap::{0}::allocate_slots]: forward function *)
-Definition hash_map_allocate_slots_fwd
-  (T : Type) (n : nat) (slots : vec (List_t T)) (n0 : usize) :
-  result (vec (List_t T))
+(** [hashmap::{hashmap::HashMap<T>}::allocate_slots]: forward function
+    Source: 'src/hashmap.rs', lines 50:4-50:76 *)
+Definition hashMap_allocate_slots
+  (T : Type) (n : nat) (slots : alloc_vec_Vec (List_t T)) (n0 : usize) :
+  result (alloc_vec_Vec (List_t T))
   :=
-  hash_map_allocate_slots_loop_fwd T n slots n0
+  hashMap_allocate_slots_loop T n slots n0
 .
 
-(** [hashmap::HashMap::{0}::new_with_capacity]: forward function *)
-Definition hash_map_new_with_capacity_fwd
+(** [hashmap::{hashmap::HashMap<T>}::new_with_capacity]: forward function
+    Source: 'src/hashmap.rs', lines 59:4-63:13 *)
+Definition hashMap_new_with_capacity
   (T : Type) (n : nat) (capacity : usize) (max_load_dividend : usize)
   (max_load_divisor : usize) :
-  result (Hash_map_t T)
+  result (HashMap_t T)
   :=
-  let v := vec_new (List_t T) in
-  slots <- hash_map_allocate_slots_fwd T n v capacity;
+  let v := alloc_vec_Vec_new (List_t T) in
+  slots <- hashMap_allocate_slots T n v capacity;
   i <- usize_mul capacity max_load_dividend;
   i0 <- usize_div i max_load_divisor;
   Return
     {|
-      Hash_map_num_entries := 0%usize;
-      Hash_map_max_load_factor := (max_load_dividend, max_load_divisor);
-      Hash_map_max_load := i0;
-      Hash_map_slots := slots
+      hashMap_num_entries := 0%usize;
+      hashMap_max_load_factor := (max_load_dividend, max_load_divisor);
+      hashMap_max_load := i0;
+      hashMap_slots := slots
     |}
 .
 
-(** [hashmap::HashMap::{0}::new]: forward function *)
-Definition hash_map_new_fwd (T : Type) (n : nat) : result (Hash_map_t T) :=
-  hash_map_new_with_capacity_fwd T n 32%usize 4%usize 5%usize
+(** [hashmap::{hashmap::HashMap<T>}::new]: forward function
+    Source: 'src/hashmap.rs', lines 75:4-75:24 *)
+Definition hashMap_new (T : Type) (n : nat) : result (HashMap_t T) :=
+  hashMap_new_with_capacity T n 32%usize 4%usize 5%usize
 .
 
-(** [hashmap::HashMap::{0}::clear]: loop 0: merged forward/backward function
-    (there is a single backward function, and the forward function returns ()) *)
-Fixpoint hash_map_clear_loop_fwd_back
-  (T : Type) (n : nat) (slots : vec (List_t T)) (i : usize) :
-  result (vec (List_t T))
+(** [hashmap::{hashmap::HashMap<T>}::clear]: loop 0: merged forward/backward function
+    (there is a single backward function, and the forward function returns ())
+    Source: 'src/hashmap.rs', lines 80:4-88:5 *)
+Fixpoint hashMap_clear_loop
+  (T : Type) (n : nat) (slots : alloc_vec_Vec (List_t T)) (i : usize) :
+  result (alloc_vec_Vec (List_t T))
   :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
-    let i0 := vec_len (List_t T) slots in
+    let i0 := alloc_vec_Vec_len (List_t T) slots in
     if i s< i0
     then (
       i1 <- usize_add i 1%usize;
-      slots0 <- vec_index_mut_back (List_t T) slots i ListNil;
-      hash_map_clear_loop_fwd_back T n0 slots0 i1)
+      slots0 <-
+        alloc_vec_Vec_index_mut_back (List_t T) usize
+          (core_slice_index_SliceIndexUsizeSliceTInst (List_t T)) slots i
+          List_Nil;
+      hashMap_clear_loop T n0 slots0 i1)
     else Return slots
   end
 .
 
-(** [hashmap::HashMap::{0}::clear]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ()) *)
-Definition hash_map_clear_fwd_back
-  (T : Type) (n : nat) (self : Hash_map_t T) : result (Hash_map_t T) :=
-  v <- hash_map_clear_loop_fwd_back T n self.(Hash_map_slots) 0%usize;
+(** [hashmap::{hashmap::HashMap<T>}::clear]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ())
+    Source: 'src/hashmap.rs', lines 80:4-80:27 *)
+Definition hashMap_clear
+  (T : Type) (n : nat) (self : HashMap_t T) : result (HashMap_t T) :=
+  v <- hashMap_clear_loop T n self.(hashMap_slots) 0%usize;
   Return
     {|
-      Hash_map_num_entries := 0%usize;
-      Hash_map_max_load_factor := self.(Hash_map_max_load_factor);
-      Hash_map_max_load := self.(Hash_map_max_load);
-      Hash_map_slots := v
+      hashMap_num_entries := 0%usize;
+      hashMap_max_load_factor := self.(hashMap_max_load_factor);
+      hashMap_max_load := self.(hashMap_max_load);
+      hashMap_slots := v
     |}
 .
 
-(** [hashmap::HashMap::{0}::len]: forward function *)
-Definition hash_map_len_fwd (T : Type) (self : Hash_map_t T) : result usize :=
-  Return self.(Hash_map_num_entries)
+(** [hashmap::{hashmap::HashMap<T>}::len]: forward function
+    Source: 'src/hashmap.rs', lines 90:4-90:30 *)
+Definition hashMap_len (T : Type) (self : HashMap_t T) : result usize :=
+  Return self.(hashMap_num_entries)
 .
 
-(** [hashmap::HashMap::{0}::insert_in_list]: loop 0: forward function *)
-Fixpoint hash_map_insert_in_list_loop_fwd
+(** [hashmap::{hashmap::HashMap<T>}::insert_in_list]: loop 0: forward function
+    Source: 'src/hashmap.rs', lines 97:4-114:5 *)
+Fixpoint hashMap_insert_in_list_loop
   (T : Type) (n : nat) (key : usize) (value : T) (ls : List_t T) :
   result bool
   :=
@@ -110,25 +122,27 @@ Fixpoint hash_map_insert_in_list_loop_fwd
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls with
-    | ListCons ckey cvalue tl =>
+    | List_Cons ckey cvalue tl =>
       if ckey s= key
       then Return false
-      else hash_map_insert_in_list_loop_fwd T n0 key value tl
-    | ListNil => Return true
+      else hashMap_insert_in_list_loop T n0 key value tl
+    | List_Nil => Return true
     end
   end
 .
 
-(** [hashmap::HashMap::{0}::insert_in_list]: forward function *)
-Definition hash_map_insert_in_list_fwd
+(** [hashmap::{hashmap::HashMap<T>}::insert_in_list]: forward function
+    Source: 'src/hashmap.rs', lines 97:4-97:71 *)
+Definition hashMap_insert_in_list
   (T : Type) (n : nat) (key : usize) (value : T) (ls : List_t T) :
   result bool
   :=
-  hash_map_insert_in_list_loop_fwd T n key value ls
+  hashMap_insert_in_list_loop T n key value ls
 .
 
-(** [hashmap::HashMap::{0}::insert_in_list]: loop 0: backward function 0 *)
-Fixpoint hash_map_insert_in_list_loop_back
+(** [hashmap::{hashmap::HashMap<T>}::insert_in_list]: loop 0: backward function 0
+    Source: 'src/hashmap.rs', lines 97:4-114:5 *)
+Fixpoint hashMap_insert_in_list_loop_back
   (T : Type) (n : nat) (key : usize) (value : T) (ls : List_t T) :
   result (List_t T)
   :=
@@ -136,259 +150,290 @@ Fixpoint hash_map_insert_in_list_loop_back
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls with
-    | ListCons ckey cvalue tl =>
+    | List_Cons ckey cvalue tl =>
       if ckey s= key
-      then Return (ListCons ckey value tl)
+      then Return (List_Cons ckey value tl)
       else (
-        tl0 <- hash_map_insert_in_list_loop_back T n0 key value tl;
-        Return (ListCons ckey cvalue tl0))
-    | ListNil => let l := ListNil in Return (ListCons key value l)
+        tl0 <- hashMap_insert_in_list_loop_back T n0 key value tl;
+        Return (List_Cons ckey cvalue tl0))
+    | List_Nil => let l := List_Nil in Return (List_Cons key value l)
     end
   end
 .
 
-(** [hashmap::HashMap::{0}::insert_in_list]: backward function 0 *)
-Definition hash_map_insert_in_list_back
+(** [hashmap::{hashmap::HashMap<T>}::insert_in_list]: backward function 0
+    Source: 'src/hashmap.rs', lines 97:4-97:71 *)
+Definition hashMap_insert_in_list_back
   (T : Type) (n : nat) (key : usize) (value : T) (ls : List_t T) :
   result (List_t T)
   :=
-  hash_map_insert_in_list_loop_back T n key value ls
+  hashMap_insert_in_list_loop_back T n key value ls
 .
 
-(** [hashmap::HashMap::{0}::insert_no_resize]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ()) *)
-Definition hash_map_insert_no_resize_fwd_back
-  (T : Type) (n : nat) (self : Hash_map_t T) (key : usize) (value : T) :
-  result (Hash_map_t T)
+(** [hashmap::{hashmap::HashMap<T>}::insert_no_resize]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ())
+    Source: 'src/hashmap.rs', lines 117:4-117:54 *)
+Definition hashMap_insert_no_resize
+  (T : Type) (n : nat) (self : HashMap_t T) (key : usize) (value : T) :
+  result (HashMap_t T)
   :=
-  hash <- hash_key_fwd key;
-  let i := vec_len (List_t T) self.(Hash_map_slots) in
+  hash <- hash_key key;
+  let i := alloc_vec_Vec_len (List_t T) self.(hashMap_slots) in
   hash_mod <- usize_rem hash i;
-  l <- vec_index_mut_fwd (List_t T) self.(Hash_map_slots) hash_mod;
-  inserted <- hash_map_insert_in_list_fwd T n key value l;
+  l <-
+    alloc_vec_Vec_index_mut (List_t T) usize
+      (core_slice_index_SliceIndexUsizeSliceTInst (List_t T))
+      self.(hashMap_slots) hash_mod;
+  inserted <- hashMap_insert_in_list T n key value l;
   if inserted
   then (
-    i0 <- usize_add self.(Hash_map_num_entries) 1%usize;
-    l0 <- hash_map_insert_in_list_back T n key value l;
-    v <- vec_index_mut_back (List_t T) self.(Hash_map_slots) hash_mod l0;
+    i0 <- usize_add self.(hashMap_num_entries) 1%usize;
+    l0 <- hashMap_insert_in_list_back T n key value l;
+    v <-
+      alloc_vec_Vec_index_mut_back (List_t T) usize
+        (core_slice_index_SliceIndexUsizeSliceTInst (List_t T))
+        self.(hashMap_slots) hash_mod l0;
     Return
       {|
-        Hash_map_num_entries := i0;
-        Hash_map_max_load_factor := self.(Hash_map_max_load_factor);
-        Hash_map_max_load := self.(Hash_map_max_load);
-        Hash_map_slots := v
+        hashMap_num_entries := i0;
+        hashMap_max_load_factor := self.(hashMap_max_load_factor);
+        hashMap_max_load := self.(hashMap_max_load);
+        hashMap_slots := v
       |})
   else (
-    l0 <- hash_map_insert_in_list_back T n key value l;
-    v <- vec_index_mut_back (List_t T) self.(Hash_map_slots) hash_mod l0;
+    l0 <- hashMap_insert_in_list_back T n key value l;
+    v <-
+      alloc_vec_Vec_index_mut_back (List_t T) usize
+        (core_slice_index_SliceIndexUsizeSliceTInst (List_t T))
+        self.(hashMap_slots) hash_mod l0;
     Return
       {|
-        Hash_map_num_entries := self.(Hash_map_num_entries);
-        Hash_map_max_load_factor := self.(Hash_map_max_load_factor);
-        Hash_map_max_load := self.(Hash_map_max_load);
-        Hash_map_slots := v
+        hashMap_num_entries := self.(hashMap_num_entries);
+        hashMap_max_load_factor := self.(hashMap_max_load_factor);
+        hashMap_max_load := self.(hashMap_max_load);
+        hashMap_slots := v
       |})
 .
 
-(** [core::num::u32::{8}::MAX] *)
-Definition core_num_u32_max_body : result u32 := Return 4294967295%u32.
-Definition core_num_u32_max_c : u32 := core_num_u32_max_body%global.
-
-(** [hashmap::HashMap::{0}::move_elements_from_list]: loop 0: merged forward/backward function
-    (there is a single backward function, and the forward function returns ()) *)
-Fixpoint hash_map_move_elements_from_list_loop_fwd_back
-  (T : Type) (n : nat) (ntable : Hash_map_t T) (ls : List_t T) :
-  result (Hash_map_t T)
+(** [hashmap::{hashmap::HashMap<T>}::move_elements_from_list]: loop 0: merged forward/backward function
+    (there is a single backward function, and the forward function returns ())
+    Source: 'src/hashmap.rs', lines 183:4-196:5 *)
+Fixpoint hashMap_move_elements_from_list_loop
+  (T : Type) (n : nat) (ntable : HashMap_t T) (ls : List_t T) :
+  result (HashMap_t T)
   :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls with
-    | ListCons k v tl =>
-      ntable0 <- hash_map_insert_no_resize_fwd_back T n0 ntable k v;
-      hash_map_move_elements_from_list_loop_fwd_back T n0 ntable0 tl
-    | ListNil => Return ntable
+    | List_Cons k v tl =>
+      ntable0 <- hashMap_insert_no_resize T n0 ntable k v;
+      hashMap_move_elements_from_list_loop T n0 ntable0 tl
+    | List_Nil => Return ntable
     end
   end
 .
 
-(** [hashmap::HashMap::{0}::move_elements_from_list]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ()) *)
-Definition hash_map_move_elements_from_list_fwd_back
-  (T : Type) (n : nat) (ntable : Hash_map_t T) (ls : List_t T) :
-  result (Hash_map_t T)
+(** [hashmap::{hashmap::HashMap<T>}::move_elements_from_list]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ())
+    Source: 'src/hashmap.rs', lines 183:4-183:72 *)
+Definition hashMap_move_elements_from_list
+  (T : Type) (n : nat) (ntable : HashMap_t T) (ls : List_t T) :
+  result (HashMap_t T)
   :=
-  hash_map_move_elements_from_list_loop_fwd_back T n ntable ls
+  hashMap_move_elements_from_list_loop T n ntable ls
 .
 
-(** [hashmap::HashMap::{0}::move_elements]: loop 0: merged forward/backward function
-    (there is a single backward function, and the forward function returns ()) *)
-Fixpoint hash_map_move_elements_loop_fwd_back
-  (T : Type) (n : nat) (ntable : Hash_map_t T) (slots : vec (List_t T))
-  (i : usize) :
-  result ((Hash_map_t T) * (vec (List_t T)))
+(** [hashmap::{hashmap::HashMap<T>}::move_elements]: loop 0: merged forward/backward function
+    (there is a single backward function, and the forward function returns ())
+    Source: 'src/hashmap.rs', lines 171:4-180:5 *)
+Fixpoint hashMap_move_elements_loop
+  (T : Type) (n : nat) (ntable : HashMap_t T)
+  (slots : alloc_vec_Vec (List_t T)) (i : usize) :
+  result ((HashMap_t T) * (alloc_vec_Vec (List_t T)))
   :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
-    let i0 := vec_len (List_t T) slots in
+    let i0 := alloc_vec_Vec_len (List_t T) slots in
     if i s< i0
     then (
-      l <- vec_index_mut_fwd (List_t T) slots i;
-      let ls := mem_replace_fwd (List_t T) l ListNil in
-      ntable0 <- hash_map_move_elements_from_list_fwd_back T n0 ntable ls;
+      l <-
+        alloc_vec_Vec_index_mut (List_t T) usize
+          (core_slice_index_SliceIndexUsizeSliceTInst (List_t T)) slots i;
+      let ls := core_mem_replace (List_t T) l List_Nil in
+      ntable0 <- hashMap_move_elements_from_list T n0 ntable ls;
       i1 <- usize_add i 1%usize;
-      let l0 := mem_replace_back (List_t T) l ListNil in
-      slots0 <- vec_index_mut_back (List_t T) slots i l0;
-      hash_map_move_elements_loop_fwd_back T n0 ntable0 slots0 i1)
+      let l0 := core_mem_replace_back (List_t T) l List_Nil in
+      slots0 <-
+        alloc_vec_Vec_index_mut_back (List_t T) usize
+          (core_slice_index_SliceIndexUsizeSliceTInst (List_t T)) slots i l0;
+      hashMap_move_elements_loop T n0 ntable0 slots0 i1)
     else Return (ntable, slots)
   end
 .
 
-(** [hashmap::HashMap::{0}::move_elements]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ()) *)
-Definition hash_map_move_elements_fwd_back
-  (T : Type) (n : nat) (ntable : Hash_map_t T) (slots : vec (List_t T))
-  (i : usize) :
-  result ((Hash_map_t T) * (vec (List_t T)))
+(** [hashmap::{hashmap::HashMap<T>}::move_elements]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ())
+    Source: 'src/hashmap.rs', lines 171:4-171:95 *)
+Definition hashMap_move_elements
+  (T : Type) (n : nat) (ntable : HashMap_t T)
+  (slots : alloc_vec_Vec (List_t T)) (i : usize) :
+  result ((HashMap_t T) * (alloc_vec_Vec (List_t T)))
   :=
-  hash_map_move_elements_loop_fwd_back T n ntable slots i
+  hashMap_move_elements_loop T n ntable slots i
 .
 
-(** [hashmap::HashMap::{0}::try_resize]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ()) *)
-Definition hash_map_try_resize_fwd_back
-  (T : Type) (n : nat) (self : Hash_map_t T) : result (Hash_map_t T) :=
-  max_usize <- scalar_cast U32 Usize core_num_u32_max_c;
-  let capacity := vec_len (List_t T) self.(Hash_map_slots) in
+(** [hashmap::{hashmap::HashMap<T>}::try_resize]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ())
+    Source: 'src/hashmap.rs', lines 140:4-140:28 *)
+Definition hashMap_try_resize
+  (T : Type) (n : nat) (self : HashMap_t T) : result (HashMap_t T) :=
+  max_usize <- scalar_cast U32 Usize core_u32_max;
+  let capacity := alloc_vec_Vec_len (List_t T) self.(hashMap_slots) in
   n1 <- usize_div max_usize 2%usize;
-  let (i, i0) := self.(Hash_map_max_load_factor) in
+  let (i, i0) := self.(hashMap_max_load_factor) in
   i1 <- usize_div n1 i;
   if capacity s<= i1
   then (
     i2 <- usize_mul capacity 2%usize;
-    ntable <- hash_map_new_with_capacity_fwd T n i2 i i0;
-    p <-
-      hash_map_move_elements_fwd_back T n ntable self.(Hash_map_slots) 0%usize;
+    ntable <- hashMap_new_with_capacity T n i2 i i0;
+    p <- hashMap_move_elements T n ntable self.(hashMap_slots) 0%usize;
     let (ntable0, _) := p in
     Return
       {|
-        Hash_map_num_entries := self.(Hash_map_num_entries);
-        Hash_map_max_load_factor := (i, i0);
-        Hash_map_max_load := ntable0.(Hash_map_max_load);
-        Hash_map_slots := ntable0.(Hash_map_slots)
+        hashMap_num_entries := self.(hashMap_num_entries);
+        hashMap_max_load_factor := (i, i0);
+        hashMap_max_load := ntable0.(hashMap_max_load);
+        hashMap_slots := ntable0.(hashMap_slots)
       |})
   else
     Return
       {|
-        Hash_map_num_entries := self.(Hash_map_num_entries);
-        Hash_map_max_load_factor := (i, i0);
-        Hash_map_max_load := self.(Hash_map_max_load);
-        Hash_map_slots := self.(Hash_map_slots)
+        hashMap_num_entries := self.(hashMap_num_entries);
+        hashMap_max_load_factor := (i, i0);
+        hashMap_max_load := self.(hashMap_max_load);
+        hashMap_slots := self.(hashMap_slots)
       |}
 .
 
-(** [hashmap::HashMap::{0}::insert]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ()) *)
-Definition hash_map_insert_fwd_back
-  (T : Type) (n : nat) (self : Hash_map_t T) (key : usize) (value : T) :
-  result (Hash_map_t T)
+(** [hashmap::{hashmap::HashMap<T>}::insert]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ())
+    Source: 'src/hashmap.rs', lines 129:4-129:48 *)
+Definition hashMap_insert
+  (T : Type) (n : nat) (self : HashMap_t T) (key : usize) (value : T) :
+  result (HashMap_t T)
   :=
-  self0 <- hash_map_insert_no_resize_fwd_back T n self key value;
-  i <- hash_map_len_fwd T self0;
-  if i s> self0.(Hash_map_max_load)
-  then hash_map_try_resize_fwd_back T n self0
+  self0 <- hashMap_insert_no_resize T n self key value;
+  i <- hashMap_len T self0;
+  if i s> self0.(hashMap_max_load)
+  then hashMap_try_resize T n self0
   else Return self0
 .
 
-(** [hashmap::HashMap::{0}::contains_key_in_list]: loop 0: forward function *)
-Fixpoint hash_map_contains_key_in_list_loop_fwd
+(** [hashmap::{hashmap::HashMap<T>}::contains_key_in_list]: loop 0: forward function
+    Source: 'src/hashmap.rs', lines 206:4-219:5 *)
+Fixpoint hashMap_contains_key_in_list_loop
   (T : Type) (n : nat) (key : usize) (ls : List_t T) : result bool :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls with
-    | ListCons ckey t tl =>
+    | List_Cons ckey t tl =>
       if ckey s= key
       then Return true
-      else hash_map_contains_key_in_list_loop_fwd T n0 key tl
-    | ListNil => Return false
+      else hashMap_contains_key_in_list_loop T n0 key tl
+    | List_Nil => Return false
     end
   end
 .
 
-(** [hashmap::HashMap::{0}::contains_key_in_list]: forward function *)
-Definition hash_map_contains_key_in_list_fwd
+(** [hashmap::{hashmap::HashMap<T>}::contains_key_in_list]: forward function
+    Source: 'src/hashmap.rs', lines 206:4-206:68 *)
+Definition hashMap_contains_key_in_list
   (T : Type) (n : nat) (key : usize) (ls : List_t T) : result bool :=
-  hash_map_contains_key_in_list_loop_fwd T n key ls
+  hashMap_contains_key_in_list_loop T n key ls
 .
 
-(** [hashmap::HashMap::{0}::contains_key]: forward function *)
-Definition hash_map_contains_key_fwd
-  (T : Type) (n : nat) (self : Hash_map_t T) (key : usize) : result bool :=
-  hash <- hash_key_fwd key;
-  let i := vec_len (List_t T) self.(Hash_map_slots) in
+(** [hashmap::{hashmap::HashMap<T>}::contains_key]: forward function
+    Source: 'src/hashmap.rs', lines 199:4-199:49 *)
+Definition hashMap_contains_key
+  (T : Type) (n : nat) (self : HashMap_t T) (key : usize) : result bool :=
+  hash <- hash_key key;
+  let i := alloc_vec_Vec_len (List_t T) self.(hashMap_slots) in
   hash_mod <- usize_rem hash i;
-  l <- vec_index_fwd (List_t T) self.(Hash_map_slots) hash_mod;
-  hash_map_contains_key_in_list_fwd T n key l
+  l <-
+    alloc_vec_Vec_index (List_t T) usize
+      (core_slice_index_SliceIndexUsizeSliceTInst (List_t T))
+      self.(hashMap_slots) hash_mod;
+  hashMap_contains_key_in_list T n key l
 .
 
-(** [hashmap::HashMap::{0}::get_in_list]: loop 0: forward function *)
-Fixpoint hash_map_get_in_list_loop_fwd
+(** [hashmap::{hashmap::HashMap<T>}::get_in_list]: loop 0: forward function
+    Source: 'src/hashmap.rs', lines 224:4-237:5 *)
+Fixpoint hashMap_get_in_list_loop
   (T : Type) (n : nat) (key : usize) (ls : List_t T) : result T :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls with
-    | ListCons ckey cvalue tl =>
+    | List_Cons ckey cvalue tl =>
       if ckey s= key
       then Return cvalue
-      else hash_map_get_in_list_loop_fwd T n0 key tl
-    | ListNil => Fail_ Failure
+      else hashMap_get_in_list_loop T n0 key tl
+    | List_Nil => Fail_ Failure
     end
   end
 .
 
-(** [hashmap::HashMap::{0}::get_in_list]: forward function *)
-Definition hash_map_get_in_list_fwd
+(** [hashmap::{hashmap::HashMap<T>}::get_in_list]: forward function
+    Source: 'src/hashmap.rs', lines 224:4-224:70 *)
+Definition hashMap_get_in_list
   (T : Type) (n : nat) (key : usize) (ls : List_t T) : result T :=
-  hash_map_get_in_list_loop_fwd T n key ls
+  hashMap_get_in_list_loop T n key ls
 .
 
-(** [hashmap::HashMap::{0}::get]: forward function *)
-Definition hash_map_get_fwd
-  (T : Type) (n : nat) (self : Hash_map_t T) (key : usize) : result T :=
-  hash <- hash_key_fwd key;
-  let i := vec_len (List_t T) self.(Hash_map_slots) in
+(** [hashmap::{hashmap::HashMap<T>}::get]: forward function
+    Source: 'src/hashmap.rs', lines 239:4-239:55 *)
+Definition hashMap_get
+  (T : Type) (n : nat) (self : HashMap_t T) (key : usize) : result T :=
+  hash <- hash_key key;
+  let i := alloc_vec_Vec_len (List_t T) self.(hashMap_slots) in
   hash_mod <- usize_rem hash i;
-  l <- vec_index_fwd (List_t T) self.(Hash_map_slots) hash_mod;
-  hash_map_get_in_list_fwd T n key l
+  l <-
+    alloc_vec_Vec_index (List_t T) usize
+      (core_slice_index_SliceIndexUsizeSliceTInst (List_t T))
+      self.(hashMap_slots) hash_mod;
+  hashMap_get_in_list T n key l
 .
 
-(** [hashmap::HashMap::{0}::get_mut_in_list]: loop 0: forward function *)
-Fixpoint hash_map_get_mut_in_list_loop_fwd
+(** [hashmap::{hashmap::HashMap<T>}::get_mut_in_list]: loop 0: forward function
+    Source: 'src/hashmap.rs', lines 245:4-254:5 *)
+Fixpoint hashMap_get_mut_in_list_loop
   (T : Type) (n : nat) (ls : List_t T) (key : usize) : result T :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls with
-    | ListCons ckey cvalue tl =>
+    | List_Cons ckey cvalue tl =>
       if ckey s= key
       then Return cvalue
-      else hash_map_get_mut_in_list_loop_fwd T n0 tl key
-    | ListNil => Fail_ Failure
+      else hashMap_get_mut_in_list_loop T n0 tl key
+    | List_Nil => Fail_ Failure
     end
   end
 .
 
-(** [hashmap::HashMap::{0}::get_mut_in_list]: forward function *)
-Definition hash_map_get_mut_in_list_fwd
+(** [hashmap::{hashmap::HashMap<T>}::get_mut_in_list]: forward function
+    Source: 'src/hashmap.rs', lines 245:4-245:86 *)
+Definition hashMap_get_mut_in_list
   (T : Type) (n : nat) (ls : List_t T) (key : usize) : result T :=
-  hash_map_get_mut_in_list_loop_fwd T n ls key
+  hashMap_get_mut_in_list_loop T n ls key
 .
 
-(** [hashmap::HashMap::{0}::get_mut_in_list]: loop 0: backward function 0 *)
-Fixpoint hash_map_get_mut_in_list_loop_back
+(** [hashmap::{hashmap::HashMap<T>}::get_mut_in_list]: loop 0: backward function 0
+    Source: 'src/hashmap.rs', lines 245:4-254:5 *)
+Fixpoint hashMap_get_mut_in_list_loop_back
   (T : Type) (n : nat) (ls : List_t T) (key : usize) (ret : T) :
   result (List_t T)
   :=
@@ -396,198 +441,231 @@ Fixpoint hash_map_get_mut_in_list_loop_back
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls with
-    | ListCons ckey cvalue tl =>
+    | List_Cons ckey cvalue tl =>
       if ckey s= key
-      then Return (ListCons ckey ret tl)
+      then Return (List_Cons ckey ret tl)
       else (
-        tl0 <- hash_map_get_mut_in_list_loop_back T n0 tl key ret;
-        Return (ListCons ckey cvalue tl0))
-    | ListNil => Fail_ Failure
+        tl0 <- hashMap_get_mut_in_list_loop_back T n0 tl key ret;
+        Return (List_Cons ckey cvalue tl0))
+    | List_Nil => Fail_ Failure
     end
   end
 .
 
-(** [hashmap::HashMap::{0}::get_mut_in_list]: backward function 0 *)
-Definition hash_map_get_mut_in_list_back
+(** [hashmap::{hashmap::HashMap<T>}::get_mut_in_list]: backward function 0
+    Source: 'src/hashmap.rs', lines 245:4-245:86 *)
+Definition hashMap_get_mut_in_list_back
   (T : Type) (n : nat) (ls : List_t T) (key : usize) (ret : T) :
   result (List_t T)
   :=
-  hash_map_get_mut_in_list_loop_back T n ls key ret
+  hashMap_get_mut_in_list_loop_back T n ls key ret
 .
 
-(** [hashmap::HashMap::{0}::get_mut]: forward function *)
-Definition hash_map_get_mut_fwd
-  (T : Type) (n : nat) (self : Hash_map_t T) (key : usize) : result T :=
-  hash <- hash_key_fwd key;
-  let i := vec_len (List_t T) self.(Hash_map_slots) in
+(** [hashmap::{hashmap::HashMap<T>}::get_mut]: forward function
+    Source: 'src/hashmap.rs', lines 257:4-257:67 *)
+Definition hashMap_get_mut
+  (T : Type) (n : nat) (self : HashMap_t T) (key : usize) : result T :=
+  hash <- hash_key key;
+  let i := alloc_vec_Vec_len (List_t T) self.(hashMap_slots) in
   hash_mod <- usize_rem hash i;
-  l <- vec_index_mut_fwd (List_t T) self.(Hash_map_slots) hash_mod;
-  hash_map_get_mut_in_list_fwd T n l key
-.
-
-(** [hashmap::HashMap::{0}::get_mut]: backward function 0 *)
-Definition hash_map_get_mut_back
-  (T : Type) (n : nat) (self : Hash_map_t T) (key : usize) (ret : T) :
-  result (Hash_map_t T)
+  l <-
+    alloc_vec_Vec_index_mut (List_t T) usize
+      (core_slice_index_SliceIndexUsizeSliceTInst (List_t T))
+      self.(hashMap_slots) hash_mod;
+  hashMap_get_mut_in_list T n l key
+.
+
+(** [hashmap::{hashmap::HashMap<T>}::get_mut]: backward function 0
+    Source: 'src/hashmap.rs', lines 257:4-257:67 *)
+Definition hashMap_get_mut_back
+  (T : Type) (n : nat) (self : HashMap_t T) (key : usize) (ret : T) :
+  result (HashMap_t T)
   :=
-  hash <- hash_key_fwd key;
-  let i := vec_len (List_t T) self.(Hash_map_slots) in
+  hash <- hash_key key;
+  let i := alloc_vec_Vec_len (List_t T) self.(hashMap_slots) in
   hash_mod <- usize_rem hash i;
-  l <- vec_index_mut_fwd (List_t T) self.(Hash_map_slots) hash_mod;
-  l0 <- hash_map_get_mut_in_list_back T n l key ret;
-  v <- vec_index_mut_back (List_t T) self.(Hash_map_slots) hash_mod l0;
+  l <-
+    alloc_vec_Vec_index_mut (List_t T) usize
+      (core_slice_index_SliceIndexUsizeSliceTInst (List_t T))
+      self.(hashMap_slots) hash_mod;
+  l0 <- hashMap_get_mut_in_list_back T n l key ret;
+  v <-
+    alloc_vec_Vec_index_mut_back (List_t T) usize
+      (core_slice_index_SliceIndexUsizeSliceTInst (List_t T))
+      self.(hashMap_slots) hash_mod l0;
   Return
     {|
-      Hash_map_num_entries := self.(Hash_map_num_entries);
-      Hash_map_max_load_factor := self.(Hash_map_max_load_factor);
-      Hash_map_max_load := self.(Hash_map_max_load);
-      Hash_map_slots := v
+      hashMap_num_entries := self.(hashMap_num_entries);
+      hashMap_max_load_factor := self.(hashMap_max_load_factor);
+      hashMap_max_load := self.(hashMap_max_load);
+      hashMap_slots := v
     |}
 .
 
-(** [hashmap::HashMap::{0}::remove_from_list]: loop 0: forward function *)
-Fixpoint hash_map_remove_from_list_loop_fwd
+(** [hashmap::{hashmap::HashMap<T>}::remove_from_list]: loop 0: forward function
+    Source: 'src/hashmap.rs', lines 265:4-291:5 *)
+Fixpoint hashMap_remove_from_list_loop
   (T : Type) (n : nat) (key : usize) (ls : List_t T) : result (option T) :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls with
-    | ListCons ckey t tl =>
+    | List_Cons ckey t tl =>
       if ckey s= key
       then
-        let mv_ls := mem_replace_fwd (List_t T) (ListCons ckey t tl) ListNil in
+        let mv_ls := core_mem_replace (List_t T) (List_Cons ckey t tl) List_Nil
+          in
         match mv_ls with
-        | ListCons i cvalue tl0 => Return (Some cvalue)
-        | ListNil => Fail_ Failure
+        | List_Cons i cvalue tl0 => Return (Some cvalue)
+        | List_Nil => Fail_ Failure
         end
-      else hash_map_remove_from_list_loop_fwd T n0 key tl
-    | ListNil => Return None
+      else hashMap_remove_from_list_loop T n0 key tl
+    | List_Nil => Return None
     end
   end
 .
 
-(** [hashmap::HashMap::{0}::remove_from_list]: forward function *)
-Definition hash_map_remove_from_list_fwd
+(** [hashmap::{hashmap::HashMap<T>}::remove_from_list]: forward function
+    Source: 'src/hashmap.rs', lines 265:4-265:69 *)
+Definition hashMap_remove_from_list
   (T : Type) (n : nat) (key : usize) (ls : List_t T) : result (option T) :=
-  hash_map_remove_from_list_loop_fwd T n key ls
+  hashMap_remove_from_list_loop T n key ls
 .
 
-(** [hashmap::HashMap::{0}::remove_from_list]: loop 0: backward function 1 *)
-Fixpoint hash_map_remove_from_list_loop_back
+(** [hashmap::{hashmap::HashMap<T>}::remove_from_list]: loop 0: backward function 1
+    Source: 'src/hashmap.rs', lines 265:4-291:5 *)
+Fixpoint hashMap_remove_from_list_loop_back
   (T : Type) (n : nat) (key : usize) (ls : List_t T) : result (List_t T) :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls with
-    | ListCons ckey t tl =>
+    | List_Cons ckey t tl =>
       if ckey s= key
       then
-        let mv_ls := mem_replace_fwd (List_t T) (ListCons ckey t tl) ListNil in
+        let mv_ls := core_mem_replace (List_t T) (List_Cons ckey t tl) List_Nil
+          in
         match mv_ls with
-        | ListCons i cvalue tl0 => Return tl0
-        | ListNil => Fail_ Failure
+        | List_Cons i cvalue tl0 => Return tl0
+        | List_Nil => Fail_ Failure
         end
       else (
-        tl0 <- hash_map_remove_from_list_loop_back T n0 key tl;
-        Return (ListCons ckey t tl0))
-    | ListNil => Return ListNil
+        tl0 <- hashMap_remove_from_list_loop_back T n0 key tl;
+        Return (List_Cons ckey t tl0))
+    | List_Nil => Return List_Nil
     end
   end
 .
 
-(** [hashmap::HashMap::{0}::remove_from_list]: backward function 1 *)
-Definition hash_map_remove_from_list_back
+(** [hashmap::{hashmap::HashMap<T>}::remove_from_list]: backward function 1
+    Source: 'src/hashmap.rs', lines 265:4-265:69 *)
+Definition hashMap_remove_from_list_back
   (T : Type) (n : nat) (key : usize) (ls : List_t T) : result (List_t T) :=
-  hash_map_remove_from_list_loop_back T n key ls
+  hashMap_remove_from_list_loop_back T n key ls
 .
 
-(** [hashmap::HashMap::{0}::remove]: forward function *)
-Definition hash_map_remove_fwd
-  (T : Type) (n : nat) (self : Hash_map_t T) (key : usize) :
+(** [hashmap::{hashmap::HashMap<T>}::remove]: forward function
+    Source: 'src/hashmap.rs', lines 294:4-294:52 *)
+Definition hashMap_remove
+  (T : Type) (n : nat) (self : HashMap_t T) (key : usize) :
   result (option T)
   :=
-  hash <- hash_key_fwd key;
-  let i := vec_len (List_t T) self.(Hash_map_slots) in
+  hash <- hash_key key;
+  let i := alloc_vec_Vec_len (List_t T) self.(hashMap_slots) in
   hash_mod <- usize_rem hash i;
-  l <- vec_index_mut_fwd (List_t T) self.(Hash_map_slots) hash_mod;
-  x <- hash_map_remove_from_list_fwd T n key l;
+  l <-
+    alloc_vec_Vec_index_mut (List_t T) usize
+      (core_slice_index_SliceIndexUsizeSliceTInst (List_t T))
+      self.(hashMap_slots) hash_mod;
+  x <- hashMap_remove_from_list T n key l;
   match x with
   | None => Return None
   | Some x0 =>
-    _ <- usize_sub self.(Hash_map_num_entries) 1%usize; Return (Some x0)
+    _ <- usize_sub self.(hashMap_num_entries) 1%usize; Return (Some x0)
   end
 .
 
-(** [hashmap::HashMap::{0}::remove]: backward function 0 *)
-Definition hash_map_remove_back
-  (T : Type) (n : nat) (self : Hash_map_t T) (key : usize) :
-  result (Hash_map_t T)
+(** [hashmap::{hashmap::HashMap<T>}::remove]: backward function 0
+    Source: 'src/hashmap.rs', lines 294:4-294:52 *)
+Definition hashMap_remove_back
+  (T : Type) (n : nat) (self : HashMap_t T) (key : usize) :
+  result (HashMap_t T)
   :=
-  hash <- hash_key_fwd key;
-  let i := vec_len (List_t T) self.(Hash_map_slots) in
+  hash <- hash_key key;
+  let i := alloc_vec_Vec_len (List_t T) self.(hashMap_slots) in
   hash_mod <- usize_rem hash i;
-  l <- vec_index_mut_fwd (List_t T) self.(Hash_map_slots) hash_mod;
-  x <- hash_map_remove_from_list_fwd T n key l;
+  l <-
+    alloc_vec_Vec_index_mut (List_t T) usize
+      (core_slice_index_SliceIndexUsizeSliceTInst (List_t T))
+      self.(hashMap_slots) hash_mod;
+  x <- hashMap_remove_from_list T n key l;
   match x with
   | None =>
-    l0 <- hash_map_remove_from_list_back T n key l;
-    v <- vec_index_mut_back (List_t T) self.(Hash_map_slots) hash_mod l0;
+    l0 <- hashMap_remove_from_list_back T n key l;
+    v <-
+      alloc_vec_Vec_index_mut_back (List_t T) usize
+        (core_slice_index_SliceIndexUsizeSliceTInst (List_t T))
+        self.(hashMap_slots) hash_mod l0;
     Return
       {|
-        Hash_map_num_entries := self.(Hash_map_num_entries);
-        Hash_map_max_load_factor := self.(Hash_map_max_load_factor);
-        Hash_map_max_load := self.(Hash_map_max_load);
-        Hash_map_slots := v
+        hashMap_num_entries := self.(hashMap_num_entries);
+        hashMap_max_load_factor := self.(hashMap_max_load_factor);
+        hashMap_max_load := self.(hashMap_max_load);
+        hashMap_slots := v
       |}
   | Some x0 =>
-    i0 <- usize_sub self.(Hash_map_num_entries) 1%usize;
-    l0 <- hash_map_remove_from_list_back T n key l;
-    v <- vec_index_mut_back (List_t T) self.(Hash_map_slots) hash_mod l0;
+    i0 <- usize_sub self.(hashMap_num_entries) 1%usize;
+    l0 <- hashMap_remove_from_list_back T n key l;
+    v <-
+      alloc_vec_Vec_index_mut_back (List_t T) usize
+        (core_slice_index_SliceIndexUsizeSliceTInst (List_t T))
+        self.(hashMap_slots) hash_mod l0;
     Return
       {|
-        Hash_map_num_entries := i0;
-        Hash_map_max_load_factor := self.(Hash_map_max_load_factor);
-        Hash_map_max_load := self.(Hash_map_max_load);
-        Hash_map_slots := v
+        hashMap_num_entries := i0;
+        hashMap_max_load_factor := self.(hashMap_max_load_factor);
+        hashMap_max_load := self.(hashMap_max_load);
+        hashMap_slots := v
       |}
   end
 .
 
-(** [hashmap::test1]: forward function *)
-Definition test1_fwd (n : nat) : result unit :=
-  hm <- hash_map_new_fwd u64 n;
-  hm0 <- hash_map_insert_fwd_back u64 n hm 0%usize 42%u64;
-  hm1 <- hash_map_insert_fwd_back u64 n hm0 128%usize 18%u64;
-  hm2 <- hash_map_insert_fwd_back u64 n hm1 1024%usize 138%u64;
-  hm3 <- hash_map_insert_fwd_back u64 n hm2 1056%usize 256%u64;
-  i <- hash_map_get_fwd u64 n hm3 128%usize;
+(** [hashmap::test1]: forward function
+    Source: 'src/hashmap.rs', lines 315:0-315:10 *)
+Definition test1 (n : nat) : result unit :=
+  hm <- hashMap_new u64 n;
+  hm0 <- hashMap_insert u64 n hm 0%usize 42%u64;
+  hm1 <- hashMap_insert u64 n hm0 128%usize 18%u64;
+  hm2 <- hashMap_insert u64 n hm1 1024%usize 138%u64;
+  hm3 <- hashMap_insert u64 n hm2 1056%usize 256%u64;
+  i <- hashMap_get u64 n hm3 128%usize;
   if negb (i s= 18%u64)
   then Fail_ Failure
   else (
-    hm4 <- hash_map_get_mut_back u64 n hm3 1024%usize 56%u64;
-    i0 <- hash_map_get_fwd u64 n hm4 1024%usize;
+    hm4 <- hashMap_get_mut_back u64 n hm3 1024%usize 56%u64;
+    i0 <- hashMap_get u64 n hm4 1024%usize;
     if negb (i0 s= 56%u64)
     then Fail_ Failure
     else (
-      x <- hash_map_remove_fwd u64 n hm4 1024%usize;
+      x <- hashMap_remove u64 n hm4 1024%usize;
       match x with
       | None => Fail_ Failure
       | Some x0 =>
         if negb (x0 s= 56%u64)
         then Fail_ Failure
         else (
-          hm5 <- hash_map_remove_back u64 n hm4 1024%usize;
-          i1 <- hash_map_get_fwd u64 n hm5 0%usize;
+          hm5 <- hashMap_remove_back u64 n hm4 1024%usize;
+          i1 <- hashMap_get u64 n hm5 0%usize;
           if negb (i1 s= 42%u64)
           then Fail_ Failure
           else (
-            i2 <- hash_map_get_fwd u64 n hm5 128%usize;
+            i2 <- hashMap_get u64 n hm5 128%usize;
             if negb (i2 s= 18%u64)
             then Fail_ Failure
             else (
-              i3 <- hash_map_get_fwd u64 n hm5 1056%usize;
+              i3 <- hashMap_get u64 n hm5 1056%usize;
               if negb (i3 s= 256%u64) then Fail_ Failure else Return tt)))
       end))
 .
 
-End Hashmap_Funs .
+End Hashmap_Funs.
diff --git a/tests/coq/hashmap/Hashmap_Types.v b/tests/coq/hashmap/Hashmap_Types.v
index dbde6be9..80a43593 100644
--- a/tests/coq/hashmap/Hashmap_Types.v
+++ b/tests/coq/hashmap/Hashmap_Types.v
@@ -8,29 +8,31 @@ Import ListNotations.
 Local Open Scope Primitives_scope.
 Module Hashmap_Types.
 
-(** [hashmap::List] *)
+(** [hashmap::List]
+    Source: 'src/hashmap.rs', lines 19:0-19:16 *)
 Inductive List_t (T : Type) :=
-| ListCons : usize -> T -> List_t T -> List_t T
-| ListNil : List_t T
+| List_Cons : usize -> T -> List_t T -> List_t T
+| List_Nil : List_t T
 .
 
-Arguments ListCons {T} _ _ _.
-Arguments ListNil {T}.
+Arguments List_Cons { _ }.
+Arguments List_Nil { _ }.
 
-(** [hashmap::HashMap] *)
-Record Hash_map_t (T : Type) :=
-mkHash_map_t {
-  Hash_map_num_entries : usize;
-  Hash_map_max_load_factor : (usize * usize);
-  Hash_map_max_load : usize;
-  Hash_map_slots : vec (List_t T);
+(** [hashmap::HashMap]
+    Source: 'src/hashmap.rs', lines 35:0-35:21 *)
+Record HashMap_t (T : Type) :=
+mkHashMap_t {
+  hashMap_num_entries : usize;
+  hashMap_max_load_factor : (usize * usize);
+  hashMap_max_load : usize;
+  hashMap_slots : alloc_vec_Vec (List_t T);
 }
 .
 
-Arguments mkHash_map_t {T} _ _ _ _.
-Arguments Hash_map_num_entries {T}.
-Arguments Hash_map_max_load_factor {T}.
-Arguments Hash_map_max_load {T}.
-Arguments Hash_map_slots {T}.
+Arguments mkHashMap_t { _ }.
+Arguments hashMap_num_entries { _ }.
+Arguments hashMap_max_load_factor { _ }.
+Arguments hashMap_max_load { _ }.
+Arguments hashMap_slots { _ }.
 
-End Hashmap_Types .
+End Hashmap_Types.
diff --git a/tests/coq/hashmap/Primitives.v b/tests/coq/hashmap/Primitives.v
index 71a2d9c3..99ffe070 100644
--- a/tests/coq/hashmap/Primitives.v
+++ b/tests/coq/hashmap/Primitives.v
@@ -63,13 +63,15 @@ Check (if true then Return (1 + 2) else Fail_ Failure)%global = 3.
 
 (*** Misc *)
 
-
 Definition string := Coq.Strings.String.string.
 Definition char := Coq.Strings.Ascii.ascii.
 Definition char_of_byte := Coq.Strings.Ascii.ascii_of_byte.
 
-Definition mem_replace_fwd (a : Type) (x : a) (y : a) : a := x .
-Definition mem_replace_back (a : Type) (x : a) (y : a) : a := y .
+Definition core_mem_replace (a : Type) (x : a) (y : a) : a := x .
+Definition core_mem_replace_back (a : Type) (x : a) (y : a) : a := y .
+
+Record mut_raw_ptr (T : Type) := { mut_raw_ptr_v : T }.
+Record const_raw_ptr (T : Type) := { const_raw_ptr_v : T }.
 
 (*** Scalars *)
 
@@ -253,6 +255,12 @@ Definition scalar_rem {ty} (x y: scalar ty) : result (scalar ty) := mk_scalar ty
   
 Definition scalar_neg {ty} (x: scalar ty) : result (scalar ty) := mk_scalar ty (-(to_Z x)).
 
+Axiom scalar_xor : forall ty, scalar ty -> scalar ty -> scalar ty. (* TODO *)
+Axiom scalar_or : forall ty, scalar ty -> scalar ty -> scalar ty. (* TODO *)
+Axiom scalar_and : forall ty, scalar ty -> scalar ty -> scalar ty. (* TODO *)
+Axiom scalar_shl : forall ty0 ty1, scalar ty0 -> scalar ty1 -> result (scalar ty0). (* TODO *)
+Axiom scalar_shr : forall ty0 ty1, scalar ty0 -> scalar ty1 -> result (scalar ty0). (* TODO *)
+
 (** Cast an integer from a [src_ty] to a [tgt_ty] *)
 (* TODO: check the semantics of casts in Rust *)
 Definition scalar_cast (src_ty tgt_ty : scalar_ty) (x : scalar src_ty) : result (scalar tgt_ty) :=
@@ -370,6 +378,76 @@ Definition u32_mul   := @scalar_mul U32.
 Definition u64_mul   := @scalar_mul U64.
 Definition u128_mul  := @scalar_mul U128.
 
+(** Xor *)
+Definition u8_xor := @scalar_xor U8.
+Definition u16_xor := @scalar_xor U16.
+Definition u32_xor := @scalar_xor U32.
+Definition u64_xor := @scalar_xor U64.
+Definition u128_xor := @scalar_xor U128.
+Definition usize_xor := @scalar_xor Usize.
+Definition i8_xor := @scalar_xor I8.
+Definition i16_xor := @scalar_xor I16.
+Definition i32_xor := @scalar_xor I32.
+Definition i64_xor := @scalar_xor I64.
+Definition i128_xor := @scalar_xor I128.
+Definition isize_xor := @scalar_xor Isize.
+
+(** Or *)
+Definition u8_or := @scalar_or U8.
+Definition u16_or := @scalar_or U16.
+Definition u32_or := @scalar_or U32.
+Definition u64_or := @scalar_or U64.
+Definition u128_or := @scalar_or U128.
+Definition usize_or := @scalar_or Usize.
+Definition i8_or := @scalar_or I8.
+Definition i16_or := @scalar_or I16.
+Definition i32_or := @scalar_or I32.
+Definition i64_or := @scalar_or I64.
+Definition i128_or := @scalar_or I128.
+Definition isize_or := @scalar_or Isize.
+
+(** And *)
+Definition u8_and := @scalar_and U8.
+Definition u16_and := @scalar_and U16.
+Definition u32_and := @scalar_and U32.
+Definition u64_and := @scalar_and U64.
+Definition u128_and := @scalar_and U128.
+Definition usize_and := @scalar_and Usize.
+Definition i8_and := @scalar_and I8.
+Definition i16_and := @scalar_and I16.
+Definition i32_and := @scalar_and I32.
+Definition i64_and := @scalar_and I64.
+Definition i128_and := @scalar_and I128.
+Definition isize_and := @scalar_and Isize.
+
+(** Shift left *)
+Definition u8_shl {ty} := @scalar_shl U8 ty.
+Definition u16_shl {ty} := @scalar_shl U16 ty.
+Definition u32_shl {ty} := @scalar_shl U32 ty.
+Definition u64_shl {ty} := @scalar_shl U64 ty.
+Definition u128_shl {ty} := @scalar_shl U128 ty.
+Definition usize_shl {ty} := @scalar_shl Usize ty.
+Definition i8_shl {ty} := @scalar_shl I8 ty.
+Definition i16_shl {ty} := @scalar_shl I16 ty.
+Definition i32_shl {ty} := @scalar_shl I32 ty.
+Definition i64_shl {ty} := @scalar_shl I64 ty.
+Definition i128_shl {ty} := @scalar_shl I128 ty.
+Definition isize_shl {ty} := @scalar_shl Isize ty.
+
+(** Shift right *)
+Definition u8_shr {ty} := @scalar_shr U8 ty.
+Definition u16_shr {ty} := @scalar_shr U16 ty.
+Definition u32_shr {ty} := @scalar_shr U32 ty.
+Definition u64_shr {ty} := @scalar_shr U64 ty.
+Definition u128_shr {ty} := @scalar_shr U128 ty.
+Definition usize_shr {ty} := @scalar_shr Usize ty.
+Definition i8_shr {ty} := @scalar_shr I8 ty.
+Definition i16_shr {ty} := @scalar_shr I16 ty.
+Definition i32_shr {ty} := @scalar_shr I32 ty.
+Definition i64_shr {ty} := @scalar_shr I64 ty.
+Definition i128_shr {ty} := @scalar_shr I128 ty.
+Definition isize_shr {ty} := @scalar_shr Isize ty.
+
 (** Small utility *)
 Definition usize_to_nat (x: usize) : nat := Z.to_nat (to_Z x).
 
@@ -394,12 +472,89 @@ Notation "x s< y" := (scalar_ltb x y)  (at level 80) : Primitives_scope.
 Notation "x s>= y" := (scalar_geb x y)  (at level 80) : Primitives_scope.
 Notation "x s> y" := (scalar_gtb x y)  (at level 80) : Primitives_scope.
 
-(*** Range *)
-Record range (T : Type) := mk_range {
-  start: T;
-  end_: T;
+(** Constants *)
+Definition core_u8_max    := u8_max %u32.
+Definition core_u16_max   := u16_max %u32.
+Definition core_u32_max   := u32_max %u32.
+Definition core_u64_max   := u64_max %u64.
+Definition core_u128_max  := u64_max %u128.
+Axiom core_usize_max : usize. (** TODO *)
+Definition core_i8_max    := i8_max %i32.
+Definition core_i16_max   := i16_max %i32.
+Definition core_i32_max   := i32_max %i32.
+Definition core_i64_max   := i64_max %i64.
+Definition core_i128_max  := i64_max %i128.
+Axiom core_isize_max : isize. (** TODO *)
+
+(*** core::ops *)
+
+(* Trait declaration: [core::ops::index::Index] *)
+Record core_ops_index_Index (Self Idx : Type) := mk_core_ops_index_Index {
+  core_ops_index_Index_Output : Type;
+  core_ops_index_Index_index : Self -> Idx -> result core_ops_index_Index_Output;
+}.
+Arguments mk_core_ops_index_Index {_ _}.
+Arguments core_ops_index_Index_Output {_ _}.
+Arguments core_ops_index_Index_index {_ _}.
+
+(* Trait declaration: [core::ops::index::IndexMut] *)
+Record core_ops_index_IndexMut (Self Idx : Type) := mk_core_ops_index_IndexMut {
+  core_ops_index_IndexMut_indexInst : core_ops_index_Index Self Idx;
+  core_ops_index_IndexMut_index_mut : Self -> Idx -> result core_ops_index_IndexMut_indexInst.(core_ops_index_Index_Output);
+  core_ops_index_IndexMut_index_mut_back : Self -> Idx -> core_ops_index_IndexMut_indexInst.(core_ops_index_Index_Output) -> result Self;
+}.
+Arguments mk_core_ops_index_IndexMut {_ _}.
+Arguments core_ops_index_IndexMut_indexInst {_ _}.
+Arguments core_ops_index_IndexMut_index_mut {_ _}.
+Arguments core_ops_index_IndexMut_index_mut_back {_ _}.
+
+(* Trait declaration [core::ops::deref::Deref] *)
+Record core_ops_deref_Deref (Self : Type) := mk_core_ops_deref_Deref {
+  core_ops_deref_Deref_target : Type;
+  core_ops_deref_Deref_deref : Self -> result core_ops_deref_Deref_target;
 }.
-Arguments mk_range {_}.
+Arguments mk_core_ops_deref_Deref {_}.
+Arguments core_ops_deref_Deref_target {_}.
+Arguments core_ops_deref_Deref_deref {_}.
+
+(* Trait declaration [core::ops::deref::DerefMut] *)
+Record core_ops_deref_DerefMut (Self : Type) := mk_core_ops_deref_DerefMut {
+  core_ops_deref_DerefMut_derefInst : core_ops_deref_Deref Self;
+  core_ops_deref_DerefMut_deref_mut : Self -> result core_ops_deref_DerefMut_derefInst.(core_ops_deref_Deref_target);
+  core_ops_deref_DerefMut_deref_mut_back : Self -> core_ops_deref_DerefMut_derefInst.(core_ops_deref_Deref_target) -> result Self;
+}.
+Arguments mk_core_ops_deref_DerefMut {_}.
+Arguments core_ops_deref_DerefMut_derefInst {_}.
+Arguments core_ops_deref_DerefMut_deref_mut {_}.
+Arguments core_ops_deref_DerefMut_deref_mut_back {_}.
+
+Record core_ops_range_Range (T : Type) := mk_core_ops_range_Range {
+  core_ops_range_Range_start : T;
+  core_ops_range_Range_end_ : T;
+}.
+Arguments mk_core_ops_range_Range {_}.
+Arguments core_ops_range_Range_start {_}.
+Arguments core_ops_range_Range_end_ {_}.
+
+(*** [alloc] *)
+
+Definition alloc_boxed_Box_deref (T : Type) (x : T) : result T := Return x.
+Definition alloc_boxed_Box_deref_mut (T : Type) (x : T) : result T := Return x.
+Definition alloc_boxed_Box_deref_mut_back (T : Type) (_ : T) (x : T) : result T := Return x.
+
+(* Trait instance *)
+Definition alloc_boxed_Box_coreopsDerefInst (Self : Type) : core_ops_deref_Deref Self := {|
+  core_ops_deref_Deref_target := Self;
+  core_ops_deref_Deref_deref := alloc_boxed_Box_deref Self;
+|}.
+
+(* Trait instance *)
+Definition alloc_boxed_Box_coreopsDerefMutInst (Self : Type) : core_ops_deref_DerefMut Self := {|
+  core_ops_deref_DerefMut_derefInst := alloc_boxed_Box_coreopsDerefInst Self;
+  core_ops_deref_DerefMut_deref_mut := alloc_boxed_Box_deref_mut Self;
+  core_ops_deref_DerefMut_deref_mut_back := alloc_boxed_Box_deref_mut_back Self;
+|}.
+
 
 (*** Arrays *)
 Definition array T (n : usize) := { l: list T | Z.of_nat (length l) = to_Z n}.
@@ -419,51 +574,50 @@ Qed.
 (* TODO: finish the definitions *)
 Axiom mk_array : forall (T : Type) (n : usize) (l : list T), array T n.
 
-Axiom array_index_shared : forall (T : Type) (n : usize) (x : array T n) (i : usize), result T.
-Axiom array_index_mut_fwd : forall (T : Type) (n : usize) (x : array T n) (i : usize), result T.
-Axiom array_index_mut_back : forall (T : Type) (n : usize) (x : array T n) (i : usize) (nx : T), result (array T n).
+(* For initialization *)
+Axiom array_repeat : forall (T : Type) (n : usize) (x : T), array T n.
+
+Axiom array_index_usize : forall (T : Type) (n : usize) (x : array T n) (i : usize), result T.
+Axiom array_update_usize : forall (T : Type) (n : usize) (x : array T n) (i : usize) (nx : T), result (array T n).
 
 (*** Slice *)
 Definition slice T := { l: list T | Z.of_nat (length l) <= usize_max}.
 
 Axiom slice_len : forall (T : Type) (s : slice T), usize.
-Axiom slice_index_shared : forall (T : Type) (x : slice T) (i : usize), result T.
-Axiom slice_index_mut_fwd : forall (T : Type) (x : slice T) (i : usize), result T.
-Axiom slice_index_mut_back : forall (T : Type) (x : slice T) (i : usize) (nx : T), result (slice T).
+Axiom slice_index_usize : forall (T : Type) (x : slice T) (i : usize), result T.
+Axiom slice_update_usize : forall (T : Type) (x : slice T) (i : usize) (nx : T), result (slice T).
 
 (*** Subslices *)
 
-Axiom array_to_slice_shared : forall (T : Type) (n : usize) (x : array T n), result (slice T).
-Axiom array_to_slice_mut_fwd : forall (T : Type) (n : usize) (x : array T n), result (slice T).
-Axiom array_to_slice_mut_back : forall (T : Type) (n : usize) (x : array T n) (s : slice T), result (array T n).
+Axiom array_to_slice : forall (T : Type) (n : usize) (x : array T n), result (slice T).
+Axiom array_from_slice : forall (T : Type) (n : usize) (x : array T n) (s : slice T), result (array T n).
 
-Axiom array_subslice_shared: forall (T : Type) (n : usize) (x : array T n) (r : range usize), result (slice T).
-Axiom array_subslice_mut_fwd: forall (T : Type) (n : usize) (x : array T n) (r : range usize), result (slice T).
-Axiom array_subslice_mut_back: forall (T : Type) (n : usize) (x : array T n) (r : range usize) (ns : slice T), result (array T n).
-Axiom slice_subslice_shared: forall (T : Type) (x : slice T) (r : range usize), result (slice T).
-Axiom slice_subslice_mut_fwd: forall (T : Type) (x : slice T) (r : range usize), result (slice T).
-Axiom slice_subslice_mut_back: forall (T : Type) (x : slice T) (r : range usize) (ns : slice T), result (slice T).
+Axiom array_subslice: forall (T : Type) (n : usize) (x : array T n) (r : core_ops_range_Range usize), result (slice T).
+Axiom array_update_subslice: forall (T : Type) (n : usize) (x : array T n) (r : core_ops_range_Range usize) (ns : slice T), result (array T n).
+
+Axiom slice_subslice: forall (T : Type) (x : slice T) (r : core_ops_range_Range usize), result (slice T).
+Axiom slice_update_subslice: forall (T : Type) (x : slice T) (r : core_ops_range_Range usize) (ns : slice T), result (slice T).
 
 (*** Vectors *)
 
-Definition vec T := { l: list T | Z.of_nat (length l) <= usize_max }.
+Definition alloc_vec_Vec T := { l: list T | Z.of_nat (length l) <= usize_max }.
 
-Definition vec_to_list {T: Type} (v: vec T) : list T := proj1_sig v.
+Definition alloc_vec_Vec_to_list {T: Type} (v: alloc_vec_Vec T) : list T := proj1_sig v.
 
-Definition vec_length {T: Type} (v: vec T) : Z := Z.of_nat (length (vec_to_list v)).
+Definition alloc_vec_Vec_length {T: Type} (v: alloc_vec_Vec T) : Z := Z.of_nat (length (alloc_vec_Vec_to_list v)).
 
-Definition vec_new (T: Type) : vec T := (exist _ [] le_0_usize_max).
+Definition alloc_vec_Vec_new (T: Type) : alloc_vec_Vec T := (exist _ [] le_0_usize_max).
 
-Lemma vec_len_in_usize {T} (v: vec T) : usize_min <= vec_length v <= usize_max.
+Lemma alloc_vec_Vec_len_in_usize {T} (v: alloc_vec_Vec T) : usize_min <= alloc_vec_Vec_length v <= usize_max.
 Proof.
-  unfold vec_length, usize_min.
+  unfold alloc_vec_Vec_length, usize_min.
   split.
   - lia.
   - apply (proj2_sig v).
 Qed.
 
-Definition vec_len (T: Type) (v: vec T) : usize :=
-  exist _ (vec_length v) (vec_len_in_usize v).
+Definition alloc_vec_Vec_len (T: Type) (v: alloc_vec_Vec T) : usize :=
+  exist _ (alloc_vec_Vec_length v) (alloc_vec_Vec_len_in_usize v).
 
 Fixpoint list_update {A} (l: list A) (n: nat) (a: A)
   : list A :=
@@ -474,50 +628,279 @@ Fixpoint list_update {A} (l: list A) (n: nat) (a: A)
     | S m => x :: (list_update t m a)
 end end.
 
-Definition vec_bind {A B} (v: vec A) (f: list A -> result (list B)) : result (vec B) :=
-  l <- f (vec_to_list v) ;
+Definition alloc_vec_Vec_bind {A B} (v: alloc_vec_Vec A) (f: list A -> result (list B)) : result (alloc_vec_Vec B) :=
+  l <- f (alloc_vec_Vec_to_list v) ;
   match sumbool_of_bool (scalar_le_max Usize (Z.of_nat (length l))) with
   | left H => Return (exist _ l (scalar_le_max_valid _ _ H))
   | right _ => Fail_ Failure
   end.
 
 (* The **forward** function shouldn't be used *)
-Definition vec_push_fwd (T: Type) (v: vec T) (x: T) : unit := tt.
+Definition alloc_vec_Vec_push_fwd (T: Type) (v: alloc_vec_Vec T) (x: T) : unit := tt.
 
-Definition vec_push_back (T: Type) (v: vec T) (x: T) : result (vec T) :=
-  vec_bind v (fun l => Return (l ++ [x])).
+Definition alloc_vec_Vec_push (T: Type) (v: alloc_vec_Vec T) (x: T) : result (alloc_vec_Vec T) :=
+  alloc_vec_Vec_bind v (fun l => Return (l ++ [x])).
 
 (* The **forward** function shouldn't be used *)
-Definition vec_insert_fwd (T: Type) (v: vec T) (i: usize) (x: T) : result unit :=
-  if to_Z i <? vec_length v then Return tt else Fail_ Failure.
+Definition alloc_vec_Vec_insert_fwd (T: Type) (v: alloc_vec_Vec T) (i: usize) (x: T) : result unit :=
+  if to_Z i <? alloc_vec_Vec_length v then Return tt else Fail_ Failure.
 
-Definition vec_insert_back (T: Type) (v: vec T) (i: usize) (x: T) : result (vec T) :=
-  vec_bind v (fun l =>
+Definition alloc_vec_Vec_insert (T: Type) (v: alloc_vec_Vec T) (i: usize) (x: T) : result (alloc_vec_Vec T) :=
+  alloc_vec_Vec_bind v (fun l =>
     if to_Z i <? Z.of_nat (length l)
     then Return (list_update l (usize_to_nat i) x)
     else Fail_ Failure).
 
-(* The **backward** function shouldn't be used *)
-Definition vec_index_fwd (T: Type) (v: vec T) (i: usize) : result T :=
-  match nth_error (vec_to_list v) (usize_to_nat i) with
-  | Some n => Return n
-  | None   => Fail_ Failure
-  end.
-
-Definition vec_index_back (T: Type) (v: vec T) (i: usize) (x: T) : result unit :=
-  if to_Z i <? vec_length v then Return tt else Fail_ Failure.
-
-(* The **backward** function shouldn't be used *)
-Definition vec_index_mut_fwd (T: Type) (v: vec T) (i: usize) : result T :=
-  match nth_error (vec_to_list v) (usize_to_nat i) with
-  | Some n => Return n
-  | None   => Fail_ Failure
+(* Helper *)
+Axiom alloc_vec_Vec_index_usize : forall {T : Type} (v : alloc_vec_Vec T) (i : usize), result T.
+
+(* Helper *)
+Axiom alloc_vec_Vec_update_usize : forall {T : Type} (v : alloc_vec_Vec T) (i : usize) (x : T), result (alloc_vec_Vec T).
+
+(* Trait declaration: [core::slice::index::private_slice_index::Sealed] *)
+Definition core_slice_index_private_slice_index_Sealed (self : Type) := unit.
+
+(* Trait declaration: [core::slice::index::SliceIndex] *)
+Record core_slice_index_SliceIndex (Self T : Type) := mk_core_slice_index_SliceIndex {
+  core_slice_index_SliceIndex_sealedInst : core_slice_index_private_slice_index_Sealed Self;
+  core_slice_index_SliceIndex_Output : Type;
+  core_slice_index_SliceIndex_get : Self -> T -> result (option core_slice_index_SliceIndex_Output);
+  core_slice_index_SliceIndex_get_mut : Self -> T -> result (option core_slice_index_SliceIndex_Output);
+  core_slice_index_SliceIndex_get_mut_back : Self -> T -> option core_slice_index_SliceIndex_Output -> result T;
+  core_slice_index_SliceIndex_get_unchecked : Self -> const_raw_ptr T -> result (const_raw_ptr core_slice_index_SliceIndex_Output);
+  core_slice_index_SliceIndex_get_unchecked_mut : Self -> mut_raw_ptr T -> result (mut_raw_ptr core_slice_index_SliceIndex_Output);
+  core_slice_index_SliceIndex_index : Self -> T -> result core_slice_index_SliceIndex_Output;
+  core_slice_index_SliceIndex_index_mut : Self -> T -> result core_slice_index_SliceIndex_Output;
+  core_slice_index_SliceIndex_index_mut_back : Self -> T -> core_slice_index_SliceIndex_Output -> result T;
+}.
+Arguments mk_core_slice_index_SliceIndex {_ _}.
+Arguments core_slice_index_SliceIndex_sealedInst {_ _}.
+Arguments core_slice_index_SliceIndex_Output {_ _}.
+Arguments core_slice_index_SliceIndex_get {_ _}.
+Arguments core_slice_index_SliceIndex_get_mut {_ _}.
+Arguments core_slice_index_SliceIndex_get_mut_back {_ _}.
+Arguments core_slice_index_SliceIndex_get_unchecked {_ _}.
+Arguments core_slice_index_SliceIndex_get_unchecked_mut {_ _}.
+Arguments core_slice_index_SliceIndex_index {_ _}.
+Arguments core_slice_index_SliceIndex_index_mut {_ _}.
+Arguments core_slice_index_SliceIndex_index_mut_back {_ _}.
+
+(* [core::slice::index::[T]::index]: forward function *)
+Definition core_slice_index_Slice_index
+  (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T))
+  (s : slice T) (i : Idx) : result inst.(core_slice_index_SliceIndex_Output) :=
+  x <- inst.(core_slice_index_SliceIndex_get) i s;
+  match x with
+  | None => Fail_ Failure
+  | Some x => Return x
   end.
 
-Definition vec_index_mut_back (T: Type) (v: vec T) (i: usize) (x: T) : result (vec T) :=
-  vec_bind v (fun l =>
-    if to_Z i <? Z.of_nat (length l)
-    then Return (list_update l (usize_to_nat i) x)
-    else Fail_ Failure).
+(* [core::slice::index::Range:::get]: forward function *)
+Axiom core_slice_index_RangeUsize_get : forall (T : Type) (i : core_ops_range_Range usize) (s : slice T), result (option (slice T)).
+
+(* [core::slice::index::Range::get_mut]: forward function *)
+Axiom core_slice_index_RangeUsize_get_mut :
+  forall (T : Type), core_ops_range_Range usize -> slice T -> result (option (slice T)).
+
+(* [core::slice::index::Range::get_mut]: backward function 0 *)
+Axiom core_slice_index_RangeUsize_get_mut_back :
+  forall (T : Type), core_ops_range_Range usize -> slice T -> option (slice T) -> result (slice T).
+
+(* [core::slice::index::Range::get_unchecked]: forward function *)
+Definition core_slice_index_RangeUsize_get_unchecked
+  (T : Type) :
+  core_ops_range_Range usize -> const_raw_ptr (slice T) -> result (const_raw_ptr (slice T)) :=
+  (* Don't know what the model should be - for now we always fail to make
+     sure code which uses it fails *)
+  fun _ _ => Fail_ Failure.
+
+(* [core::slice::index::Range::get_unchecked_mut]: forward function *)
+Definition core_slice_index_RangeUsize_get_unchecked_mut
+  (T : Type) :
+  core_ops_range_Range usize -> mut_raw_ptr (slice T) -> result (mut_raw_ptr (slice T)) :=
+  (* Don't know what the model should be - for now we always fail to make
+    sure code which uses it fails *)
+  fun _ _ => Fail_ Failure.
+
+(* [core::slice::index::Range::index]: forward function *)
+Axiom core_slice_index_RangeUsize_index :
+  forall (T : Type), core_ops_range_Range usize -> slice T -> result (slice T).
+
+(* [core::slice::index::Range::index_mut]: forward function *)
+Axiom core_slice_index_RangeUsize_index_mut :
+  forall (T : Type), core_ops_range_Range usize -> slice T -> result (slice T).
+
+(* [core::slice::index::Range::index_mut]: backward function 0 *)
+Axiom core_slice_index_RangeUsize_index_mut_back :
+  forall (T : Type), core_ops_range_Range usize -> slice T -> slice T -> result (slice T).
+
+(* [core::slice::index::[T]::index_mut]: forward function *)
+Axiom core_slice_index_Slice_index_mut :
+  forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T)),
+  slice T -> Idx -> result inst.(core_slice_index_SliceIndex_Output).
+
+(* [core::slice::index::[T]::index_mut]: backward function 0 *)
+Axiom core_slice_index_Slice_index_mut_back :
+  forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T)),
+  slice T -> Idx -> inst.(core_slice_index_SliceIndex_Output) -> result (slice T).
+
+(* [core::array::[T; N]::index]: forward function *)
+Axiom core_array_Array_index :
+  forall (T Idx : Type) (N : usize) (inst : core_ops_index_Index (slice T) Idx)
+  (a : array T N) (i : Idx), result inst.(core_ops_index_Index_Output).
+
+(* [core::array::[T; N]::index_mut]: forward function *)
+Axiom core_array_Array_index_mut :
+  forall (T Idx : Type) (N : usize) (inst : core_ops_index_IndexMut (slice T) Idx)
+  (a : array T N) (i : Idx), result inst.(core_ops_index_IndexMut_indexInst).(core_ops_index_Index_Output).
+
+(* [core::array::[T; N]::index_mut]: backward function 0 *)
+Axiom core_array_Array_index_mut_back :
+  forall (T Idx : Type) (N : usize) (inst : core_ops_index_IndexMut (slice T) Idx)
+  (a : array T N) (i : Idx) (x : inst.(core_ops_index_IndexMut_indexInst).(core_ops_index_Index_Output)), result (array T N).
+
+(* Trait implementation: [core::slice::index::private_slice_index::Range] *)
+Definition core_slice_index_private_slice_index_SealedRangeUsizeInst
+  : core_slice_index_private_slice_index_Sealed (core_ops_range_Range usize) := tt.
+
+(* Trait implementation: [core::slice::index::Range] *)
+Definition core_slice_index_SliceIndexRangeUsizeSliceTInst (T : Type) :
+  core_slice_index_SliceIndex (core_ops_range_Range usize) (slice T) := {|
+  core_slice_index_SliceIndex_sealedInst := core_slice_index_private_slice_index_SealedRangeUsizeInst;
+  core_slice_index_SliceIndex_Output := slice T;
+  core_slice_index_SliceIndex_get := core_slice_index_RangeUsize_get T;
+  core_slice_index_SliceIndex_get_mut := core_slice_index_RangeUsize_get_mut T;
+  core_slice_index_SliceIndex_get_mut_back := core_slice_index_RangeUsize_get_mut_back T;
+  core_slice_index_SliceIndex_get_unchecked := core_slice_index_RangeUsize_get_unchecked T;
+  core_slice_index_SliceIndex_get_unchecked_mut := core_slice_index_RangeUsize_get_unchecked_mut T;
+  core_slice_index_SliceIndex_index := core_slice_index_RangeUsize_index T;
+  core_slice_index_SliceIndex_index_mut := core_slice_index_RangeUsize_index_mut T;
+  core_slice_index_SliceIndex_index_mut_back := core_slice_index_RangeUsize_index_mut_back T;
+|}.
+
+(* Trait implementation: [core::slice::index::[T]] *)
+Definition core_ops_index_IndexSliceTIInst (T Idx : Type)
+  (inst : core_slice_index_SliceIndex Idx (slice T)) :
+  core_ops_index_Index (slice T) Idx := {|
+  core_ops_index_Index_Output := inst.(core_slice_index_SliceIndex_Output);
+  core_ops_index_Index_index := core_slice_index_Slice_index T Idx inst;
+|}.
+
+(* Trait implementation: [core::slice::index::[T]] *)
+Definition core_ops_index_IndexMutSliceTIInst (T Idx : Type)
+  (inst : core_slice_index_SliceIndex Idx (slice T)) :
+  core_ops_index_IndexMut (slice T) Idx := {|
+  core_ops_index_IndexMut_indexInst := core_ops_index_IndexSliceTIInst T Idx inst;
+  core_ops_index_IndexMut_index_mut := core_slice_index_Slice_index_mut T Idx inst;
+  core_ops_index_IndexMut_index_mut_back := core_slice_index_Slice_index_mut_back T Idx inst;
+|}.
+
+(* Trait implementation: [core::array::[T; N]] *)
+Definition core_ops_index_IndexArrayInst (T Idx : Type) (N : usize)
+  (inst : core_ops_index_Index (slice T) Idx) :
+  core_ops_index_Index (array T N) Idx := {|
+  core_ops_index_Index_Output := inst.(core_ops_index_Index_Output);
+  core_ops_index_Index_index := core_array_Array_index T Idx N inst;
+|}.
+
+(* Trait implementation: [core::array::[T; N]] *)
+Definition core_ops_index_IndexMutArrayInst (T Idx : Type) (N : usize)
+  (inst : core_ops_index_IndexMut (slice T) Idx) :
+  core_ops_index_IndexMut (array T N) Idx := {|
+  core_ops_index_IndexMut_indexInst := core_ops_index_IndexArrayInst T Idx N inst.(core_ops_index_IndexMut_indexInst);
+  core_ops_index_IndexMut_index_mut := core_array_Array_index_mut T Idx N inst;
+  core_ops_index_IndexMut_index_mut_back := core_array_Array_index_mut_back T Idx N inst;
+|}.
+
+(* [core::slice::index::usize::get]: forward function *)
+Axiom core_slice_index_usize_get : forall (T : Type), usize -> slice T -> result (option T).
+
+(* [core::slice::index::usize::get_mut]: forward function *)
+Axiom core_slice_index_usize_get_mut : forall (T : Type), usize -> slice T -> result (option T).
+
+(* [core::slice::index::usize::get_mut]: backward function 0 *)
+Axiom core_slice_index_usize_get_mut_back :
+  forall (T : Type), usize -> slice T -> option T -> result (slice T).
+
+(* [core::slice::index::usize::get_unchecked]: forward function *)
+Axiom core_slice_index_usize_get_unchecked :
+  forall (T : Type), usize -> const_raw_ptr (slice T) -> result (const_raw_ptr T).
+
+(* [core::slice::index::usize::get_unchecked_mut]: forward function *)
+Axiom core_slice_index_usize_get_unchecked_mut :
+  forall (T : Type), usize -> mut_raw_ptr (slice T) -> result (mut_raw_ptr T).
+
+(* [core::slice::index::usize::index]: forward function *)
+Axiom core_slice_index_usize_index : forall (T : Type), usize -> slice T -> result T.
+
+(* [core::slice::index::usize::index_mut]: forward function *)
+Axiom core_slice_index_usize_index_mut : forall (T : Type), usize -> slice T -> result T.
+
+(* [core::slice::index::usize::index_mut]: backward function 0 *)
+Axiom core_slice_index_usize_index_mut_back :
+  forall (T : Type), usize -> slice T -> T -> result (slice T).
+
+(* Trait implementation: [core::slice::index::private_slice_index::usize] *)
+Definition core_slice_index_private_slice_index_SealedUsizeInst
+  : core_slice_index_private_slice_index_Sealed usize := tt.
+
+(* Trait implementation: [core::slice::index::usize] *)
+Definition core_slice_index_SliceIndexUsizeSliceTInst (T : Type) :
+  core_slice_index_SliceIndex usize (slice T) := {|
+  core_slice_index_SliceIndex_sealedInst := core_slice_index_private_slice_index_SealedUsizeInst;
+  core_slice_index_SliceIndex_Output := T;
+  core_slice_index_SliceIndex_get := core_slice_index_usize_get T;
+  core_slice_index_SliceIndex_get_mut := core_slice_index_usize_get_mut T;
+  core_slice_index_SliceIndex_get_mut_back := core_slice_index_usize_get_mut_back T;
+  core_slice_index_SliceIndex_get_unchecked := core_slice_index_usize_get_unchecked T;
+  core_slice_index_SliceIndex_get_unchecked_mut := core_slice_index_usize_get_unchecked_mut T;
+  core_slice_index_SliceIndex_index := core_slice_index_usize_index T;
+  core_slice_index_SliceIndex_index_mut := core_slice_index_usize_index_mut T;
+  core_slice_index_SliceIndex_index_mut_back := core_slice_index_usize_index_mut_back T;
+|}.
+
+(* [alloc::vec::Vec::index]: forward function *)
+Axiom alloc_vec_Vec_index : forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T))
+  (Self : alloc_vec_Vec T) (i : Idx), result inst.(core_slice_index_SliceIndex_Output).
+
+(* [alloc::vec::Vec::index_mut]: forward function *)
+Axiom alloc_vec_Vec_index_mut : forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T))
+  (Self : alloc_vec_Vec T) (i : Idx), result inst.(core_slice_index_SliceIndex_Output).
+
+(* [alloc::vec::Vec::index_mut]: backward function 0 *)
+Axiom alloc_vec_Vec_index_mut_back :
+  forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T))
+  (Self : alloc_vec_Vec T) (i : Idx) (x : inst.(core_slice_index_SliceIndex_Output)), result (alloc_vec_Vec T).
+
+(* Trait implementation: [alloc::vec::Vec] *)
+Definition alloc_vec_Vec_coreopsindexIndexInst (T Idx : Type)
+  (inst : core_slice_index_SliceIndex Idx (slice T)) :
+  core_ops_index_Index (alloc_vec_Vec T) Idx := {|
+  core_ops_index_Index_Output := inst.(core_slice_index_SliceIndex_Output);
+  core_ops_index_Index_index := alloc_vec_Vec_index T Idx inst;
+|}.
+
+(* Trait implementation: [alloc::vec::Vec] *)
+Definition alloc_vec_Vec_coreopsindexIndexMutInst (T Idx : Type)
+  (inst : core_slice_index_SliceIndex Idx (slice T)) :
+  core_ops_index_IndexMut (alloc_vec_Vec T) Idx := {|
+  core_ops_index_IndexMut_indexInst := alloc_vec_Vec_coreopsindexIndexInst T Idx inst;
+  core_ops_index_IndexMut_index_mut := alloc_vec_Vec_index_mut T Idx inst;
+  core_ops_index_IndexMut_index_mut_back := alloc_vec_Vec_index_mut_back T Idx inst;
+|}.
+
+(*** Theorems *)
+
+Axiom alloc_vec_Vec_index_eq : forall {a : Type} (v : alloc_vec_Vec a) (i : usize) (x : a),
+  alloc_vec_Vec_index a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i =
+    alloc_vec_Vec_index_usize v i.
+
+Axiom alloc_vec_Vec_index_mut_eq : forall {a : Type} (v : alloc_vec_Vec a) (i : usize) (x : a),
+  alloc_vec_Vec_index_mut a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i =
+    alloc_vec_Vec_index_usize v i.
+
+Axiom alloc_vec_Vec_index_mut_back_eq : forall {a : Type} (v : alloc_vec_Vec a) (i : usize) (x : a),
+  alloc_vec_Vec_index_mut_back a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i x =
+    alloc_vec_Vec_update_usize v i x.
 
 End Primitives.
diff --git a/tests/coq/hashmap_on_disk/HashmapMain_Funs.v b/tests/coq/hashmap_on_disk/HashmapMain_Funs.v
index 657d5590..faba0afe 100644
--- a/tests/coq/hashmap_on_disk/HashmapMain_Funs.v
+++ b/tests/coq/hashmap_on_disk/HashmapMain_Funs.v
@@ -6,663 +6,715 @@ Require Import Coq.ZArith.ZArith.
 Require Import List.
 Import ListNotations.
 Local Open Scope Primitives_scope.
-Require Export HashmapMain_Types.
-Import HashmapMain_Types.
-Require Export HashmapMain_Opaque.
-Import HashmapMain_Opaque.
+Require Import HashmapMain_Types.
+Include HashmapMain_Types.
+Require Import HashmapMain_FunsExternal.
+Include HashmapMain_FunsExternal.
 Module HashmapMain_Funs.
 
-(** [hashmap_main::hashmap::hash_key]: forward function *)
-Definition hashmap_hash_key_fwd (k : usize) : result usize :=
+(** [hashmap_main::hashmap::hash_key]: forward function
+    Source: 'src/hashmap.rs', lines 27:0-27:32 *)
+Definition hashmap_hash_key (k : usize) : result usize :=
   Return k.
 
-(** [hashmap_main::hashmap::HashMap::{0}::allocate_slots]: loop 0: forward function *)
-Fixpoint hashmap_hash_map_allocate_slots_loop_fwd
-  (T : Type) (n : nat) (slots : vec (Hashmap_list_t T)) (n0 : usize) :
-  result (vec (Hashmap_list_t T))
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::allocate_slots]: loop 0: forward function
+    Source: 'src/hashmap.rs', lines 50:4-56:5 *)
+Fixpoint hashmap_HashMap_allocate_slots_loop
+  (T : Type) (n : nat) (slots : alloc_vec_Vec (hashmap_List_t T)) (n0 : usize)
+  :
+  result (alloc_vec_Vec (hashmap_List_t T))
   :=
   match n with
   | O => Fail_ OutOfFuel
   | S n1 =>
     if n0 s> 0%usize
     then (
-      slots0 <- vec_push_back (Hashmap_list_t T) slots HashmapListNil;
+      slots0 <- alloc_vec_Vec_push (hashmap_List_t T) slots Hashmap_List_Nil;
       n2 <- usize_sub n0 1%usize;
-      hashmap_hash_map_allocate_slots_loop_fwd T n1 slots0 n2)
+      hashmap_HashMap_allocate_slots_loop T n1 slots0 n2)
     else Return slots
   end
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::allocate_slots]: forward function *)
-Definition hashmap_hash_map_allocate_slots_fwd
-  (T : Type) (n : nat) (slots : vec (Hashmap_list_t T)) (n0 : usize) :
-  result (vec (Hashmap_list_t T))
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::allocate_slots]: forward function
+    Source: 'src/hashmap.rs', lines 50:4-50:76 *)
+Definition hashmap_HashMap_allocate_slots
+  (T : Type) (n : nat) (slots : alloc_vec_Vec (hashmap_List_t T)) (n0 : usize)
+  :
+  result (alloc_vec_Vec (hashmap_List_t T))
   :=
-  hashmap_hash_map_allocate_slots_loop_fwd T n slots n0
+  hashmap_HashMap_allocate_slots_loop T n slots n0
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::new_with_capacity]: forward function *)
-Definition hashmap_hash_map_new_with_capacity_fwd
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::new_with_capacity]: forward function
+    Source: 'src/hashmap.rs', lines 59:4-63:13 *)
+Definition hashmap_HashMap_new_with_capacity
   (T : Type) (n : nat) (capacity : usize) (max_load_dividend : usize)
   (max_load_divisor : usize) :
-  result (Hashmap_hash_map_t T)
+  result (hashmap_HashMap_t T)
   :=
-  let v := vec_new (Hashmap_list_t T) in
-  slots <- hashmap_hash_map_allocate_slots_fwd T n v capacity;
+  let v := alloc_vec_Vec_new (hashmap_List_t T) in
+  slots <- hashmap_HashMap_allocate_slots T n v capacity;
   i <- usize_mul capacity max_load_dividend;
   i0 <- usize_div i max_load_divisor;
   Return
     {|
-      Hashmap_hash_map_num_entries := 0%usize;
-      Hashmap_hash_map_max_load_factor := (max_load_dividend, max_load_divisor);
-      Hashmap_hash_map_max_load := i0;
-      Hashmap_hash_map_slots := slots
+      hashmap_HashMap_num_entries := 0%usize;
+      hashmap_HashMap_max_load_factor := (max_load_dividend, max_load_divisor);
+      hashmap_HashMap_max_load := i0;
+      hashmap_HashMap_slots := slots
     |}
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::new]: forward function *)
-Definition hashmap_hash_map_new_fwd
-  (T : Type) (n : nat) : result (Hashmap_hash_map_t T) :=
-  hashmap_hash_map_new_with_capacity_fwd T n 32%usize 4%usize 5%usize
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::new]: forward function
+    Source: 'src/hashmap.rs', lines 75:4-75:24 *)
+Definition hashmap_HashMap_new
+  (T : Type) (n : nat) : result (hashmap_HashMap_t T) :=
+  hashmap_HashMap_new_with_capacity T n 32%usize 4%usize 5%usize
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::clear]: loop 0: merged forward/backward function
-    (there is a single backward function, and the forward function returns ()) *)
-Fixpoint hashmap_hash_map_clear_loop_fwd_back
-  (T : Type) (n : nat) (slots : vec (Hashmap_list_t T)) (i : usize) :
-  result (vec (Hashmap_list_t T))
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::clear]: loop 0: merged forward/backward function
+    (there is a single backward function, and the forward function returns ())
+    Source: 'src/hashmap.rs', lines 80:4-88:5 *)
+Fixpoint hashmap_HashMap_clear_loop
+  (T : Type) (n : nat) (slots : alloc_vec_Vec (hashmap_List_t T)) (i : usize) :
+  result (alloc_vec_Vec (hashmap_List_t T))
   :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
-    let i0 := vec_len (Hashmap_list_t T) slots in
+    let i0 := alloc_vec_Vec_len (hashmap_List_t T) slots in
     if i s< i0
     then (
       i1 <- usize_add i 1%usize;
-      slots0 <- vec_index_mut_back (Hashmap_list_t T) slots i HashmapListNil;
-      hashmap_hash_map_clear_loop_fwd_back T n0 slots0 i1)
+      slots0 <-
+        alloc_vec_Vec_index_mut_back (hashmap_List_t T) usize
+          (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t T)) slots
+          i Hashmap_List_Nil;
+      hashmap_HashMap_clear_loop T n0 slots0 i1)
     else Return slots
   end
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::clear]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ()) *)
-Definition hashmap_hash_map_clear_fwd_back
-  (T : Type) (n : nat) (self : Hashmap_hash_map_t T) :
-  result (Hashmap_hash_map_t T)
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::clear]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ())
+    Source: 'src/hashmap.rs', lines 80:4-80:27 *)
+Definition hashmap_HashMap_clear
+  (T : Type) (n : nat) (self : hashmap_HashMap_t T) :
+  result (hashmap_HashMap_t T)
   :=
-  v <-
-    hashmap_hash_map_clear_loop_fwd_back T n self.(Hashmap_hash_map_slots)
-      0%usize;
+  v <- hashmap_HashMap_clear_loop T n self.(hashmap_HashMap_slots) 0%usize;
   Return
     {|
-      Hashmap_hash_map_num_entries := 0%usize;
-      Hashmap_hash_map_max_load_factor :=
-        self.(Hashmap_hash_map_max_load_factor);
-      Hashmap_hash_map_max_load := self.(Hashmap_hash_map_max_load);
-      Hashmap_hash_map_slots := v
+      hashmap_HashMap_num_entries := 0%usize;
+      hashmap_HashMap_max_load_factor := self.(hashmap_HashMap_max_load_factor);
+      hashmap_HashMap_max_load := self.(hashmap_HashMap_max_load);
+      hashmap_HashMap_slots := v
     |}
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::len]: forward function *)
-Definition hashmap_hash_map_len_fwd
-  (T : Type) (self : Hashmap_hash_map_t T) : result usize :=
-  Return self.(Hashmap_hash_map_num_entries)
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::len]: forward function
+    Source: 'src/hashmap.rs', lines 90:4-90:30 *)
+Definition hashmap_HashMap_len
+  (T : Type) (self : hashmap_HashMap_t T) : result usize :=
+  Return self.(hashmap_HashMap_num_entries)
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::insert_in_list]: loop 0: forward function *)
-Fixpoint hashmap_hash_map_insert_in_list_loop_fwd
-  (T : Type) (n : nat) (key : usize) (value : T) (ls : Hashmap_list_t T) :
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::insert_in_list]: loop 0: forward function
+    Source: 'src/hashmap.rs', lines 97:4-114:5 *)
+Fixpoint hashmap_HashMap_insert_in_list_loop
+  (T : Type) (n : nat) (key : usize) (value : T) (ls : hashmap_List_t T) :
   result bool
   :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls with
-    | HashmapListCons ckey cvalue tl =>
+    | Hashmap_List_Cons ckey cvalue tl =>
       if ckey s= key
       then Return false
-      else hashmap_hash_map_insert_in_list_loop_fwd T n0 key value tl
-    | HashmapListNil => Return true
+      else hashmap_HashMap_insert_in_list_loop T n0 key value tl
+    | Hashmap_List_Nil => Return true
     end
   end
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::insert_in_list]: forward function *)
-Definition hashmap_hash_map_insert_in_list_fwd
-  (T : Type) (n : nat) (key : usize) (value : T) (ls : Hashmap_list_t T) :
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::insert_in_list]: forward function
+    Source: 'src/hashmap.rs', lines 97:4-97:71 *)
+Definition hashmap_HashMap_insert_in_list
+  (T : Type) (n : nat) (key : usize) (value : T) (ls : hashmap_List_t T) :
   result bool
   :=
-  hashmap_hash_map_insert_in_list_loop_fwd T n key value ls
+  hashmap_HashMap_insert_in_list_loop T n key value ls
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::insert_in_list]: loop 0: backward function 0 *)
-Fixpoint hashmap_hash_map_insert_in_list_loop_back
-  (T : Type) (n : nat) (key : usize) (value : T) (ls : Hashmap_list_t T) :
-  result (Hashmap_list_t T)
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::insert_in_list]: loop 0: backward function 0
+    Source: 'src/hashmap.rs', lines 97:4-114:5 *)
+Fixpoint hashmap_HashMap_insert_in_list_loop_back
+  (T : Type) (n : nat) (key : usize) (value : T) (ls : hashmap_List_t T) :
+  result (hashmap_List_t T)
   :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls with
-    | HashmapListCons ckey cvalue tl =>
+    | Hashmap_List_Cons ckey cvalue tl =>
       if ckey s= key
-      then Return (HashmapListCons ckey value tl)
+      then Return (Hashmap_List_Cons ckey value tl)
       else (
-        tl0 <- hashmap_hash_map_insert_in_list_loop_back T n0 key value tl;
-        Return (HashmapListCons ckey cvalue tl0))
-    | HashmapListNil =>
-      let l := HashmapListNil in Return (HashmapListCons key value l)
+        tl0 <- hashmap_HashMap_insert_in_list_loop_back T n0 key value tl;
+        Return (Hashmap_List_Cons ckey cvalue tl0))
+    | Hashmap_List_Nil =>
+      let l := Hashmap_List_Nil in Return (Hashmap_List_Cons key value l)
     end
   end
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::insert_in_list]: backward function 0 *)
-Definition hashmap_hash_map_insert_in_list_back
-  (T : Type) (n : nat) (key : usize) (value : T) (ls : Hashmap_list_t T) :
-  result (Hashmap_list_t T)
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::insert_in_list]: backward function 0
+    Source: 'src/hashmap.rs', lines 97:4-97:71 *)
+Definition hashmap_HashMap_insert_in_list_back
+  (T : Type) (n : nat) (key : usize) (value : T) (ls : hashmap_List_t T) :
+  result (hashmap_List_t T)
   :=
-  hashmap_hash_map_insert_in_list_loop_back T n key value ls
+  hashmap_HashMap_insert_in_list_loop_back T n key value ls
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::insert_no_resize]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ()) *)
-Definition hashmap_hash_map_insert_no_resize_fwd_back
-  (T : Type) (n : nat) (self : Hashmap_hash_map_t T) (key : usize) (value : T)
-  :
-  result (Hashmap_hash_map_t T)
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::insert_no_resize]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ())
+    Source: 'src/hashmap.rs', lines 117:4-117:54 *)
+Definition hashmap_HashMap_insert_no_resize
+  (T : Type) (n : nat) (self : hashmap_HashMap_t T) (key : usize) (value : T) :
+  result (hashmap_HashMap_t T)
   :=
-  hash <- hashmap_hash_key_fwd key;
-  let i := vec_len (Hashmap_list_t T) self.(Hashmap_hash_map_slots) in
+  hash <- hashmap_hash_key key;
+  let i := alloc_vec_Vec_len (hashmap_List_t T) self.(hashmap_HashMap_slots) in
   hash_mod <- usize_rem hash i;
   l <-
-    vec_index_mut_fwd (Hashmap_list_t T) self.(Hashmap_hash_map_slots) hash_mod;
-  inserted <- hashmap_hash_map_insert_in_list_fwd T n key value l;
+    alloc_vec_Vec_index_mut (hashmap_List_t T) usize
+      (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t T))
+      self.(hashmap_HashMap_slots) hash_mod;
+  inserted <- hashmap_HashMap_insert_in_list T n key value l;
   if inserted
   then (
-    i0 <- usize_add self.(Hashmap_hash_map_num_entries) 1%usize;
-    l0 <- hashmap_hash_map_insert_in_list_back T n key value l;
+    i0 <- usize_add self.(hashmap_HashMap_num_entries) 1%usize;
+    l0 <- hashmap_HashMap_insert_in_list_back T n key value l;
     v <-
-      vec_index_mut_back (Hashmap_list_t T) self.(Hashmap_hash_map_slots)
-        hash_mod l0;
+      alloc_vec_Vec_index_mut_back (hashmap_List_t T) usize
+        (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t T))
+        self.(hashmap_HashMap_slots) hash_mod l0;
     Return
       {|
-        Hashmap_hash_map_num_entries := i0;
-        Hashmap_hash_map_max_load_factor :=
-          self.(Hashmap_hash_map_max_load_factor);
-        Hashmap_hash_map_max_load := self.(Hashmap_hash_map_max_load);
-        Hashmap_hash_map_slots := v
+        hashmap_HashMap_num_entries := i0;
+        hashmap_HashMap_max_load_factor :=
+          self.(hashmap_HashMap_max_load_factor);
+        hashmap_HashMap_max_load := self.(hashmap_HashMap_max_load);
+        hashmap_HashMap_slots := v
       |})
   else (
-    l0 <- hashmap_hash_map_insert_in_list_back T n key value l;
+    l0 <- hashmap_HashMap_insert_in_list_back T n key value l;
     v <-
-      vec_index_mut_back (Hashmap_list_t T) self.(Hashmap_hash_map_slots)
-        hash_mod l0;
+      alloc_vec_Vec_index_mut_back (hashmap_List_t T) usize
+        (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t T))
+        self.(hashmap_HashMap_slots) hash_mod l0;
     Return
       {|
-        Hashmap_hash_map_num_entries := self.(Hashmap_hash_map_num_entries);
-        Hashmap_hash_map_max_load_factor :=
-          self.(Hashmap_hash_map_max_load_factor);
-        Hashmap_hash_map_max_load := self.(Hashmap_hash_map_max_load);
-        Hashmap_hash_map_slots := v
+        hashmap_HashMap_num_entries := self.(hashmap_HashMap_num_entries);
+        hashmap_HashMap_max_load_factor :=
+          self.(hashmap_HashMap_max_load_factor);
+        hashmap_HashMap_max_load := self.(hashmap_HashMap_max_load);
+        hashmap_HashMap_slots := v
       |})
 .
 
-(** [core::num::u32::{8}::MAX] *)
-Definition core_num_u32_max_body : result u32 := Return 4294967295%u32.
-Definition core_num_u32_max_c : u32 := core_num_u32_max_body%global.
-
-(** [hashmap_main::hashmap::HashMap::{0}::move_elements_from_list]: loop 0: merged forward/backward function
-    (there is a single backward function, and the forward function returns ()) *)
-Fixpoint hashmap_hash_map_move_elements_from_list_loop_fwd_back
-  (T : Type) (n : nat) (ntable : Hashmap_hash_map_t T) (ls : Hashmap_list_t T)
-  :
-  result (Hashmap_hash_map_t T)
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::move_elements_from_list]: loop 0: merged forward/backward function
+    (there is a single backward function, and the forward function returns ())
+    Source: 'src/hashmap.rs', lines 183:4-196:5 *)
+Fixpoint hashmap_HashMap_move_elements_from_list_loop
+  (T : Type) (n : nat) (ntable : hashmap_HashMap_t T) (ls : hashmap_List_t T) :
+  result (hashmap_HashMap_t T)
   :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls with
-    | HashmapListCons k v tl =>
-      ntable0 <- hashmap_hash_map_insert_no_resize_fwd_back T n0 ntable k v;
-      hashmap_hash_map_move_elements_from_list_loop_fwd_back T n0 ntable0 tl
-    | HashmapListNil => Return ntable
+    | Hashmap_List_Cons k v tl =>
+      ntable0 <- hashmap_HashMap_insert_no_resize T n0 ntable k v;
+      hashmap_HashMap_move_elements_from_list_loop T n0 ntable0 tl
+    | Hashmap_List_Nil => Return ntable
     end
   end
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::move_elements_from_list]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ()) *)
-Definition hashmap_hash_map_move_elements_from_list_fwd_back
-  (T : Type) (n : nat) (ntable : Hashmap_hash_map_t T) (ls : Hashmap_list_t T)
-  :
-  result (Hashmap_hash_map_t T)
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::move_elements_from_list]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ())
+    Source: 'src/hashmap.rs', lines 183:4-183:72 *)
+Definition hashmap_HashMap_move_elements_from_list
+  (T : Type) (n : nat) (ntable : hashmap_HashMap_t T) (ls : hashmap_List_t T) :
+  result (hashmap_HashMap_t T)
   :=
-  hashmap_hash_map_move_elements_from_list_loop_fwd_back T n ntable ls
+  hashmap_HashMap_move_elements_from_list_loop T n ntable ls
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::move_elements]: loop 0: merged forward/backward function
-    (there is a single backward function, and the forward function returns ()) *)
-Fixpoint hashmap_hash_map_move_elements_loop_fwd_back
-  (T : Type) (n : nat) (ntable : Hashmap_hash_map_t T)
-  (slots : vec (Hashmap_list_t T)) (i : usize) :
-  result ((Hashmap_hash_map_t T) * (vec (Hashmap_list_t T)))
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::move_elements]: loop 0: merged forward/backward function
+    (there is a single backward function, and the forward function returns ())
+    Source: 'src/hashmap.rs', lines 171:4-180:5 *)
+Fixpoint hashmap_HashMap_move_elements_loop
+  (T : Type) (n : nat) (ntable : hashmap_HashMap_t T)
+  (slots : alloc_vec_Vec (hashmap_List_t T)) (i : usize) :
+  result ((hashmap_HashMap_t T) * (alloc_vec_Vec (hashmap_List_t T)))
   :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
-    let i0 := vec_len (Hashmap_list_t T) slots in
+    let i0 := alloc_vec_Vec_len (hashmap_List_t T) slots in
     if i s< i0
     then (
-      l <- vec_index_mut_fwd (Hashmap_list_t T) slots i;
-      let ls := mem_replace_fwd (Hashmap_list_t T) l HashmapListNil in
-      ntable0 <-
-        hashmap_hash_map_move_elements_from_list_fwd_back T n0 ntable ls;
+      l <-
+        alloc_vec_Vec_index_mut (hashmap_List_t T) usize
+          (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t T)) slots
+          i;
+      let ls := core_mem_replace (hashmap_List_t T) l Hashmap_List_Nil in
+      ntable0 <- hashmap_HashMap_move_elements_from_list T n0 ntable ls;
       i1 <- usize_add i 1%usize;
-      let l0 := mem_replace_back (Hashmap_list_t T) l HashmapListNil in
-      slots0 <- vec_index_mut_back (Hashmap_list_t T) slots i l0;
-      hashmap_hash_map_move_elements_loop_fwd_back T n0 ntable0 slots0 i1)
+      let l0 := core_mem_replace_back (hashmap_List_t T) l Hashmap_List_Nil in
+      slots0 <-
+        alloc_vec_Vec_index_mut_back (hashmap_List_t T) usize
+          (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t T)) slots
+          i l0;
+      hashmap_HashMap_move_elements_loop T n0 ntable0 slots0 i1)
     else Return (ntable, slots)
   end
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::move_elements]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ()) *)
-Definition hashmap_hash_map_move_elements_fwd_back
-  (T : Type) (n : nat) (ntable : Hashmap_hash_map_t T)
-  (slots : vec (Hashmap_list_t T)) (i : usize) :
-  result ((Hashmap_hash_map_t T) * (vec (Hashmap_list_t T)))
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::move_elements]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ())
+    Source: 'src/hashmap.rs', lines 171:4-171:95 *)
+Definition hashmap_HashMap_move_elements
+  (T : Type) (n : nat) (ntable : hashmap_HashMap_t T)
+  (slots : alloc_vec_Vec (hashmap_List_t T)) (i : usize) :
+  result ((hashmap_HashMap_t T) * (alloc_vec_Vec (hashmap_List_t T)))
   :=
-  hashmap_hash_map_move_elements_loop_fwd_back T n ntable slots i
+  hashmap_HashMap_move_elements_loop T n ntable slots i
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::try_resize]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ()) *)
-Definition hashmap_hash_map_try_resize_fwd_back
-  (T : Type) (n : nat) (self : Hashmap_hash_map_t T) :
-  result (Hashmap_hash_map_t T)
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::try_resize]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ())
+    Source: 'src/hashmap.rs', lines 140:4-140:28 *)
+Definition hashmap_HashMap_try_resize
+  (T : Type) (n : nat) (self : hashmap_HashMap_t T) :
+  result (hashmap_HashMap_t T)
   :=
-  max_usize <- scalar_cast U32 Usize core_num_u32_max_c;
-  let capacity := vec_len (Hashmap_list_t T) self.(Hashmap_hash_map_slots) in
+  max_usize <- scalar_cast U32 Usize core_u32_max;
+  let capacity :=
+    alloc_vec_Vec_len (hashmap_List_t T) self.(hashmap_HashMap_slots) in
   n1 <- usize_div max_usize 2%usize;
-  let (i, i0) := self.(Hashmap_hash_map_max_load_factor) in
+  let (i, i0) := self.(hashmap_HashMap_max_load_factor) in
   i1 <- usize_div n1 i;
   if capacity s<= i1
   then (
     i2 <- usize_mul capacity 2%usize;
-    ntable <- hashmap_hash_map_new_with_capacity_fwd T n i2 i i0;
+    ntable <- hashmap_HashMap_new_with_capacity T n i2 i i0;
     p <-
-      hashmap_hash_map_move_elements_fwd_back T n ntable
-        self.(Hashmap_hash_map_slots) 0%usize;
+      hashmap_HashMap_move_elements T n ntable self.(hashmap_HashMap_slots)
+        0%usize;
     let (ntable0, _) := p in
     Return
       {|
-        Hashmap_hash_map_num_entries := self.(Hashmap_hash_map_num_entries);
-        Hashmap_hash_map_max_load_factor := (i, i0);
-        Hashmap_hash_map_max_load := ntable0.(Hashmap_hash_map_max_load);
-        Hashmap_hash_map_slots := ntable0.(Hashmap_hash_map_slots)
+        hashmap_HashMap_num_entries := self.(hashmap_HashMap_num_entries);
+        hashmap_HashMap_max_load_factor := (i, i0);
+        hashmap_HashMap_max_load := ntable0.(hashmap_HashMap_max_load);
+        hashmap_HashMap_slots := ntable0.(hashmap_HashMap_slots)
       |})
   else
     Return
       {|
-        Hashmap_hash_map_num_entries := self.(Hashmap_hash_map_num_entries);
-        Hashmap_hash_map_max_load_factor := (i, i0);
-        Hashmap_hash_map_max_load := self.(Hashmap_hash_map_max_load);
-        Hashmap_hash_map_slots := self.(Hashmap_hash_map_slots)
+        hashmap_HashMap_num_entries := self.(hashmap_HashMap_num_entries);
+        hashmap_HashMap_max_load_factor := (i, i0);
+        hashmap_HashMap_max_load := self.(hashmap_HashMap_max_load);
+        hashmap_HashMap_slots := self.(hashmap_HashMap_slots)
       |}
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::insert]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ()) *)
-Definition hashmap_hash_map_insert_fwd_back
-  (T : Type) (n : nat) (self : Hashmap_hash_map_t T) (key : usize) (value : T)
-  :
-  result (Hashmap_hash_map_t T)
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::insert]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ())
+    Source: 'src/hashmap.rs', lines 129:4-129:48 *)
+Definition hashmap_HashMap_insert
+  (T : Type) (n : nat) (self : hashmap_HashMap_t T) (key : usize) (value : T) :
+  result (hashmap_HashMap_t T)
   :=
-  self0 <- hashmap_hash_map_insert_no_resize_fwd_back T n self key value;
-  i <- hashmap_hash_map_len_fwd T self0;
-  if i s> self0.(Hashmap_hash_map_max_load)
-  then hashmap_hash_map_try_resize_fwd_back T n self0
+  self0 <- hashmap_HashMap_insert_no_resize T n self key value;
+  i <- hashmap_HashMap_len T self0;
+  if i s> self0.(hashmap_HashMap_max_load)
+  then hashmap_HashMap_try_resize T n self0
   else Return self0
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::contains_key_in_list]: loop 0: forward function *)
-Fixpoint hashmap_hash_map_contains_key_in_list_loop_fwd
-  (T : Type) (n : nat) (key : usize) (ls : Hashmap_list_t T) : result bool :=
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::contains_key_in_list]: loop 0: forward function
+    Source: 'src/hashmap.rs', lines 206:4-219:5 *)
+Fixpoint hashmap_HashMap_contains_key_in_list_loop
+  (T : Type) (n : nat) (key : usize) (ls : hashmap_List_t T) : result bool :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls with
-    | HashmapListCons ckey t tl =>
+    | Hashmap_List_Cons ckey t tl =>
       if ckey s= key
       then Return true
-      else hashmap_hash_map_contains_key_in_list_loop_fwd T n0 key tl
-    | HashmapListNil => Return false
+      else hashmap_HashMap_contains_key_in_list_loop T n0 key tl
+    | Hashmap_List_Nil => Return false
     end
   end
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::contains_key_in_list]: forward function *)
-Definition hashmap_hash_map_contains_key_in_list_fwd
-  (T : Type) (n : nat) (key : usize) (ls : Hashmap_list_t T) : result bool :=
-  hashmap_hash_map_contains_key_in_list_loop_fwd T n key ls
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::contains_key_in_list]: forward function
+    Source: 'src/hashmap.rs', lines 206:4-206:68 *)
+Definition hashmap_HashMap_contains_key_in_list
+  (T : Type) (n : nat) (key : usize) (ls : hashmap_List_t T) : result bool :=
+  hashmap_HashMap_contains_key_in_list_loop T n key ls
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::contains_key]: forward function *)
-Definition hashmap_hash_map_contains_key_fwd
-  (T : Type) (n : nat) (self : Hashmap_hash_map_t T) (key : usize) :
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::contains_key]: forward function
+    Source: 'src/hashmap.rs', lines 199:4-199:49 *)
+Definition hashmap_HashMap_contains_key
+  (T : Type) (n : nat) (self : hashmap_HashMap_t T) (key : usize) :
   result bool
   :=
-  hash <- hashmap_hash_key_fwd key;
-  let i := vec_len (Hashmap_list_t T) self.(Hashmap_hash_map_slots) in
+  hash <- hashmap_hash_key key;
+  let i := alloc_vec_Vec_len (hashmap_List_t T) self.(hashmap_HashMap_slots) in
   hash_mod <- usize_rem hash i;
-  l <- vec_index_fwd (Hashmap_list_t T) self.(Hashmap_hash_map_slots) hash_mod;
-  hashmap_hash_map_contains_key_in_list_fwd T n key l
+  l <-
+    alloc_vec_Vec_index (hashmap_List_t T) usize
+      (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t T))
+      self.(hashmap_HashMap_slots) hash_mod;
+  hashmap_HashMap_contains_key_in_list T n key l
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::get_in_list]: loop 0: forward function *)
-Fixpoint hashmap_hash_map_get_in_list_loop_fwd
-  (T : Type) (n : nat) (key : usize) (ls : Hashmap_list_t T) : result T :=
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_in_list]: loop 0: forward function
+    Source: 'src/hashmap.rs', lines 224:4-237:5 *)
+Fixpoint hashmap_HashMap_get_in_list_loop
+  (T : Type) (n : nat) (key : usize) (ls : hashmap_List_t T) : result T :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls with
-    | HashmapListCons ckey cvalue tl =>
+    | Hashmap_List_Cons ckey cvalue tl =>
       if ckey s= key
       then Return cvalue
-      else hashmap_hash_map_get_in_list_loop_fwd T n0 key tl
-    | HashmapListNil => Fail_ Failure
+      else hashmap_HashMap_get_in_list_loop T n0 key tl
+    | Hashmap_List_Nil => Fail_ Failure
     end
   end
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::get_in_list]: forward function *)
-Definition hashmap_hash_map_get_in_list_fwd
-  (T : Type) (n : nat) (key : usize) (ls : Hashmap_list_t T) : result T :=
-  hashmap_hash_map_get_in_list_loop_fwd T n key ls
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_in_list]: forward function
+    Source: 'src/hashmap.rs', lines 224:4-224:70 *)
+Definition hashmap_HashMap_get_in_list
+  (T : Type) (n : nat) (key : usize) (ls : hashmap_List_t T) : result T :=
+  hashmap_HashMap_get_in_list_loop T n key ls
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::get]: forward function *)
-Definition hashmap_hash_map_get_fwd
-  (T : Type) (n : nat) (self : Hashmap_hash_map_t T) (key : usize) :
-  result T
-  :=
-  hash <- hashmap_hash_key_fwd key;
-  let i := vec_len (Hashmap_list_t T) self.(Hashmap_hash_map_slots) in
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get]: forward function
+    Source: 'src/hashmap.rs', lines 239:4-239:55 *)
+Definition hashmap_HashMap_get
+  (T : Type) (n : nat) (self : hashmap_HashMap_t T) (key : usize) : result T :=
+  hash <- hashmap_hash_key key;
+  let i := alloc_vec_Vec_len (hashmap_List_t T) self.(hashmap_HashMap_slots) in
   hash_mod <- usize_rem hash i;
-  l <- vec_index_fwd (Hashmap_list_t T) self.(Hashmap_hash_map_slots) hash_mod;
-  hashmap_hash_map_get_in_list_fwd T n key l
+  l <-
+    alloc_vec_Vec_index (hashmap_List_t T) usize
+      (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t T))
+      self.(hashmap_HashMap_slots) hash_mod;
+  hashmap_HashMap_get_in_list T n key l
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list]: loop 0: forward function *)
-Fixpoint hashmap_hash_map_get_mut_in_list_loop_fwd
-  (T : Type) (n : nat) (ls : Hashmap_list_t T) (key : usize) : result T :=
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_mut_in_list]: loop 0: forward function
+    Source: 'src/hashmap.rs', lines 245:4-254:5 *)
+Fixpoint hashmap_HashMap_get_mut_in_list_loop
+  (T : Type) (n : nat) (ls : hashmap_List_t T) (key : usize) : result T :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls with
-    | HashmapListCons ckey cvalue tl =>
+    | Hashmap_List_Cons ckey cvalue tl =>
       if ckey s= key
       then Return cvalue
-      else hashmap_hash_map_get_mut_in_list_loop_fwd T n0 tl key
-    | HashmapListNil => Fail_ Failure
+      else hashmap_HashMap_get_mut_in_list_loop T n0 tl key
+    | Hashmap_List_Nil => Fail_ Failure
     end
   end
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list]: forward function *)
-Definition hashmap_hash_map_get_mut_in_list_fwd
-  (T : Type) (n : nat) (ls : Hashmap_list_t T) (key : usize) : result T :=
-  hashmap_hash_map_get_mut_in_list_loop_fwd T n ls key
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_mut_in_list]: forward function
+    Source: 'src/hashmap.rs', lines 245:4-245:86 *)
+Definition hashmap_HashMap_get_mut_in_list
+  (T : Type) (n : nat) (ls : hashmap_List_t T) (key : usize) : result T :=
+  hashmap_HashMap_get_mut_in_list_loop T n ls key
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list]: loop 0: backward function 0 *)
-Fixpoint hashmap_hash_map_get_mut_in_list_loop_back
-  (T : Type) (n : nat) (ls : Hashmap_list_t T) (key : usize) (ret : T) :
-  result (Hashmap_list_t T)
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_mut_in_list]: loop 0: backward function 0
+    Source: 'src/hashmap.rs', lines 245:4-254:5 *)
+Fixpoint hashmap_HashMap_get_mut_in_list_loop_back
+  (T : Type) (n : nat) (ls : hashmap_List_t T) (key : usize) (ret : T) :
+  result (hashmap_List_t T)
   :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls with
-    | HashmapListCons ckey cvalue tl =>
+    | Hashmap_List_Cons ckey cvalue tl =>
       if ckey s= key
-      then Return (HashmapListCons ckey ret tl)
+      then Return (Hashmap_List_Cons ckey ret tl)
       else (
-        tl0 <- hashmap_hash_map_get_mut_in_list_loop_back T n0 tl key ret;
-        Return (HashmapListCons ckey cvalue tl0))
-    | HashmapListNil => Fail_ Failure
+        tl0 <- hashmap_HashMap_get_mut_in_list_loop_back T n0 tl key ret;
+        Return (Hashmap_List_Cons ckey cvalue tl0))
+    | Hashmap_List_Nil => Fail_ Failure
     end
   end
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list]: backward function 0 *)
-Definition hashmap_hash_map_get_mut_in_list_back
-  (T : Type) (n : nat) (ls : Hashmap_list_t T) (key : usize) (ret : T) :
-  result (Hashmap_list_t T)
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_mut_in_list]: backward function 0
+    Source: 'src/hashmap.rs', lines 245:4-245:86 *)
+Definition hashmap_HashMap_get_mut_in_list_back
+  (T : Type) (n : nat) (ls : hashmap_List_t T) (key : usize) (ret : T) :
+  result (hashmap_List_t T)
   :=
-  hashmap_hash_map_get_mut_in_list_loop_back T n ls key ret
+  hashmap_HashMap_get_mut_in_list_loop_back T n ls key ret
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::get_mut]: forward function *)
-Definition hashmap_hash_map_get_mut_fwd
-  (T : Type) (n : nat) (self : Hashmap_hash_map_t T) (key : usize) :
-  result T
-  :=
-  hash <- hashmap_hash_key_fwd key;
-  let i := vec_len (Hashmap_list_t T) self.(Hashmap_hash_map_slots) in
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_mut]: forward function
+    Source: 'src/hashmap.rs', lines 257:4-257:67 *)
+Definition hashmap_HashMap_get_mut
+  (T : Type) (n : nat) (self : hashmap_HashMap_t T) (key : usize) : result T :=
+  hash <- hashmap_hash_key key;
+  let i := alloc_vec_Vec_len (hashmap_List_t T) self.(hashmap_HashMap_slots) in
   hash_mod <- usize_rem hash i;
   l <-
-    vec_index_mut_fwd (Hashmap_list_t T) self.(Hashmap_hash_map_slots) hash_mod;
-  hashmap_hash_map_get_mut_in_list_fwd T n l key
+    alloc_vec_Vec_index_mut (hashmap_List_t T) usize
+      (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t T))
+      self.(hashmap_HashMap_slots) hash_mod;
+  hashmap_HashMap_get_mut_in_list T n l key
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::get_mut]: backward function 0 *)
-Definition hashmap_hash_map_get_mut_back
-  (T : Type) (n : nat) (self : Hashmap_hash_map_t T) (key : usize) (ret : T) :
-  result (Hashmap_hash_map_t T)
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_mut]: backward function 0
+    Source: 'src/hashmap.rs', lines 257:4-257:67 *)
+Definition hashmap_HashMap_get_mut_back
+  (T : Type) (n : nat) (self : hashmap_HashMap_t T) (key : usize) (ret : T) :
+  result (hashmap_HashMap_t T)
   :=
-  hash <- hashmap_hash_key_fwd key;
-  let i := vec_len (Hashmap_list_t T) self.(Hashmap_hash_map_slots) in
+  hash <- hashmap_hash_key key;
+  let i := alloc_vec_Vec_len (hashmap_List_t T) self.(hashmap_HashMap_slots) in
   hash_mod <- usize_rem hash i;
   l <-
-    vec_index_mut_fwd (Hashmap_list_t T) self.(Hashmap_hash_map_slots) hash_mod;
-  l0 <- hashmap_hash_map_get_mut_in_list_back T n l key ret;
+    alloc_vec_Vec_index_mut (hashmap_List_t T) usize
+      (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t T))
+      self.(hashmap_HashMap_slots) hash_mod;
+  l0 <- hashmap_HashMap_get_mut_in_list_back T n l key ret;
   v <-
-    vec_index_mut_back (Hashmap_list_t T) self.(Hashmap_hash_map_slots)
-      hash_mod l0;
+    alloc_vec_Vec_index_mut_back (hashmap_List_t T) usize
+      (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t T))
+      self.(hashmap_HashMap_slots) hash_mod l0;
   Return
     {|
-      Hashmap_hash_map_num_entries := self.(Hashmap_hash_map_num_entries);
-      Hashmap_hash_map_max_load_factor :=
-        self.(Hashmap_hash_map_max_load_factor);
-      Hashmap_hash_map_max_load := self.(Hashmap_hash_map_max_load);
-      Hashmap_hash_map_slots := v
+      hashmap_HashMap_num_entries := self.(hashmap_HashMap_num_entries);
+      hashmap_HashMap_max_load_factor := self.(hashmap_HashMap_max_load_factor);
+      hashmap_HashMap_max_load := self.(hashmap_HashMap_max_load);
+      hashmap_HashMap_slots := v
     |}
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::remove_from_list]: loop 0: forward function *)
-Fixpoint hashmap_hash_map_remove_from_list_loop_fwd
-  (T : Type) (n : nat) (key : usize) (ls : Hashmap_list_t T) :
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::remove_from_list]: loop 0: forward function
+    Source: 'src/hashmap.rs', lines 265:4-291:5 *)
+Fixpoint hashmap_HashMap_remove_from_list_loop
+  (T : Type) (n : nat) (key : usize) (ls : hashmap_List_t T) :
   result (option T)
   :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls with
-    | HashmapListCons ckey t tl =>
+    | Hashmap_List_Cons ckey t tl =>
       if ckey s= key
       then
         let mv_ls :=
-          mem_replace_fwd (Hashmap_list_t T) (HashmapListCons ckey t tl)
-            HashmapListNil in
+          core_mem_replace (hashmap_List_t T) (Hashmap_List_Cons ckey t tl)
+            Hashmap_List_Nil in
         match mv_ls with
-        | HashmapListCons i cvalue tl0 => Return (Some cvalue)
-        | HashmapListNil => Fail_ Failure
+        | Hashmap_List_Cons i cvalue tl0 => Return (Some cvalue)
+        | Hashmap_List_Nil => Fail_ Failure
         end
-      else hashmap_hash_map_remove_from_list_loop_fwd T n0 key tl
-    | HashmapListNil => Return None
+      else hashmap_HashMap_remove_from_list_loop T n0 key tl
+    | Hashmap_List_Nil => Return None
     end
   end
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::remove_from_list]: forward function *)
-Definition hashmap_hash_map_remove_from_list_fwd
-  (T : Type) (n : nat) (key : usize) (ls : Hashmap_list_t T) :
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::remove_from_list]: forward function
+    Source: 'src/hashmap.rs', lines 265:4-265:69 *)
+Definition hashmap_HashMap_remove_from_list
+  (T : Type) (n : nat) (key : usize) (ls : hashmap_List_t T) :
   result (option T)
   :=
-  hashmap_hash_map_remove_from_list_loop_fwd T n key ls
+  hashmap_HashMap_remove_from_list_loop T n key ls
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::remove_from_list]: loop 0: backward function 1 *)
-Fixpoint hashmap_hash_map_remove_from_list_loop_back
-  (T : Type) (n : nat) (key : usize) (ls : Hashmap_list_t T) :
-  result (Hashmap_list_t T)
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::remove_from_list]: loop 0: backward function 1
+    Source: 'src/hashmap.rs', lines 265:4-291:5 *)
+Fixpoint hashmap_HashMap_remove_from_list_loop_back
+  (T : Type) (n : nat) (key : usize) (ls : hashmap_List_t T) :
+  result (hashmap_List_t T)
   :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls with
-    | HashmapListCons ckey t tl =>
+    | Hashmap_List_Cons ckey t tl =>
       if ckey s= key
       then
         let mv_ls :=
-          mem_replace_fwd (Hashmap_list_t T) (HashmapListCons ckey t tl)
-            HashmapListNil in
+          core_mem_replace (hashmap_List_t T) (Hashmap_List_Cons ckey t tl)
+            Hashmap_List_Nil in
         match mv_ls with
-        | HashmapListCons i cvalue tl0 => Return tl0
-        | HashmapListNil => Fail_ Failure
+        | Hashmap_List_Cons i cvalue tl0 => Return tl0
+        | Hashmap_List_Nil => Fail_ Failure
         end
       else (
-        tl0 <- hashmap_hash_map_remove_from_list_loop_back T n0 key tl;
-        Return (HashmapListCons ckey t tl0))
-    | HashmapListNil => Return HashmapListNil
+        tl0 <- hashmap_HashMap_remove_from_list_loop_back T n0 key tl;
+        Return (Hashmap_List_Cons ckey t tl0))
+    | Hashmap_List_Nil => Return Hashmap_List_Nil
     end
   end
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::remove_from_list]: backward function 1 *)
-Definition hashmap_hash_map_remove_from_list_back
-  (T : Type) (n : nat) (key : usize) (ls : Hashmap_list_t T) :
-  result (Hashmap_list_t T)
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::remove_from_list]: backward function 1
+    Source: 'src/hashmap.rs', lines 265:4-265:69 *)
+Definition hashmap_HashMap_remove_from_list_back
+  (T : Type) (n : nat) (key : usize) (ls : hashmap_List_t T) :
+  result (hashmap_List_t T)
   :=
-  hashmap_hash_map_remove_from_list_loop_back T n key ls
+  hashmap_HashMap_remove_from_list_loop_back T n key ls
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::remove]: forward function *)
-Definition hashmap_hash_map_remove_fwd
-  (T : Type) (n : nat) (self : Hashmap_hash_map_t T) (key : usize) :
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::remove]: forward function
+    Source: 'src/hashmap.rs', lines 294:4-294:52 *)
+Definition hashmap_HashMap_remove
+  (T : Type) (n : nat) (self : hashmap_HashMap_t T) (key : usize) :
   result (option T)
   :=
-  hash <- hashmap_hash_key_fwd key;
-  let i := vec_len (Hashmap_list_t T) self.(Hashmap_hash_map_slots) in
+  hash <- hashmap_hash_key key;
+  let i := alloc_vec_Vec_len (hashmap_List_t T) self.(hashmap_HashMap_slots) in
   hash_mod <- usize_rem hash i;
   l <-
-    vec_index_mut_fwd (Hashmap_list_t T) self.(Hashmap_hash_map_slots) hash_mod;
-  x <- hashmap_hash_map_remove_from_list_fwd T n key l;
+    alloc_vec_Vec_index_mut (hashmap_List_t T) usize
+      (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t T))
+      self.(hashmap_HashMap_slots) hash_mod;
+  x <- hashmap_HashMap_remove_from_list T n key l;
   match x with
   | None => Return None
   | Some x0 =>
-    _ <- usize_sub self.(Hashmap_hash_map_num_entries) 1%usize;
-    Return (Some x0)
+    _ <- usize_sub self.(hashmap_HashMap_num_entries) 1%usize; Return (Some x0)
   end
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::remove]: backward function 0 *)
-Definition hashmap_hash_map_remove_back
-  (T : Type) (n : nat) (self : Hashmap_hash_map_t T) (key : usize) :
-  result (Hashmap_hash_map_t T)
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::remove]: backward function 0
+    Source: 'src/hashmap.rs', lines 294:4-294:52 *)
+Definition hashmap_HashMap_remove_back
+  (T : Type) (n : nat) (self : hashmap_HashMap_t T) (key : usize) :
+  result (hashmap_HashMap_t T)
   :=
-  hash <- hashmap_hash_key_fwd key;
-  let i := vec_len (Hashmap_list_t T) self.(Hashmap_hash_map_slots) in
+  hash <- hashmap_hash_key key;
+  let i := alloc_vec_Vec_len (hashmap_List_t T) self.(hashmap_HashMap_slots) in
   hash_mod <- usize_rem hash i;
   l <-
-    vec_index_mut_fwd (Hashmap_list_t T) self.(Hashmap_hash_map_slots) hash_mod;
-  x <- hashmap_hash_map_remove_from_list_fwd T n key l;
+    alloc_vec_Vec_index_mut (hashmap_List_t T) usize
+      (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t T))
+      self.(hashmap_HashMap_slots) hash_mod;
+  x <- hashmap_HashMap_remove_from_list T n key l;
   match x with
   | None =>
-    l0 <- hashmap_hash_map_remove_from_list_back T n key l;
+    l0 <- hashmap_HashMap_remove_from_list_back T n key l;
     v <-
-      vec_index_mut_back (Hashmap_list_t T) self.(Hashmap_hash_map_slots)
-        hash_mod l0;
+      alloc_vec_Vec_index_mut_back (hashmap_List_t T) usize
+        (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t T))
+        self.(hashmap_HashMap_slots) hash_mod l0;
     Return
       {|
-        Hashmap_hash_map_num_entries := self.(Hashmap_hash_map_num_entries);
-        Hashmap_hash_map_max_load_factor :=
-          self.(Hashmap_hash_map_max_load_factor);
-        Hashmap_hash_map_max_load := self.(Hashmap_hash_map_max_load);
-        Hashmap_hash_map_slots := v
+        hashmap_HashMap_num_entries := self.(hashmap_HashMap_num_entries);
+        hashmap_HashMap_max_load_factor :=
+          self.(hashmap_HashMap_max_load_factor);
+        hashmap_HashMap_max_load := self.(hashmap_HashMap_max_load);
+        hashmap_HashMap_slots := v
       |}
   | Some x0 =>
-    i0 <- usize_sub self.(Hashmap_hash_map_num_entries) 1%usize;
-    l0 <- hashmap_hash_map_remove_from_list_back T n key l;
+    i0 <- usize_sub self.(hashmap_HashMap_num_entries) 1%usize;
+    l0 <- hashmap_HashMap_remove_from_list_back T n key l;
     v <-
-      vec_index_mut_back (Hashmap_list_t T) self.(Hashmap_hash_map_slots)
-        hash_mod l0;
+      alloc_vec_Vec_index_mut_back (hashmap_List_t T) usize
+        (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t T))
+        self.(hashmap_HashMap_slots) hash_mod l0;
     Return
       {|
-        Hashmap_hash_map_num_entries := i0;
-        Hashmap_hash_map_max_load_factor :=
-          self.(Hashmap_hash_map_max_load_factor);
-        Hashmap_hash_map_max_load := self.(Hashmap_hash_map_max_load);
-        Hashmap_hash_map_slots := v
+        hashmap_HashMap_num_entries := i0;
+        hashmap_HashMap_max_load_factor :=
+          self.(hashmap_HashMap_max_load_factor);
+        hashmap_HashMap_max_load := self.(hashmap_HashMap_max_load);
+        hashmap_HashMap_slots := v
       |}
   end
 .
 
-(** [hashmap_main::hashmap::test1]: forward function *)
-Definition hashmap_test1_fwd (n : nat) : result unit :=
-  hm <- hashmap_hash_map_new_fwd u64 n;
-  hm0 <- hashmap_hash_map_insert_fwd_back u64 n hm 0%usize 42%u64;
-  hm1 <- hashmap_hash_map_insert_fwd_back u64 n hm0 128%usize 18%u64;
-  hm2 <- hashmap_hash_map_insert_fwd_back u64 n hm1 1024%usize 138%u64;
-  hm3 <- hashmap_hash_map_insert_fwd_back u64 n hm2 1056%usize 256%u64;
-  i <- hashmap_hash_map_get_fwd u64 n hm3 128%usize;
+(** [hashmap_main::hashmap::test1]: forward function
+    Source: 'src/hashmap.rs', lines 315:0-315:10 *)
+Definition hashmap_test1 (n : nat) : result unit :=
+  hm <- hashmap_HashMap_new u64 n;
+  hm0 <- hashmap_HashMap_insert u64 n hm 0%usize 42%u64;
+  hm1 <- hashmap_HashMap_insert u64 n hm0 128%usize 18%u64;
+  hm2 <- hashmap_HashMap_insert u64 n hm1 1024%usize 138%u64;
+  hm3 <- hashmap_HashMap_insert u64 n hm2 1056%usize 256%u64;
+  i <- hashmap_HashMap_get u64 n hm3 128%usize;
   if negb (i s= 18%u64)
   then Fail_ Failure
   else (
-    hm4 <- hashmap_hash_map_get_mut_back u64 n hm3 1024%usize 56%u64;
-    i0 <- hashmap_hash_map_get_fwd u64 n hm4 1024%usize;
+    hm4 <- hashmap_HashMap_get_mut_back u64 n hm3 1024%usize 56%u64;
+    i0 <- hashmap_HashMap_get u64 n hm4 1024%usize;
     if negb (i0 s= 56%u64)
     then Fail_ Failure
     else (
-      x <- hashmap_hash_map_remove_fwd u64 n hm4 1024%usize;
+      x <- hashmap_HashMap_remove u64 n hm4 1024%usize;
       match x with
       | None => Fail_ Failure
       | Some x0 =>
         if negb (x0 s= 56%u64)
         then Fail_ Failure
         else (
-          hm5 <- hashmap_hash_map_remove_back u64 n hm4 1024%usize;
-          i1 <- hashmap_hash_map_get_fwd u64 n hm5 0%usize;
+          hm5 <- hashmap_HashMap_remove_back u64 n hm4 1024%usize;
+          i1 <- hashmap_HashMap_get u64 n hm5 0%usize;
           if negb (i1 s= 42%u64)
           then Fail_ Failure
           else (
-            i2 <- hashmap_hash_map_get_fwd u64 n hm5 128%usize;
+            i2 <- hashmap_HashMap_get u64 n hm5 128%usize;
             if negb (i2 s= 18%u64)
             then Fail_ Failure
             else (
-              i3 <- hashmap_hash_map_get_fwd u64 n hm5 1056%usize;
+              i3 <- hashmap_HashMap_get u64 n hm5 1056%usize;
               if negb (i3 s= 256%u64) then Fail_ Failure else Return tt)))
       end))
 .
 
-(** [hashmap_main::insert_on_disk]: forward function *)
-Definition insert_on_disk_fwd
+(** [hashmap_main::insert_on_disk]: forward function
+    Source: 'src/hashmap_main.rs', lines 7:0-7:43 *)
+Definition insert_on_disk
   (n : nat) (key : usize) (value : u64) (st : state) : result (state * unit) :=
-  p <- hashmap_utils_deserialize_fwd st;
+  p <- hashmap_utils_deserialize st;
   let (st0, hm) := p in
-  hm0 <- hashmap_hash_map_insert_fwd_back u64 n hm key value;
-  p0 <- hashmap_utils_serialize_fwd hm0 st0;
+  hm0 <- hashmap_HashMap_insert u64 n hm key value;
+  p0 <- hashmap_utils_serialize hm0 st0;
   let (st1, _) := p0 in
   Return (st1, tt)
 .
 
-(** [hashmap_main::main]: forward function *)
-Definition main_fwd : result unit :=
+(** [hashmap_main::main]: forward function
+    Source: 'src/hashmap_main.rs', lines 16:0-16:13 *)
+Definition main : result unit :=
   Return tt.
 
-(** Unit test for [hashmap_main::main] *)
-Check (main_fwd )%return.
-
-End HashmapMain_Funs .
+End HashmapMain_Funs.
diff --git a/tests/coq/hashmap_on_disk/HashmapMain_FunsExternal.v b/tests/coq/hashmap_on_disk/HashmapMain_FunsExternal.v
new file mode 100644
index 00000000..a03dc407
--- /dev/null
+++ b/tests/coq/hashmap_on_disk/HashmapMain_FunsExternal.v
@@ -0,0 +1,25 @@
+(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
+(** [hashmap_main]: external function declarations *)
+Require Import Primitives.
+Import Primitives.
+Require Import Coq.ZArith.ZArith.
+Require Import List.
+Import ListNotations.
+Local Open Scope Primitives_scope.
+Require Export HashmapMain_Types.
+Import HashmapMain_Types.
+Module HashmapMain_FunsExternal.
+
+(** [hashmap_main::hashmap_utils::deserialize]: forward function
+    Source: 'src/hashmap_utils.rs', lines 10:0-10:43 *)
+Axiom hashmap_utils_deserialize
+  : state -> result (state * (hashmap_HashMap_t u64))
+.
+
+(** [hashmap_main::hashmap_utils::serialize]: forward function
+    Source: 'src/hashmap_utils.rs', lines 5:0-5:42 *)
+Axiom hashmap_utils_serialize
+  : hashmap_HashMap_t u64 -> state -> result (state * unit)
+.
+
+End HashmapMain_FunsExternal.
diff --git a/tests/coq/hashmap_on_disk/HashmapMain_FunsExternal_Template.v b/tests/coq/hashmap_on_disk/HashmapMain_FunsExternal_Template.v
new file mode 100644
index 00000000..e10d02f6
--- /dev/null
+++ b/tests/coq/hashmap_on_disk/HashmapMain_FunsExternal_Template.v
@@ -0,0 +1,26 @@
+(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
+(** [hashmap_main]: external functions.
+-- This is a template file: rename it to "FunsExternal.lean" and fill the holes. *)
+Require Import Primitives.
+Import Primitives.
+Require Import Coq.ZArith.ZArith.
+Require Import List.
+Import ListNotations.
+Local Open Scope Primitives_scope.
+Require Import HashmapMain_Types.
+Include HashmapMain_Types.
+Module HashmapMain_FunsExternal_Template.
+
+(** [hashmap_main::hashmap_utils::deserialize]: forward function
+    Source: 'src/hashmap_utils.rs', lines 10:0-10:43 *)
+Axiom hashmap_utils_deserialize
+  : state -> result (state * (hashmap_HashMap_t u64))
+.
+
+(** [hashmap_main::hashmap_utils::serialize]: forward function
+    Source: 'src/hashmap_utils.rs', lines 5:0-5:42 *)
+Axiom hashmap_utils_serialize
+  : hashmap_HashMap_t u64 -> state -> result (state * unit)
+.
+
+End HashmapMain_FunsExternal_Template.
diff --git a/tests/coq/hashmap_on_disk/HashmapMain_Opaque.v b/tests/coq/hashmap_on_disk/HashmapMain_Opaque.v
deleted file mode 100644
index 2d17cc29..00000000
--- a/tests/coq/hashmap_on_disk/HashmapMain_Opaque.v
+++ /dev/null
@@ -1,23 +0,0 @@
-(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
-(** [hashmap_main]: external function declarations *)
-Require Import Primitives.
-Import Primitives.
-Require Import Coq.ZArith.ZArith.
-Require Import List.
-Import ListNotations.
-Local Open Scope Primitives_scope.
-Require Export HashmapMain_Types.
-Import HashmapMain_Types.
-Module HashmapMain_Opaque.
-
-(** [hashmap_main::hashmap_utils::deserialize]: forward function *)
-Axiom hashmap_utils_deserialize_fwd
-  : state -> result (state * (Hashmap_hash_map_t u64))
-.
-
-(** [hashmap_main::hashmap_utils::serialize]: forward function *)
-Axiom hashmap_utils_serialize_fwd
-  : Hashmap_hash_map_t u64 -> state -> result (state * unit)
-.
-
-End HashmapMain_Opaque .
diff --git a/tests/coq/hashmap_on_disk/HashmapMain_Types.v b/tests/coq/hashmap_on_disk/HashmapMain_Types.v
index 36aaaf25..8d3d72aa 100644
--- a/tests/coq/hashmap_on_disk/HashmapMain_Types.v
+++ b/tests/coq/hashmap_on_disk/HashmapMain_Types.v
@@ -6,34 +6,35 @@ Require Import Coq.ZArith.ZArith.
 Require Import List.
 Import ListNotations.
 Local Open Scope Primitives_scope.
+Require Import HashmapMain_TypesExternal.
+Include HashmapMain_TypesExternal.
 Module HashmapMain_Types.
 
-(** [hashmap_main::hashmap::List] *)
-Inductive Hashmap_list_t (T : Type) :=
-| HashmapListCons : usize -> T -> Hashmap_list_t T -> Hashmap_list_t T
-| HashmapListNil : Hashmap_list_t T
+(** [hashmap_main::hashmap::List]
+    Source: 'src/hashmap.rs', lines 19:0-19:16 *)
+Inductive hashmap_List_t (T : Type) :=
+| Hashmap_List_Cons : usize -> T -> hashmap_List_t T -> hashmap_List_t T
+| Hashmap_List_Nil : hashmap_List_t T
 .
 
-Arguments HashmapListCons {T} _ _ _.
-Arguments HashmapListNil {T}.
+Arguments Hashmap_List_Cons { _ }.
+Arguments Hashmap_List_Nil { _ }.
 
-(** [hashmap_main::hashmap::HashMap] *)
-Record Hashmap_hash_map_t (T : Type) :=
-mkHashmap_hash_map_t {
-  Hashmap_hash_map_num_entries : usize;
-  Hashmap_hash_map_max_load_factor : (usize * usize);
-  Hashmap_hash_map_max_load : usize;
-  Hashmap_hash_map_slots : vec (Hashmap_list_t T);
+(** [hashmap_main::hashmap::HashMap]
+    Source: 'src/hashmap.rs', lines 35:0-35:21 *)
+Record hashmap_HashMap_t (T : Type) :=
+mkhashmap_HashMap_t {
+  hashmap_HashMap_num_entries : usize;
+  hashmap_HashMap_max_load_factor : (usize * usize);
+  hashmap_HashMap_max_load : usize;
+  hashmap_HashMap_slots : alloc_vec_Vec (hashmap_List_t T);
 }
 .
 
-Arguments mkHashmap_hash_map_t {T} _ _ _ _.
-Arguments Hashmap_hash_map_num_entries {T}.
-Arguments Hashmap_hash_map_max_load_factor {T}.
-Arguments Hashmap_hash_map_max_load {T}.
-Arguments Hashmap_hash_map_slots {T}.
+Arguments mkhashmap_HashMap_t { _ }.
+Arguments hashmap_HashMap_num_entries { _ }.
+Arguments hashmap_HashMap_max_load_factor { _ }.
+Arguments hashmap_HashMap_max_load { _ }.
+Arguments hashmap_HashMap_slots { _ }.
 
-(** The state type used in the state-error monad *)
-Axiom state : Type.
-
-End HashmapMain_Types .
+End HashmapMain_Types.
diff --git a/tests/coq/hashmap_on_disk/HashmapMain_TypesExternal.v b/tests/coq/hashmap_on_disk/HashmapMain_TypesExternal.v
new file mode 100644
index 00000000..87568232
--- /dev/null
+++ b/tests/coq/hashmap_on_disk/HashmapMain_TypesExternal.v
@@ -0,0 +1,15 @@
+(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
+(** [hashmap_main]: external types.
+-- This is a template file: rename it to "TypesExternal.lean" and fill the holes. *)
+Require Import Primitives.
+Import Primitives.
+Require Import Coq.ZArith.ZArith.
+Require Import List.
+Import ListNotations.
+Local Open Scope Primitives_scope.
+Module HashmapMain_TypesExternal.
+
+(** The state type used in the state-error monad *)
+Axiom state : Type.
+
+End HashmapMain_TypesExternal.
diff --git a/tests/coq/hashmap_on_disk/HashmapMain_TypesExternal_Template.v b/tests/coq/hashmap_on_disk/HashmapMain_TypesExternal_Template.v
new file mode 100644
index 00000000..391b2775
--- /dev/null
+++ b/tests/coq/hashmap_on_disk/HashmapMain_TypesExternal_Template.v
@@ -0,0 +1,15 @@
+(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
+(** [hashmap_main]: external types.
+-- This is a template file: rename it to "TypesExternal.lean" and fill the holes. *)
+Require Import Primitives.
+Import Primitives.
+Require Import Coq.ZArith.ZArith.
+Require Import List.
+Import ListNotations.
+Local Open Scope Primitives_scope.
+Module HashmapMain_TypesExternal_Template.
+
+(** The state type used in the state-error monad *)
+Axiom state : Type.
+
+End HashmapMain_TypesExternal_Template.
diff --git a/tests/coq/hashmap_on_disk/Primitives.v b/tests/coq/hashmap_on_disk/Primitives.v
index 71a2d9c3..99ffe070 100644
--- a/tests/coq/hashmap_on_disk/Primitives.v
+++ b/tests/coq/hashmap_on_disk/Primitives.v
@@ -63,13 +63,15 @@ Check (if true then Return (1 + 2) else Fail_ Failure)%global = 3.
 
 (*** Misc *)
 
-
 Definition string := Coq.Strings.String.string.
 Definition char := Coq.Strings.Ascii.ascii.
 Definition char_of_byte := Coq.Strings.Ascii.ascii_of_byte.
 
-Definition mem_replace_fwd (a : Type) (x : a) (y : a) : a := x .
-Definition mem_replace_back (a : Type) (x : a) (y : a) : a := y .
+Definition core_mem_replace (a : Type) (x : a) (y : a) : a := x .
+Definition core_mem_replace_back (a : Type) (x : a) (y : a) : a := y .
+
+Record mut_raw_ptr (T : Type) := { mut_raw_ptr_v : T }.
+Record const_raw_ptr (T : Type) := { const_raw_ptr_v : T }.
 
 (*** Scalars *)
 
@@ -253,6 +255,12 @@ Definition scalar_rem {ty} (x y: scalar ty) : result (scalar ty) := mk_scalar ty
   
 Definition scalar_neg {ty} (x: scalar ty) : result (scalar ty) := mk_scalar ty (-(to_Z x)).
 
+Axiom scalar_xor : forall ty, scalar ty -> scalar ty -> scalar ty. (* TODO *)
+Axiom scalar_or : forall ty, scalar ty -> scalar ty -> scalar ty. (* TODO *)
+Axiom scalar_and : forall ty, scalar ty -> scalar ty -> scalar ty. (* TODO *)
+Axiom scalar_shl : forall ty0 ty1, scalar ty0 -> scalar ty1 -> result (scalar ty0). (* TODO *)
+Axiom scalar_shr : forall ty0 ty1, scalar ty0 -> scalar ty1 -> result (scalar ty0). (* TODO *)
+
 (** Cast an integer from a [src_ty] to a [tgt_ty] *)
 (* TODO: check the semantics of casts in Rust *)
 Definition scalar_cast (src_ty tgt_ty : scalar_ty) (x : scalar src_ty) : result (scalar tgt_ty) :=
@@ -370,6 +378,76 @@ Definition u32_mul   := @scalar_mul U32.
 Definition u64_mul   := @scalar_mul U64.
 Definition u128_mul  := @scalar_mul U128.
 
+(** Xor *)
+Definition u8_xor := @scalar_xor U8.
+Definition u16_xor := @scalar_xor U16.
+Definition u32_xor := @scalar_xor U32.
+Definition u64_xor := @scalar_xor U64.
+Definition u128_xor := @scalar_xor U128.
+Definition usize_xor := @scalar_xor Usize.
+Definition i8_xor := @scalar_xor I8.
+Definition i16_xor := @scalar_xor I16.
+Definition i32_xor := @scalar_xor I32.
+Definition i64_xor := @scalar_xor I64.
+Definition i128_xor := @scalar_xor I128.
+Definition isize_xor := @scalar_xor Isize.
+
+(** Or *)
+Definition u8_or := @scalar_or U8.
+Definition u16_or := @scalar_or U16.
+Definition u32_or := @scalar_or U32.
+Definition u64_or := @scalar_or U64.
+Definition u128_or := @scalar_or U128.
+Definition usize_or := @scalar_or Usize.
+Definition i8_or := @scalar_or I8.
+Definition i16_or := @scalar_or I16.
+Definition i32_or := @scalar_or I32.
+Definition i64_or := @scalar_or I64.
+Definition i128_or := @scalar_or I128.
+Definition isize_or := @scalar_or Isize.
+
+(** And *)
+Definition u8_and := @scalar_and U8.
+Definition u16_and := @scalar_and U16.
+Definition u32_and := @scalar_and U32.
+Definition u64_and := @scalar_and U64.
+Definition u128_and := @scalar_and U128.
+Definition usize_and := @scalar_and Usize.
+Definition i8_and := @scalar_and I8.
+Definition i16_and := @scalar_and I16.
+Definition i32_and := @scalar_and I32.
+Definition i64_and := @scalar_and I64.
+Definition i128_and := @scalar_and I128.
+Definition isize_and := @scalar_and Isize.
+
+(** Shift left *)
+Definition u8_shl {ty} := @scalar_shl U8 ty.
+Definition u16_shl {ty} := @scalar_shl U16 ty.
+Definition u32_shl {ty} := @scalar_shl U32 ty.
+Definition u64_shl {ty} := @scalar_shl U64 ty.
+Definition u128_shl {ty} := @scalar_shl U128 ty.
+Definition usize_shl {ty} := @scalar_shl Usize ty.
+Definition i8_shl {ty} := @scalar_shl I8 ty.
+Definition i16_shl {ty} := @scalar_shl I16 ty.
+Definition i32_shl {ty} := @scalar_shl I32 ty.
+Definition i64_shl {ty} := @scalar_shl I64 ty.
+Definition i128_shl {ty} := @scalar_shl I128 ty.
+Definition isize_shl {ty} := @scalar_shl Isize ty.
+
+(** Shift right *)
+Definition u8_shr {ty} := @scalar_shr U8 ty.
+Definition u16_shr {ty} := @scalar_shr U16 ty.
+Definition u32_shr {ty} := @scalar_shr U32 ty.
+Definition u64_shr {ty} := @scalar_shr U64 ty.
+Definition u128_shr {ty} := @scalar_shr U128 ty.
+Definition usize_shr {ty} := @scalar_shr Usize ty.
+Definition i8_shr {ty} := @scalar_shr I8 ty.
+Definition i16_shr {ty} := @scalar_shr I16 ty.
+Definition i32_shr {ty} := @scalar_shr I32 ty.
+Definition i64_shr {ty} := @scalar_shr I64 ty.
+Definition i128_shr {ty} := @scalar_shr I128 ty.
+Definition isize_shr {ty} := @scalar_shr Isize ty.
+
 (** Small utility *)
 Definition usize_to_nat (x: usize) : nat := Z.to_nat (to_Z x).
 
@@ -394,12 +472,89 @@ Notation "x s< y" := (scalar_ltb x y)  (at level 80) : Primitives_scope.
 Notation "x s>= y" := (scalar_geb x y)  (at level 80) : Primitives_scope.
 Notation "x s> y" := (scalar_gtb x y)  (at level 80) : Primitives_scope.
 
-(*** Range *)
-Record range (T : Type) := mk_range {
-  start: T;
-  end_: T;
+(** Constants *)
+Definition core_u8_max    := u8_max %u32.
+Definition core_u16_max   := u16_max %u32.
+Definition core_u32_max   := u32_max %u32.
+Definition core_u64_max   := u64_max %u64.
+Definition core_u128_max  := u64_max %u128.
+Axiom core_usize_max : usize. (** TODO *)
+Definition core_i8_max    := i8_max %i32.
+Definition core_i16_max   := i16_max %i32.
+Definition core_i32_max   := i32_max %i32.
+Definition core_i64_max   := i64_max %i64.
+Definition core_i128_max  := i64_max %i128.
+Axiom core_isize_max : isize. (** TODO *)
+
+(*** core::ops *)
+
+(* Trait declaration: [core::ops::index::Index] *)
+Record core_ops_index_Index (Self Idx : Type) := mk_core_ops_index_Index {
+  core_ops_index_Index_Output : Type;
+  core_ops_index_Index_index : Self -> Idx -> result core_ops_index_Index_Output;
+}.
+Arguments mk_core_ops_index_Index {_ _}.
+Arguments core_ops_index_Index_Output {_ _}.
+Arguments core_ops_index_Index_index {_ _}.
+
+(* Trait declaration: [core::ops::index::IndexMut] *)
+Record core_ops_index_IndexMut (Self Idx : Type) := mk_core_ops_index_IndexMut {
+  core_ops_index_IndexMut_indexInst : core_ops_index_Index Self Idx;
+  core_ops_index_IndexMut_index_mut : Self -> Idx -> result core_ops_index_IndexMut_indexInst.(core_ops_index_Index_Output);
+  core_ops_index_IndexMut_index_mut_back : Self -> Idx -> core_ops_index_IndexMut_indexInst.(core_ops_index_Index_Output) -> result Self;
+}.
+Arguments mk_core_ops_index_IndexMut {_ _}.
+Arguments core_ops_index_IndexMut_indexInst {_ _}.
+Arguments core_ops_index_IndexMut_index_mut {_ _}.
+Arguments core_ops_index_IndexMut_index_mut_back {_ _}.
+
+(* Trait declaration [core::ops::deref::Deref] *)
+Record core_ops_deref_Deref (Self : Type) := mk_core_ops_deref_Deref {
+  core_ops_deref_Deref_target : Type;
+  core_ops_deref_Deref_deref : Self -> result core_ops_deref_Deref_target;
 }.
-Arguments mk_range {_}.
+Arguments mk_core_ops_deref_Deref {_}.
+Arguments core_ops_deref_Deref_target {_}.
+Arguments core_ops_deref_Deref_deref {_}.
+
+(* Trait declaration [core::ops::deref::DerefMut] *)
+Record core_ops_deref_DerefMut (Self : Type) := mk_core_ops_deref_DerefMut {
+  core_ops_deref_DerefMut_derefInst : core_ops_deref_Deref Self;
+  core_ops_deref_DerefMut_deref_mut : Self -> result core_ops_deref_DerefMut_derefInst.(core_ops_deref_Deref_target);
+  core_ops_deref_DerefMut_deref_mut_back : Self -> core_ops_deref_DerefMut_derefInst.(core_ops_deref_Deref_target) -> result Self;
+}.
+Arguments mk_core_ops_deref_DerefMut {_}.
+Arguments core_ops_deref_DerefMut_derefInst {_}.
+Arguments core_ops_deref_DerefMut_deref_mut {_}.
+Arguments core_ops_deref_DerefMut_deref_mut_back {_}.
+
+Record core_ops_range_Range (T : Type) := mk_core_ops_range_Range {
+  core_ops_range_Range_start : T;
+  core_ops_range_Range_end_ : T;
+}.
+Arguments mk_core_ops_range_Range {_}.
+Arguments core_ops_range_Range_start {_}.
+Arguments core_ops_range_Range_end_ {_}.
+
+(*** [alloc] *)
+
+Definition alloc_boxed_Box_deref (T : Type) (x : T) : result T := Return x.
+Definition alloc_boxed_Box_deref_mut (T : Type) (x : T) : result T := Return x.
+Definition alloc_boxed_Box_deref_mut_back (T : Type) (_ : T) (x : T) : result T := Return x.
+
+(* Trait instance *)
+Definition alloc_boxed_Box_coreopsDerefInst (Self : Type) : core_ops_deref_Deref Self := {|
+  core_ops_deref_Deref_target := Self;
+  core_ops_deref_Deref_deref := alloc_boxed_Box_deref Self;
+|}.
+
+(* Trait instance *)
+Definition alloc_boxed_Box_coreopsDerefMutInst (Self : Type) : core_ops_deref_DerefMut Self := {|
+  core_ops_deref_DerefMut_derefInst := alloc_boxed_Box_coreopsDerefInst Self;
+  core_ops_deref_DerefMut_deref_mut := alloc_boxed_Box_deref_mut Self;
+  core_ops_deref_DerefMut_deref_mut_back := alloc_boxed_Box_deref_mut_back Self;
+|}.
+
 
 (*** Arrays *)
 Definition array T (n : usize) := { l: list T | Z.of_nat (length l) = to_Z n}.
@@ -419,51 +574,50 @@ Qed.
 (* TODO: finish the definitions *)
 Axiom mk_array : forall (T : Type) (n : usize) (l : list T), array T n.
 
-Axiom array_index_shared : forall (T : Type) (n : usize) (x : array T n) (i : usize), result T.
-Axiom array_index_mut_fwd : forall (T : Type) (n : usize) (x : array T n) (i : usize), result T.
-Axiom array_index_mut_back : forall (T : Type) (n : usize) (x : array T n) (i : usize) (nx : T), result (array T n).
+(* For initialization *)
+Axiom array_repeat : forall (T : Type) (n : usize) (x : T), array T n.
+
+Axiom array_index_usize : forall (T : Type) (n : usize) (x : array T n) (i : usize), result T.
+Axiom array_update_usize : forall (T : Type) (n : usize) (x : array T n) (i : usize) (nx : T), result (array T n).
 
 (*** Slice *)
 Definition slice T := { l: list T | Z.of_nat (length l) <= usize_max}.
 
 Axiom slice_len : forall (T : Type) (s : slice T), usize.
-Axiom slice_index_shared : forall (T : Type) (x : slice T) (i : usize), result T.
-Axiom slice_index_mut_fwd : forall (T : Type) (x : slice T) (i : usize), result T.
-Axiom slice_index_mut_back : forall (T : Type) (x : slice T) (i : usize) (nx : T), result (slice T).
+Axiom slice_index_usize : forall (T : Type) (x : slice T) (i : usize), result T.
+Axiom slice_update_usize : forall (T : Type) (x : slice T) (i : usize) (nx : T), result (slice T).
 
 (*** Subslices *)
 
-Axiom array_to_slice_shared : forall (T : Type) (n : usize) (x : array T n), result (slice T).
-Axiom array_to_slice_mut_fwd : forall (T : Type) (n : usize) (x : array T n), result (slice T).
-Axiom array_to_slice_mut_back : forall (T : Type) (n : usize) (x : array T n) (s : slice T), result (array T n).
+Axiom array_to_slice : forall (T : Type) (n : usize) (x : array T n), result (slice T).
+Axiom array_from_slice : forall (T : Type) (n : usize) (x : array T n) (s : slice T), result (array T n).
 
-Axiom array_subslice_shared: forall (T : Type) (n : usize) (x : array T n) (r : range usize), result (slice T).
-Axiom array_subslice_mut_fwd: forall (T : Type) (n : usize) (x : array T n) (r : range usize), result (slice T).
-Axiom array_subslice_mut_back: forall (T : Type) (n : usize) (x : array T n) (r : range usize) (ns : slice T), result (array T n).
-Axiom slice_subslice_shared: forall (T : Type) (x : slice T) (r : range usize), result (slice T).
-Axiom slice_subslice_mut_fwd: forall (T : Type) (x : slice T) (r : range usize), result (slice T).
-Axiom slice_subslice_mut_back: forall (T : Type) (x : slice T) (r : range usize) (ns : slice T), result (slice T).
+Axiom array_subslice: forall (T : Type) (n : usize) (x : array T n) (r : core_ops_range_Range usize), result (slice T).
+Axiom array_update_subslice: forall (T : Type) (n : usize) (x : array T n) (r : core_ops_range_Range usize) (ns : slice T), result (array T n).
+
+Axiom slice_subslice: forall (T : Type) (x : slice T) (r : core_ops_range_Range usize), result (slice T).
+Axiom slice_update_subslice: forall (T : Type) (x : slice T) (r : core_ops_range_Range usize) (ns : slice T), result (slice T).
 
 (*** Vectors *)
 
-Definition vec T := { l: list T | Z.of_nat (length l) <= usize_max }.
+Definition alloc_vec_Vec T := { l: list T | Z.of_nat (length l) <= usize_max }.
 
-Definition vec_to_list {T: Type} (v: vec T) : list T := proj1_sig v.
+Definition alloc_vec_Vec_to_list {T: Type} (v: alloc_vec_Vec T) : list T := proj1_sig v.
 
-Definition vec_length {T: Type} (v: vec T) : Z := Z.of_nat (length (vec_to_list v)).
+Definition alloc_vec_Vec_length {T: Type} (v: alloc_vec_Vec T) : Z := Z.of_nat (length (alloc_vec_Vec_to_list v)).
 
-Definition vec_new (T: Type) : vec T := (exist _ [] le_0_usize_max).
+Definition alloc_vec_Vec_new (T: Type) : alloc_vec_Vec T := (exist _ [] le_0_usize_max).
 
-Lemma vec_len_in_usize {T} (v: vec T) : usize_min <= vec_length v <= usize_max.
+Lemma alloc_vec_Vec_len_in_usize {T} (v: alloc_vec_Vec T) : usize_min <= alloc_vec_Vec_length v <= usize_max.
 Proof.
-  unfold vec_length, usize_min.
+  unfold alloc_vec_Vec_length, usize_min.
   split.
   - lia.
   - apply (proj2_sig v).
 Qed.
 
-Definition vec_len (T: Type) (v: vec T) : usize :=
-  exist _ (vec_length v) (vec_len_in_usize v).
+Definition alloc_vec_Vec_len (T: Type) (v: alloc_vec_Vec T) : usize :=
+  exist _ (alloc_vec_Vec_length v) (alloc_vec_Vec_len_in_usize v).
 
 Fixpoint list_update {A} (l: list A) (n: nat) (a: A)
   : list A :=
@@ -474,50 +628,279 @@ Fixpoint list_update {A} (l: list A) (n: nat) (a: A)
     | S m => x :: (list_update t m a)
 end end.
 
-Definition vec_bind {A B} (v: vec A) (f: list A -> result (list B)) : result (vec B) :=
-  l <- f (vec_to_list v) ;
+Definition alloc_vec_Vec_bind {A B} (v: alloc_vec_Vec A) (f: list A -> result (list B)) : result (alloc_vec_Vec B) :=
+  l <- f (alloc_vec_Vec_to_list v) ;
   match sumbool_of_bool (scalar_le_max Usize (Z.of_nat (length l))) with
   | left H => Return (exist _ l (scalar_le_max_valid _ _ H))
   | right _ => Fail_ Failure
   end.
 
 (* The **forward** function shouldn't be used *)
-Definition vec_push_fwd (T: Type) (v: vec T) (x: T) : unit := tt.
+Definition alloc_vec_Vec_push_fwd (T: Type) (v: alloc_vec_Vec T) (x: T) : unit := tt.
 
-Definition vec_push_back (T: Type) (v: vec T) (x: T) : result (vec T) :=
-  vec_bind v (fun l => Return (l ++ [x])).
+Definition alloc_vec_Vec_push (T: Type) (v: alloc_vec_Vec T) (x: T) : result (alloc_vec_Vec T) :=
+  alloc_vec_Vec_bind v (fun l => Return (l ++ [x])).
 
 (* The **forward** function shouldn't be used *)
-Definition vec_insert_fwd (T: Type) (v: vec T) (i: usize) (x: T) : result unit :=
-  if to_Z i <? vec_length v then Return tt else Fail_ Failure.
+Definition alloc_vec_Vec_insert_fwd (T: Type) (v: alloc_vec_Vec T) (i: usize) (x: T) : result unit :=
+  if to_Z i <? alloc_vec_Vec_length v then Return tt else Fail_ Failure.
 
-Definition vec_insert_back (T: Type) (v: vec T) (i: usize) (x: T) : result (vec T) :=
-  vec_bind v (fun l =>
+Definition alloc_vec_Vec_insert (T: Type) (v: alloc_vec_Vec T) (i: usize) (x: T) : result (alloc_vec_Vec T) :=
+  alloc_vec_Vec_bind v (fun l =>
     if to_Z i <? Z.of_nat (length l)
     then Return (list_update l (usize_to_nat i) x)
     else Fail_ Failure).
 
-(* The **backward** function shouldn't be used *)
-Definition vec_index_fwd (T: Type) (v: vec T) (i: usize) : result T :=
-  match nth_error (vec_to_list v) (usize_to_nat i) with
-  | Some n => Return n
-  | None   => Fail_ Failure
-  end.
-
-Definition vec_index_back (T: Type) (v: vec T) (i: usize) (x: T) : result unit :=
-  if to_Z i <? vec_length v then Return tt else Fail_ Failure.
-
-(* The **backward** function shouldn't be used *)
-Definition vec_index_mut_fwd (T: Type) (v: vec T) (i: usize) : result T :=
-  match nth_error (vec_to_list v) (usize_to_nat i) with
-  | Some n => Return n
-  | None   => Fail_ Failure
+(* Helper *)
+Axiom alloc_vec_Vec_index_usize : forall {T : Type} (v : alloc_vec_Vec T) (i : usize), result T.
+
+(* Helper *)
+Axiom alloc_vec_Vec_update_usize : forall {T : Type} (v : alloc_vec_Vec T) (i : usize) (x : T), result (alloc_vec_Vec T).
+
+(* Trait declaration: [core::slice::index::private_slice_index::Sealed] *)
+Definition core_slice_index_private_slice_index_Sealed (self : Type) := unit.
+
+(* Trait declaration: [core::slice::index::SliceIndex] *)
+Record core_slice_index_SliceIndex (Self T : Type) := mk_core_slice_index_SliceIndex {
+  core_slice_index_SliceIndex_sealedInst : core_slice_index_private_slice_index_Sealed Self;
+  core_slice_index_SliceIndex_Output : Type;
+  core_slice_index_SliceIndex_get : Self -> T -> result (option core_slice_index_SliceIndex_Output);
+  core_slice_index_SliceIndex_get_mut : Self -> T -> result (option core_slice_index_SliceIndex_Output);
+  core_slice_index_SliceIndex_get_mut_back : Self -> T -> option core_slice_index_SliceIndex_Output -> result T;
+  core_slice_index_SliceIndex_get_unchecked : Self -> const_raw_ptr T -> result (const_raw_ptr core_slice_index_SliceIndex_Output);
+  core_slice_index_SliceIndex_get_unchecked_mut : Self -> mut_raw_ptr T -> result (mut_raw_ptr core_slice_index_SliceIndex_Output);
+  core_slice_index_SliceIndex_index : Self -> T -> result core_slice_index_SliceIndex_Output;
+  core_slice_index_SliceIndex_index_mut : Self -> T -> result core_slice_index_SliceIndex_Output;
+  core_slice_index_SliceIndex_index_mut_back : Self -> T -> core_slice_index_SliceIndex_Output -> result T;
+}.
+Arguments mk_core_slice_index_SliceIndex {_ _}.
+Arguments core_slice_index_SliceIndex_sealedInst {_ _}.
+Arguments core_slice_index_SliceIndex_Output {_ _}.
+Arguments core_slice_index_SliceIndex_get {_ _}.
+Arguments core_slice_index_SliceIndex_get_mut {_ _}.
+Arguments core_slice_index_SliceIndex_get_mut_back {_ _}.
+Arguments core_slice_index_SliceIndex_get_unchecked {_ _}.
+Arguments core_slice_index_SliceIndex_get_unchecked_mut {_ _}.
+Arguments core_slice_index_SliceIndex_index {_ _}.
+Arguments core_slice_index_SliceIndex_index_mut {_ _}.
+Arguments core_slice_index_SliceIndex_index_mut_back {_ _}.
+
+(* [core::slice::index::[T]::index]: forward function *)
+Definition core_slice_index_Slice_index
+  (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T))
+  (s : slice T) (i : Idx) : result inst.(core_slice_index_SliceIndex_Output) :=
+  x <- inst.(core_slice_index_SliceIndex_get) i s;
+  match x with
+  | None => Fail_ Failure
+  | Some x => Return x
   end.
 
-Definition vec_index_mut_back (T: Type) (v: vec T) (i: usize) (x: T) : result (vec T) :=
-  vec_bind v (fun l =>
-    if to_Z i <? Z.of_nat (length l)
-    then Return (list_update l (usize_to_nat i) x)
-    else Fail_ Failure).
+(* [core::slice::index::Range:::get]: forward function *)
+Axiom core_slice_index_RangeUsize_get : forall (T : Type) (i : core_ops_range_Range usize) (s : slice T), result (option (slice T)).
+
+(* [core::slice::index::Range::get_mut]: forward function *)
+Axiom core_slice_index_RangeUsize_get_mut :
+  forall (T : Type), core_ops_range_Range usize -> slice T -> result (option (slice T)).
+
+(* [core::slice::index::Range::get_mut]: backward function 0 *)
+Axiom core_slice_index_RangeUsize_get_mut_back :
+  forall (T : Type), core_ops_range_Range usize -> slice T -> option (slice T) -> result (slice T).
+
+(* [core::slice::index::Range::get_unchecked]: forward function *)
+Definition core_slice_index_RangeUsize_get_unchecked
+  (T : Type) :
+  core_ops_range_Range usize -> const_raw_ptr (slice T) -> result (const_raw_ptr (slice T)) :=
+  (* Don't know what the model should be - for now we always fail to make
+     sure code which uses it fails *)
+  fun _ _ => Fail_ Failure.
+
+(* [core::slice::index::Range::get_unchecked_mut]: forward function *)
+Definition core_slice_index_RangeUsize_get_unchecked_mut
+  (T : Type) :
+  core_ops_range_Range usize -> mut_raw_ptr (slice T) -> result (mut_raw_ptr (slice T)) :=
+  (* Don't know what the model should be - for now we always fail to make
+    sure code which uses it fails *)
+  fun _ _ => Fail_ Failure.
+
+(* [core::slice::index::Range::index]: forward function *)
+Axiom core_slice_index_RangeUsize_index :
+  forall (T : Type), core_ops_range_Range usize -> slice T -> result (slice T).
+
+(* [core::slice::index::Range::index_mut]: forward function *)
+Axiom core_slice_index_RangeUsize_index_mut :
+  forall (T : Type), core_ops_range_Range usize -> slice T -> result (slice T).
+
+(* [core::slice::index::Range::index_mut]: backward function 0 *)
+Axiom core_slice_index_RangeUsize_index_mut_back :
+  forall (T : Type), core_ops_range_Range usize -> slice T -> slice T -> result (slice T).
+
+(* [core::slice::index::[T]::index_mut]: forward function *)
+Axiom core_slice_index_Slice_index_mut :
+  forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T)),
+  slice T -> Idx -> result inst.(core_slice_index_SliceIndex_Output).
+
+(* [core::slice::index::[T]::index_mut]: backward function 0 *)
+Axiom core_slice_index_Slice_index_mut_back :
+  forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T)),
+  slice T -> Idx -> inst.(core_slice_index_SliceIndex_Output) -> result (slice T).
+
+(* [core::array::[T; N]::index]: forward function *)
+Axiom core_array_Array_index :
+  forall (T Idx : Type) (N : usize) (inst : core_ops_index_Index (slice T) Idx)
+  (a : array T N) (i : Idx), result inst.(core_ops_index_Index_Output).
+
+(* [core::array::[T; N]::index_mut]: forward function *)
+Axiom core_array_Array_index_mut :
+  forall (T Idx : Type) (N : usize) (inst : core_ops_index_IndexMut (slice T) Idx)
+  (a : array T N) (i : Idx), result inst.(core_ops_index_IndexMut_indexInst).(core_ops_index_Index_Output).
+
+(* [core::array::[T; N]::index_mut]: backward function 0 *)
+Axiom core_array_Array_index_mut_back :
+  forall (T Idx : Type) (N : usize) (inst : core_ops_index_IndexMut (slice T) Idx)
+  (a : array T N) (i : Idx) (x : inst.(core_ops_index_IndexMut_indexInst).(core_ops_index_Index_Output)), result (array T N).
+
+(* Trait implementation: [core::slice::index::private_slice_index::Range] *)
+Definition core_slice_index_private_slice_index_SealedRangeUsizeInst
+  : core_slice_index_private_slice_index_Sealed (core_ops_range_Range usize) := tt.
+
+(* Trait implementation: [core::slice::index::Range] *)
+Definition core_slice_index_SliceIndexRangeUsizeSliceTInst (T : Type) :
+  core_slice_index_SliceIndex (core_ops_range_Range usize) (slice T) := {|
+  core_slice_index_SliceIndex_sealedInst := core_slice_index_private_slice_index_SealedRangeUsizeInst;
+  core_slice_index_SliceIndex_Output := slice T;
+  core_slice_index_SliceIndex_get := core_slice_index_RangeUsize_get T;
+  core_slice_index_SliceIndex_get_mut := core_slice_index_RangeUsize_get_mut T;
+  core_slice_index_SliceIndex_get_mut_back := core_slice_index_RangeUsize_get_mut_back T;
+  core_slice_index_SliceIndex_get_unchecked := core_slice_index_RangeUsize_get_unchecked T;
+  core_slice_index_SliceIndex_get_unchecked_mut := core_slice_index_RangeUsize_get_unchecked_mut T;
+  core_slice_index_SliceIndex_index := core_slice_index_RangeUsize_index T;
+  core_slice_index_SliceIndex_index_mut := core_slice_index_RangeUsize_index_mut T;
+  core_slice_index_SliceIndex_index_mut_back := core_slice_index_RangeUsize_index_mut_back T;
+|}.
+
+(* Trait implementation: [core::slice::index::[T]] *)
+Definition core_ops_index_IndexSliceTIInst (T Idx : Type)
+  (inst : core_slice_index_SliceIndex Idx (slice T)) :
+  core_ops_index_Index (slice T) Idx := {|
+  core_ops_index_Index_Output := inst.(core_slice_index_SliceIndex_Output);
+  core_ops_index_Index_index := core_slice_index_Slice_index T Idx inst;
+|}.
+
+(* Trait implementation: [core::slice::index::[T]] *)
+Definition core_ops_index_IndexMutSliceTIInst (T Idx : Type)
+  (inst : core_slice_index_SliceIndex Idx (slice T)) :
+  core_ops_index_IndexMut (slice T) Idx := {|
+  core_ops_index_IndexMut_indexInst := core_ops_index_IndexSliceTIInst T Idx inst;
+  core_ops_index_IndexMut_index_mut := core_slice_index_Slice_index_mut T Idx inst;
+  core_ops_index_IndexMut_index_mut_back := core_slice_index_Slice_index_mut_back T Idx inst;
+|}.
+
+(* Trait implementation: [core::array::[T; N]] *)
+Definition core_ops_index_IndexArrayInst (T Idx : Type) (N : usize)
+  (inst : core_ops_index_Index (slice T) Idx) :
+  core_ops_index_Index (array T N) Idx := {|
+  core_ops_index_Index_Output := inst.(core_ops_index_Index_Output);
+  core_ops_index_Index_index := core_array_Array_index T Idx N inst;
+|}.
+
+(* Trait implementation: [core::array::[T; N]] *)
+Definition core_ops_index_IndexMutArrayInst (T Idx : Type) (N : usize)
+  (inst : core_ops_index_IndexMut (slice T) Idx) :
+  core_ops_index_IndexMut (array T N) Idx := {|
+  core_ops_index_IndexMut_indexInst := core_ops_index_IndexArrayInst T Idx N inst.(core_ops_index_IndexMut_indexInst);
+  core_ops_index_IndexMut_index_mut := core_array_Array_index_mut T Idx N inst;
+  core_ops_index_IndexMut_index_mut_back := core_array_Array_index_mut_back T Idx N inst;
+|}.
+
+(* [core::slice::index::usize::get]: forward function *)
+Axiom core_slice_index_usize_get : forall (T : Type), usize -> slice T -> result (option T).
+
+(* [core::slice::index::usize::get_mut]: forward function *)
+Axiom core_slice_index_usize_get_mut : forall (T : Type), usize -> slice T -> result (option T).
+
+(* [core::slice::index::usize::get_mut]: backward function 0 *)
+Axiom core_slice_index_usize_get_mut_back :
+  forall (T : Type), usize -> slice T -> option T -> result (slice T).
+
+(* [core::slice::index::usize::get_unchecked]: forward function *)
+Axiom core_slice_index_usize_get_unchecked :
+  forall (T : Type), usize -> const_raw_ptr (slice T) -> result (const_raw_ptr T).
+
+(* [core::slice::index::usize::get_unchecked_mut]: forward function *)
+Axiom core_slice_index_usize_get_unchecked_mut :
+  forall (T : Type), usize -> mut_raw_ptr (slice T) -> result (mut_raw_ptr T).
+
+(* [core::slice::index::usize::index]: forward function *)
+Axiom core_slice_index_usize_index : forall (T : Type), usize -> slice T -> result T.
+
+(* [core::slice::index::usize::index_mut]: forward function *)
+Axiom core_slice_index_usize_index_mut : forall (T : Type), usize -> slice T -> result T.
+
+(* [core::slice::index::usize::index_mut]: backward function 0 *)
+Axiom core_slice_index_usize_index_mut_back :
+  forall (T : Type), usize -> slice T -> T -> result (slice T).
+
+(* Trait implementation: [core::slice::index::private_slice_index::usize] *)
+Definition core_slice_index_private_slice_index_SealedUsizeInst
+  : core_slice_index_private_slice_index_Sealed usize := tt.
+
+(* Trait implementation: [core::slice::index::usize] *)
+Definition core_slice_index_SliceIndexUsizeSliceTInst (T : Type) :
+  core_slice_index_SliceIndex usize (slice T) := {|
+  core_slice_index_SliceIndex_sealedInst := core_slice_index_private_slice_index_SealedUsizeInst;
+  core_slice_index_SliceIndex_Output := T;
+  core_slice_index_SliceIndex_get := core_slice_index_usize_get T;
+  core_slice_index_SliceIndex_get_mut := core_slice_index_usize_get_mut T;
+  core_slice_index_SliceIndex_get_mut_back := core_slice_index_usize_get_mut_back T;
+  core_slice_index_SliceIndex_get_unchecked := core_slice_index_usize_get_unchecked T;
+  core_slice_index_SliceIndex_get_unchecked_mut := core_slice_index_usize_get_unchecked_mut T;
+  core_slice_index_SliceIndex_index := core_slice_index_usize_index T;
+  core_slice_index_SliceIndex_index_mut := core_slice_index_usize_index_mut T;
+  core_slice_index_SliceIndex_index_mut_back := core_slice_index_usize_index_mut_back T;
+|}.
+
+(* [alloc::vec::Vec::index]: forward function *)
+Axiom alloc_vec_Vec_index : forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T))
+  (Self : alloc_vec_Vec T) (i : Idx), result inst.(core_slice_index_SliceIndex_Output).
+
+(* [alloc::vec::Vec::index_mut]: forward function *)
+Axiom alloc_vec_Vec_index_mut : forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T))
+  (Self : alloc_vec_Vec T) (i : Idx), result inst.(core_slice_index_SliceIndex_Output).
+
+(* [alloc::vec::Vec::index_mut]: backward function 0 *)
+Axiom alloc_vec_Vec_index_mut_back :
+  forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T))
+  (Self : alloc_vec_Vec T) (i : Idx) (x : inst.(core_slice_index_SliceIndex_Output)), result (alloc_vec_Vec T).
+
+(* Trait implementation: [alloc::vec::Vec] *)
+Definition alloc_vec_Vec_coreopsindexIndexInst (T Idx : Type)
+  (inst : core_slice_index_SliceIndex Idx (slice T)) :
+  core_ops_index_Index (alloc_vec_Vec T) Idx := {|
+  core_ops_index_Index_Output := inst.(core_slice_index_SliceIndex_Output);
+  core_ops_index_Index_index := alloc_vec_Vec_index T Idx inst;
+|}.
+
+(* Trait implementation: [alloc::vec::Vec] *)
+Definition alloc_vec_Vec_coreopsindexIndexMutInst (T Idx : Type)
+  (inst : core_slice_index_SliceIndex Idx (slice T)) :
+  core_ops_index_IndexMut (alloc_vec_Vec T) Idx := {|
+  core_ops_index_IndexMut_indexInst := alloc_vec_Vec_coreopsindexIndexInst T Idx inst;
+  core_ops_index_IndexMut_index_mut := alloc_vec_Vec_index_mut T Idx inst;
+  core_ops_index_IndexMut_index_mut_back := alloc_vec_Vec_index_mut_back T Idx inst;
+|}.
+
+(*** Theorems *)
+
+Axiom alloc_vec_Vec_index_eq : forall {a : Type} (v : alloc_vec_Vec a) (i : usize) (x : a),
+  alloc_vec_Vec_index a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i =
+    alloc_vec_Vec_index_usize v i.
+
+Axiom alloc_vec_Vec_index_mut_eq : forall {a : Type} (v : alloc_vec_Vec a) (i : usize) (x : a),
+  alloc_vec_Vec_index_mut a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i =
+    alloc_vec_Vec_index_usize v i.
+
+Axiom alloc_vec_Vec_index_mut_back_eq : forall {a : Type} (v : alloc_vec_Vec a) (i : usize) (x : a),
+  alloc_vec_Vec_index_mut_back a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i x =
+    alloc_vec_Vec_update_usize v i x.
 
 End Primitives.
diff --git a/tests/coq/hashmap_on_disk/_CoqProject b/tests/coq/hashmap_on_disk/_CoqProject
index b78c7b5f..41945494 100644
--- a/tests/coq/hashmap_on_disk/_CoqProject
+++ b/tests/coq/hashmap_on_disk/_CoqProject
@@ -6,4 +6,7 @@
 HashmapMain_Types.v
 Primitives.v
 HashmapMain_Funs.v
-HashmapMain_Opaque.v
+HashmapMain_TypesExternal.v
+HashmapMain_FunsExternal_Template.v
+HashmapMain_FunsExternal.v
+HashmapMain_TypesExternal_Template.v
diff --git a/tests/coq/misc/Bitwise.v b/tests/coq/misc/Bitwise.v
new file mode 100644
index 00000000..94771b37
--- /dev/null
+++ b/tests/coq/misc/Bitwise.v
@@ -0,0 +1,38 @@
+(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
+(** [bitwise] *)
+Require Import Primitives.
+Import Primitives.
+Require Import Coq.ZArith.ZArith.
+Require Import List.
+Import ListNotations.
+Local Open Scope Primitives_scope.
+Module Bitwise.
+
+(** [bitwise::shift_u32]: forward function
+    Source: 'src/bitwise.rs', lines 3:0-3:31 *)
+Definition shift_u32 (a : u32) : result u32 :=
+  t <- u32_shr a 16%usize; u32_shl t 16%usize
+.
+
+(** [bitwise::shift_i32]: forward function
+    Source: 'src/bitwise.rs', lines 10:0-10:31 *)
+Definition shift_i32 (a : i32) : result i32 :=
+  t <- i32_shr a 16%isize; i32_shl t 16%isize
+.
+
+(** [bitwise::xor_u32]: forward function
+    Source: 'src/bitwise.rs', lines 17:0-17:37 *)
+Definition xor_u32 (a : u32) (b : u32) : result u32 :=
+  Return (u32_xor a b).
+
+(** [bitwise::or_u32]: forward function
+    Source: 'src/bitwise.rs', lines 21:0-21:36 *)
+Definition or_u32 (a : u32) (b : u32) : result u32 :=
+  Return (u32_or a b).
+
+(** [bitwise::and_u32]: forward function
+    Source: 'src/bitwise.rs', lines 25:0-25:37 *)
+Definition and_u32 (a : u32) (b : u32) : result u32 :=
+  Return (u32_and a b).
+
+End Bitwise.
diff --git a/tests/coq/misc/Constants.v b/tests/coq/misc/Constants.v
index f1c32730..ad899f25 100644
--- a/tests/coq/misc/Constants.v
+++ b/tests/coq/misc/Constants.v
@@ -8,131 +8,153 @@ Import ListNotations.
 Local Open Scope Primitives_scope.
 Module Constants.
 
-(** [constants::X0] *)
+(** [constants::X0]
+    Source: 'src/constants.rs', lines 5:0-5:17 *)
 Definition x0_body : result u32 := Return 0%u32.
 Definition x0_c : u32 := x0_body%global.
 
-(** [core::num::u32::{8}::MAX] *)
-Definition core_num_u32_max_body : result u32 := Return 4294967295%u32.
-Definition core_num_u32_max_c : u32 := core_num_u32_max_body%global.
-
-(** [constants::X1] *)
-Definition x1_body : result u32 := Return core_num_u32_max_c.
+(** [constants::X1]
+    Source: 'src/constants.rs', lines 7:0-7:17 *)
+Definition x1_body : result u32 := Return core_u32_max.
 Definition x1_c : u32 := x1_body%global.
 
-(** [constants::X2] *)
+(** [constants::X2]
+    Source: 'src/constants.rs', lines 10:0-10:17 *)
 Definition x2_body : result u32 := Return 3%u32.
 Definition x2_c : u32 := x2_body%global.
 
-(** [constants::incr]: forward function *)
-Definition incr_fwd (n : u32) : result u32 :=
+(** [constants::incr]: forward function
+    Source: 'src/constants.rs', lines 17:0-17:32 *)
+Definition incr (n : u32) : result u32 :=
   u32_add n 1%u32.
 
-(** [constants::X3] *)
-Definition x3_body : result u32 := incr_fwd 32%u32.
+(** [constants::X3]
+    Source: 'src/constants.rs', lines 15:0-15:17 *)
+Definition x3_body : result u32 := incr 32%u32.
 Definition x3_c : u32 := x3_body%global.
 
-(** [constants::mk_pair0]: forward function *)
-Definition mk_pair0_fwd (x : u32) (y : u32) : result (u32 * u32) :=
-  Return (x, y)
-.
+(** [constants::mk_pair0]: forward function
+    Source: 'src/constants.rs', lines 23:0-23:51 *)
+Definition mk_pair0 (x : u32) (y : u32) : result (u32 * u32) :=
+  Return (x, y).
 
-(** [constants::Pair] *)
-Record Pair_t (T1 T2 : Type) := mkPair_t { Pair_x : T1; Pair_y : T2; }.
+(** [constants::Pair]
+    Source: 'src/constants.rs', lines 36:0-36:23 *)
+Record Pair_t (T1 T2 : Type) := mkPair_t { pair_x : T1; pair_y : T2; }.
 
-Arguments mkPair_t {T1} {T2} _ _.
-Arguments Pair_x {T1} {T2}.
-Arguments Pair_y {T1} {T2}.
+Arguments mkPair_t { _ _ }.
+Arguments pair_x { _ _ }.
+Arguments pair_y { _ _ }.
 
-(** [constants::mk_pair1]: forward function *)
-Definition mk_pair1_fwd (x : u32) (y : u32) : result (Pair_t u32 u32) :=
-  Return {| Pair_x := x; Pair_y := y |}
+(** [constants::mk_pair1]: forward function
+    Source: 'src/constants.rs', lines 27:0-27:55 *)
+Definition mk_pair1 (x : u32) (y : u32) : result (Pair_t u32 u32) :=
+  Return {| pair_x := x; pair_y := y |}
 .
 
-(** [constants::P0] *)
-Definition p0_body : result (u32 * u32) := mk_pair0_fwd 0%u32 1%u32.
+(** [constants::P0]
+    Source: 'src/constants.rs', lines 31:0-31:24 *)
+Definition p0_body : result (u32 * u32) := mk_pair0 0%u32 1%u32.
 Definition p0_c : (u32 * u32) := p0_body%global.
 
-(** [constants::P1] *)
-Definition p1_body : result (Pair_t u32 u32) := mk_pair1_fwd 0%u32 1%u32.
+(** [constants::P1]
+    Source: 'src/constants.rs', lines 32:0-32:28 *)
+Definition p1_body : result (Pair_t u32 u32) := mk_pair1 0%u32 1%u32.
 Definition p1_c : Pair_t u32 u32 := p1_body%global.
 
-(** [constants::P2] *)
+(** [constants::P2]
+    Source: 'src/constants.rs', lines 33:0-33:24 *)
 Definition p2_body : result (u32 * u32) := Return (0%u32, 1%u32).
 Definition p2_c : (u32 * u32) := p2_body%global.
 
-(** [constants::P3] *)
+(** [constants::P3]
+    Source: 'src/constants.rs', lines 34:0-34:28 *)
 Definition p3_body : result (Pair_t u32 u32) :=
-  Return {| Pair_x := 0%u32; Pair_y := 1%u32 |}
+  Return {| pair_x := 0%u32; pair_y := 1%u32 |}
 .
 Definition p3_c : Pair_t u32 u32 := p3_body%global.
 
-(** [constants::Wrap] *)
-Record Wrap_t (T : Type) := mkWrap_t { Wrap_val : T; }.
+(** [constants::Wrap]
+    Source: 'src/constants.rs', lines 49:0-49:18 *)
+Record Wrap_t (T : Type) := mkWrap_t { wrap_value : T; }.
 
-Arguments mkWrap_t {T} _.
-Arguments Wrap_val {T}.
+Arguments mkWrap_t { _ }.
+Arguments wrap_value { _ }.
 
-(** [constants::Wrap::{0}::new]: forward function *)
-Definition wrap_new_fwd (T : Type) (val : T) : result (Wrap_t T) :=
-  Return {| Wrap_val := val |}
+(** [constants::{constants::Wrap<T>}::new]: forward function
+    Source: 'src/constants.rs', lines 54:4-54:41 *)
+Definition wrap_new (T : Type) (value : T) : result (Wrap_t T) :=
+  Return {| wrap_value := value |}
 .
 
-(** [constants::Y] *)
-Definition y_body : result (Wrap_t i32) := wrap_new_fwd i32 2%i32.
+(** [constants::Y]
+    Source: 'src/constants.rs', lines 41:0-41:22 *)
+Definition y_body : result (Wrap_t i32) := wrap_new i32 2%i32.
 Definition y_c : Wrap_t i32 := y_body%global.
 
-(** [constants::unwrap_y]: forward function *)
-Definition unwrap_y_fwd : result i32 :=
-  Return y_c.(Wrap_val).
+(** [constants::unwrap_y]: forward function
+    Source: 'src/constants.rs', lines 43:0-43:30 *)
+Definition unwrap_y : result i32 :=
+  Return y_c.(wrap_value).
 
-(** [constants::YVAL] *)
-Definition yval_body : result i32 := unwrap_y_fwd.
+(** [constants::YVAL]
+    Source: 'src/constants.rs', lines 47:0-47:19 *)
+Definition yval_body : result i32 := unwrap_y.
 Definition yval_c : i32 := yval_body%global.
 
-(** [constants::get_z1::Z1] *)
+(** [constants::get_z1::Z1]
+    Source: 'src/constants.rs', lines 62:4-62:17 *)
 Definition get_z1_z1_body : result i32 := Return 3%i32.
 Definition get_z1_z1_c : i32 := get_z1_z1_body%global.
 
-(** [constants::get_z1]: forward function *)
-Definition get_z1_fwd : result i32 :=
+(** [constants::get_z1]: forward function
+    Source: 'src/constants.rs', lines 61:0-61:28 *)
+Definition get_z1 : result i32 :=
   Return get_z1_z1_c.
 
-(** [constants::add]: forward function *)
-Definition add_fwd (a : i32) (b : i32) : result i32 :=
+(** [constants::add]: forward function
+    Source: 'src/constants.rs', lines 66:0-66:39 *)
+Definition add (a : i32) (b : i32) : result i32 :=
   i32_add a b.
 
-(** [constants::Q1] *)
+(** [constants::Q1]
+    Source: 'src/constants.rs', lines 74:0-74:17 *)
 Definition q1_body : result i32 := Return 5%i32.
 Definition q1_c : i32 := q1_body%global.
 
-(** [constants::Q2] *)
+(** [constants::Q2]
+    Source: 'src/constants.rs', lines 75:0-75:17 *)
 Definition q2_body : result i32 := Return q1_c.
 Definition q2_c : i32 := q2_body%global.
 
-(** [constants::Q3] *)
-Definition q3_body : result i32 := add_fwd q2_c 3%i32.
+(** [constants::Q3]
+    Source: 'src/constants.rs', lines 76:0-76:17 *)
+Definition q3_body : result i32 := add q2_c 3%i32.
 Definition q3_c : i32 := q3_body%global.
 
-(** [constants::get_z2]: forward function *)
-Definition get_z2_fwd : result i32 :=
-  i <- get_z1_fwd; i0 <- add_fwd i q3_c; add_fwd q1_c i0
-.
+(** [constants::get_z2]: forward function
+    Source: 'src/constants.rs', lines 70:0-70:28 *)
+Definition get_z2 : result i32 :=
+  i <- get_z1; i0 <- add i q3_c; add q1_c i0.
 
-(** [constants::S1] *)
+(** [constants::S1]
+    Source: 'src/constants.rs', lines 80:0-80:18 *)
 Definition s1_body : result u32 := Return 6%u32.
 Definition s1_c : u32 := s1_body%global.
 
-(** [constants::S2] *)
-Definition s2_body : result u32 := incr_fwd s1_c.
+(** [constants::S2]
+    Source: 'src/constants.rs', lines 81:0-81:18 *)
+Definition s2_body : result u32 := incr s1_c.
 Definition s2_c : u32 := s2_body%global.
 
-(** [constants::S3] *)
+(** [constants::S3]
+    Source: 'src/constants.rs', lines 82:0-82:29 *)
 Definition s3_body : result (Pair_t u32 u32) := Return p3_c.
 Definition s3_c : Pair_t u32 u32 := s3_body%global.
 
-(** [constants::S4] *)
-Definition s4_body : result (Pair_t u32 u32) := mk_pair1_fwd 7%u32 8%u32.
+(** [constants::S4]
+    Source: 'src/constants.rs', lines 83:0-83:29 *)
+Definition s4_body : result (Pair_t u32 u32) := mk_pair1 7%u32 8%u32.
 Definition s4_c : Pair_t u32 u32 := s4_body%global.
 
-End Constants .
+End Constants.
diff --git a/tests/coq/misc/External_Funs.v b/tests/coq/misc/External_Funs.v
index 28370b2b..e9d39f66 100644
--- a/tests/coq/misc/External_Funs.v
+++ b/tests/coq/misc/External_Funs.v
@@ -6,16 +6,17 @@ Require Import Coq.ZArith.ZArith.
 Require Import List.
 Import ListNotations.
 Local Open Scope Primitives_scope.
-Require Export External_Types.
-Import External_Types.
-Require Export External_Opaque.
-Import External_Opaque.
+Require Import External_Types.
+Include External_Types.
+Require Import External_FunsExternal.
+Include External_FunsExternal.
 Module External_Funs.
 
-(** [external::swap]: forward function *)
-Definition swap_fwd
+(** [external::swap]: forward function
+    Source: 'src/external.rs', lines 6:0-6:46 *)
+Definition swap
   (T : Type) (x : T) (y : T) (st : state) : result (state * unit) :=
-  p <- core_mem_swap_fwd T x y st;
+  p <- core_mem_swap T x y st;
   let (st0, _) := p in
   p0 <- core_mem_swap_back0 T x y st st0;
   let (st1, _) := p0 in
@@ -24,12 +25,13 @@ Definition swap_fwd
   Return (st2, tt)
 .
 
-(** [external::swap]: backward function 0 *)
+(** [external::swap]: backward function 0
+    Source: 'src/external.rs', lines 6:0-6:46 *)
 Definition swap_back
   (T : Type) (x : T) (y : T) (st : state) (st0 : state) :
   result (state * (T * T))
   :=
-  p <- core_mem_swap_fwd T x y st;
+  p <- core_mem_swap T x y st;
   let (st1, _) := p in
   p0 <- core_mem_swap_back0 T x y st st1;
   let (st2, x0) := p0 in
@@ -38,26 +40,31 @@ Definition swap_back
   Return (st0, (x0, y0))
 .
 
-(** [external::test_new_non_zero_u32]: forward function *)
-Definition test_new_non_zero_u32_fwd
-  (x : u32) (st : state) : result (state * Core_num_nonzero_non_zero_u32_t) :=
-  p <- core_num_nonzero_non_zero_u32_new_fwd x st;
-  let (st0, opt) := p in
-  core_option_option_unwrap_fwd Core_num_nonzero_non_zero_u32_t opt st0
+(** [external::test_new_non_zero_u32]: forward function
+    Source: 'src/external.rs', lines 11:0-11:60 *)
+Definition test_new_non_zero_u32
+  (x : u32) (st : state) : result (state * core_num_nonzero_NonZeroU32_t) :=
+  p <- core_num_nonzero_NonZeroU32_new x st;
+  let (st0, o) := p in
+  core_option_Option_unwrap core_num_nonzero_NonZeroU32_t o st0
 .
 
-(** [external::test_vec]: forward function *)
-Definition test_vec_fwd : result unit :=
-  let v := vec_new u32 in _ <- vec_push_back u32 v 0%u32; Return tt
+(** [external::test_vec]: forward function
+    Source: 'src/external.rs', lines 17:0-17:17 *)
+Definition test_vec : result unit :=
+  let v := alloc_vec_Vec_new u32 in
+  _ <- alloc_vec_Vec_push u32 v 0%u32;
+  Return tt
 .
 
 (** Unit test for [external::test_vec] *)
-Check (test_vec_fwd )%return.
+Check (test_vec )%return.
 
-(** [external::custom_swap]: forward function *)
-Definition custom_swap_fwd
+(** [external::custom_swap]: forward function
+    Source: 'src/external.rs', lines 24:0-24:66 *)
+Definition custom_swap
   (T : Type) (x : T) (y : T) (st : state) : result (state * T) :=
-  p <- core_mem_swap_fwd T x y st;
+  p <- core_mem_swap T x y st;
   let (st0, _) := p in
   p0 <- core_mem_swap_back0 T x y st st0;
   let (st1, x0) := p0 in
@@ -66,12 +73,13 @@ Definition custom_swap_fwd
   Return (st2, x0)
 .
 
-(** [external::custom_swap]: backward function 0 *)
+(** [external::custom_swap]: backward function 0
+    Source: 'src/external.rs', lines 24:0-24:66 *)
 Definition custom_swap_back
   (T : Type) (x : T) (y : T) (st : state) (ret : T) (st0 : state) :
   result (state * (T * T))
   :=
-  p <- core_mem_swap_fwd T x y st;
+  p <- core_mem_swap T x y st;
   let (st1, _) := p in
   p0 <- core_mem_swap_back0 T x y st st1;
   let (st2, _) := p0 in
@@ -80,13 +88,15 @@ Definition custom_swap_back
   Return (st0, (ret, y0))
 .
 
-(** [external::test_custom_swap]: forward function *)
-Definition test_custom_swap_fwd
+(** [external::test_custom_swap]: forward function
+    Source: 'src/external.rs', lines 29:0-29:59 *)
+Definition test_custom_swap
   (x : u32) (y : u32) (st : state) : result (state * unit) :=
-  p <- custom_swap_fwd u32 x y st; let (st0, _) := p in Return (st0, tt)
+  p <- custom_swap u32 x y st; let (st0, _) := p in Return (st0, tt)
 .
 
-(** [external::test_custom_swap]: backward function 0 *)
+(** [external::test_custom_swap]: backward function 0
+    Source: 'src/external.rs', lines 29:0-29:59 *)
 Definition test_custom_swap_back
   (x : u32) (y : u32) (st : state) (st0 : state) :
   result (state * (u32 * u32))
@@ -94,10 +104,10 @@ Definition test_custom_swap_back
   custom_swap_back u32 x y st 1%u32 st0
 .
 
-(** [external::test_swap_non_zero]: forward function *)
-Definition test_swap_non_zero_fwd
-  (x : u32) (st : state) : result (state * u32) :=
-  p <- swap_fwd u32 x 0%u32 st;
+(** [external::test_swap_non_zero]: forward function
+    Source: 'src/external.rs', lines 35:0-35:44 *)
+Definition test_swap_non_zero (x : u32) (st : state) : result (state * u32) :=
+  p <- swap u32 x 0%u32 st;
   let (st0, _) := p in
   p0 <- swap_back u32 x 0%u32 st st0;
   let (st1, p1) := p0 in
@@ -105,4 +115,4 @@ Definition test_swap_non_zero_fwd
   if x0 s= 0%u32 then Fail_ Failure else Return (st1, x0)
 .
 
-End External_Funs .
+End External_Funs.
diff --git a/tests/coq/misc/External_FunsExternal.v b/tests/coq/misc/External_FunsExternal.v
new file mode 100644
index 00000000..a8c5756a
--- /dev/null
+++ b/tests/coq/misc/External_FunsExternal.v
@@ -0,0 +1,43 @@
+(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
+(** [external]: external function declarations *)
+Require Import Primitives.
+Import Primitives.
+Require Import Coq.ZArith.ZArith.
+Require Import List.
+Import ListNotations.
+Local Open Scope Primitives_scope.
+Require Export External_Types.
+Include External_Types.
+Module External_FunsExternal.
+
+(** [core::mem::swap]: forward function
+    Source: '/rustc/d59363ad0b6391b7fc5bbb02c9ccf9300eef3753/library/core/src/mem/mod.rs', lines 726:0-726:42 *)
+Axiom core_mem_swap :
+  forall(T : Type), T -> T -> state -> result (state * unit)
+.
+
+(** [core::mem::swap]: backward function 0
+    Source: '/rustc/d59363ad0b6391b7fc5bbb02c9ccf9300eef3753/library/core/src/mem/mod.rs', lines 726:0-726:42 *)
+Axiom core_mem_swap_back0 :
+  forall(T : Type), T -> T -> state -> state -> result (state * T)
+.
+
+(** [core::mem::swap]: backward function 1
+    Source: '/rustc/d59363ad0b6391b7fc5bbb02c9ccf9300eef3753/library/core/src/mem/mod.rs', lines 726:0-726:42 *)
+Axiom core_mem_swap_back1 :
+  forall(T : Type), T -> T -> state -> state -> result (state * T)
+.
+
+(** [core::num::nonzero::{core::num::nonzero::NonZeroU32#14}::new]: forward function
+    Source: '/rustc/d59363ad0b6391b7fc5bbb02c9ccf9300eef3753/library/core/src/num/nonzero.rs', lines 79:16-79:57 *)
+Axiom core_num_nonzero_NonZeroU32_new
+  : u32 -> state -> result (state * (option core_num_nonzero_NonZeroU32_t))
+.
+
+(** [core::option::{core::option::Option<T>}::unwrap]: forward function
+    Source: '/rustc/d59363ad0b6391b7fc5bbb02c9ccf9300eef3753/library/core/src/option.rs', lines 932:4-932:34 *)
+Axiom core_option_Option_unwrap :
+  forall(T : Type), option T -> state -> result (state * T)
+.
+
+End External_FunsExternal.
diff --git a/tests/coq/misc/External_FunsExternal_Template.v b/tests/coq/misc/External_FunsExternal_Template.v
new file mode 100644
index 00000000..31e69c39
--- /dev/null
+++ b/tests/coq/misc/External_FunsExternal_Template.v
@@ -0,0 +1,44 @@
+(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
+(** [external]: external functions.
+-- This is a template file: rename it to "FunsExternal.lean" and fill the holes. *)
+Require Import Primitives.
+Import Primitives.
+Require Import Coq.ZArith.ZArith.
+Require Import List.
+Import ListNotations.
+Local Open Scope Primitives_scope.
+Require Import External_Types.
+Include External_Types.
+Module External_FunsExternal_Template.
+
+(** [core::mem::swap]: forward function
+    Source: '/rustc/d59363ad0b6391b7fc5bbb02c9ccf9300eef3753/library/core/src/mem/mod.rs', lines 726:0-726:42 *)
+Axiom core_mem_swap :
+  forall(T : Type), T -> T -> state -> result (state * unit)
+.
+
+(** [core::mem::swap]: backward function 0
+    Source: '/rustc/d59363ad0b6391b7fc5bbb02c9ccf9300eef3753/library/core/src/mem/mod.rs', lines 726:0-726:42 *)
+Axiom core_mem_swap_back0 :
+  forall(T : Type), T -> T -> state -> state -> result (state * T)
+.
+
+(** [core::mem::swap]: backward function 1
+    Source: '/rustc/d59363ad0b6391b7fc5bbb02c9ccf9300eef3753/library/core/src/mem/mod.rs', lines 726:0-726:42 *)
+Axiom core_mem_swap_back1 :
+  forall(T : Type), T -> T -> state -> state -> result (state * T)
+.
+
+(** [core::num::nonzero::{core::num::nonzero::NonZeroU32#14}::new]: forward function
+    Source: '/rustc/d59363ad0b6391b7fc5bbb02c9ccf9300eef3753/library/core/src/num/nonzero.rs', lines 79:16-79:57 *)
+Axiom core_num_nonzero_NonZeroU32_new
+  : u32 -> state -> result (state * (option core_num_nonzero_NonZeroU32_t))
+.
+
+(** [core::option::{core::option::Option<T>}::unwrap]: forward function
+    Source: '/rustc/d59363ad0b6391b7fc5bbb02c9ccf9300eef3753/library/core/src/option.rs', lines 932:4-932:34 *)
+Axiom core_option_Option_unwrap :
+  forall(T : Type), option T -> state -> result (state * T)
+.
+
+End External_FunsExternal_Template.
diff --git a/tests/coq/misc/External_Opaque.v b/tests/coq/misc/External_Opaque.v
deleted file mode 100644
index d2ee42d4..00000000
--- a/tests/coq/misc/External_Opaque.v
+++ /dev/null
@@ -1,38 +0,0 @@
-(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
-(** [external]: external function declarations *)
-Require Import Primitives.
-Import Primitives.
-Require Import Coq.ZArith.ZArith.
-Require Import List.
-Import ListNotations.
-Local Open Scope Primitives_scope.
-Require Export External_Types.
-Import External_Types.
-Module External_Opaque.
-
-(** [core::mem::swap]: forward function *)
-Axiom core_mem_swap_fwd :
-  forall(T : Type), T -> T -> state -> result (state * unit)
-.
-
-(** [core::mem::swap]: backward function 0 *)
-Axiom core_mem_swap_back0 :
-  forall(T : Type), T -> T -> state -> state -> result (state * T)
-.
-
-(** [core::mem::swap]: backward function 1 *)
-Axiom core_mem_swap_back1 :
-  forall(T : Type), T -> T -> state -> state -> result (state * T)
-.
-
-(** [core::num::nonzero::NonZeroU32::{14}::new]: forward function *)
-Axiom core_num_nonzero_non_zero_u32_new_fwd
-  : u32 -> state -> result (state * (option Core_num_nonzero_non_zero_u32_t))
-.
-
-(** [core::option::Option::{0}::unwrap]: forward function *)
-Axiom core_option_option_unwrap_fwd :
-  forall(T : Type), option T -> state -> result (state * T)
-.
-
-End External_Opaque .
diff --git a/tests/coq/misc/External_Types.v b/tests/coq/misc/External_Types.v
index 1883fa6c..b42c2ecf 100644
--- a/tests/coq/misc/External_Types.v
+++ b/tests/coq/misc/External_Types.v
@@ -6,12 +6,8 @@ Require Import Coq.ZArith.ZArith.
 Require Import List.
 Import ListNotations.
 Local Open Scope Primitives_scope.
+Require Import External_TypesExternal.
+Include External_TypesExternal.
 Module External_Types.
 
-(** [core::num::nonzero::NonZeroU32] *)
-Axiom Core_num_nonzero_non_zero_u32_t : Type.
-
-(** The state type used in the state-error monad *)
-Axiom state : Type.
-
-End External_Types .
+End External_Types.
diff --git a/tests/coq/misc/External_TypesExternal.v b/tests/coq/misc/External_TypesExternal.v
new file mode 100644
index 00000000..3f02b839
--- /dev/null
+++ b/tests/coq/misc/External_TypesExternal.v
@@ -0,0 +1,19 @@
+(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
+(** [external]: external types.
+-- This is a template file: rename it to "TypesExternal.lean" and fill the holes. *)
+Require Import Primitives.
+Import Primitives.
+Require Import Coq.ZArith.ZArith.
+Require Import List.
+Import ListNotations.
+Local Open Scope Primitives_scope.
+Module External_TypesExternal.
+
+(** [core::num::nonzero::NonZeroU32]
+    Source: '/rustc/d59363ad0b6391b7fc5bbb02c9ccf9300eef3753/library/core/src/num/nonzero.rs', lines 50:12-50:33 *)
+Axiom core_num_nonzero_NonZeroU32_t : Type.
+
+(** The state type used in the state-error monad *)
+Axiom state : Type.
+
+End External_TypesExternal.
diff --git a/tests/coq/misc/External_TypesExternal_Template.v b/tests/coq/misc/External_TypesExternal_Template.v
new file mode 100644
index 00000000..7ba79d8e
--- /dev/null
+++ b/tests/coq/misc/External_TypesExternal_Template.v
@@ -0,0 +1,19 @@
+(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
+(** [external]: external types.
+-- This is a template file: rename it to "TypesExternal.lean" and fill the holes. *)
+Require Import Primitives.
+Import Primitives.
+Require Import Coq.ZArith.ZArith.
+Require Import List.
+Import ListNotations.
+Local Open Scope Primitives_scope.
+Module External_TypesExternal_Template.
+
+(** [core::num::nonzero::NonZeroU32]
+    Source: '/rustc/d59363ad0b6391b7fc5bbb02c9ccf9300eef3753/library/core/src/num/nonzero.rs', lines 50:12-50:33 *)
+Axiom core_num_nonzero_NonZeroU32_t : Type.
+
+(** The state type used in the state-error monad *)
+Axiom state : Type.
+
+End External_TypesExternal_Template.
diff --git a/tests/coq/misc/Loops.v b/tests/coq/misc/Loops.v
index 82e57576..83c249c1 100644
--- a/tests/coq/misc/Loops.v
+++ b/tests/coq/misc/Loops.v
@@ -8,24 +8,27 @@ Import ListNotations.
 Local Open Scope Primitives_scope.
 Module Loops.
 
-(** [loops::sum]: loop 0: forward function *)
-Fixpoint sum_loop_fwd (n : nat) (max : u32) (i : u32) (s : u32) : result u32 :=
+(** [loops::sum]: loop 0: forward function
+    Source: 'src/loops.rs', lines 4:0-14:1 *)
+Fixpoint sum_loop (n : nat) (max : u32) (i : u32) (s : u32) : result u32 :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
     if i s< max
-    then (s0 <- u32_add s i; i0 <- u32_add i 1%u32; sum_loop_fwd n0 max i0 s0)
+    then (s0 <- u32_add s i; i0 <- u32_add i 1%u32; sum_loop n0 max i0 s0)
     else u32_mul s 2%u32
   end
 .
 
-(** [loops::sum]: forward function *)
-Definition sum_fwd (n : nat) (max : u32) : result u32 :=
-  sum_loop_fwd n max 0%u32 0%u32
+(** [loops::sum]: forward function
+    Source: 'src/loops.rs', lines 4:0-4:27 *)
+Definition sum (n : nat) (max : u32) : result u32 :=
+  sum_loop n max 0%u32 0%u32
 .
 
-(** [loops::sum_with_mut_borrows]: loop 0: forward function *)
-Fixpoint sum_with_mut_borrows_loop_fwd
+(** [loops::sum_with_mut_borrows]: loop 0: forward function
+    Source: 'src/loops.rs', lines 19:0-31:1 *)
+Fixpoint sum_with_mut_borrows_loop
   (n : nat) (max : u32) (mi : u32) (ms : u32) : result u32 :=
   match n with
   | O => Fail_ OutOfFuel
@@ -34,18 +37,20 @@ Fixpoint sum_with_mut_borrows_loop_fwd
     then (
       ms0 <- u32_add ms mi;
       mi0 <- u32_add mi 1%u32;
-      sum_with_mut_borrows_loop_fwd n0 max mi0 ms0)
+      sum_with_mut_borrows_loop n0 max mi0 ms0)
     else u32_mul ms 2%u32
   end
 .
 
-(** [loops::sum_with_mut_borrows]: forward function *)
-Definition sum_with_mut_borrows_fwd (n : nat) (max : u32) : result u32 :=
-  sum_with_mut_borrows_loop_fwd n max 0%u32 0%u32
+(** [loops::sum_with_mut_borrows]: forward function
+    Source: 'src/loops.rs', lines 19:0-19:44 *)
+Definition sum_with_mut_borrows (n : nat) (max : u32) : result u32 :=
+  sum_with_mut_borrows_loop n max 0%u32 0%u32
 .
 
-(** [loops::sum_with_shared_borrows]: loop 0: forward function *)
-Fixpoint sum_with_shared_borrows_loop_fwd
+(** [loops::sum_with_shared_borrows]: loop 0: forward function
+    Source: 'src/loops.rs', lines 34:0-48:1 *)
+Fixpoint sum_with_shared_borrows_loop
   (n : nat) (max : u32) (i : u32) (s : u32) : result u32 :=
   match n with
   | O => Fail_ OutOfFuel
@@ -54,90 +59,100 @@ Fixpoint sum_with_shared_borrows_loop_fwd
     then (
       i0 <- u32_add i 1%u32;
       s0 <- u32_add s i0;
-      sum_with_shared_borrows_loop_fwd n0 max i0 s0)
+      sum_with_shared_borrows_loop n0 max i0 s0)
     else u32_mul s 2%u32
   end
 .
 
-(** [loops::sum_with_shared_borrows]: forward function *)
-Definition sum_with_shared_borrows_fwd (n : nat) (max : u32) : result u32 :=
-  sum_with_shared_borrows_loop_fwd n max 0%u32 0%u32
+(** [loops::sum_with_shared_borrows]: forward function
+    Source: 'src/loops.rs', lines 34:0-34:47 *)
+Definition sum_with_shared_borrows (n : nat) (max : u32) : result u32 :=
+  sum_with_shared_borrows_loop n max 0%u32 0%u32
 .
 
 (** [loops::clear]: loop 0: merged forward/backward function
-    (there is a single backward function, and the forward function returns ()) *)
-Fixpoint clear_loop_fwd_back
-  (n : nat) (v : vec u32) (i : usize) : result (vec u32) :=
+    (there is a single backward function, and the forward function returns ())
+    Source: 'src/loops.rs', lines 52:0-58:1 *)
+Fixpoint clear_loop
+  (n : nat) (v : alloc_vec_Vec u32) (i : usize) : result (alloc_vec_Vec u32) :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
-    let i0 := vec_len u32 v in
+    let i0 := alloc_vec_Vec_len u32 v in
     if i s< i0
     then (
       i1 <- usize_add i 1%usize;
-      v0 <- vec_index_mut_back u32 v i 0%u32;
-      clear_loop_fwd_back n0 v0 i1)
+      v0 <-
+        alloc_vec_Vec_index_mut_back u32 usize
+          (core_slice_index_SliceIndexUsizeSliceTInst u32) v i 0%u32;
+      clear_loop n0 v0 i1)
     else Return v
   end
 .
 
 (** [loops::clear]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ()) *)
-Definition clear_fwd_back (n : nat) (v : vec u32) : result (vec u32) :=
-  clear_loop_fwd_back n v 0%usize
+    (there is a single backward function, and the forward function returns ())
+    Source: 'src/loops.rs', lines 52:0-52:30 *)
+Definition clear
+  (n : nat) (v : alloc_vec_Vec u32) : result (alloc_vec_Vec u32) :=
+  clear_loop n v 0%usize
 .
 
-(** [loops::List] *)
+(** [loops::List]
+    Source: 'src/loops.rs', lines 60:0-60:16 *)
 Inductive List_t (T : Type) :=
-| ListCons : T -> List_t T -> List_t T
-| ListNil : List_t T
+| List_Cons : T -> List_t T -> List_t T
+| List_Nil : List_t T
 .
 
-Arguments ListCons {T} _ _.
-Arguments ListNil {T}.
+Arguments List_Cons { _ }.
+Arguments List_Nil { _ }.
 
-(** [loops::list_mem]: loop 0: forward function *)
-Fixpoint list_mem_loop_fwd
-  (n : nat) (x : u32) (ls : List_t u32) : result bool :=
+(** [loops::list_mem]: loop 0: forward function
+    Source: 'src/loops.rs', lines 66:0-75:1 *)
+Fixpoint list_mem_loop (n : nat) (x : u32) (ls : List_t u32) : result bool :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls with
-    | ListCons y tl =>
-      if y s= x then Return true else list_mem_loop_fwd n0 x tl
-    | ListNil => Return false
+    | List_Cons y tl => if y s= x then Return true else list_mem_loop n0 x tl
+    | List_Nil => Return false
     end
   end
 .
 
-(** [loops::list_mem]: forward function *)
-Definition list_mem_fwd (n : nat) (x : u32) (ls : List_t u32) : result bool :=
-  list_mem_loop_fwd n x ls
+(** [loops::list_mem]: forward function
+    Source: 'src/loops.rs', lines 66:0-66:52 *)
+Definition list_mem (n : nat) (x : u32) (ls : List_t u32) : result bool :=
+  list_mem_loop n x ls
 .
 
-(** [loops::list_nth_mut_loop]: loop 0: forward function *)
-Fixpoint list_nth_mut_loop_loop_fwd
+(** [loops::list_nth_mut_loop]: loop 0: forward function
+    Source: 'src/loops.rs', lines 78:0-88:1 *)
+Fixpoint list_nth_mut_loop_loop
   (T : Type) (n : nat) (ls : List_t T) (i : u32) : result T :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls with
-    | ListCons x tl =>
+    | List_Cons x tl =>
       if i s= 0%u32
       then Return x
-      else (i0 <- u32_sub i 1%u32; list_nth_mut_loop_loop_fwd T n0 tl i0)
-    | ListNil => Fail_ Failure
+      else (i0 <- u32_sub i 1%u32; list_nth_mut_loop_loop T n0 tl i0)
+    | List_Nil => Fail_ Failure
     end
   end
 .
 
-(** [loops::list_nth_mut_loop]: forward function *)
-Definition list_nth_mut_loop_fwd
+(** [loops::list_nth_mut_loop]: forward function
+    Source: 'src/loops.rs', lines 78:0-78:71 *)
+Definition list_nth_mut_loop
   (T : Type) (n : nat) (ls : List_t T) (i : u32) : result T :=
-  list_nth_mut_loop_loop_fwd T n ls i
+  list_nth_mut_loop_loop T n ls i
 .
 
-(** [loops::list_nth_mut_loop]: loop 0: backward function 0 *)
+(** [loops::list_nth_mut_loop]: loop 0: backward function 0
+    Source: 'src/loops.rs', lines 78:0-88:1 *)
 Fixpoint list_nth_mut_loop_loop_back
   (T : Type) (n : nat) (ls : List_t T) (i : u32) (ret : T) :
   result (List_t T)
@@ -146,19 +161,20 @@ Fixpoint list_nth_mut_loop_loop_back
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls with
-    | ListCons x tl =>
+    | List_Cons x tl =>
       if i s= 0%u32
-      then Return (ListCons ret tl)
+      then Return (List_Cons ret tl)
       else (
         i0 <- u32_sub i 1%u32;
         tl0 <- list_nth_mut_loop_loop_back T n0 tl i0 ret;
-        Return (ListCons x tl0))
-    | ListNil => Fail_ Failure
+        Return (List_Cons x tl0))
+    | List_Nil => Fail_ Failure
     end
   end
 .
 
-(** [loops::list_nth_mut_loop]: backward function 0 *)
+(** [loops::list_nth_mut_loop]: backward function 0
+    Source: 'src/loops.rs', lines 78:0-78:71 *)
 Definition list_nth_mut_loop_back
   (T : Type) (n : nat) (ls : List_t T) (i : u32) (ret : T) :
   result (List_t T)
@@ -166,50 +182,58 @@ Definition list_nth_mut_loop_back
   list_nth_mut_loop_loop_back T n ls i ret
 .
 
-(** [loops::list_nth_shared_loop]: loop 0: forward function *)
-Fixpoint list_nth_shared_loop_loop_fwd
+(** [loops::list_nth_shared_loop]: loop 0: forward function
+    Source: 'src/loops.rs', lines 91:0-101:1 *)
+Fixpoint list_nth_shared_loop_loop
   (T : Type) (n : nat) (ls : List_t T) (i : u32) : result T :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls with
-    | ListCons x tl =>
+    | List_Cons x tl =>
       if i s= 0%u32
       then Return x
-      else (i0 <- u32_sub i 1%u32; list_nth_shared_loop_loop_fwd T n0 tl i0)
-    | ListNil => Fail_ Failure
+      else (i0 <- u32_sub i 1%u32; list_nth_shared_loop_loop T n0 tl i0)
+    | List_Nil => Fail_ Failure
     end
   end
 .
 
-(** [loops::list_nth_shared_loop]: forward function *)
-Definition list_nth_shared_loop_fwd
+(** [loops::list_nth_shared_loop]: forward function
+    Source: 'src/loops.rs', lines 91:0-91:66 *)
+Definition list_nth_shared_loop
   (T : Type) (n : nat) (ls : List_t T) (i : u32) : result T :=
-  list_nth_shared_loop_loop_fwd T n ls i
+  list_nth_shared_loop_loop T n ls i
 .
 
-(** [loops::get_elem_mut]: loop 0: forward function *)
-Fixpoint get_elem_mut_loop_fwd
+(** [loops::get_elem_mut]: loop 0: forward function
+    Source: 'src/loops.rs', lines 103:0-117:1 *)
+Fixpoint get_elem_mut_loop
   (n : nat) (x : usize) (ls : List_t usize) : result usize :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls with
-    | ListCons y tl =>
-      if y s= x then Return y else get_elem_mut_loop_fwd n0 x tl
-    | ListNil => Fail_ Failure
+    | List_Cons y tl => if y s= x then Return y else get_elem_mut_loop n0 x tl
+    | List_Nil => Fail_ Failure
     end
   end
 .
 
-(** [loops::get_elem_mut]: forward function *)
-Definition get_elem_mut_fwd
-  (n : nat) (slots : vec (List_t usize)) (x : usize) : result usize :=
-  l <- vec_index_mut_fwd (List_t usize) slots 0%usize;
-  get_elem_mut_loop_fwd n x l
+(** [loops::get_elem_mut]: forward function
+    Source: 'src/loops.rs', lines 103:0-103:73 *)
+Definition get_elem_mut
+  (n : nat) (slots : alloc_vec_Vec (List_t usize)) (x : usize) :
+  result usize
+  :=
+  l <-
+    alloc_vec_Vec_index_mut (List_t usize) usize
+      (core_slice_index_SliceIndexUsizeSliceTInst (List_t usize)) slots 0%usize;
+  get_elem_mut_loop n x l
 .
 
-(** [loops::get_elem_mut]: loop 0: backward function 0 *)
+(** [loops::get_elem_mut]: loop 0: backward function 0
+    Source: 'src/loops.rs', lines 103:0-117:1 *)
 Fixpoint get_elem_mut_loop_back
   (n : nat) (x : usize) (ls : List_t usize) (ret : usize) :
   result (List_t usize)
@@ -218,86 +242,102 @@ Fixpoint get_elem_mut_loop_back
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls with
-    | ListCons y tl =>
+    | List_Cons y tl =>
       if y s= x
-      then Return (ListCons ret tl)
-      else (tl0 <- get_elem_mut_loop_back n0 x tl ret; Return (ListCons y tl0))
-    | ListNil => Fail_ Failure
+      then Return (List_Cons ret tl)
+      else (
+        tl0 <- get_elem_mut_loop_back n0 x tl ret; Return (List_Cons y tl0))
+    | List_Nil => Fail_ Failure
     end
   end
 .
 
-(** [loops::get_elem_mut]: backward function 0 *)
+(** [loops::get_elem_mut]: backward function 0
+    Source: 'src/loops.rs', lines 103:0-103:73 *)
 Definition get_elem_mut_back
-  (n : nat) (slots : vec (List_t usize)) (x : usize) (ret : usize) :
-  result (vec (List_t usize))
+  (n : nat) (slots : alloc_vec_Vec (List_t usize)) (x : usize) (ret : usize) :
+  result (alloc_vec_Vec (List_t usize))
   :=
-  l <- vec_index_mut_fwd (List_t usize) slots 0%usize;
+  l <-
+    alloc_vec_Vec_index_mut (List_t usize) usize
+      (core_slice_index_SliceIndexUsizeSliceTInst (List_t usize)) slots 0%usize;
   l0 <- get_elem_mut_loop_back n x l ret;
-  vec_index_mut_back (List_t usize) slots 0%usize l0
+  alloc_vec_Vec_index_mut_back (List_t usize) usize
+    (core_slice_index_SliceIndexUsizeSliceTInst (List_t usize)) slots 0%usize
+    l0
 .
 
-(** [loops::get_elem_shared]: loop 0: forward function *)
-Fixpoint get_elem_shared_loop_fwd
+(** [loops::get_elem_shared]: loop 0: forward function
+    Source: 'src/loops.rs', lines 119:0-133:1 *)
+Fixpoint get_elem_shared_loop
   (n : nat) (x : usize) (ls : List_t usize) : result usize :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls with
-    | ListCons y tl =>
-      if y s= x then Return y else get_elem_shared_loop_fwd n0 x tl
-    | ListNil => Fail_ Failure
+    | List_Cons y tl =>
+      if y s= x then Return y else get_elem_shared_loop n0 x tl
+    | List_Nil => Fail_ Failure
     end
   end
 .
 
-(** [loops::get_elem_shared]: forward function *)
-Definition get_elem_shared_fwd
-  (n : nat) (slots : vec (List_t usize)) (x : usize) : result usize :=
-  l <- vec_index_fwd (List_t usize) slots 0%usize;
-  get_elem_shared_loop_fwd n x l
+(** [loops::get_elem_shared]: forward function
+    Source: 'src/loops.rs', lines 119:0-119:68 *)
+Definition get_elem_shared
+  (n : nat) (slots : alloc_vec_Vec (List_t usize)) (x : usize) :
+  result usize
+  :=
+  l <-
+    alloc_vec_Vec_index (List_t usize) usize
+      (core_slice_index_SliceIndexUsizeSliceTInst (List_t usize)) slots 0%usize;
+  get_elem_shared_loop n x l
 .
 
-(** [loops::id_mut]: forward function *)
-Definition id_mut_fwd (T : Type) (ls : List_t T) : result (List_t T) :=
-  Return ls
-.
+(** [loops::id_mut]: forward function
+    Source: 'src/loops.rs', lines 135:0-135:50 *)
+Definition id_mut (T : Type) (ls : List_t T) : result (List_t T) :=
+  Return ls.
 
-(** [loops::id_mut]: backward function 0 *)
+(** [loops::id_mut]: backward function 0
+    Source: 'src/loops.rs', lines 135:0-135:50 *)
 Definition id_mut_back
   (T : Type) (ls : List_t T) (ret : List_t T) : result (List_t T) :=
   Return ret
 .
 
-(** [loops::id_shared]: forward function *)
-Definition id_shared_fwd (T : Type) (ls : List_t T) : result (List_t T) :=
+(** [loops::id_shared]: forward function
+    Source: 'src/loops.rs', lines 139:0-139:45 *)
+Definition id_shared (T : Type) (ls : List_t T) : result (List_t T) :=
   Return ls
 .
 
-(** [loops::list_nth_mut_loop_with_id]: loop 0: forward function *)
-Fixpoint list_nth_mut_loop_with_id_loop_fwd
+(** [loops::list_nth_mut_loop_with_id]: loop 0: forward function
+    Source: 'src/loops.rs', lines 144:0-155:1 *)
+Fixpoint list_nth_mut_loop_with_id_loop
   (T : Type) (n : nat) (i : u32) (ls : List_t T) : result T :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls with
-    | ListCons x tl =>
+    | List_Cons x tl =>
       if i s= 0%u32
       then Return x
-      else (
-        i0 <- u32_sub i 1%u32; list_nth_mut_loop_with_id_loop_fwd T n0 i0 tl)
-    | ListNil => Fail_ Failure
+      else (i0 <- u32_sub i 1%u32; list_nth_mut_loop_with_id_loop T n0 i0 tl)
+    | List_Nil => Fail_ Failure
     end
   end
 .
 
-(** [loops::list_nth_mut_loop_with_id]: forward function *)
-Definition list_nth_mut_loop_with_id_fwd
+(** [loops::list_nth_mut_loop_with_id]: forward function
+    Source: 'src/loops.rs', lines 144:0-144:75 *)
+Definition list_nth_mut_loop_with_id
   (T : Type) (n : nat) (ls : List_t T) (i : u32) : result T :=
-  ls0 <- id_mut_fwd T ls; list_nth_mut_loop_with_id_loop_fwd T n i ls0
+  ls0 <- id_mut T ls; list_nth_mut_loop_with_id_loop T n i ls0
 .
 
-(** [loops::list_nth_mut_loop_with_id]: loop 0: backward function 0 *)
+(** [loops::list_nth_mut_loop_with_id]: loop 0: backward function 0
+    Source: 'src/loops.rs', lines 144:0-155:1 *)
 Fixpoint list_nth_mut_loop_with_id_loop_back
   (T : Type) (n : nat) (i : u32) (ls : List_t T) (ret : T) :
   result (List_t T)
@@ -306,53 +346,57 @@ Fixpoint list_nth_mut_loop_with_id_loop_back
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls with
-    | ListCons x tl =>
+    | List_Cons x tl =>
       if i s= 0%u32
-      then Return (ListCons ret tl)
+      then Return (List_Cons ret tl)
       else (
         i0 <- u32_sub i 1%u32;
         tl0 <- list_nth_mut_loop_with_id_loop_back T n0 i0 tl ret;
-        Return (ListCons x tl0))
-    | ListNil => Fail_ Failure
+        Return (List_Cons x tl0))
+    | List_Nil => Fail_ Failure
     end
   end
 .
 
-(** [loops::list_nth_mut_loop_with_id]: backward function 0 *)
+(** [loops::list_nth_mut_loop_with_id]: backward function 0
+    Source: 'src/loops.rs', lines 144:0-144:75 *)
 Definition list_nth_mut_loop_with_id_back
   (T : Type) (n : nat) (ls : List_t T) (i : u32) (ret : T) :
   result (List_t T)
   :=
-  ls0 <- id_mut_fwd T ls;
+  ls0 <- id_mut T ls;
   l <- list_nth_mut_loop_with_id_loop_back T n i ls0 ret;
   id_mut_back T ls l
 .
 
-(** [loops::list_nth_shared_loop_with_id]: loop 0: forward function *)
-Fixpoint list_nth_shared_loop_with_id_loop_fwd
+(** [loops::list_nth_shared_loop_with_id]: loop 0: forward function
+    Source: 'src/loops.rs', lines 158:0-169:1 *)
+Fixpoint list_nth_shared_loop_with_id_loop
   (T : Type) (n : nat) (i : u32) (ls : List_t T) : result T :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls with
-    | ListCons x tl =>
+    | List_Cons x tl =>
       if i s= 0%u32
       then Return x
       else (
-        i0 <- u32_sub i 1%u32; list_nth_shared_loop_with_id_loop_fwd T n0 i0 tl)
-    | ListNil => Fail_ Failure
+        i0 <- u32_sub i 1%u32; list_nth_shared_loop_with_id_loop T n0 i0 tl)
+    | List_Nil => Fail_ Failure
     end
   end
 .
 
-(** [loops::list_nth_shared_loop_with_id]: forward function *)
-Definition list_nth_shared_loop_with_id_fwd
+(** [loops::list_nth_shared_loop_with_id]: forward function
+    Source: 'src/loops.rs', lines 158:0-158:70 *)
+Definition list_nth_shared_loop_with_id
   (T : Type) (n : nat) (ls : List_t T) (i : u32) : result T :=
-  ls0 <- id_shared_fwd T ls; list_nth_shared_loop_with_id_loop_fwd T n i ls0
+  ls0 <- id_shared T ls; list_nth_shared_loop_with_id_loop T n i ls0
 .
 
-(** [loops::list_nth_mut_loop_pair]: loop 0: forward function *)
-Fixpoint list_nth_mut_loop_pair_loop_fwd
+(** [loops::list_nth_mut_loop_pair]: loop 0: forward function
+    Source: 'src/loops.rs', lines 174:0-195:1 *)
+Fixpoint list_nth_mut_loop_pair_loop
   (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) :
   result (T * T)
   :=
@@ -360,30 +404,31 @@ Fixpoint list_nth_mut_loop_pair_loop_fwd
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls0 with
-    | ListCons x0 tl0 =>
+    | List_Cons x0 tl0 =>
       match ls1 with
-      | ListCons x1 tl1 =>
+      | List_Cons x1 tl1 =>
         if i s= 0%u32
         then Return (x0, x1)
         else (
-          i0 <- u32_sub i 1%u32;
-          list_nth_mut_loop_pair_loop_fwd T n0 tl0 tl1 i0)
-      | ListNil => Fail_ Failure
+          i0 <- u32_sub i 1%u32; list_nth_mut_loop_pair_loop T n0 tl0 tl1 i0)
+      | List_Nil => Fail_ Failure
       end
-    | ListNil => Fail_ Failure
+    | List_Nil => Fail_ Failure
     end
   end
 .
 
-(** [loops::list_nth_mut_loop_pair]: forward function *)
-Definition list_nth_mut_loop_pair_fwd
+(** [loops::list_nth_mut_loop_pair]: forward function
+    Source: 'src/loops.rs', lines 174:0-178:27 *)
+Definition list_nth_mut_loop_pair
   (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) :
   result (T * T)
   :=
-  list_nth_mut_loop_pair_loop_fwd T n ls0 ls1 i
+  list_nth_mut_loop_pair_loop T n ls0 ls1 i
 .
 
-(** [loops::list_nth_mut_loop_pair]: loop 0: backward function 0 *)
+(** [loops::list_nth_mut_loop_pair]: loop 0: backward function 0
+    Source: 'src/loops.rs', lines 174:0-195:1 *)
 Fixpoint list_nth_mut_loop_pair_loop_back'a
   (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) (ret : T) :
   result (List_t T)
@@ -392,23 +437,24 @@ Fixpoint list_nth_mut_loop_pair_loop_back'a
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls0 with
-    | ListCons x0 tl0 =>
+    | List_Cons x0 tl0 =>
       match ls1 with
-      | ListCons x1 tl1 =>
+      | List_Cons x1 tl1 =>
         if i s= 0%u32
-        then Return (ListCons ret tl0)
+        then Return (List_Cons ret tl0)
         else (
           i0 <- u32_sub i 1%u32;
           tl00 <- list_nth_mut_loop_pair_loop_back'a T n0 tl0 tl1 i0 ret;
-          Return (ListCons x0 tl00))
-      | ListNil => Fail_ Failure
+          Return (List_Cons x0 tl00))
+      | List_Nil => Fail_ Failure
       end
-    | ListNil => Fail_ Failure
+    | List_Nil => Fail_ Failure
     end
   end
 .
 
-(** [loops::list_nth_mut_loop_pair]: backward function 0 *)
+(** [loops::list_nth_mut_loop_pair]: backward function 0
+    Source: 'src/loops.rs', lines 174:0-178:27 *)
 Definition list_nth_mut_loop_pair_back'a
   (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) (ret : T) :
   result (List_t T)
@@ -416,7 +462,8 @@ Definition list_nth_mut_loop_pair_back'a
   list_nth_mut_loop_pair_loop_back'a T n ls0 ls1 i ret
 .
 
-(** [loops::list_nth_mut_loop_pair]: loop 0: backward function 1 *)
+(** [loops::list_nth_mut_loop_pair]: loop 0: backward function 1
+    Source: 'src/loops.rs', lines 174:0-195:1 *)
 Fixpoint list_nth_mut_loop_pair_loop_back'b
   (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) (ret : T) :
   result (List_t T)
@@ -425,23 +472,24 @@ Fixpoint list_nth_mut_loop_pair_loop_back'b
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls0 with
-    | ListCons x0 tl0 =>
+    | List_Cons x0 tl0 =>
       match ls1 with
-      | ListCons x1 tl1 =>
+      | List_Cons x1 tl1 =>
         if i s= 0%u32
-        then Return (ListCons ret tl1)
+        then Return (List_Cons ret tl1)
         else (
           i0 <- u32_sub i 1%u32;
           tl10 <- list_nth_mut_loop_pair_loop_back'b T n0 tl0 tl1 i0 ret;
-          Return (ListCons x1 tl10))
-      | ListNil => Fail_ Failure
+          Return (List_Cons x1 tl10))
+      | List_Nil => Fail_ Failure
       end
-    | ListNil => Fail_ Failure
+    | List_Nil => Fail_ Failure
     end
   end
 .
 
-(** [loops::list_nth_mut_loop_pair]: backward function 1 *)
+(** [loops::list_nth_mut_loop_pair]: backward function 1
+    Source: 'src/loops.rs', lines 174:0-178:27 *)
 Definition list_nth_mut_loop_pair_back'b
   (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) (ret : T) :
   result (List_t T)
@@ -449,8 +497,9 @@ Definition list_nth_mut_loop_pair_back'b
   list_nth_mut_loop_pair_loop_back'b T n ls0 ls1 i ret
 .
 
-(** [loops::list_nth_shared_loop_pair]: loop 0: forward function *)
-Fixpoint list_nth_shared_loop_pair_loop_fwd
+(** [loops::list_nth_shared_loop_pair]: loop 0: forward function
+    Source: 'src/loops.rs', lines 198:0-219:1 *)
+Fixpoint list_nth_shared_loop_pair_loop
   (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) :
   result (T * T)
   :=
@@ -458,31 +507,32 @@ Fixpoint list_nth_shared_loop_pair_loop_fwd
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls0 with
-    | ListCons x0 tl0 =>
+    | List_Cons x0 tl0 =>
       match ls1 with
-      | ListCons x1 tl1 =>
+      | List_Cons x1 tl1 =>
         if i s= 0%u32
         then Return (x0, x1)
         else (
-          i0 <- u32_sub i 1%u32;
-          list_nth_shared_loop_pair_loop_fwd T n0 tl0 tl1 i0)
-      | ListNil => Fail_ Failure
+          i0 <- u32_sub i 1%u32; list_nth_shared_loop_pair_loop T n0 tl0 tl1 i0)
+      | List_Nil => Fail_ Failure
       end
-    | ListNil => Fail_ Failure
+    | List_Nil => Fail_ Failure
     end
   end
 .
 
-(** [loops::list_nth_shared_loop_pair]: forward function *)
-Definition list_nth_shared_loop_pair_fwd
+(** [loops::list_nth_shared_loop_pair]: forward function
+    Source: 'src/loops.rs', lines 198:0-202:19 *)
+Definition list_nth_shared_loop_pair
   (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) :
   result (T * T)
   :=
-  list_nth_shared_loop_pair_loop_fwd T n ls0 ls1 i
+  list_nth_shared_loop_pair_loop T n ls0 ls1 i
 .
 
-(** [loops::list_nth_mut_loop_pair_merge]: loop 0: forward function *)
-Fixpoint list_nth_mut_loop_pair_merge_loop_fwd
+(** [loops::list_nth_mut_loop_pair_merge]: loop 0: forward function
+    Source: 'src/loops.rs', lines 223:0-238:1 *)
+Fixpoint list_nth_mut_loop_pair_merge_loop
   (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) :
   result (T * T)
   :=
@@ -490,30 +540,32 @@ Fixpoint list_nth_mut_loop_pair_merge_loop_fwd
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls0 with
-    | ListCons x0 tl0 =>
+    | List_Cons x0 tl0 =>
       match ls1 with
-      | ListCons x1 tl1 =>
+      | List_Cons x1 tl1 =>
         if i s= 0%u32
         then Return (x0, x1)
         else (
           i0 <- u32_sub i 1%u32;
-          list_nth_mut_loop_pair_merge_loop_fwd T n0 tl0 tl1 i0)
-      | ListNil => Fail_ Failure
+          list_nth_mut_loop_pair_merge_loop T n0 tl0 tl1 i0)
+      | List_Nil => Fail_ Failure
       end
-    | ListNil => Fail_ Failure
+    | List_Nil => Fail_ Failure
     end
   end
 .
 
-(** [loops::list_nth_mut_loop_pair_merge]: forward function *)
-Definition list_nth_mut_loop_pair_merge_fwd
+(** [loops::list_nth_mut_loop_pair_merge]: forward function
+    Source: 'src/loops.rs', lines 223:0-227:27 *)
+Definition list_nth_mut_loop_pair_merge
   (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) :
   result (T * T)
   :=
-  list_nth_mut_loop_pair_merge_loop_fwd T n ls0 ls1 i
+  list_nth_mut_loop_pair_merge_loop T n ls0 ls1 i
 .
 
-(** [loops::list_nth_mut_loop_pair_merge]: loop 0: backward function 0 *)
+(** [loops::list_nth_mut_loop_pair_merge]: loop 0: backward function 0
+    Source: 'src/loops.rs', lines 223:0-238:1 *)
 Fixpoint list_nth_mut_loop_pair_merge_loop_back
   (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32)
   (ret : (T * T)) :
@@ -523,24 +575,25 @@ Fixpoint list_nth_mut_loop_pair_merge_loop_back
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls0 with
-    | ListCons x0 tl0 =>
+    | List_Cons x0 tl0 =>
       match ls1 with
-      | ListCons x1 tl1 =>
+      | List_Cons x1 tl1 =>
         if i s= 0%u32
-        then let (t, t0) := ret in Return (ListCons t tl0, ListCons t0 tl1)
+        then let (t, t0) := ret in Return (List_Cons t tl0, List_Cons t0 tl1)
         else (
           i0 <- u32_sub i 1%u32;
           p <- list_nth_mut_loop_pair_merge_loop_back T n0 tl0 tl1 i0 ret;
           let (tl00, tl10) := p in
-          Return (ListCons x0 tl00, ListCons x1 tl10))
-      | ListNil => Fail_ Failure
+          Return (List_Cons x0 tl00, List_Cons x1 tl10))
+      | List_Nil => Fail_ Failure
       end
-    | ListNil => Fail_ Failure
+    | List_Nil => Fail_ Failure
     end
   end
 .
 
-(** [loops::list_nth_mut_loop_pair_merge]: backward function 0 *)
+(** [loops::list_nth_mut_loop_pair_merge]: backward function 0
+    Source: 'src/loops.rs', lines 223:0-227:27 *)
 Definition list_nth_mut_loop_pair_merge_back
   (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32)
   (ret : (T * T)) :
@@ -549,8 +602,9 @@ Definition list_nth_mut_loop_pair_merge_back
   list_nth_mut_loop_pair_merge_loop_back T n ls0 ls1 i ret
 .
 
-(** [loops::list_nth_shared_loop_pair_merge]: loop 0: forward function *)
-Fixpoint list_nth_shared_loop_pair_merge_loop_fwd
+(** [loops::list_nth_shared_loop_pair_merge]: loop 0: forward function
+    Source: 'src/loops.rs', lines 241:0-256:1 *)
+Fixpoint list_nth_shared_loop_pair_merge_loop
   (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) :
   result (T * T)
   :=
@@ -558,31 +612,33 @@ Fixpoint list_nth_shared_loop_pair_merge_loop_fwd
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls0 with
-    | ListCons x0 tl0 =>
+    | List_Cons x0 tl0 =>
       match ls1 with
-      | ListCons x1 tl1 =>
+      | List_Cons x1 tl1 =>
         if i s= 0%u32
         then Return (x0, x1)
         else (
           i0 <- u32_sub i 1%u32;
-          list_nth_shared_loop_pair_merge_loop_fwd T n0 tl0 tl1 i0)
-      | ListNil => Fail_ Failure
+          list_nth_shared_loop_pair_merge_loop T n0 tl0 tl1 i0)
+      | List_Nil => Fail_ Failure
       end
-    | ListNil => Fail_ Failure
+    | List_Nil => Fail_ Failure
     end
   end
 .
 
-(** [loops::list_nth_shared_loop_pair_merge]: forward function *)
-Definition list_nth_shared_loop_pair_merge_fwd
+(** [loops::list_nth_shared_loop_pair_merge]: forward function
+    Source: 'src/loops.rs', lines 241:0-245:19 *)
+Definition list_nth_shared_loop_pair_merge
   (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) :
   result (T * T)
   :=
-  list_nth_shared_loop_pair_merge_loop_fwd T n ls0 ls1 i
+  list_nth_shared_loop_pair_merge_loop T n ls0 ls1 i
 .
 
-(** [loops::list_nth_mut_shared_loop_pair]: loop 0: forward function *)
-Fixpoint list_nth_mut_shared_loop_pair_loop_fwd
+(** [loops::list_nth_mut_shared_loop_pair]: loop 0: forward function
+    Source: 'src/loops.rs', lines 259:0-274:1 *)
+Fixpoint list_nth_mut_shared_loop_pair_loop
   (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) :
   result (T * T)
   :=
@@ -590,30 +646,32 @@ Fixpoint list_nth_mut_shared_loop_pair_loop_fwd
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls0 with
-    | ListCons x0 tl0 =>
+    | List_Cons x0 tl0 =>
       match ls1 with
-      | ListCons x1 tl1 =>
+      | List_Cons x1 tl1 =>
         if i s= 0%u32
         then Return (x0, x1)
         else (
           i0 <- u32_sub i 1%u32;
-          list_nth_mut_shared_loop_pair_loop_fwd T n0 tl0 tl1 i0)
-      | ListNil => Fail_ Failure
+          list_nth_mut_shared_loop_pair_loop T n0 tl0 tl1 i0)
+      | List_Nil => Fail_ Failure
       end
-    | ListNil => Fail_ Failure
+    | List_Nil => Fail_ Failure
     end
   end
 .
 
-(** [loops::list_nth_mut_shared_loop_pair]: forward function *)
-Definition list_nth_mut_shared_loop_pair_fwd
+(** [loops::list_nth_mut_shared_loop_pair]: forward function
+    Source: 'src/loops.rs', lines 259:0-263:23 *)
+Definition list_nth_mut_shared_loop_pair
   (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) :
   result (T * T)
   :=
-  list_nth_mut_shared_loop_pair_loop_fwd T n ls0 ls1 i
+  list_nth_mut_shared_loop_pair_loop T n ls0 ls1 i
 .
 
-(** [loops::list_nth_mut_shared_loop_pair]: loop 0: backward function 0 *)
+(** [loops::list_nth_mut_shared_loop_pair]: loop 0: backward function 0
+    Source: 'src/loops.rs', lines 259:0-274:1 *)
 Fixpoint list_nth_mut_shared_loop_pair_loop_back
   (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) (ret : T) :
   result (List_t T)
@@ -622,23 +680,24 @@ Fixpoint list_nth_mut_shared_loop_pair_loop_back
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls0 with
-    | ListCons x0 tl0 =>
+    | List_Cons x0 tl0 =>
       match ls1 with
-      | ListCons x1 tl1 =>
+      | List_Cons x1 tl1 =>
         if i s= 0%u32
-        then Return (ListCons ret tl0)
+        then Return (List_Cons ret tl0)
         else (
           i0 <- u32_sub i 1%u32;
           tl00 <- list_nth_mut_shared_loop_pair_loop_back T n0 tl0 tl1 i0 ret;
-          Return (ListCons x0 tl00))
-      | ListNil => Fail_ Failure
+          Return (List_Cons x0 tl00))
+      | List_Nil => Fail_ Failure
       end
-    | ListNil => Fail_ Failure
+    | List_Nil => Fail_ Failure
     end
   end
 .
 
-(** [loops::list_nth_mut_shared_loop_pair]: backward function 0 *)
+(** [loops::list_nth_mut_shared_loop_pair]: backward function 0
+    Source: 'src/loops.rs', lines 259:0-263:23 *)
 Definition list_nth_mut_shared_loop_pair_back
   (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) (ret : T) :
   result (List_t T)
@@ -646,8 +705,9 @@ Definition list_nth_mut_shared_loop_pair_back
   list_nth_mut_shared_loop_pair_loop_back T n ls0 ls1 i ret
 .
 
-(** [loops::list_nth_mut_shared_loop_pair_merge]: loop 0: forward function *)
-Fixpoint list_nth_mut_shared_loop_pair_merge_loop_fwd
+(** [loops::list_nth_mut_shared_loop_pair_merge]: loop 0: forward function
+    Source: 'src/loops.rs', lines 278:0-293:1 *)
+Fixpoint list_nth_mut_shared_loop_pair_merge_loop
   (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) :
   result (T * T)
   :=
@@ -655,30 +715,32 @@ Fixpoint list_nth_mut_shared_loop_pair_merge_loop_fwd
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls0 with
-    | ListCons x0 tl0 =>
+    | List_Cons x0 tl0 =>
       match ls1 with
-      | ListCons x1 tl1 =>
+      | List_Cons x1 tl1 =>
         if i s= 0%u32
         then Return (x0, x1)
         else (
           i0 <- u32_sub i 1%u32;
-          list_nth_mut_shared_loop_pair_merge_loop_fwd T n0 tl0 tl1 i0)
-      | ListNil => Fail_ Failure
+          list_nth_mut_shared_loop_pair_merge_loop T n0 tl0 tl1 i0)
+      | List_Nil => Fail_ Failure
       end
-    | ListNil => Fail_ Failure
+    | List_Nil => Fail_ Failure
     end
   end
 .
 
-(** [loops::list_nth_mut_shared_loop_pair_merge]: forward function *)
-Definition list_nth_mut_shared_loop_pair_merge_fwd
+(** [loops::list_nth_mut_shared_loop_pair_merge]: forward function
+    Source: 'src/loops.rs', lines 278:0-282:23 *)
+Definition list_nth_mut_shared_loop_pair_merge
   (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) :
   result (T * T)
   :=
-  list_nth_mut_shared_loop_pair_merge_loop_fwd T n ls0 ls1 i
+  list_nth_mut_shared_loop_pair_merge_loop T n ls0 ls1 i
 .
 
-(** [loops::list_nth_mut_shared_loop_pair_merge]: loop 0: backward function 0 *)
+(** [loops::list_nth_mut_shared_loop_pair_merge]: loop 0: backward function 0
+    Source: 'src/loops.rs', lines 278:0-293:1 *)
 Fixpoint list_nth_mut_shared_loop_pair_merge_loop_back
   (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) (ret : T) :
   result (List_t T)
@@ -687,24 +749,25 @@ Fixpoint list_nth_mut_shared_loop_pair_merge_loop_back
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls0 with
-    | ListCons x0 tl0 =>
+    | List_Cons x0 tl0 =>
       match ls1 with
-      | ListCons x1 tl1 =>
+      | List_Cons x1 tl1 =>
         if i s= 0%u32
-        then Return (ListCons ret tl0)
+        then Return (List_Cons ret tl0)
         else (
           i0 <- u32_sub i 1%u32;
           tl00 <-
             list_nth_mut_shared_loop_pair_merge_loop_back T n0 tl0 tl1 i0 ret;
-          Return (ListCons x0 tl00))
-      | ListNil => Fail_ Failure
+          Return (List_Cons x0 tl00))
+      | List_Nil => Fail_ Failure
       end
-    | ListNil => Fail_ Failure
+    | List_Nil => Fail_ Failure
     end
   end
 .
 
-(** [loops::list_nth_mut_shared_loop_pair_merge]: backward function 0 *)
+(** [loops::list_nth_mut_shared_loop_pair_merge]: backward function 0
+    Source: 'src/loops.rs', lines 278:0-282:23 *)
 Definition list_nth_mut_shared_loop_pair_merge_back
   (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) (ret : T) :
   result (List_t T)
@@ -712,8 +775,9 @@ Definition list_nth_mut_shared_loop_pair_merge_back
   list_nth_mut_shared_loop_pair_merge_loop_back T n ls0 ls1 i ret
 .
 
-(** [loops::list_nth_shared_mut_loop_pair]: loop 0: forward function *)
-Fixpoint list_nth_shared_mut_loop_pair_loop_fwd
+(** [loops::list_nth_shared_mut_loop_pair]: loop 0: forward function
+    Source: 'src/loops.rs', lines 297:0-312:1 *)
+Fixpoint list_nth_shared_mut_loop_pair_loop
   (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) :
   result (T * T)
   :=
@@ -721,30 +785,32 @@ Fixpoint list_nth_shared_mut_loop_pair_loop_fwd
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls0 with
-    | ListCons x0 tl0 =>
+    | List_Cons x0 tl0 =>
       match ls1 with
-      | ListCons x1 tl1 =>
+      | List_Cons x1 tl1 =>
         if i s= 0%u32
         then Return (x0, x1)
         else (
           i0 <- u32_sub i 1%u32;
-          list_nth_shared_mut_loop_pair_loop_fwd T n0 tl0 tl1 i0)
-      | ListNil => Fail_ Failure
+          list_nth_shared_mut_loop_pair_loop T n0 tl0 tl1 i0)
+      | List_Nil => Fail_ Failure
       end
-    | ListNil => Fail_ Failure
+    | List_Nil => Fail_ Failure
     end
   end
 .
 
-(** [loops::list_nth_shared_mut_loop_pair]: forward function *)
-Definition list_nth_shared_mut_loop_pair_fwd
+(** [loops::list_nth_shared_mut_loop_pair]: forward function
+    Source: 'src/loops.rs', lines 297:0-301:23 *)
+Definition list_nth_shared_mut_loop_pair
   (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) :
   result (T * T)
   :=
-  list_nth_shared_mut_loop_pair_loop_fwd T n ls0 ls1 i
+  list_nth_shared_mut_loop_pair_loop T n ls0 ls1 i
 .
 
-(** [loops::list_nth_shared_mut_loop_pair]: loop 0: backward function 1 *)
+(** [loops::list_nth_shared_mut_loop_pair]: loop 0: backward function 1
+    Source: 'src/loops.rs', lines 297:0-312:1 *)
 Fixpoint list_nth_shared_mut_loop_pair_loop_back
   (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) (ret : T) :
   result (List_t T)
@@ -753,23 +819,24 @@ Fixpoint list_nth_shared_mut_loop_pair_loop_back
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls0 with
-    | ListCons x0 tl0 =>
+    | List_Cons x0 tl0 =>
       match ls1 with
-      | ListCons x1 tl1 =>
+      | List_Cons x1 tl1 =>
         if i s= 0%u32
-        then Return (ListCons ret tl1)
+        then Return (List_Cons ret tl1)
         else (
           i0 <- u32_sub i 1%u32;
           tl10 <- list_nth_shared_mut_loop_pair_loop_back T n0 tl0 tl1 i0 ret;
-          Return (ListCons x1 tl10))
-      | ListNil => Fail_ Failure
+          Return (List_Cons x1 tl10))
+      | List_Nil => Fail_ Failure
       end
-    | ListNil => Fail_ Failure
+    | List_Nil => Fail_ Failure
     end
   end
 .
 
-(** [loops::list_nth_shared_mut_loop_pair]: backward function 1 *)
+(** [loops::list_nth_shared_mut_loop_pair]: backward function 1
+    Source: 'src/loops.rs', lines 297:0-301:23 *)
 Definition list_nth_shared_mut_loop_pair_back
   (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) (ret : T) :
   result (List_t T)
@@ -777,8 +844,9 @@ Definition list_nth_shared_mut_loop_pair_back
   list_nth_shared_mut_loop_pair_loop_back T n ls0 ls1 i ret
 .
 
-(** [loops::list_nth_shared_mut_loop_pair_merge]: loop 0: forward function *)
-Fixpoint list_nth_shared_mut_loop_pair_merge_loop_fwd
+(** [loops::list_nth_shared_mut_loop_pair_merge]: loop 0: forward function
+    Source: 'src/loops.rs', lines 316:0-331:1 *)
+Fixpoint list_nth_shared_mut_loop_pair_merge_loop
   (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) :
   result (T * T)
   :=
@@ -786,30 +854,32 @@ Fixpoint list_nth_shared_mut_loop_pair_merge_loop_fwd
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls0 with
-    | ListCons x0 tl0 =>
+    | List_Cons x0 tl0 =>
       match ls1 with
-      | ListCons x1 tl1 =>
+      | List_Cons x1 tl1 =>
         if i s= 0%u32
         then Return (x0, x1)
         else (
           i0 <- u32_sub i 1%u32;
-          list_nth_shared_mut_loop_pair_merge_loop_fwd T n0 tl0 tl1 i0)
-      | ListNil => Fail_ Failure
+          list_nth_shared_mut_loop_pair_merge_loop T n0 tl0 tl1 i0)
+      | List_Nil => Fail_ Failure
       end
-    | ListNil => Fail_ Failure
+    | List_Nil => Fail_ Failure
     end
   end
 .
 
-(** [loops::list_nth_shared_mut_loop_pair_merge]: forward function *)
-Definition list_nth_shared_mut_loop_pair_merge_fwd
+(** [loops::list_nth_shared_mut_loop_pair_merge]: forward function
+    Source: 'src/loops.rs', lines 316:0-320:23 *)
+Definition list_nth_shared_mut_loop_pair_merge
   (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) :
   result (T * T)
   :=
-  list_nth_shared_mut_loop_pair_merge_loop_fwd T n ls0 ls1 i
+  list_nth_shared_mut_loop_pair_merge_loop T n ls0 ls1 i
 .
 
-(** [loops::list_nth_shared_mut_loop_pair_merge]: loop 0: backward function 0 *)
+(** [loops::list_nth_shared_mut_loop_pair_merge]: loop 0: backward function 0
+    Source: 'src/loops.rs', lines 316:0-331:1 *)
 Fixpoint list_nth_shared_mut_loop_pair_merge_loop_back
   (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) (ret : T) :
   result (List_t T)
@@ -818,24 +888,25 @@ Fixpoint list_nth_shared_mut_loop_pair_merge_loop_back
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls0 with
-    | ListCons x0 tl0 =>
+    | List_Cons x0 tl0 =>
       match ls1 with
-      | ListCons x1 tl1 =>
+      | List_Cons x1 tl1 =>
         if i s= 0%u32
-        then Return (ListCons ret tl1)
+        then Return (List_Cons ret tl1)
         else (
           i0 <- u32_sub i 1%u32;
           tl10 <-
             list_nth_shared_mut_loop_pair_merge_loop_back T n0 tl0 tl1 i0 ret;
-          Return (ListCons x1 tl10))
-      | ListNil => Fail_ Failure
+          Return (List_Cons x1 tl10))
+      | List_Nil => Fail_ Failure
       end
-    | ListNil => Fail_ Failure
+    | List_Nil => Fail_ Failure
     end
   end
 .
 
-(** [loops::list_nth_shared_mut_loop_pair_merge]: backward function 0 *)
+(** [loops::list_nth_shared_mut_loop_pair_merge]: backward function 0
+    Source: 'src/loops.rs', lines 316:0-320:23 *)
 Definition list_nth_shared_mut_loop_pair_merge_back
   (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) (ret : T) :
   result (List_t T)
@@ -843,4 +914,4 @@ Definition list_nth_shared_mut_loop_pair_merge_back
   list_nth_shared_mut_loop_pair_merge_loop_back T n ls0 ls1 i ret
 .
 
-End Loops .
+End Loops.
diff --git a/tests/coq/misc/NoNestedBorrows.v b/tests/coq/misc/NoNestedBorrows.v
index c1c24e00..1a0014c0 100644
--- a/tests/coq/misc/NoNestedBorrows.v
+++ b/tests/coq/misc/NoNestedBorrows.v
@@ -8,114 +8,207 @@ Import ListNotations.
 Local Open Scope Primitives_scope.
 Module NoNestedBorrows.
 
-(** [no_nested_borrows::Pair] *)
-Record Pair_t (T1 T2 : Type) := mkPair_t { Pair_x : T1; Pair_y : T2; }.
+(** [no_nested_borrows::Pair]
+    Source: 'src/no_nested_borrows.rs', lines 4:0-4:23 *)
+Record Pair_t (T1 T2 : Type) := mkPair_t { pair_x : T1; pair_y : T2; }.
 
-Arguments mkPair_t {T1} {T2} _ _.
-Arguments Pair_x {T1} {T2}.
-Arguments Pair_y {T1} {T2}.
+Arguments mkPair_t { _ _ }.
+Arguments pair_x { _ _ }.
+Arguments pair_y { _ _ }.
 
-(** [no_nested_borrows::List] *)
+(** [no_nested_borrows::List]
+    Source: 'src/no_nested_borrows.rs', lines 9:0-9:16 *)
 Inductive List_t (T : Type) :=
-| ListCons : T -> List_t T -> List_t T
-| ListNil : List_t T
+| List_Cons : T -> List_t T -> List_t T
+| List_Nil : List_t T
 .
 
-Arguments ListCons {T} _ _.
-Arguments ListNil {T}.
+Arguments List_Cons { _ }.
+Arguments List_Nil { _ }.
 
-(** [no_nested_borrows::One] *)
-Inductive One_t (T1 : Type) := | OneOne : T1 -> One_t T1.
+(** [no_nested_borrows::One]
+    Source: 'src/no_nested_borrows.rs', lines 20:0-20:16 *)
+Inductive One_t (T1 : Type) := | One_One : T1 -> One_t T1.
 
-Arguments OneOne {T1} _.
+Arguments One_One { _ }.
 
-(** [no_nested_borrows::EmptyEnum] *)
-Inductive Empty_enum_t := | EmptyEnumEmpty : Empty_enum_t.
+(** [no_nested_borrows::EmptyEnum]
+    Source: 'src/no_nested_borrows.rs', lines 26:0-26:18 *)
+Inductive EmptyEnum_t := | EmptyEnum_Empty : EmptyEnum_t.
 
-(** [no_nested_borrows::Enum] *)
-Inductive Enum_t := | EnumVariant1 : Enum_t | EnumVariant2 : Enum_t.
+(** [no_nested_borrows::Enum]
+    Source: 'src/no_nested_borrows.rs', lines 32:0-32:13 *)
+Inductive Enum_t := | Enum_Variant1 : Enum_t | Enum_Variant2 : Enum_t.
 
-(** [no_nested_borrows::EmptyStruct] *)
-Record Empty_struct_t := mkEmpty_struct_t {  }.
+(** [no_nested_borrows::EmptyStruct]
+    Source: 'src/no_nested_borrows.rs', lines 39:0-39:22 *)
+Record EmptyStruct_t := mkEmptyStruct_t {  }.
 
-(** [no_nested_borrows::Sum] *)
+(** [no_nested_borrows::Sum]
+    Source: 'src/no_nested_borrows.rs', lines 41:0-41:20 *)
 Inductive Sum_t (T1 T2 : Type) :=
-| SumLeft : T1 -> Sum_t T1 T2
-| SumRight : T2 -> Sum_t T1 T2
+| Sum_Left : T1 -> Sum_t T1 T2
+| Sum_Right : T2 -> Sum_t T1 T2
 .
 
-Arguments SumLeft {T1} {T2} _.
-Arguments SumRight {T1} {T2} _.
+Arguments Sum_Left { _ _ }.
+Arguments Sum_Right { _ _ }.
 
-(** [no_nested_borrows::neg_test]: forward function *)
-Definition neg_test_fwd (x : i32) : result i32 :=
+(** [no_nested_borrows::neg_test]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 48:0-48:30 *)
+Definition neg_test (x : i32) : result i32 :=
   i32_neg x.
 
-(** [no_nested_borrows::add_test]: forward function *)
-Definition add_test_fwd (x : u32) (y : u32) : result u32 :=
+(** [no_nested_borrows::add_u32]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 54:0-54:37 *)
+Definition add_u32 (x : u32) (y : u32) : result u32 :=
   u32_add x y.
 
-(** [no_nested_borrows::subs_test]: forward function *)
-Definition subs_test_fwd (x : u32) (y : u32) : result u32 :=
+(** [no_nested_borrows::subs_u32]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 60:0-60:38 *)
+Definition subs_u32 (x : u32) (y : u32) : result u32 :=
   u32_sub x y.
 
-(** [no_nested_borrows::div_test]: forward function *)
-Definition div_test_fwd (x : u32) (y : u32) : result u32 :=
+(** [no_nested_borrows::div_u32]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 66:0-66:37 *)
+Definition div_u32 (x : u32) (y : u32) : result u32 :=
   u32_div x y.
 
-(** [no_nested_borrows::div_test1]: forward function *)
-Definition div_test1_fwd (x : u32) : result u32 :=
+(** [no_nested_borrows::div_u32_const]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 73:0-73:35 *)
+Definition div_u32_const (x : u32) : result u32 :=
   u32_div x 2%u32.
 
-(** [no_nested_borrows::rem_test]: forward function *)
-Definition rem_test_fwd (x : u32) (y : u32) : result u32 :=
+(** [no_nested_borrows::rem_u32]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 78:0-78:37 *)
+Definition rem_u32 (x : u32) (y : u32) : result u32 :=
   u32_rem x y.
 
-(** [no_nested_borrows::cast_test]: forward function *)
-Definition cast_test_fwd (x : u32) : result i32 :=
+(** [no_nested_borrows::mul_u32]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 82:0-82:37 *)
+Definition mul_u32 (x : u32) (y : u32) : result u32 :=
+  u32_mul x y.
+
+(** [no_nested_borrows::add_i32]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 88:0-88:37 *)
+Definition add_i32 (x : i32) (y : i32) : result i32 :=
+  i32_add x y.
+
+(** [no_nested_borrows::subs_i32]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 92:0-92:38 *)
+Definition subs_i32 (x : i32) (y : i32) : result i32 :=
+  i32_sub x y.
+
+(** [no_nested_borrows::div_i32]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 96:0-96:37 *)
+Definition div_i32 (x : i32) (y : i32) : result i32 :=
+  i32_div x y.
+
+(** [no_nested_borrows::div_i32_const]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 100:0-100:35 *)
+Definition div_i32_const (x : i32) : result i32 :=
+  i32_div x 2%i32.
+
+(** [no_nested_borrows::rem_i32]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 104:0-104:37 *)
+Definition rem_i32 (x : i32) (y : i32) : result i32 :=
+  i32_rem x y.
+
+(** [no_nested_borrows::mul_i32]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 108:0-108:37 *)
+Definition mul_i32 (x : i32) (y : i32) : result i32 :=
+  i32_mul x y.
+
+(** [no_nested_borrows::mix_arith_u32]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 112:0-112:51 *)
+Definition mix_arith_u32 (x : u32) (y : u32) (z : u32) : result u32 :=
+  i <- u32_add x y;
+  i0 <- u32_div x y;
+  i1 <- u32_mul i i0;
+  i2 <- u32_rem z y;
+  i3 <- u32_sub x i2;
+  i4 <- u32_add i1 i3;
+  i5 <- u32_add x y;
+  i6 <- u32_add i5 z;
+  u32_rem i4 i6
+.
+
+(** [no_nested_borrows::mix_arith_i32]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 116:0-116:51 *)
+Definition mix_arith_i32 (x : i32) (y : i32) (z : i32) : result i32 :=
+  i <- i32_add x y;
+  i0 <- i32_div x y;
+  i1 <- i32_mul i i0;
+  i2 <- i32_rem z y;
+  i3 <- i32_sub x i2;
+  i4 <- i32_add i1 i3;
+  i5 <- i32_add x y;
+  i6 <- i32_add i5 z;
+  i32_rem i4 i6
+.
+
+(** [no_nested_borrows::CONST0]
+    Source: 'src/no_nested_borrows.rs', lines 125:0-125:23 *)
+Definition const0_body : result usize := usize_add 1%usize 1%usize.
+Definition const0_c : usize := const0_body%global.
+
+(** [no_nested_borrows::CONST1]
+    Source: 'src/no_nested_borrows.rs', lines 126:0-126:23 *)
+Definition const1_body : result usize := usize_mul 2%usize 2%usize.
+Definition const1_c : usize := const1_body%global.
+
+(** [no_nested_borrows::cast_test]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 128:0-128:31 *)
+Definition cast_test (x : u32) : result i32 :=
   scalar_cast U32 I32 x.
 
-(** [no_nested_borrows::test2]: forward function *)
-Definition test2_fwd : result unit :=
+(** [no_nested_borrows::test2]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 133:0-133:14 *)
+Definition test2 : result unit :=
   _ <- u32_add 23%u32 44%u32; Return tt.
 
 (** Unit test for [no_nested_borrows::test2] *)
-Check (test2_fwd )%return.
+Check (test2 )%return.
 
-(** [no_nested_borrows::get_max]: forward function *)
-Definition get_max_fwd (x : u32) (y : u32) : result u32 :=
+(** [no_nested_borrows::get_max]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 145:0-145:37 *)
+Definition get_max (x : u32) (y : u32) : result u32 :=
   if x s>= y then Return x else Return y
 .
 
-(** [no_nested_borrows::test3]: forward function *)
-Definition test3_fwd : result unit :=
-  x <- get_max_fwd 4%u32 3%u32;
-  y <- get_max_fwd 10%u32 11%u32;
+(** [no_nested_borrows::test3]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 153:0-153:14 *)
+Definition test3 : result unit :=
+  x <- get_max 4%u32 3%u32;
+  y <- get_max 10%u32 11%u32;
   z <- u32_add x y;
   if negb (z s= 15%u32) then Fail_ Failure else Return tt
 .
 
 (** Unit test for [no_nested_borrows::test3] *)
-Check (test3_fwd )%return.
+Check (test3 )%return.
 
-(** [no_nested_borrows::test_neg1]: forward function *)
-Definition test_neg1_fwd : result unit :=
+(** [no_nested_borrows::test_neg1]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 160:0-160:18 *)
+Definition test_neg1 : result unit :=
   y <- i32_neg 3%i32; if negb (y s= (-3)%i32) then Fail_ Failure else Return tt
 .
 
 (** Unit test for [no_nested_borrows::test_neg1] *)
-Check (test_neg1_fwd )%return.
+Check (test_neg1 )%return.
 
-(** [no_nested_borrows::refs_test1]: forward function *)
-Definition refs_test1_fwd : result unit :=
+(** [no_nested_borrows::refs_test1]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 167:0-167:19 *)
+Definition refs_test1 : result unit :=
   if negb (1%i32 s= 1%i32) then Fail_ Failure else Return tt
 .
 
 (** Unit test for [no_nested_borrows::refs_test1] *)
-Check (refs_test1_fwd )%return.
+Check (refs_test1 )%return.
 
-(** [no_nested_borrows::refs_test2]: forward function *)
-Definition refs_test2_fwd : result unit :=
+(** [no_nested_borrows::refs_test2]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 178:0-178:19 *)
+Definition refs_test2 : result unit :=
   if negb (2%i32 s= 2%i32)
   then Fail_ Failure
   else
@@ -128,97 +221,109 @@ Definition refs_test2_fwd : result unit :=
 .
 
 (** Unit test for [no_nested_borrows::refs_test2] *)
-Check (refs_test2_fwd )%return.
+Check (refs_test2 )%return.
 
-(** [no_nested_borrows::test_list1]: forward function *)
-Definition test_list1_fwd : result unit :=
+(** [no_nested_borrows::test_list1]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 194:0-194:19 *)
+Definition test_list1 : result unit :=
   Return tt.
 
 (** Unit test for [no_nested_borrows::test_list1] *)
-Check (test_list1_fwd )%return.
-
-(** [no_nested_borrows::test_box1]: forward function *)
-Definition test_box1_fwd : result unit :=
-  let b := 1%i32 in
-  let x := b in
+Check (test_list1 )%return.
+
+(** [no_nested_borrows::test_box1]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 199:0-199:18 *)
+Definition test_box1 : result unit :=
+  let b := 0%i32 in
+  b0 <- alloc_boxed_Box_deref_mut_back i32 b 1%i32;
+  x <- alloc_boxed_Box_deref i32 b0;
   if negb (x s= 1%i32) then Fail_ Failure else Return tt
 .
 
 (** Unit test for [no_nested_borrows::test_box1] *)
-Check (test_box1_fwd )%return.
+Check (test_box1 )%return.
 
-(** [no_nested_borrows::copy_int]: forward function *)
-Definition copy_int_fwd (x : i32) : result i32 :=
+(** [no_nested_borrows::copy_int]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 209:0-209:30 *)
+Definition copy_int (x : i32) : result i32 :=
   Return x.
 
-(** [no_nested_borrows::test_unreachable]: forward function *)
-Definition test_unreachable_fwd (b : bool) : result unit :=
+(** [no_nested_borrows::test_unreachable]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 215:0-215:32 *)
+Definition test_unreachable (b : bool) : result unit :=
   if b then Fail_ Failure else Return tt
 .
 
-(** [no_nested_borrows::test_panic]: forward function *)
-Definition test_panic_fwd (b : bool) : result unit :=
+(** [no_nested_borrows::test_panic]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 223:0-223:26 *)
+Definition test_panic (b : bool) : result unit :=
   if b then Fail_ Failure else Return tt
 .
 
-(** [no_nested_borrows::test_copy_int]: forward function *)
-Definition test_copy_int_fwd : result unit :=
-  y <- copy_int_fwd 0%i32;
-  if negb (0%i32 s= y) then Fail_ Failure else Return tt
+(** [no_nested_borrows::test_copy_int]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 230:0-230:22 *)
+Definition test_copy_int : result unit :=
+  y <- copy_int 0%i32; if negb (0%i32 s= y) then Fail_ Failure else Return tt
 .
 
 (** Unit test for [no_nested_borrows::test_copy_int] *)
-Check (test_copy_int_fwd )%return.
+Check (test_copy_int )%return.
 
-(** [no_nested_borrows::is_cons]: forward function *)
-Definition is_cons_fwd (T : Type) (l : List_t T) : result bool :=
-  match l with | ListCons t l0 => Return true | ListNil => Return false end
+(** [no_nested_borrows::is_cons]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 237:0-237:38 *)
+Definition is_cons (T : Type) (l : List_t T) : result bool :=
+  match l with | List_Cons t l0 => Return true | List_Nil => Return false end
 .
 
-(** [no_nested_borrows::test_is_cons]: forward function *)
-Definition test_is_cons_fwd : result unit :=
-  let l := ListNil in
-  b <- is_cons_fwd i32 (ListCons 0%i32 l);
+(** [no_nested_borrows::test_is_cons]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 244:0-244:21 *)
+Definition test_is_cons : result unit :=
+  let l := List_Nil in
+  b <- is_cons i32 (List_Cons 0%i32 l);
   if negb b then Fail_ Failure else Return tt
 .
 
 (** Unit test for [no_nested_borrows::test_is_cons] *)
-Check (test_is_cons_fwd )%return.
+Check (test_is_cons )%return.
 
-(** [no_nested_borrows::split_list]: forward function *)
-Definition split_list_fwd
-  (T : Type) (l : List_t T) : result (T * (List_t T)) :=
+(** [no_nested_borrows::split_list]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 250:0-250:48 *)
+Definition split_list (T : Type) (l : List_t T) : result (T * (List_t T)) :=
   match l with
-  | ListCons hd tl => Return (hd, tl)
-  | ListNil => Fail_ Failure
+  | List_Cons hd tl => Return (hd, tl)
+  | List_Nil => Fail_ Failure
   end
 .
 
-(** [no_nested_borrows::test_split_list]: forward function *)
-Definition test_split_list_fwd : result unit :=
-  let l := ListNil in
-  p <- split_list_fwd i32 (ListCons 0%i32 l);
+(** [no_nested_borrows::test_split_list]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 258:0-258:24 *)
+Definition test_split_list : result unit :=
+  let l := List_Nil in
+  p <- split_list i32 (List_Cons 0%i32 l);
   let (hd, _) := p in
   if negb (hd s= 0%i32) then Fail_ Failure else Return tt
 .
 
 (** Unit test for [no_nested_borrows::test_split_list] *)
-Check (test_split_list_fwd )%return.
+Check (test_split_list )%return.
 
-(** [no_nested_borrows::choose]: forward function *)
-Definition choose_fwd (T : Type) (b : bool) (x : T) (y : T) : result T :=
+(** [no_nested_borrows::choose]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 265:0-265:70 *)
+Definition choose (T : Type) (b : bool) (x : T) (y : T) : result T :=
   if b then Return x else Return y
 .
 
-(** [no_nested_borrows::choose]: backward function 0 *)
+(** [no_nested_borrows::choose]: backward function 0
+    Source: 'src/no_nested_borrows.rs', lines 265:0-265:70 *)
 Definition choose_back
   (T : Type) (b : bool) (x : T) (y : T) (ret : T) : result (T * T) :=
   if b then Return (ret, y) else Return (x, ret)
 .
 
-(** [no_nested_borrows::choose_test]: forward function *)
-Definition choose_test_fwd : result unit :=
-  z <- choose_fwd i32 true 0%i32 0%i32;
+(** [no_nested_borrows::choose_test]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 273:0-273:20 *)
+Definition choose_test : result unit :=
+  z <- choose i32 true 0%i32 0%i32;
   z0 <- i32_add z 1%i32;
   if negb (z0 s= 1%i32)
   then Fail_ Failure
@@ -231,284 +336,312 @@ Definition choose_test_fwd : result unit :=
 .
 
 (** Unit test for [no_nested_borrows::choose_test] *)
-Check (choose_test_fwd )%return.
+Check (choose_test )%return.
 
-(** [no_nested_borrows::test_char]: forward function *)
-Definition test_char_fwd : result char :=
-  Return (char_of_byte Coq.Init.Byte.x61)
-.
+(** [no_nested_borrows::test_char]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 285:0-285:26 *)
+Definition test_char : result char :=
+  Return (char_of_byte Coq.Init.Byte.x61).
 
-(** [no_nested_borrows::Tree] *)
+(** [no_nested_borrows::Tree]
+    Source: 'src/no_nested_borrows.rs', lines 290:0-290:16 *)
 Inductive Tree_t (T : Type) :=
-| TreeLeaf : T -> Tree_t T
-| TreeNode : T -> Node_elem_t T -> Tree_t T -> Tree_t T
+| Tree_Leaf : T -> Tree_t T
+| Tree_Node : T -> NodeElem_t T -> Tree_t T -> Tree_t T
 
-(** [no_nested_borrows::NodeElem] *)
-with Node_elem_t (T : Type) :=
-| NodeElemCons : Tree_t T -> Node_elem_t T -> Node_elem_t T
-| NodeElemNil : Node_elem_t T
+(** [no_nested_borrows::NodeElem]
+    Source: 'src/no_nested_borrows.rs', lines 295:0-295:20 *)
+with NodeElem_t (T : Type) :=
+| NodeElem_Cons : Tree_t T -> NodeElem_t T -> NodeElem_t T
+| NodeElem_Nil : NodeElem_t T
 .
 
-Arguments TreeLeaf {T} _.
-Arguments TreeNode {T} _ _ _.
+Arguments Tree_Leaf { _ }.
+Arguments Tree_Node { _ }.
 
-Arguments NodeElemCons {T} _ _.
-Arguments NodeElemNil {T}.
+Arguments NodeElem_Cons { _ }.
+Arguments NodeElem_Nil { _ }.
 
-(** [no_nested_borrows::list_length]: forward function *)
-Fixpoint list_length_fwd (T : Type) (l : List_t T) : result u32 :=
+(** [no_nested_borrows::list_length]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 330:0-330:48 *)
+Fixpoint list_length (T : Type) (l : List_t T) : result u32 :=
   match l with
-  | ListCons t l1 => i <- list_length_fwd T l1; u32_add 1%u32 i
-  | ListNil => Return 0%u32
+  | List_Cons t l1 => i <- list_length T l1; u32_add 1%u32 i
+  | List_Nil => Return 0%u32
   end
 .
 
-(** [no_nested_borrows::list_nth_shared]: forward function *)
-Fixpoint list_nth_shared_fwd (T : Type) (l : List_t T) (i : u32) : result T :=
+(** [no_nested_borrows::list_nth_shared]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 338:0-338:62 *)
+Fixpoint list_nth_shared (T : Type) (l : List_t T) (i : u32) : result T :=
   match l with
-  | ListCons x tl =>
+  | List_Cons x tl =>
     if i s= 0%u32
     then Return x
-    else (i0 <- u32_sub i 1%u32; list_nth_shared_fwd T tl i0)
-  | ListNil => Fail_ Failure
+    else (i0 <- u32_sub i 1%u32; list_nth_shared T tl i0)
+  | List_Nil => Fail_ Failure
   end
 .
 
-(** [no_nested_borrows::list_nth_mut]: forward function *)
-Fixpoint list_nth_mut_fwd (T : Type) (l : List_t T) (i : u32) : result T :=
+(** [no_nested_borrows::list_nth_mut]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 354:0-354:67 *)
+Fixpoint list_nth_mut (T : Type) (l : List_t T) (i : u32) : result T :=
   match l with
-  | ListCons x tl =>
+  | List_Cons x tl =>
     if i s= 0%u32
     then Return x
-    else (i0 <- u32_sub i 1%u32; list_nth_mut_fwd T tl i0)
-  | ListNil => Fail_ Failure
+    else (i0 <- u32_sub i 1%u32; list_nth_mut T tl i0)
+  | List_Nil => Fail_ Failure
   end
 .
 
-(** [no_nested_borrows::list_nth_mut]: backward function 0 *)
+(** [no_nested_borrows::list_nth_mut]: backward function 0
+    Source: 'src/no_nested_borrows.rs', lines 354:0-354:67 *)
 Fixpoint list_nth_mut_back
   (T : Type) (l : List_t T) (i : u32) (ret : T) : result (List_t T) :=
   match l with
-  | ListCons x tl =>
+  | List_Cons x tl =>
     if i s= 0%u32
-    then Return (ListCons ret tl)
+    then Return (List_Cons ret tl)
     else (
       i0 <- u32_sub i 1%u32;
       tl0 <- list_nth_mut_back T tl i0 ret;
-      Return (ListCons x tl0))
-  | ListNil => Fail_ Failure
+      Return (List_Cons x tl0))
+  | List_Nil => Fail_ Failure
   end
 .
 
-(** [no_nested_borrows::list_rev_aux]: forward function *)
-Fixpoint list_rev_aux_fwd
+(** [no_nested_borrows::list_rev_aux]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 370:0-370:63 *)
+Fixpoint list_rev_aux
   (T : Type) (li : List_t T) (lo : List_t T) : result (List_t T) :=
   match li with
-  | ListCons hd tl => list_rev_aux_fwd T tl (ListCons hd lo)
-  | ListNil => Return lo
+  | List_Cons hd tl => list_rev_aux T tl (List_Cons hd lo)
+  | List_Nil => Return lo
   end
 .
 
 (** [no_nested_borrows::list_rev]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ()) *)
-Definition list_rev_fwd_back (T : Type) (l : List_t T) : result (List_t T) :=
-  let li := mem_replace_fwd (List_t T) l ListNil in
-  list_rev_aux_fwd T li ListNil
-.
-
-(** [no_nested_borrows::test_list_functions]: forward function *)
-Definition test_list_functions_fwd : result unit :=
-  let l := ListNil in
-  let l0 := ListCons 2%i32 l in
-  let l1 := ListCons 1%i32 l0 in
-  i <- list_length_fwd i32 (ListCons 0%i32 l1);
+    (there is a single backward function, and the forward function returns ())
+    Source: 'src/no_nested_borrows.rs', lines 384:0-384:42 *)
+Definition list_rev (T : Type) (l : List_t T) : result (List_t T) :=
+  let li := core_mem_replace (List_t T) l List_Nil in
+  list_rev_aux T li List_Nil
+.
+
+(** [no_nested_borrows::test_list_functions]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 389:0-389:28 *)
+Definition test_list_functions : result unit :=
+  let l := List_Nil in
+  let l0 := List_Cons 2%i32 l in
+  let l1 := List_Cons 1%i32 l0 in
+  i <- list_length i32 (List_Cons 0%i32 l1);
   if negb (i s= 3%u32)
   then Fail_ Failure
   else (
-    i0 <- list_nth_shared_fwd i32 (ListCons 0%i32 l1) 0%u32;
+    i0 <- list_nth_shared i32 (List_Cons 0%i32 l1) 0%u32;
     if negb (i0 s= 0%i32)
     then Fail_ Failure
     else (
-      i1 <- list_nth_shared_fwd i32 (ListCons 0%i32 l1) 1%u32;
+      i1 <- list_nth_shared i32 (List_Cons 0%i32 l1) 1%u32;
       if negb (i1 s= 1%i32)
       then Fail_ Failure
       else (
-        i2 <- list_nth_shared_fwd i32 (ListCons 0%i32 l1) 2%u32;
+        i2 <- list_nth_shared i32 (List_Cons 0%i32 l1) 2%u32;
         if negb (i2 s= 2%i32)
         then Fail_ Failure
         else (
-          ls <- list_nth_mut_back i32 (ListCons 0%i32 l1) 1%u32 3%i32;
-          i3 <- list_nth_shared_fwd i32 ls 0%u32;
+          ls <- list_nth_mut_back i32 (List_Cons 0%i32 l1) 1%u32 3%i32;
+          i3 <- list_nth_shared i32 ls 0%u32;
           if negb (i3 s= 0%i32)
           then Fail_ Failure
           else (
-            i4 <- list_nth_shared_fwd i32 ls 1%u32;
+            i4 <- list_nth_shared i32 ls 1%u32;
             if negb (i4 s= 3%i32)
             then Fail_ Failure
             else (
-              i5 <- list_nth_shared_fwd i32 ls 2%u32;
+              i5 <- list_nth_shared i32 ls 2%u32;
               if negb (i5 s= 2%i32) then Fail_ Failure else Return tt))))))
 .
 
 (** Unit test for [no_nested_borrows::test_list_functions] *)
-Check (test_list_functions_fwd )%return.
+Check (test_list_functions )%return.
 
-(** [no_nested_borrows::id_mut_pair1]: forward function *)
-Definition id_mut_pair1_fwd
-  (T1 T2 : Type) (x : T1) (y : T2) : result (T1 * T2) :=
+(** [no_nested_borrows::id_mut_pair1]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 405:0-405:89 *)
+Definition id_mut_pair1 (T1 T2 : Type) (x : T1) (y : T2) : result (T1 * T2) :=
   Return (x, y)
 .
 
-(** [no_nested_borrows::id_mut_pair1]: backward function 0 *)
+(** [no_nested_borrows::id_mut_pair1]: backward function 0
+    Source: 'src/no_nested_borrows.rs', lines 405:0-405:89 *)
 Definition id_mut_pair1_back
   (T1 T2 : Type) (x : T1) (y : T2) (ret : (T1 * T2)) : result (T1 * T2) :=
   let (t, t0) := ret in Return (t, t0)
 .
 
-(** [no_nested_borrows::id_mut_pair2]: forward function *)
-Definition id_mut_pair2_fwd
-  (T1 T2 : Type) (p : (T1 * T2)) : result (T1 * T2) :=
+(** [no_nested_borrows::id_mut_pair2]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 409:0-409:88 *)
+Definition id_mut_pair2 (T1 T2 : Type) (p : (T1 * T2)) : result (T1 * T2) :=
   let (t, t0) := p in Return (t, t0)
 .
 
-(** [no_nested_borrows::id_mut_pair2]: backward function 0 *)
+(** [no_nested_borrows::id_mut_pair2]: backward function 0
+    Source: 'src/no_nested_borrows.rs', lines 409:0-409:88 *)
 Definition id_mut_pair2_back
   (T1 T2 : Type) (p : (T1 * T2)) (ret : (T1 * T2)) : result (T1 * T2) :=
   let (t, t0) := ret in Return (t, t0)
 .
 
-(** [no_nested_borrows::id_mut_pair3]: forward function *)
-Definition id_mut_pair3_fwd
-  (T1 T2 : Type) (x : T1) (y : T2) : result (T1 * T2) :=
+(** [no_nested_borrows::id_mut_pair3]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 413:0-413:93 *)
+Definition id_mut_pair3 (T1 T2 : Type) (x : T1) (y : T2) : result (T1 * T2) :=
   Return (x, y)
 .
 
-(** [no_nested_borrows::id_mut_pair3]: backward function 0 *)
+(** [no_nested_borrows::id_mut_pair3]: backward function 0
+    Source: 'src/no_nested_borrows.rs', lines 413:0-413:93 *)
 Definition id_mut_pair3_back'a
   (T1 T2 : Type) (x : T1) (y : T2) (ret : T1) : result T1 :=
   Return ret
 .
 
-(** [no_nested_borrows::id_mut_pair3]: backward function 1 *)
+(** [no_nested_borrows::id_mut_pair3]: backward function 1
+    Source: 'src/no_nested_borrows.rs', lines 413:0-413:93 *)
 Definition id_mut_pair3_back'b
   (T1 T2 : Type) (x : T1) (y : T2) (ret : T2) : result T2 :=
   Return ret
 .
 
-(** [no_nested_borrows::id_mut_pair4]: forward function *)
-Definition id_mut_pair4_fwd
-  (T1 T2 : Type) (p : (T1 * T2)) : result (T1 * T2) :=
+(** [no_nested_borrows::id_mut_pair4]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 417:0-417:92 *)
+Definition id_mut_pair4 (T1 T2 : Type) (p : (T1 * T2)) : result (T1 * T2) :=
   let (t, t0) := p in Return (t, t0)
 .
 
-(** [no_nested_borrows::id_mut_pair4]: backward function 0 *)
+(** [no_nested_borrows::id_mut_pair4]: backward function 0
+    Source: 'src/no_nested_borrows.rs', lines 417:0-417:92 *)
 Definition id_mut_pair4_back'a
   (T1 T2 : Type) (p : (T1 * T2)) (ret : T1) : result T1 :=
   Return ret
 .
 
-(** [no_nested_borrows::id_mut_pair4]: backward function 1 *)
+(** [no_nested_borrows::id_mut_pair4]: backward function 1
+    Source: 'src/no_nested_borrows.rs', lines 417:0-417:92 *)
 Definition id_mut_pair4_back'b
   (T1 T2 : Type) (p : (T1 * T2)) (ret : T2) : result T2 :=
   Return ret
 .
 
-(** [no_nested_borrows::StructWithTuple] *)
-Record Struct_with_tuple_t (T1 T2 : Type) :=
-mkStruct_with_tuple_t {
-  Struct_with_tuple_p : (T1 * T2);
+(** [no_nested_borrows::StructWithTuple]
+    Source: 'src/no_nested_borrows.rs', lines 424:0-424:34 *)
+Record StructWithTuple_t (T1 T2 : Type) :=
+mkStructWithTuple_t {
+  structWithTuple_p : (T1 * T2);
 }
 .
 
-Arguments mkStruct_with_tuple_t {T1} {T2} _.
-Arguments Struct_with_tuple_p {T1} {T2}.
+Arguments mkStructWithTuple_t { _ _ }.
+Arguments structWithTuple_p { _ _ }.
 
-(** [no_nested_borrows::new_tuple1]: forward function *)
-Definition new_tuple1_fwd : result (Struct_with_tuple_t u32 u32) :=
-  Return {| Struct_with_tuple_p := (1%u32, 2%u32) |}
+(** [no_nested_borrows::new_tuple1]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 428:0-428:48 *)
+Definition new_tuple1 : result (StructWithTuple_t u32 u32) :=
+  Return {| structWithTuple_p := (1%u32, 2%u32) |}
 .
 
-(** [no_nested_borrows::new_tuple2]: forward function *)
-Definition new_tuple2_fwd : result (Struct_with_tuple_t i16 i16) :=
-  Return {| Struct_with_tuple_p := (1%i16, 2%i16) |}
+(** [no_nested_borrows::new_tuple2]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 432:0-432:48 *)
+Definition new_tuple2 : result (StructWithTuple_t i16 i16) :=
+  Return {| structWithTuple_p := (1%i16, 2%i16) |}
 .
 
-(** [no_nested_borrows::new_tuple3]: forward function *)
-Definition new_tuple3_fwd : result (Struct_with_tuple_t u64 i64) :=
-  Return {| Struct_with_tuple_p := (1%u64, 2%i64) |}
+(** [no_nested_borrows::new_tuple3]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 436:0-436:48 *)
+Definition new_tuple3 : result (StructWithTuple_t u64 i64) :=
+  Return {| structWithTuple_p := (1%u64, 2%i64) |}
 .
 
-(** [no_nested_borrows::StructWithPair] *)
-Record Struct_with_pair_t (T1 T2 : Type) :=
-mkStruct_with_pair_t {
-  Struct_with_pair_p : Pair_t T1 T2;
+(** [no_nested_borrows::StructWithPair]
+    Source: 'src/no_nested_borrows.rs', lines 441:0-441:33 *)
+Record StructWithPair_t (T1 T2 : Type) :=
+mkStructWithPair_t {
+  structWithPair_p : Pair_t T1 T2;
 }
 .
 
-Arguments mkStruct_with_pair_t {T1} {T2} _.
-Arguments Struct_with_pair_p {T1} {T2}.
+Arguments mkStructWithPair_t { _ _ }.
+Arguments structWithPair_p { _ _ }.
 
-(** [no_nested_borrows::new_pair1]: forward function *)
-Definition new_pair1_fwd : result (Struct_with_pair_t u32 u32) :=
-  Return {| Struct_with_pair_p := {| Pair_x := 1%u32; Pair_y := 2%u32 |} |}
+(** [no_nested_borrows::new_pair1]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 445:0-445:46 *)
+Definition new_pair1 : result (StructWithPair_t u32 u32) :=
+  Return {| structWithPair_p := {| pair_x := 1%u32; pair_y := 2%u32 |} |}
 .
 
-(** [no_nested_borrows::test_constants]: forward function *)
-Definition test_constants_fwd : result unit :=
-  swt <- new_tuple1_fwd;
-  let (i, _) := swt.(Struct_with_tuple_p) in
+(** [no_nested_borrows::test_constants]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 453:0-453:23 *)
+Definition test_constants : result unit :=
+  swt <- new_tuple1;
+  let (i, _) := swt.(structWithTuple_p) in
   if negb (i s= 1%u32)
   then Fail_ Failure
   else (
-    swt0 <- new_tuple2_fwd;
-    let (i0, _) := swt0.(Struct_with_tuple_p) in
+    swt0 <- new_tuple2;
+    let (i0, _) := swt0.(structWithTuple_p) in
     if negb (i0 s= 1%i16)
     then Fail_ Failure
     else (
-      swt1 <- new_tuple3_fwd;
-      let (i1, _) := swt1.(Struct_with_tuple_p) in
+      swt1 <- new_tuple3;
+      let (i1, _) := swt1.(structWithTuple_p) in
       if negb (i1 s= 1%u64)
       then Fail_ Failure
       else (
-        swp <- new_pair1_fwd;
-        if negb (swp.(Struct_with_pair_p).(Pair_x) s= 1%u32)
+        swp <- new_pair1;
+        if negb (swp.(structWithPair_p).(pair_x) s= 1%u32)
         then Fail_ Failure
         else Return tt)))
 .
 
 (** Unit test for [no_nested_borrows::test_constants] *)
-Check (test_constants_fwd )%return.
+Check (test_constants )%return.
 
-(** [no_nested_borrows::test_weird_borrows1]: forward function *)
-Definition test_weird_borrows1_fwd : result unit :=
+(** [no_nested_borrows::test_weird_borrows1]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 462:0-462:28 *)
+Definition test_weird_borrows1 : result unit :=
   Return tt.
 
 (** Unit test for [no_nested_borrows::test_weird_borrows1] *)
-Check (test_weird_borrows1_fwd )%return.
+Check (test_weird_borrows1 )%return.
 
 (** [no_nested_borrows::test_mem_replace]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ()) *)
-Definition test_mem_replace_fwd_back (px : u32) : result u32 :=
-  let y := mem_replace_fwd u32 px 1%u32 in
+    (there is a single backward function, and the forward function returns ())
+    Source: 'src/no_nested_borrows.rs', lines 472:0-472:37 *)
+Definition test_mem_replace (px : u32) : result u32 :=
+  let y := core_mem_replace u32 px 1%u32 in
   if negb (y s= 0%u32) then Fail_ Failure else Return 2%u32
 .
 
-(** [no_nested_borrows::test_shared_borrow_bool1]: forward function *)
-Definition test_shared_borrow_bool1_fwd (b : bool) : result u32 :=
+(** [no_nested_borrows::test_shared_borrow_bool1]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 479:0-479:47 *)
+Definition test_shared_borrow_bool1 (b : bool) : result u32 :=
   if b then Return 0%u32 else Return 1%u32
 .
 
-(** [no_nested_borrows::test_shared_borrow_bool2]: forward function *)
-Definition test_shared_borrow_bool2_fwd : result u32 :=
+(** [no_nested_borrows::test_shared_borrow_bool2]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 492:0-492:40 *)
+Definition test_shared_borrow_bool2 : result u32 :=
   Return 0%u32.
 
-(** [no_nested_borrows::test_shared_borrow_enum1]: forward function *)
-Definition test_shared_borrow_enum1_fwd (l : List_t u32) : result u32 :=
-  match l with | ListCons i l0 => Return 1%u32 | ListNil => Return 0%u32 end
+(** [no_nested_borrows::test_shared_borrow_enum1]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 507:0-507:52 *)
+Definition test_shared_borrow_enum1 (l : List_t u32) : result u32 :=
+  match l with | List_Cons i l0 => Return 1%u32 | List_Nil => Return 0%u32 end
 .
 
-(** [no_nested_borrows::test_shared_borrow_enum2]: forward function *)
-Definition test_shared_borrow_enum2_fwd : result u32 :=
+(** [no_nested_borrows::test_shared_borrow_enum2]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 519:0-519:40 *)
+Definition test_shared_borrow_enum2 : result u32 :=
   Return 0%u32.
 
-End NoNestedBorrows .
+End NoNestedBorrows.
diff --git a/tests/coq/misc/Paper.v b/tests/coq/misc/Paper.v
index 175a523d..6b110193 100644
--- a/tests/coq/misc/Paper.v
+++ b/tests/coq/misc/Paper.v
@@ -9,33 +9,37 @@ Local Open Scope Primitives_scope.
 Module Paper.
 
 (** [paper::ref_incr]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ()) *)
-Definition ref_incr_fwd_back (x : i32) : result i32 :=
+    (there is a single backward function, and the forward function returns ())
+    Source: 'src/paper.rs', lines 4:0-4:28 *)
+Definition ref_incr (x : i32) : result i32 :=
   i32_add x 1%i32.
 
-(** [paper::test_incr]: forward function *)
-Definition test_incr_fwd : result unit :=
-  x <- ref_incr_fwd_back 0%i32;
-  if negb (x s= 1%i32) then Fail_ Failure else Return tt
+(** [paper::test_incr]: forward function
+    Source: 'src/paper.rs', lines 8:0-8:18 *)
+Definition test_incr : result unit :=
+  x <- ref_incr 0%i32; if negb (x s= 1%i32) then Fail_ Failure else Return tt
 .
 
 (** Unit test for [paper::test_incr] *)
-Check (test_incr_fwd )%return.
+Check (test_incr )%return.
 
-(** [paper::choose]: forward function *)
-Definition choose_fwd (T : Type) (b : bool) (x : T) (y : T) : result T :=
+(** [paper::choose]: forward function
+    Source: 'src/paper.rs', lines 15:0-15:70 *)
+Definition choose (T : Type) (b : bool) (x : T) (y : T) : result T :=
   if b then Return x else Return y
 .
 
-(** [paper::choose]: backward function 0 *)
+(** [paper::choose]: backward function 0
+    Source: 'src/paper.rs', lines 15:0-15:70 *)
 Definition choose_back
   (T : Type) (b : bool) (x : T) (y : T) (ret : T) : result (T * T) :=
   if b then Return (ret, y) else Return (x, ret)
 .
 
-(** [paper::test_choose]: forward function *)
-Definition test_choose_fwd : result unit :=
-  z <- choose_fwd i32 true 0%i32 0%i32;
+(** [paper::test_choose]: forward function
+    Source: 'src/paper.rs', lines 23:0-23:20 *)
+Definition test_choose : result unit :=
+  z <- choose i32 true 0%i32 0%i32;
   z0 <- i32_add z 1%i32;
   if negb (z0 s= 1%i32)
   then Fail_ Failure
@@ -48,74 +52,80 @@ Definition test_choose_fwd : result unit :=
 .
 
 (** Unit test for [paper::test_choose] *)
-Check (test_choose_fwd )%return.
+Check (test_choose )%return.
 
-(** [paper::List] *)
+(** [paper::List]
+    Source: 'src/paper.rs', lines 35:0-35:16 *)
 Inductive List_t (T : Type) :=
-| ListCons : T -> List_t T -> List_t T
-| ListNil : List_t T
+| List_Cons : T -> List_t T -> List_t T
+| List_Nil : List_t T
 .
 
-Arguments ListCons {T} _ _.
-Arguments ListNil {T}.
+Arguments List_Cons { _ }.
+Arguments List_Nil { _ }.
 
-(** [paper::list_nth_mut]: forward function *)
-Fixpoint list_nth_mut_fwd (T : Type) (l : List_t T) (i : u32) : result T :=
+(** [paper::list_nth_mut]: forward function
+    Source: 'src/paper.rs', lines 42:0-42:67 *)
+Fixpoint list_nth_mut (T : Type) (l : List_t T) (i : u32) : result T :=
   match l with
-  | ListCons x tl =>
+  | List_Cons x tl =>
     if i s= 0%u32
     then Return x
-    else (i0 <- u32_sub i 1%u32; list_nth_mut_fwd T tl i0)
-  | ListNil => Fail_ Failure
+    else (i0 <- u32_sub i 1%u32; list_nth_mut T tl i0)
+  | List_Nil => Fail_ Failure
   end
 .
 
-(** [paper::list_nth_mut]: backward function 0 *)
+(** [paper::list_nth_mut]: backward function 0
+    Source: 'src/paper.rs', lines 42:0-42:67 *)
 Fixpoint list_nth_mut_back
   (T : Type) (l : List_t T) (i : u32) (ret : T) : result (List_t T) :=
   match l with
-  | ListCons x tl =>
+  | List_Cons x tl =>
     if i s= 0%u32
-    then Return (ListCons ret tl)
+    then Return (List_Cons ret tl)
     else (
       i0 <- u32_sub i 1%u32;
       tl0 <- list_nth_mut_back T tl i0 ret;
-      Return (ListCons x tl0))
-  | ListNil => Fail_ Failure
+      Return (List_Cons x tl0))
+  | List_Nil => Fail_ Failure
   end
 .
 
-(** [paper::sum]: forward function *)
-Fixpoint sum_fwd (l : List_t i32) : result i32 :=
+(** [paper::sum]: forward function
+    Source: 'src/paper.rs', lines 57:0-57:32 *)
+Fixpoint sum (l : List_t i32) : result i32 :=
   match l with
-  | ListCons x tl => i <- sum_fwd tl; i32_add x i
-  | ListNil => Return 0%i32
+  | List_Cons x tl => i <- sum tl; i32_add x i
+  | List_Nil => Return 0%i32
   end
 .
 
-(** [paper::test_nth]: forward function *)
-Definition test_nth_fwd : result unit :=
-  let l := ListNil in
-  let l0 := ListCons 3%i32 l in
-  let l1 := ListCons 2%i32 l0 in
-  x <- list_nth_mut_fwd i32 (ListCons 1%i32 l1) 2%u32;
+(** [paper::test_nth]: forward function
+    Source: 'src/paper.rs', lines 68:0-68:17 *)
+Definition test_nth : result unit :=
+  let l := List_Nil in
+  let l0 := List_Cons 3%i32 l in
+  let l1 := List_Cons 2%i32 l0 in
+  x <- list_nth_mut i32 (List_Cons 1%i32 l1) 2%u32;
   x0 <- i32_add x 1%i32;
-  l2 <- list_nth_mut_back i32 (ListCons 1%i32 l1) 2%u32 x0;
-  i <- sum_fwd l2;
+  l2 <- list_nth_mut_back i32 (List_Cons 1%i32 l1) 2%u32 x0;
+  i <- sum l2;
   if negb (i s= 7%i32) then Fail_ Failure else Return tt
 .
 
 (** Unit test for [paper::test_nth] *)
-Check (test_nth_fwd )%return.
+Check (test_nth )%return.
 
-(** [paper::call_choose]: forward function *)
-Definition call_choose_fwd (p : (u32 * u32)) : result u32 :=
+(** [paper::call_choose]: forward function
+    Source: 'src/paper.rs', lines 76:0-76:44 *)
+Definition call_choose (p : (u32 * u32)) : result u32 :=
   let (px, py) := p in
-  pz <- choose_fwd u32 true px py;
+  pz <- choose u32 true px py;
   pz0 <- u32_add pz 1%u32;
   p0 <- choose_back u32 true px py pz0;
   let (px0, _) := p0 in
   Return px0
 .
 
-End Paper .
+End Paper.
diff --git a/tests/coq/misc/PoloniusList.v b/tests/coq/misc/PoloniusList.v
index 54021bdf..2371b1cc 100644
--- a/tests/coq/misc/PoloniusList.v
+++ b/tests/coq/misc/PoloniusList.v
@@ -8,34 +8,37 @@ Import ListNotations.
 Local Open Scope Primitives_scope.
 Module PoloniusList.
 
-(** [polonius_list::List] *)
+(** [polonius_list::List]
+    Source: 'src/polonius_list.rs', lines 3:0-3:16 *)
 Inductive List_t (T : Type) :=
-| ListCons : T -> List_t T -> List_t T
-| ListNil : List_t T
+| List_Cons : T -> List_t T -> List_t T
+| List_Nil : List_t T
 .
 
-Arguments ListCons {T} _ _.
-Arguments ListNil {T}.
+Arguments List_Cons { _ }.
+Arguments List_Nil { _ }.
 
-(** [polonius_list::get_list_at_x]: forward function *)
-Fixpoint get_list_at_x_fwd (ls : List_t u32) (x : u32) : result (List_t u32) :=
+(** [polonius_list::get_list_at_x]: forward function
+    Source: 'src/polonius_list.rs', lines 13:0-13:76 *)
+Fixpoint get_list_at_x (ls : List_t u32) (x : u32) : result (List_t u32) :=
   match ls with
-  | ListCons hd tl =>
-    if hd s= x then Return (ListCons hd tl) else get_list_at_x_fwd tl x
-  | ListNil => Return ListNil
+  | List_Cons hd tl =>
+    if hd s= x then Return (List_Cons hd tl) else get_list_at_x tl x
+  | List_Nil => Return List_Nil
   end
 .
 
-(** [polonius_list::get_list_at_x]: backward function 0 *)
+(** [polonius_list::get_list_at_x]: backward function 0
+    Source: 'src/polonius_list.rs', lines 13:0-13:76 *)
 Fixpoint get_list_at_x_back
   (ls : List_t u32) (x : u32) (ret : List_t u32) : result (List_t u32) :=
   match ls with
-  | ListCons hd tl =>
+  | List_Cons hd tl =>
     if hd s= x
     then Return ret
-    else (tl0 <- get_list_at_x_back tl x ret; Return (ListCons hd tl0))
-  | ListNil => Return ret
+    else (tl0 <- get_list_at_x_back tl x ret; Return (List_Cons hd tl0))
+  | List_Nil => Return ret
   end
 .
 
-End PoloniusList .
+End PoloniusList.
diff --git a/tests/coq/misc/Primitives.v b/tests/coq/misc/Primitives.v
index 71a2d9c3..99ffe070 100644
--- a/tests/coq/misc/Primitives.v
+++ b/tests/coq/misc/Primitives.v
@@ -63,13 +63,15 @@ Check (if true then Return (1 + 2) else Fail_ Failure)%global = 3.
 
 (*** Misc *)
 
-
 Definition string := Coq.Strings.String.string.
 Definition char := Coq.Strings.Ascii.ascii.
 Definition char_of_byte := Coq.Strings.Ascii.ascii_of_byte.
 
-Definition mem_replace_fwd (a : Type) (x : a) (y : a) : a := x .
-Definition mem_replace_back (a : Type) (x : a) (y : a) : a := y .
+Definition core_mem_replace (a : Type) (x : a) (y : a) : a := x .
+Definition core_mem_replace_back (a : Type) (x : a) (y : a) : a := y .
+
+Record mut_raw_ptr (T : Type) := { mut_raw_ptr_v : T }.
+Record const_raw_ptr (T : Type) := { const_raw_ptr_v : T }.
 
 (*** Scalars *)
 
@@ -253,6 +255,12 @@ Definition scalar_rem {ty} (x y: scalar ty) : result (scalar ty) := mk_scalar ty
   
 Definition scalar_neg {ty} (x: scalar ty) : result (scalar ty) := mk_scalar ty (-(to_Z x)).
 
+Axiom scalar_xor : forall ty, scalar ty -> scalar ty -> scalar ty. (* TODO *)
+Axiom scalar_or : forall ty, scalar ty -> scalar ty -> scalar ty. (* TODO *)
+Axiom scalar_and : forall ty, scalar ty -> scalar ty -> scalar ty. (* TODO *)
+Axiom scalar_shl : forall ty0 ty1, scalar ty0 -> scalar ty1 -> result (scalar ty0). (* TODO *)
+Axiom scalar_shr : forall ty0 ty1, scalar ty0 -> scalar ty1 -> result (scalar ty0). (* TODO *)
+
 (** Cast an integer from a [src_ty] to a [tgt_ty] *)
 (* TODO: check the semantics of casts in Rust *)
 Definition scalar_cast (src_ty tgt_ty : scalar_ty) (x : scalar src_ty) : result (scalar tgt_ty) :=
@@ -370,6 +378,76 @@ Definition u32_mul   := @scalar_mul U32.
 Definition u64_mul   := @scalar_mul U64.
 Definition u128_mul  := @scalar_mul U128.
 
+(** Xor *)
+Definition u8_xor := @scalar_xor U8.
+Definition u16_xor := @scalar_xor U16.
+Definition u32_xor := @scalar_xor U32.
+Definition u64_xor := @scalar_xor U64.
+Definition u128_xor := @scalar_xor U128.
+Definition usize_xor := @scalar_xor Usize.
+Definition i8_xor := @scalar_xor I8.
+Definition i16_xor := @scalar_xor I16.
+Definition i32_xor := @scalar_xor I32.
+Definition i64_xor := @scalar_xor I64.
+Definition i128_xor := @scalar_xor I128.
+Definition isize_xor := @scalar_xor Isize.
+
+(** Or *)
+Definition u8_or := @scalar_or U8.
+Definition u16_or := @scalar_or U16.
+Definition u32_or := @scalar_or U32.
+Definition u64_or := @scalar_or U64.
+Definition u128_or := @scalar_or U128.
+Definition usize_or := @scalar_or Usize.
+Definition i8_or := @scalar_or I8.
+Definition i16_or := @scalar_or I16.
+Definition i32_or := @scalar_or I32.
+Definition i64_or := @scalar_or I64.
+Definition i128_or := @scalar_or I128.
+Definition isize_or := @scalar_or Isize.
+
+(** And *)
+Definition u8_and := @scalar_and U8.
+Definition u16_and := @scalar_and U16.
+Definition u32_and := @scalar_and U32.
+Definition u64_and := @scalar_and U64.
+Definition u128_and := @scalar_and U128.
+Definition usize_and := @scalar_and Usize.
+Definition i8_and := @scalar_and I8.
+Definition i16_and := @scalar_and I16.
+Definition i32_and := @scalar_and I32.
+Definition i64_and := @scalar_and I64.
+Definition i128_and := @scalar_and I128.
+Definition isize_and := @scalar_and Isize.
+
+(** Shift left *)
+Definition u8_shl {ty} := @scalar_shl U8 ty.
+Definition u16_shl {ty} := @scalar_shl U16 ty.
+Definition u32_shl {ty} := @scalar_shl U32 ty.
+Definition u64_shl {ty} := @scalar_shl U64 ty.
+Definition u128_shl {ty} := @scalar_shl U128 ty.
+Definition usize_shl {ty} := @scalar_shl Usize ty.
+Definition i8_shl {ty} := @scalar_shl I8 ty.
+Definition i16_shl {ty} := @scalar_shl I16 ty.
+Definition i32_shl {ty} := @scalar_shl I32 ty.
+Definition i64_shl {ty} := @scalar_shl I64 ty.
+Definition i128_shl {ty} := @scalar_shl I128 ty.
+Definition isize_shl {ty} := @scalar_shl Isize ty.
+
+(** Shift right *)
+Definition u8_shr {ty} := @scalar_shr U8 ty.
+Definition u16_shr {ty} := @scalar_shr U16 ty.
+Definition u32_shr {ty} := @scalar_shr U32 ty.
+Definition u64_shr {ty} := @scalar_shr U64 ty.
+Definition u128_shr {ty} := @scalar_shr U128 ty.
+Definition usize_shr {ty} := @scalar_shr Usize ty.
+Definition i8_shr {ty} := @scalar_shr I8 ty.
+Definition i16_shr {ty} := @scalar_shr I16 ty.
+Definition i32_shr {ty} := @scalar_shr I32 ty.
+Definition i64_shr {ty} := @scalar_shr I64 ty.
+Definition i128_shr {ty} := @scalar_shr I128 ty.
+Definition isize_shr {ty} := @scalar_shr Isize ty.
+
 (** Small utility *)
 Definition usize_to_nat (x: usize) : nat := Z.to_nat (to_Z x).
 
@@ -394,12 +472,89 @@ Notation "x s< y" := (scalar_ltb x y)  (at level 80) : Primitives_scope.
 Notation "x s>= y" := (scalar_geb x y)  (at level 80) : Primitives_scope.
 Notation "x s> y" := (scalar_gtb x y)  (at level 80) : Primitives_scope.
 
-(*** Range *)
-Record range (T : Type) := mk_range {
-  start: T;
-  end_: T;
+(** Constants *)
+Definition core_u8_max    := u8_max %u32.
+Definition core_u16_max   := u16_max %u32.
+Definition core_u32_max   := u32_max %u32.
+Definition core_u64_max   := u64_max %u64.
+Definition core_u128_max  := u64_max %u128.
+Axiom core_usize_max : usize. (** TODO *)
+Definition core_i8_max    := i8_max %i32.
+Definition core_i16_max   := i16_max %i32.
+Definition core_i32_max   := i32_max %i32.
+Definition core_i64_max   := i64_max %i64.
+Definition core_i128_max  := i64_max %i128.
+Axiom core_isize_max : isize. (** TODO *)
+
+(*** core::ops *)
+
+(* Trait declaration: [core::ops::index::Index] *)
+Record core_ops_index_Index (Self Idx : Type) := mk_core_ops_index_Index {
+  core_ops_index_Index_Output : Type;
+  core_ops_index_Index_index : Self -> Idx -> result core_ops_index_Index_Output;
+}.
+Arguments mk_core_ops_index_Index {_ _}.
+Arguments core_ops_index_Index_Output {_ _}.
+Arguments core_ops_index_Index_index {_ _}.
+
+(* Trait declaration: [core::ops::index::IndexMut] *)
+Record core_ops_index_IndexMut (Self Idx : Type) := mk_core_ops_index_IndexMut {
+  core_ops_index_IndexMut_indexInst : core_ops_index_Index Self Idx;
+  core_ops_index_IndexMut_index_mut : Self -> Idx -> result core_ops_index_IndexMut_indexInst.(core_ops_index_Index_Output);
+  core_ops_index_IndexMut_index_mut_back : Self -> Idx -> core_ops_index_IndexMut_indexInst.(core_ops_index_Index_Output) -> result Self;
+}.
+Arguments mk_core_ops_index_IndexMut {_ _}.
+Arguments core_ops_index_IndexMut_indexInst {_ _}.
+Arguments core_ops_index_IndexMut_index_mut {_ _}.
+Arguments core_ops_index_IndexMut_index_mut_back {_ _}.
+
+(* Trait declaration [core::ops::deref::Deref] *)
+Record core_ops_deref_Deref (Self : Type) := mk_core_ops_deref_Deref {
+  core_ops_deref_Deref_target : Type;
+  core_ops_deref_Deref_deref : Self -> result core_ops_deref_Deref_target;
 }.
-Arguments mk_range {_}.
+Arguments mk_core_ops_deref_Deref {_}.
+Arguments core_ops_deref_Deref_target {_}.
+Arguments core_ops_deref_Deref_deref {_}.
+
+(* Trait declaration [core::ops::deref::DerefMut] *)
+Record core_ops_deref_DerefMut (Self : Type) := mk_core_ops_deref_DerefMut {
+  core_ops_deref_DerefMut_derefInst : core_ops_deref_Deref Self;
+  core_ops_deref_DerefMut_deref_mut : Self -> result core_ops_deref_DerefMut_derefInst.(core_ops_deref_Deref_target);
+  core_ops_deref_DerefMut_deref_mut_back : Self -> core_ops_deref_DerefMut_derefInst.(core_ops_deref_Deref_target) -> result Self;
+}.
+Arguments mk_core_ops_deref_DerefMut {_}.
+Arguments core_ops_deref_DerefMut_derefInst {_}.
+Arguments core_ops_deref_DerefMut_deref_mut {_}.
+Arguments core_ops_deref_DerefMut_deref_mut_back {_}.
+
+Record core_ops_range_Range (T : Type) := mk_core_ops_range_Range {
+  core_ops_range_Range_start : T;
+  core_ops_range_Range_end_ : T;
+}.
+Arguments mk_core_ops_range_Range {_}.
+Arguments core_ops_range_Range_start {_}.
+Arguments core_ops_range_Range_end_ {_}.
+
+(*** [alloc] *)
+
+Definition alloc_boxed_Box_deref (T : Type) (x : T) : result T := Return x.
+Definition alloc_boxed_Box_deref_mut (T : Type) (x : T) : result T := Return x.
+Definition alloc_boxed_Box_deref_mut_back (T : Type) (_ : T) (x : T) : result T := Return x.
+
+(* Trait instance *)
+Definition alloc_boxed_Box_coreopsDerefInst (Self : Type) : core_ops_deref_Deref Self := {|
+  core_ops_deref_Deref_target := Self;
+  core_ops_deref_Deref_deref := alloc_boxed_Box_deref Self;
+|}.
+
+(* Trait instance *)
+Definition alloc_boxed_Box_coreopsDerefMutInst (Self : Type) : core_ops_deref_DerefMut Self := {|
+  core_ops_deref_DerefMut_derefInst := alloc_boxed_Box_coreopsDerefInst Self;
+  core_ops_deref_DerefMut_deref_mut := alloc_boxed_Box_deref_mut Self;
+  core_ops_deref_DerefMut_deref_mut_back := alloc_boxed_Box_deref_mut_back Self;
+|}.
+
 
 (*** Arrays *)
 Definition array T (n : usize) := { l: list T | Z.of_nat (length l) = to_Z n}.
@@ -419,51 +574,50 @@ Qed.
 (* TODO: finish the definitions *)
 Axiom mk_array : forall (T : Type) (n : usize) (l : list T), array T n.
 
-Axiom array_index_shared : forall (T : Type) (n : usize) (x : array T n) (i : usize), result T.
-Axiom array_index_mut_fwd : forall (T : Type) (n : usize) (x : array T n) (i : usize), result T.
-Axiom array_index_mut_back : forall (T : Type) (n : usize) (x : array T n) (i : usize) (nx : T), result (array T n).
+(* For initialization *)
+Axiom array_repeat : forall (T : Type) (n : usize) (x : T), array T n.
+
+Axiom array_index_usize : forall (T : Type) (n : usize) (x : array T n) (i : usize), result T.
+Axiom array_update_usize : forall (T : Type) (n : usize) (x : array T n) (i : usize) (nx : T), result (array T n).
 
 (*** Slice *)
 Definition slice T := { l: list T | Z.of_nat (length l) <= usize_max}.
 
 Axiom slice_len : forall (T : Type) (s : slice T), usize.
-Axiom slice_index_shared : forall (T : Type) (x : slice T) (i : usize), result T.
-Axiom slice_index_mut_fwd : forall (T : Type) (x : slice T) (i : usize), result T.
-Axiom slice_index_mut_back : forall (T : Type) (x : slice T) (i : usize) (nx : T), result (slice T).
+Axiom slice_index_usize : forall (T : Type) (x : slice T) (i : usize), result T.
+Axiom slice_update_usize : forall (T : Type) (x : slice T) (i : usize) (nx : T), result (slice T).
 
 (*** Subslices *)
 
-Axiom array_to_slice_shared : forall (T : Type) (n : usize) (x : array T n), result (slice T).
-Axiom array_to_slice_mut_fwd : forall (T : Type) (n : usize) (x : array T n), result (slice T).
-Axiom array_to_slice_mut_back : forall (T : Type) (n : usize) (x : array T n) (s : slice T), result (array T n).
+Axiom array_to_slice : forall (T : Type) (n : usize) (x : array T n), result (slice T).
+Axiom array_from_slice : forall (T : Type) (n : usize) (x : array T n) (s : slice T), result (array T n).
 
-Axiom array_subslice_shared: forall (T : Type) (n : usize) (x : array T n) (r : range usize), result (slice T).
-Axiom array_subslice_mut_fwd: forall (T : Type) (n : usize) (x : array T n) (r : range usize), result (slice T).
-Axiom array_subslice_mut_back: forall (T : Type) (n : usize) (x : array T n) (r : range usize) (ns : slice T), result (array T n).
-Axiom slice_subslice_shared: forall (T : Type) (x : slice T) (r : range usize), result (slice T).
-Axiom slice_subslice_mut_fwd: forall (T : Type) (x : slice T) (r : range usize), result (slice T).
-Axiom slice_subslice_mut_back: forall (T : Type) (x : slice T) (r : range usize) (ns : slice T), result (slice T).
+Axiom array_subslice: forall (T : Type) (n : usize) (x : array T n) (r : core_ops_range_Range usize), result (slice T).
+Axiom array_update_subslice: forall (T : Type) (n : usize) (x : array T n) (r : core_ops_range_Range usize) (ns : slice T), result (array T n).
+
+Axiom slice_subslice: forall (T : Type) (x : slice T) (r : core_ops_range_Range usize), result (slice T).
+Axiom slice_update_subslice: forall (T : Type) (x : slice T) (r : core_ops_range_Range usize) (ns : slice T), result (slice T).
 
 (*** Vectors *)
 
-Definition vec T := { l: list T | Z.of_nat (length l) <= usize_max }.
+Definition alloc_vec_Vec T := { l: list T | Z.of_nat (length l) <= usize_max }.
 
-Definition vec_to_list {T: Type} (v: vec T) : list T := proj1_sig v.
+Definition alloc_vec_Vec_to_list {T: Type} (v: alloc_vec_Vec T) : list T := proj1_sig v.
 
-Definition vec_length {T: Type} (v: vec T) : Z := Z.of_nat (length (vec_to_list v)).
+Definition alloc_vec_Vec_length {T: Type} (v: alloc_vec_Vec T) : Z := Z.of_nat (length (alloc_vec_Vec_to_list v)).
 
-Definition vec_new (T: Type) : vec T := (exist _ [] le_0_usize_max).
+Definition alloc_vec_Vec_new (T: Type) : alloc_vec_Vec T := (exist _ [] le_0_usize_max).
 
-Lemma vec_len_in_usize {T} (v: vec T) : usize_min <= vec_length v <= usize_max.
+Lemma alloc_vec_Vec_len_in_usize {T} (v: alloc_vec_Vec T) : usize_min <= alloc_vec_Vec_length v <= usize_max.
 Proof.
-  unfold vec_length, usize_min.
+  unfold alloc_vec_Vec_length, usize_min.
   split.
   - lia.
   - apply (proj2_sig v).
 Qed.
 
-Definition vec_len (T: Type) (v: vec T) : usize :=
-  exist _ (vec_length v) (vec_len_in_usize v).
+Definition alloc_vec_Vec_len (T: Type) (v: alloc_vec_Vec T) : usize :=
+  exist _ (alloc_vec_Vec_length v) (alloc_vec_Vec_len_in_usize v).
 
 Fixpoint list_update {A} (l: list A) (n: nat) (a: A)
   : list A :=
@@ -474,50 +628,279 @@ Fixpoint list_update {A} (l: list A) (n: nat) (a: A)
     | S m => x :: (list_update t m a)
 end end.
 
-Definition vec_bind {A B} (v: vec A) (f: list A -> result (list B)) : result (vec B) :=
-  l <- f (vec_to_list v) ;
+Definition alloc_vec_Vec_bind {A B} (v: alloc_vec_Vec A) (f: list A -> result (list B)) : result (alloc_vec_Vec B) :=
+  l <- f (alloc_vec_Vec_to_list v) ;
   match sumbool_of_bool (scalar_le_max Usize (Z.of_nat (length l))) with
   | left H => Return (exist _ l (scalar_le_max_valid _ _ H))
   | right _ => Fail_ Failure
   end.
 
 (* The **forward** function shouldn't be used *)
-Definition vec_push_fwd (T: Type) (v: vec T) (x: T) : unit := tt.
+Definition alloc_vec_Vec_push_fwd (T: Type) (v: alloc_vec_Vec T) (x: T) : unit := tt.
 
-Definition vec_push_back (T: Type) (v: vec T) (x: T) : result (vec T) :=
-  vec_bind v (fun l => Return (l ++ [x])).
+Definition alloc_vec_Vec_push (T: Type) (v: alloc_vec_Vec T) (x: T) : result (alloc_vec_Vec T) :=
+  alloc_vec_Vec_bind v (fun l => Return (l ++ [x])).
 
 (* The **forward** function shouldn't be used *)
-Definition vec_insert_fwd (T: Type) (v: vec T) (i: usize) (x: T) : result unit :=
-  if to_Z i <? vec_length v then Return tt else Fail_ Failure.
+Definition alloc_vec_Vec_insert_fwd (T: Type) (v: alloc_vec_Vec T) (i: usize) (x: T) : result unit :=
+  if to_Z i <? alloc_vec_Vec_length v then Return tt else Fail_ Failure.
 
-Definition vec_insert_back (T: Type) (v: vec T) (i: usize) (x: T) : result (vec T) :=
-  vec_bind v (fun l =>
+Definition alloc_vec_Vec_insert (T: Type) (v: alloc_vec_Vec T) (i: usize) (x: T) : result (alloc_vec_Vec T) :=
+  alloc_vec_Vec_bind v (fun l =>
     if to_Z i <? Z.of_nat (length l)
     then Return (list_update l (usize_to_nat i) x)
     else Fail_ Failure).
 
-(* The **backward** function shouldn't be used *)
-Definition vec_index_fwd (T: Type) (v: vec T) (i: usize) : result T :=
-  match nth_error (vec_to_list v) (usize_to_nat i) with
-  | Some n => Return n
-  | None   => Fail_ Failure
-  end.
-
-Definition vec_index_back (T: Type) (v: vec T) (i: usize) (x: T) : result unit :=
-  if to_Z i <? vec_length v then Return tt else Fail_ Failure.
-
-(* The **backward** function shouldn't be used *)
-Definition vec_index_mut_fwd (T: Type) (v: vec T) (i: usize) : result T :=
-  match nth_error (vec_to_list v) (usize_to_nat i) with
-  | Some n => Return n
-  | None   => Fail_ Failure
+(* Helper *)
+Axiom alloc_vec_Vec_index_usize : forall {T : Type} (v : alloc_vec_Vec T) (i : usize), result T.
+
+(* Helper *)
+Axiom alloc_vec_Vec_update_usize : forall {T : Type} (v : alloc_vec_Vec T) (i : usize) (x : T), result (alloc_vec_Vec T).
+
+(* Trait declaration: [core::slice::index::private_slice_index::Sealed] *)
+Definition core_slice_index_private_slice_index_Sealed (self : Type) := unit.
+
+(* Trait declaration: [core::slice::index::SliceIndex] *)
+Record core_slice_index_SliceIndex (Self T : Type) := mk_core_slice_index_SliceIndex {
+  core_slice_index_SliceIndex_sealedInst : core_slice_index_private_slice_index_Sealed Self;
+  core_slice_index_SliceIndex_Output : Type;
+  core_slice_index_SliceIndex_get : Self -> T -> result (option core_slice_index_SliceIndex_Output);
+  core_slice_index_SliceIndex_get_mut : Self -> T -> result (option core_slice_index_SliceIndex_Output);
+  core_slice_index_SliceIndex_get_mut_back : Self -> T -> option core_slice_index_SliceIndex_Output -> result T;
+  core_slice_index_SliceIndex_get_unchecked : Self -> const_raw_ptr T -> result (const_raw_ptr core_slice_index_SliceIndex_Output);
+  core_slice_index_SliceIndex_get_unchecked_mut : Self -> mut_raw_ptr T -> result (mut_raw_ptr core_slice_index_SliceIndex_Output);
+  core_slice_index_SliceIndex_index : Self -> T -> result core_slice_index_SliceIndex_Output;
+  core_slice_index_SliceIndex_index_mut : Self -> T -> result core_slice_index_SliceIndex_Output;
+  core_slice_index_SliceIndex_index_mut_back : Self -> T -> core_slice_index_SliceIndex_Output -> result T;
+}.
+Arguments mk_core_slice_index_SliceIndex {_ _}.
+Arguments core_slice_index_SliceIndex_sealedInst {_ _}.
+Arguments core_slice_index_SliceIndex_Output {_ _}.
+Arguments core_slice_index_SliceIndex_get {_ _}.
+Arguments core_slice_index_SliceIndex_get_mut {_ _}.
+Arguments core_slice_index_SliceIndex_get_mut_back {_ _}.
+Arguments core_slice_index_SliceIndex_get_unchecked {_ _}.
+Arguments core_slice_index_SliceIndex_get_unchecked_mut {_ _}.
+Arguments core_slice_index_SliceIndex_index {_ _}.
+Arguments core_slice_index_SliceIndex_index_mut {_ _}.
+Arguments core_slice_index_SliceIndex_index_mut_back {_ _}.
+
+(* [core::slice::index::[T]::index]: forward function *)
+Definition core_slice_index_Slice_index
+  (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T))
+  (s : slice T) (i : Idx) : result inst.(core_slice_index_SliceIndex_Output) :=
+  x <- inst.(core_slice_index_SliceIndex_get) i s;
+  match x with
+  | None => Fail_ Failure
+  | Some x => Return x
   end.
 
-Definition vec_index_mut_back (T: Type) (v: vec T) (i: usize) (x: T) : result (vec T) :=
-  vec_bind v (fun l =>
-    if to_Z i <? Z.of_nat (length l)
-    then Return (list_update l (usize_to_nat i) x)
-    else Fail_ Failure).
+(* [core::slice::index::Range:::get]: forward function *)
+Axiom core_slice_index_RangeUsize_get : forall (T : Type) (i : core_ops_range_Range usize) (s : slice T), result (option (slice T)).
+
+(* [core::slice::index::Range::get_mut]: forward function *)
+Axiom core_slice_index_RangeUsize_get_mut :
+  forall (T : Type), core_ops_range_Range usize -> slice T -> result (option (slice T)).
+
+(* [core::slice::index::Range::get_mut]: backward function 0 *)
+Axiom core_slice_index_RangeUsize_get_mut_back :
+  forall (T : Type), core_ops_range_Range usize -> slice T -> option (slice T) -> result (slice T).
+
+(* [core::slice::index::Range::get_unchecked]: forward function *)
+Definition core_slice_index_RangeUsize_get_unchecked
+  (T : Type) :
+  core_ops_range_Range usize -> const_raw_ptr (slice T) -> result (const_raw_ptr (slice T)) :=
+  (* Don't know what the model should be - for now we always fail to make
+     sure code which uses it fails *)
+  fun _ _ => Fail_ Failure.
+
+(* [core::slice::index::Range::get_unchecked_mut]: forward function *)
+Definition core_slice_index_RangeUsize_get_unchecked_mut
+  (T : Type) :
+  core_ops_range_Range usize -> mut_raw_ptr (slice T) -> result (mut_raw_ptr (slice T)) :=
+  (* Don't know what the model should be - for now we always fail to make
+    sure code which uses it fails *)
+  fun _ _ => Fail_ Failure.
+
+(* [core::slice::index::Range::index]: forward function *)
+Axiom core_slice_index_RangeUsize_index :
+  forall (T : Type), core_ops_range_Range usize -> slice T -> result (slice T).
+
+(* [core::slice::index::Range::index_mut]: forward function *)
+Axiom core_slice_index_RangeUsize_index_mut :
+  forall (T : Type), core_ops_range_Range usize -> slice T -> result (slice T).
+
+(* [core::slice::index::Range::index_mut]: backward function 0 *)
+Axiom core_slice_index_RangeUsize_index_mut_back :
+  forall (T : Type), core_ops_range_Range usize -> slice T -> slice T -> result (slice T).
+
+(* [core::slice::index::[T]::index_mut]: forward function *)
+Axiom core_slice_index_Slice_index_mut :
+  forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T)),
+  slice T -> Idx -> result inst.(core_slice_index_SliceIndex_Output).
+
+(* [core::slice::index::[T]::index_mut]: backward function 0 *)
+Axiom core_slice_index_Slice_index_mut_back :
+  forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T)),
+  slice T -> Idx -> inst.(core_slice_index_SliceIndex_Output) -> result (slice T).
+
+(* [core::array::[T; N]::index]: forward function *)
+Axiom core_array_Array_index :
+  forall (T Idx : Type) (N : usize) (inst : core_ops_index_Index (slice T) Idx)
+  (a : array T N) (i : Idx), result inst.(core_ops_index_Index_Output).
+
+(* [core::array::[T; N]::index_mut]: forward function *)
+Axiom core_array_Array_index_mut :
+  forall (T Idx : Type) (N : usize) (inst : core_ops_index_IndexMut (slice T) Idx)
+  (a : array T N) (i : Idx), result inst.(core_ops_index_IndexMut_indexInst).(core_ops_index_Index_Output).
+
+(* [core::array::[T; N]::index_mut]: backward function 0 *)
+Axiom core_array_Array_index_mut_back :
+  forall (T Idx : Type) (N : usize) (inst : core_ops_index_IndexMut (slice T) Idx)
+  (a : array T N) (i : Idx) (x : inst.(core_ops_index_IndexMut_indexInst).(core_ops_index_Index_Output)), result (array T N).
+
+(* Trait implementation: [core::slice::index::private_slice_index::Range] *)
+Definition core_slice_index_private_slice_index_SealedRangeUsizeInst
+  : core_slice_index_private_slice_index_Sealed (core_ops_range_Range usize) := tt.
+
+(* Trait implementation: [core::slice::index::Range] *)
+Definition core_slice_index_SliceIndexRangeUsizeSliceTInst (T : Type) :
+  core_slice_index_SliceIndex (core_ops_range_Range usize) (slice T) := {|
+  core_slice_index_SliceIndex_sealedInst := core_slice_index_private_slice_index_SealedRangeUsizeInst;
+  core_slice_index_SliceIndex_Output := slice T;
+  core_slice_index_SliceIndex_get := core_slice_index_RangeUsize_get T;
+  core_slice_index_SliceIndex_get_mut := core_slice_index_RangeUsize_get_mut T;
+  core_slice_index_SliceIndex_get_mut_back := core_slice_index_RangeUsize_get_mut_back T;
+  core_slice_index_SliceIndex_get_unchecked := core_slice_index_RangeUsize_get_unchecked T;
+  core_slice_index_SliceIndex_get_unchecked_mut := core_slice_index_RangeUsize_get_unchecked_mut T;
+  core_slice_index_SliceIndex_index := core_slice_index_RangeUsize_index T;
+  core_slice_index_SliceIndex_index_mut := core_slice_index_RangeUsize_index_mut T;
+  core_slice_index_SliceIndex_index_mut_back := core_slice_index_RangeUsize_index_mut_back T;
+|}.
+
+(* Trait implementation: [core::slice::index::[T]] *)
+Definition core_ops_index_IndexSliceTIInst (T Idx : Type)
+  (inst : core_slice_index_SliceIndex Idx (slice T)) :
+  core_ops_index_Index (slice T) Idx := {|
+  core_ops_index_Index_Output := inst.(core_slice_index_SliceIndex_Output);
+  core_ops_index_Index_index := core_slice_index_Slice_index T Idx inst;
+|}.
+
+(* Trait implementation: [core::slice::index::[T]] *)
+Definition core_ops_index_IndexMutSliceTIInst (T Idx : Type)
+  (inst : core_slice_index_SliceIndex Idx (slice T)) :
+  core_ops_index_IndexMut (slice T) Idx := {|
+  core_ops_index_IndexMut_indexInst := core_ops_index_IndexSliceTIInst T Idx inst;
+  core_ops_index_IndexMut_index_mut := core_slice_index_Slice_index_mut T Idx inst;
+  core_ops_index_IndexMut_index_mut_back := core_slice_index_Slice_index_mut_back T Idx inst;
+|}.
+
+(* Trait implementation: [core::array::[T; N]] *)
+Definition core_ops_index_IndexArrayInst (T Idx : Type) (N : usize)
+  (inst : core_ops_index_Index (slice T) Idx) :
+  core_ops_index_Index (array T N) Idx := {|
+  core_ops_index_Index_Output := inst.(core_ops_index_Index_Output);
+  core_ops_index_Index_index := core_array_Array_index T Idx N inst;
+|}.
+
+(* Trait implementation: [core::array::[T; N]] *)
+Definition core_ops_index_IndexMutArrayInst (T Idx : Type) (N : usize)
+  (inst : core_ops_index_IndexMut (slice T) Idx) :
+  core_ops_index_IndexMut (array T N) Idx := {|
+  core_ops_index_IndexMut_indexInst := core_ops_index_IndexArrayInst T Idx N inst.(core_ops_index_IndexMut_indexInst);
+  core_ops_index_IndexMut_index_mut := core_array_Array_index_mut T Idx N inst;
+  core_ops_index_IndexMut_index_mut_back := core_array_Array_index_mut_back T Idx N inst;
+|}.
+
+(* [core::slice::index::usize::get]: forward function *)
+Axiom core_slice_index_usize_get : forall (T : Type), usize -> slice T -> result (option T).
+
+(* [core::slice::index::usize::get_mut]: forward function *)
+Axiom core_slice_index_usize_get_mut : forall (T : Type), usize -> slice T -> result (option T).
+
+(* [core::slice::index::usize::get_mut]: backward function 0 *)
+Axiom core_slice_index_usize_get_mut_back :
+  forall (T : Type), usize -> slice T -> option T -> result (slice T).
+
+(* [core::slice::index::usize::get_unchecked]: forward function *)
+Axiom core_slice_index_usize_get_unchecked :
+  forall (T : Type), usize -> const_raw_ptr (slice T) -> result (const_raw_ptr T).
+
+(* [core::slice::index::usize::get_unchecked_mut]: forward function *)
+Axiom core_slice_index_usize_get_unchecked_mut :
+  forall (T : Type), usize -> mut_raw_ptr (slice T) -> result (mut_raw_ptr T).
+
+(* [core::slice::index::usize::index]: forward function *)
+Axiom core_slice_index_usize_index : forall (T : Type), usize -> slice T -> result T.
+
+(* [core::slice::index::usize::index_mut]: forward function *)
+Axiom core_slice_index_usize_index_mut : forall (T : Type), usize -> slice T -> result T.
+
+(* [core::slice::index::usize::index_mut]: backward function 0 *)
+Axiom core_slice_index_usize_index_mut_back :
+  forall (T : Type), usize -> slice T -> T -> result (slice T).
+
+(* Trait implementation: [core::slice::index::private_slice_index::usize] *)
+Definition core_slice_index_private_slice_index_SealedUsizeInst
+  : core_slice_index_private_slice_index_Sealed usize := tt.
+
+(* Trait implementation: [core::slice::index::usize] *)
+Definition core_slice_index_SliceIndexUsizeSliceTInst (T : Type) :
+  core_slice_index_SliceIndex usize (slice T) := {|
+  core_slice_index_SliceIndex_sealedInst := core_slice_index_private_slice_index_SealedUsizeInst;
+  core_slice_index_SliceIndex_Output := T;
+  core_slice_index_SliceIndex_get := core_slice_index_usize_get T;
+  core_slice_index_SliceIndex_get_mut := core_slice_index_usize_get_mut T;
+  core_slice_index_SliceIndex_get_mut_back := core_slice_index_usize_get_mut_back T;
+  core_slice_index_SliceIndex_get_unchecked := core_slice_index_usize_get_unchecked T;
+  core_slice_index_SliceIndex_get_unchecked_mut := core_slice_index_usize_get_unchecked_mut T;
+  core_slice_index_SliceIndex_index := core_slice_index_usize_index T;
+  core_slice_index_SliceIndex_index_mut := core_slice_index_usize_index_mut T;
+  core_slice_index_SliceIndex_index_mut_back := core_slice_index_usize_index_mut_back T;
+|}.
+
+(* [alloc::vec::Vec::index]: forward function *)
+Axiom alloc_vec_Vec_index : forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T))
+  (Self : alloc_vec_Vec T) (i : Idx), result inst.(core_slice_index_SliceIndex_Output).
+
+(* [alloc::vec::Vec::index_mut]: forward function *)
+Axiom alloc_vec_Vec_index_mut : forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T))
+  (Self : alloc_vec_Vec T) (i : Idx), result inst.(core_slice_index_SliceIndex_Output).
+
+(* [alloc::vec::Vec::index_mut]: backward function 0 *)
+Axiom alloc_vec_Vec_index_mut_back :
+  forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T))
+  (Self : alloc_vec_Vec T) (i : Idx) (x : inst.(core_slice_index_SliceIndex_Output)), result (alloc_vec_Vec T).
+
+(* Trait implementation: [alloc::vec::Vec] *)
+Definition alloc_vec_Vec_coreopsindexIndexInst (T Idx : Type)
+  (inst : core_slice_index_SliceIndex Idx (slice T)) :
+  core_ops_index_Index (alloc_vec_Vec T) Idx := {|
+  core_ops_index_Index_Output := inst.(core_slice_index_SliceIndex_Output);
+  core_ops_index_Index_index := alloc_vec_Vec_index T Idx inst;
+|}.
+
+(* Trait implementation: [alloc::vec::Vec] *)
+Definition alloc_vec_Vec_coreopsindexIndexMutInst (T Idx : Type)
+  (inst : core_slice_index_SliceIndex Idx (slice T)) :
+  core_ops_index_IndexMut (alloc_vec_Vec T) Idx := {|
+  core_ops_index_IndexMut_indexInst := alloc_vec_Vec_coreopsindexIndexInst T Idx inst;
+  core_ops_index_IndexMut_index_mut := alloc_vec_Vec_index_mut T Idx inst;
+  core_ops_index_IndexMut_index_mut_back := alloc_vec_Vec_index_mut_back T Idx inst;
+|}.
+
+(*** Theorems *)
+
+Axiom alloc_vec_Vec_index_eq : forall {a : Type} (v : alloc_vec_Vec a) (i : usize) (x : a),
+  alloc_vec_Vec_index a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i =
+    alloc_vec_Vec_index_usize v i.
+
+Axiom alloc_vec_Vec_index_mut_eq : forall {a : Type} (v : alloc_vec_Vec a) (i : usize) (x : a),
+  alloc_vec_Vec_index_mut a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i =
+    alloc_vec_Vec_index_usize v i.
+
+Axiom alloc_vec_Vec_index_mut_back_eq : forall {a : Type} (v : alloc_vec_Vec a) (i : usize) (x : a),
+  alloc_vec_Vec_index_mut_back a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i x =
+    alloc_vec_Vec_update_usize v i x.
 
 End Primitives.
diff --git a/tests/coq/misc/_CoqProject b/tests/coq/misc/_CoqProject
index db6c2742..869cdb4d 100644
--- a/tests/coq/misc/_CoqProject
+++ b/tests/coq/misc/_CoqProject
@@ -4,11 +4,15 @@
 -arg all
 
 Loops.v
+External_Types.v
 Primitives.v
 External_Funs.v
+External_TypesExternal.v
 Constants.v
 PoloniusList.v
-External_Types.v
-NoNestedBorrows.v
-External_Opaque.v
 Paper.v
+NoNestedBorrows.v
+External_FunsExternal.v
+Bitwise.v
+External_TypesExternal_Template.v
+External_FunsExternal_Template.v
diff --git a/tests/coq/traits/Makefile b/tests/coq/traits/Makefile
new file mode 100644
index 00000000..1a5aee4a
--- /dev/null
+++ b/tests/coq/traits/Makefile
@@ -0,0 +1,23 @@
+# This file was automatically generated - modify ../Makefile.template instead
+# Makefile originally taken from coq-club
+
+%: Makefile.coq phony
+	+make -f Makefile.coq $@
+
+all: Makefile.coq
+	+make -f Makefile.coq all
+
+clean: Makefile.coq
+	+make -f Makefile.coq clean
+	rm -f Makefile.coq
+
+Makefile.coq: _CoqProject Makefile
+	coq_makefile -f _CoqProject | sed 's/$$(COQCHK) $$(COQCHKFLAGS) $$(COQLIBS)/$$(COQCHK) $$(COQCHKFLAGS) $$(subst -Q,-R,$$(COQLIBS))/' > Makefile.coq
+
+_CoqProject: ;
+
+Makefile: ;
+
+phony: ;
+
+.PHONY: all clean phony
diff --git a/tests/coq/traits/Primitives.v b/tests/coq/traits/Primitives.v
new file mode 100644
index 00000000..99ffe070
--- /dev/null
+++ b/tests/coq/traits/Primitives.v
@@ -0,0 +1,906 @@
+Require Import Lia.
+Require Coq.Strings.Ascii.
+Require Coq.Strings.String.
+Require Import Coq.Program.Equality.
+Require Import Coq.ZArith.ZArith.
+Require Import Coq.ZArith.Znat.
+Require Import List.
+Import ListNotations.
+
+Module Primitives.
+
+  (* TODO: use more *)
+Declare Scope Primitives_scope.
+
+(*** Result *)
+
+Inductive error :=
+  | Failure
+  | OutOfFuel.
+
+Inductive result A :=
+  | Return : A -> result A
+  | Fail_ : error -> result A.
+
+Arguments Return {_} a.
+Arguments Fail_ {_}.
+
+Definition bind {A B} (m: result A) (f: A -> result B) : result B :=
+  match m with
+  | Fail_ e => Fail_ e
+  | Return x => f x
+  end.
+
+Definition return_ {A: Type} (x: A) : result A := Return x.
+Definition fail_ {A: Type} (e: error) : result A := Fail_ e.
+
+Notation "x <- c1 ; c2" := (bind c1 (fun x => c2))
+  (at level 61, c1 at next level, right associativity).
+
+(** Monadic assert *)
+Definition massert (b: bool) : result unit :=
+  if b then Return tt else Fail_ Failure.
+
+(** Normalize and unwrap a successful result (used for globals) *)
+Definition eval_result_refl {A} {x} (a: result A) (p: a = Return x) : A :=
+  match a as r return (r = Return x -> A) with
+  | Return a' => fun _  => a'
+  | Fail_ e   => fun p' =>
+      False_rect _ (eq_ind (Fail_ e)
+          (fun e : result A =>
+          match e with
+          | Return _ => False
+          | Fail_ e => True
+          end)
+        I (Return x) p')
+  end p.
+
+Notation "x %global" := (eval_result_refl x eq_refl) (at level 40).
+Notation "x %return" := (eval_result_refl x eq_refl) (at level 40).
+
+(* Sanity check *)
+Check (if true then Return (1 + 2) else Fail_ Failure)%global = 3.
+
+(*** Misc *)
+
+Definition string := Coq.Strings.String.string.
+Definition char := Coq.Strings.Ascii.ascii.
+Definition char_of_byte := Coq.Strings.Ascii.ascii_of_byte.
+
+Definition core_mem_replace (a : Type) (x : a) (y : a) : a := x .
+Definition core_mem_replace_back (a : Type) (x : a) (y : a) : a := y .
+
+Record mut_raw_ptr (T : Type) := { mut_raw_ptr_v : T }.
+Record const_raw_ptr (T : Type) := { const_raw_ptr_v : T }.
+
+(*** Scalars *)
+
+Definition i8_min   : Z := -128%Z.
+Definition i8_max   : Z := 127%Z.
+Definition i16_min  : Z := -32768%Z.
+Definition i16_max  : Z := 32767%Z.
+Definition i32_min  : Z := -2147483648%Z.
+Definition i32_max  : Z := 2147483647%Z.
+Definition i64_min  : Z := -9223372036854775808%Z.
+Definition i64_max  : Z := 9223372036854775807%Z.
+Definition i128_min : Z := -170141183460469231731687303715884105728%Z.
+Definition i128_max : Z := 170141183460469231731687303715884105727%Z.
+Definition u8_min   : Z := 0%Z.
+Definition u8_max   : Z := 255%Z.
+Definition u16_min  : Z := 0%Z.
+Definition u16_max  : Z := 65535%Z.
+Definition u32_min  : Z := 0%Z.
+Definition u32_max  : Z := 4294967295%Z.
+Definition u64_min  : Z := 0%Z.
+Definition u64_max  : Z := 18446744073709551615%Z.
+Definition u128_min : Z := 0%Z.
+Definition u128_max : Z := 340282366920938463463374607431768211455%Z.
+
+(** The bounds of [isize] and [usize] vary with the architecture. *)
+Axiom isize_min : Z.
+Axiom isize_max : Z.
+Definition usize_min : Z := 0%Z.
+Axiom usize_max : Z.
+
+Open Scope Z_scope.
+
+(** We provide those lemmas to reason about the bounds of [isize] and [usize] *)
+Axiom isize_min_bound : isize_min <= i32_min.
+Axiom isize_max_bound : i32_max <= isize_max.
+Axiom usize_max_bound : u32_max <= usize_max.
+
+Inductive scalar_ty :=
+  | Isize
+  | I8
+  | I16
+  | I32
+  | I64
+  | I128
+  | Usize
+  | U8
+  | U16
+  | U32
+  | U64
+  | U128
+.
+
+Definition scalar_min (ty: scalar_ty) : Z :=
+  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
+end.
+
+Definition scalar_max (ty: scalar_ty) : Z :=
+  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
+end.
+
+(** We use the following conservative bounds to make sure we can compute bound
+    checks in most situations *)
+Definition scalar_min_cons (ty: scalar_ty) : Z :=
+  match ty with
+  | Isize => i32_min
+  | Usize => u32_min
+  | _ => scalar_min ty
+end.
+
+Definition scalar_max_cons (ty: scalar_ty) : Z :=
+  match ty with
+  | Isize => i32_max
+  | Usize => u32_max
+  | _ => scalar_max ty
+end.
+
+Lemma scalar_min_cons_valid : forall ty, scalar_min ty <= scalar_min_cons ty .
+Proof.
+  destruct ty; unfold scalar_min_cons, scalar_min; try lia.
+  - pose isize_min_bound; lia.
+  - apply Z.le_refl.
+Qed.
+
+Lemma scalar_max_cons_valid : forall ty, scalar_max ty >= scalar_max_cons ty .
+Proof.
+  destruct ty; unfold scalar_max_cons, scalar_max; try lia.
+  - pose isize_max_bound; lia.
+  - pose usize_max_bound. lia.
+Qed.
+
+Definition scalar (ty: scalar_ty) : Type :=
+ { x: Z | scalar_min ty <= x <= scalar_max ty }.
+
+Definition to_Z {ty} (x: scalar ty) : Z := proj1_sig x.
+
+(** Bounds checks: we start by using the conservative bounds, to make sure we
+    can compute in most situations, then we use the real bounds (for [isize]
+    and [usize]). *)
+Definition scalar_ge_min (ty: scalar_ty) (x: Z) : bool :=
+  Z.leb (scalar_min_cons ty) x || Z.leb (scalar_min ty) x.
+
+Definition scalar_le_max (ty: scalar_ty) (x: Z) : bool :=
+  Z.leb x (scalar_max_cons ty) || Z.leb x (scalar_max ty).
+
+Lemma scalar_ge_min_valid (ty: scalar_ty) (x: Z) :
+  scalar_ge_min ty x = true -> scalar_min ty <= x .
+Proof.
+  unfold scalar_ge_min.
+  pose (scalar_min_cons_valid ty).
+  lia.
+Qed.
+
+Lemma scalar_le_max_valid (ty: scalar_ty) (x: Z) :
+  scalar_le_max ty x = true -> x <= scalar_max ty .
+Proof.
+  unfold scalar_le_max.
+  pose (scalar_max_cons_valid ty).
+  lia.
+Qed.
+
+Definition scalar_in_bounds (ty: scalar_ty) (x: Z) : bool :=
+  scalar_ge_min ty x && scalar_le_max ty x .
+
+Lemma scalar_in_bounds_valid (ty: scalar_ty) (x: Z) :
+  scalar_in_bounds ty x = true -> scalar_min ty <= x <= scalar_max ty .
+Proof.
+  unfold scalar_in_bounds.
+  intros H.
+  destruct (scalar_ge_min ty x) eqn:Hmin.
+  - destruct (scalar_le_max ty x) eqn:Hmax.
+    + pose (scalar_ge_min_valid ty x Hmin).
+      pose (scalar_le_max_valid ty x Hmax).
+      lia.
+    + inversion H.
+  - inversion H.
+Qed.
+
+Import Sumbool.
+
+Definition mk_scalar (ty: scalar_ty) (x: Z) : result (scalar ty) :=
+  match sumbool_of_bool (scalar_in_bounds ty x) with
+  | left H => Return (exist _ x (scalar_in_bounds_valid _ _ H))
+  | right _ => Fail_ Failure
+  end.
+
+Definition scalar_add {ty} (x y: scalar ty) : result (scalar ty) := mk_scalar ty (to_Z x + to_Z y).
+
+Definition scalar_sub {ty} (x y: scalar ty) : result (scalar ty) := mk_scalar ty (to_Z x - to_Z y).
+
+Definition scalar_mul {ty} (x y: scalar ty) : result (scalar ty) := mk_scalar ty (to_Z x * to_Z y).
+
+Definition scalar_div {ty} (x y: scalar ty) : result (scalar ty) :=
+  if to_Z y =? 0 then Fail_ Failure else
+  mk_scalar ty (to_Z x / to_Z y).
+
+Definition scalar_rem {ty} (x y: scalar ty) : result (scalar ty) := mk_scalar ty (Z.rem (to_Z x) (to_Z y)).
+  
+Definition scalar_neg {ty} (x: scalar ty) : result (scalar ty) := mk_scalar ty (-(to_Z x)).
+
+Axiom scalar_xor : forall ty, scalar ty -> scalar ty -> scalar ty. (* TODO *)
+Axiom scalar_or : forall ty, scalar ty -> scalar ty -> scalar ty. (* TODO *)
+Axiom scalar_and : forall ty, scalar ty -> scalar ty -> scalar ty. (* TODO *)
+Axiom scalar_shl : forall ty0 ty1, scalar ty0 -> scalar ty1 -> result (scalar ty0). (* TODO *)
+Axiom scalar_shr : forall ty0 ty1, scalar ty0 -> scalar ty1 -> result (scalar ty0). (* TODO *)
+
+(** Cast an integer from a [src_ty] to a [tgt_ty] *)
+(* TODO: check the semantics of casts in Rust *)
+Definition scalar_cast (src_ty tgt_ty : scalar_ty) (x : scalar src_ty) : result (scalar tgt_ty) :=
+  mk_scalar tgt_ty (to_Z x).
+
+(** Comparisons *)
+Definition scalar_leb {ty : scalar_ty} (x : scalar ty) (y : scalar ty) : bool :=
+  Z.leb (to_Z x) (to_Z y) .
+
+Definition scalar_ltb {ty : scalar_ty} (x : scalar ty) (y : scalar ty) : bool :=
+  Z.ltb (to_Z x) (to_Z y) .
+
+Definition scalar_geb {ty : scalar_ty} (x : scalar ty) (y : scalar ty) : bool :=
+  Z.geb (to_Z x) (to_Z y) .
+
+Definition scalar_gtb {ty : scalar_ty} (x : scalar ty) (y : scalar ty) : bool :=
+  Z.gtb (to_Z x) (to_Z y) .
+
+Definition scalar_eqb {ty : scalar_ty} (x : scalar ty) (y : scalar ty) : bool :=
+  Z.eqb (to_Z x) (to_Z y) .
+
+Definition scalar_neqb {ty : scalar_ty} (x : scalar ty) (y : scalar ty) : bool :=
+  negb (Z.eqb (to_Z x) (to_Z y)) .
+
+
+(** The scalar types *)
+Definition isize := scalar Isize.
+Definition i8    := scalar I8.
+Definition i16   := scalar I16.
+Definition i32   := scalar I32.
+Definition i64   := scalar I64.
+Definition i128  := scalar I128.
+Definition usize := scalar Usize.
+Definition u8    := scalar U8.
+Definition u16   := scalar U16.
+Definition u32   := scalar U32.
+Definition u64   := scalar U64.
+Definition u128  := scalar U128.
+
+(** Negaion *)
+Definition isize_neg := @scalar_neg Isize.
+Definition i8_neg    := @scalar_neg I8.
+Definition i16_neg   := @scalar_neg I16.
+Definition i32_neg   := @scalar_neg I32.
+Definition i64_neg   := @scalar_neg I64.
+Definition i128_neg  := @scalar_neg I128.
+
+(** Division *)
+Definition isize_div := @scalar_div Isize.
+Definition i8_div    := @scalar_div I8.
+Definition i16_div   := @scalar_div I16.
+Definition i32_div   := @scalar_div I32.
+Definition i64_div   := @scalar_div I64.
+Definition i128_div  := @scalar_div I128.
+Definition usize_div := @scalar_div Usize.
+Definition u8_div    := @scalar_div U8.
+Definition u16_div   := @scalar_div U16.
+Definition u32_div   := @scalar_div U32.
+Definition u64_div   := @scalar_div U64.
+Definition u128_div  := @scalar_div U128.
+
+(** Remainder *)
+Definition isize_rem := @scalar_rem Isize.
+Definition i8_rem    := @scalar_rem I8.
+Definition i16_rem   := @scalar_rem I16.
+Definition i32_rem   := @scalar_rem I32.
+Definition i64_rem   := @scalar_rem I64.
+Definition i128_rem  := @scalar_rem I128.
+Definition usize_rem := @scalar_rem Usize.
+Definition u8_rem    := @scalar_rem U8.
+Definition u16_rem   := @scalar_rem U16.
+Definition u32_rem   := @scalar_rem U32.
+Definition u64_rem   := @scalar_rem U64.
+Definition u128_rem  := @scalar_rem U128.
+
+(** Addition *)
+Definition isize_add := @scalar_add Isize.
+Definition i8_add    := @scalar_add I8.
+Definition i16_add   := @scalar_add I16.
+Definition i32_add   := @scalar_add I32.
+Definition i64_add   := @scalar_add I64.
+Definition i128_add  := @scalar_add I128.
+Definition usize_add := @scalar_add Usize.
+Definition u8_add    := @scalar_add U8.
+Definition u16_add   := @scalar_add U16.
+Definition u32_add   := @scalar_add U32.
+Definition u64_add   := @scalar_add U64.
+Definition u128_add  := @scalar_add U128.
+
+(** Substraction *)
+Definition isize_sub := @scalar_sub Isize.
+Definition i8_sub    := @scalar_sub I8.
+Definition i16_sub   := @scalar_sub I16.
+Definition i32_sub   := @scalar_sub I32.
+Definition i64_sub   := @scalar_sub I64.
+Definition i128_sub  := @scalar_sub I128.
+Definition usize_sub := @scalar_sub Usize.
+Definition u8_sub    := @scalar_sub U8.
+Definition u16_sub   := @scalar_sub U16.
+Definition u32_sub   := @scalar_sub U32.
+Definition u64_sub   := @scalar_sub U64.
+Definition u128_sub  := @scalar_sub U128.
+
+(** Multiplication *)
+Definition isize_mul := @scalar_mul Isize.
+Definition i8_mul    := @scalar_mul I8.
+Definition i16_mul   := @scalar_mul I16.
+Definition i32_mul   := @scalar_mul I32.
+Definition i64_mul   := @scalar_mul I64.
+Definition i128_mul  := @scalar_mul I128.
+Definition usize_mul := @scalar_mul Usize.
+Definition u8_mul    := @scalar_mul U8.
+Definition u16_mul   := @scalar_mul U16.
+Definition u32_mul   := @scalar_mul U32.
+Definition u64_mul   := @scalar_mul U64.
+Definition u128_mul  := @scalar_mul U128.
+
+(** Xor *)
+Definition u8_xor := @scalar_xor U8.
+Definition u16_xor := @scalar_xor U16.
+Definition u32_xor := @scalar_xor U32.
+Definition u64_xor := @scalar_xor U64.
+Definition u128_xor := @scalar_xor U128.
+Definition usize_xor := @scalar_xor Usize.
+Definition i8_xor := @scalar_xor I8.
+Definition i16_xor := @scalar_xor I16.
+Definition i32_xor := @scalar_xor I32.
+Definition i64_xor := @scalar_xor I64.
+Definition i128_xor := @scalar_xor I128.
+Definition isize_xor := @scalar_xor Isize.
+
+(** Or *)
+Definition u8_or := @scalar_or U8.
+Definition u16_or := @scalar_or U16.
+Definition u32_or := @scalar_or U32.
+Definition u64_or := @scalar_or U64.
+Definition u128_or := @scalar_or U128.
+Definition usize_or := @scalar_or Usize.
+Definition i8_or := @scalar_or I8.
+Definition i16_or := @scalar_or I16.
+Definition i32_or := @scalar_or I32.
+Definition i64_or := @scalar_or I64.
+Definition i128_or := @scalar_or I128.
+Definition isize_or := @scalar_or Isize.
+
+(** And *)
+Definition u8_and := @scalar_and U8.
+Definition u16_and := @scalar_and U16.
+Definition u32_and := @scalar_and U32.
+Definition u64_and := @scalar_and U64.
+Definition u128_and := @scalar_and U128.
+Definition usize_and := @scalar_and Usize.
+Definition i8_and := @scalar_and I8.
+Definition i16_and := @scalar_and I16.
+Definition i32_and := @scalar_and I32.
+Definition i64_and := @scalar_and I64.
+Definition i128_and := @scalar_and I128.
+Definition isize_and := @scalar_and Isize.
+
+(** Shift left *)
+Definition u8_shl {ty} := @scalar_shl U8 ty.
+Definition u16_shl {ty} := @scalar_shl U16 ty.
+Definition u32_shl {ty} := @scalar_shl U32 ty.
+Definition u64_shl {ty} := @scalar_shl U64 ty.
+Definition u128_shl {ty} := @scalar_shl U128 ty.
+Definition usize_shl {ty} := @scalar_shl Usize ty.
+Definition i8_shl {ty} := @scalar_shl I8 ty.
+Definition i16_shl {ty} := @scalar_shl I16 ty.
+Definition i32_shl {ty} := @scalar_shl I32 ty.
+Definition i64_shl {ty} := @scalar_shl I64 ty.
+Definition i128_shl {ty} := @scalar_shl I128 ty.
+Definition isize_shl {ty} := @scalar_shl Isize ty.
+
+(** Shift right *)
+Definition u8_shr {ty} := @scalar_shr U8 ty.
+Definition u16_shr {ty} := @scalar_shr U16 ty.
+Definition u32_shr {ty} := @scalar_shr U32 ty.
+Definition u64_shr {ty} := @scalar_shr U64 ty.
+Definition u128_shr {ty} := @scalar_shr U128 ty.
+Definition usize_shr {ty} := @scalar_shr Usize ty.
+Definition i8_shr {ty} := @scalar_shr I8 ty.
+Definition i16_shr {ty} := @scalar_shr I16 ty.
+Definition i32_shr {ty} := @scalar_shr I32 ty.
+Definition i64_shr {ty} := @scalar_shr I64 ty.
+Definition i128_shr {ty} := @scalar_shr I128 ty.
+Definition isize_shr {ty} := @scalar_shr Isize ty.
+
+(** Small utility *)
+Definition usize_to_nat (x: usize) : nat := Z.to_nat (to_Z x).
+
+(** Notations *)
+Notation "x %isize" := ((mk_scalar Isize x)%return) (at level 9).
+Notation "x %i8"    := ((mk_scalar I8    x)%return) (at level 9).
+Notation "x %i16"   := ((mk_scalar I16   x)%return) (at level 9).
+Notation "x %i32"   := ((mk_scalar I32   x)%return) (at level 9).
+Notation "x %i64"   := ((mk_scalar I64   x)%return) (at level 9).
+Notation "x %i128"  := ((mk_scalar I128  x)%return) (at level 9).
+Notation "x %usize" := ((mk_scalar Usize x)%return) (at level 9).
+Notation "x %u8"    := ((mk_scalar U8    x)%return) (at level 9).
+Notation "x %u16"   := ((mk_scalar U16   x)%return) (at level 9).
+Notation "x %u32"   := ((mk_scalar U32   x)%return) (at level 9).
+Notation "x %u64"   := ((mk_scalar U64   x)%return) (at level 9).
+Notation "x %u128"  := ((mk_scalar U128  x)%return) (at level 9).
+
+Notation "x s= y" := (scalar_eqb x y)  (at level 80) : Primitives_scope.
+Notation "x s<> y" := (scalar_neqb x y) (at level 80) : Primitives_scope.
+Notation "x s<= y" := (scalar_leb x y)  (at level 80) : Primitives_scope.
+Notation "x s< y" := (scalar_ltb x y)  (at level 80) : Primitives_scope.
+Notation "x s>= y" := (scalar_geb x y)  (at level 80) : Primitives_scope.
+Notation "x s> y" := (scalar_gtb x y)  (at level 80) : Primitives_scope.
+
+(** Constants *)
+Definition core_u8_max    := u8_max %u32.
+Definition core_u16_max   := u16_max %u32.
+Definition core_u32_max   := u32_max %u32.
+Definition core_u64_max   := u64_max %u64.
+Definition core_u128_max  := u64_max %u128.
+Axiom core_usize_max : usize. (** TODO *)
+Definition core_i8_max    := i8_max %i32.
+Definition core_i16_max   := i16_max %i32.
+Definition core_i32_max   := i32_max %i32.
+Definition core_i64_max   := i64_max %i64.
+Definition core_i128_max  := i64_max %i128.
+Axiom core_isize_max : isize. (** TODO *)
+
+(*** core::ops *)
+
+(* Trait declaration: [core::ops::index::Index] *)
+Record core_ops_index_Index (Self Idx : Type) := mk_core_ops_index_Index {
+  core_ops_index_Index_Output : Type;
+  core_ops_index_Index_index : Self -> Idx -> result core_ops_index_Index_Output;
+}.
+Arguments mk_core_ops_index_Index {_ _}.
+Arguments core_ops_index_Index_Output {_ _}.
+Arguments core_ops_index_Index_index {_ _}.
+
+(* Trait declaration: [core::ops::index::IndexMut] *)
+Record core_ops_index_IndexMut (Self Idx : Type) := mk_core_ops_index_IndexMut {
+  core_ops_index_IndexMut_indexInst : core_ops_index_Index Self Idx;
+  core_ops_index_IndexMut_index_mut : Self -> Idx -> result core_ops_index_IndexMut_indexInst.(core_ops_index_Index_Output);
+  core_ops_index_IndexMut_index_mut_back : Self -> Idx -> core_ops_index_IndexMut_indexInst.(core_ops_index_Index_Output) -> result Self;
+}.
+Arguments mk_core_ops_index_IndexMut {_ _}.
+Arguments core_ops_index_IndexMut_indexInst {_ _}.
+Arguments core_ops_index_IndexMut_index_mut {_ _}.
+Arguments core_ops_index_IndexMut_index_mut_back {_ _}.
+
+(* Trait declaration [core::ops::deref::Deref] *)
+Record core_ops_deref_Deref (Self : Type) := mk_core_ops_deref_Deref {
+  core_ops_deref_Deref_target : Type;
+  core_ops_deref_Deref_deref : Self -> result core_ops_deref_Deref_target;
+}.
+Arguments mk_core_ops_deref_Deref {_}.
+Arguments core_ops_deref_Deref_target {_}.
+Arguments core_ops_deref_Deref_deref {_}.
+
+(* Trait declaration [core::ops::deref::DerefMut] *)
+Record core_ops_deref_DerefMut (Self : Type) := mk_core_ops_deref_DerefMut {
+  core_ops_deref_DerefMut_derefInst : core_ops_deref_Deref Self;
+  core_ops_deref_DerefMut_deref_mut : Self -> result core_ops_deref_DerefMut_derefInst.(core_ops_deref_Deref_target);
+  core_ops_deref_DerefMut_deref_mut_back : Self -> core_ops_deref_DerefMut_derefInst.(core_ops_deref_Deref_target) -> result Self;
+}.
+Arguments mk_core_ops_deref_DerefMut {_}.
+Arguments core_ops_deref_DerefMut_derefInst {_}.
+Arguments core_ops_deref_DerefMut_deref_mut {_}.
+Arguments core_ops_deref_DerefMut_deref_mut_back {_}.
+
+Record core_ops_range_Range (T : Type) := mk_core_ops_range_Range {
+  core_ops_range_Range_start : T;
+  core_ops_range_Range_end_ : T;
+}.
+Arguments mk_core_ops_range_Range {_}.
+Arguments core_ops_range_Range_start {_}.
+Arguments core_ops_range_Range_end_ {_}.
+
+(*** [alloc] *)
+
+Definition alloc_boxed_Box_deref (T : Type) (x : T) : result T := Return x.
+Definition alloc_boxed_Box_deref_mut (T : Type) (x : T) : result T := Return x.
+Definition alloc_boxed_Box_deref_mut_back (T : Type) (_ : T) (x : T) : result T := Return x.
+
+(* Trait instance *)
+Definition alloc_boxed_Box_coreopsDerefInst (Self : Type) : core_ops_deref_Deref Self := {|
+  core_ops_deref_Deref_target := Self;
+  core_ops_deref_Deref_deref := alloc_boxed_Box_deref Self;
+|}.
+
+(* Trait instance *)
+Definition alloc_boxed_Box_coreopsDerefMutInst (Self : Type) : core_ops_deref_DerefMut Self := {|
+  core_ops_deref_DerefMut_derefInst := alloc_boxed_Box_coreopsDerefInst Self;
+  core_ops_deref_DerefMut_deref_mut := alloc_boxed_Box_deref_mut Self;
+  core_ops_deref_DerefMut_deref_mut_back := alloc_boxed_Box_deref_mut_back Self;
+|}.
+
+
+(*** Arrays *)
+Definition array T (n : usize) := { l: list T | Z.of_nat (length l) = to_Z n}.
+
+Lemma le_0_usize_max : 0 <= usize_max.
+Proof.
+  pose (H := usize_max_bound).
+  unfold u32_max in H.
+  lia.
+Qed.
+
+Lemma eqb_imp_eq (x y : Z) : Z.eqb x y = true -> x = y.
+Proof.
+  lia.
+Qed.
+
+(* TODO: finish the definitions *)
+Axiom mk_array : forall (T : Type) (n : usize) (l : list T), array T n.
+
+(* For initialization *)
+Axiom array_repeat : forall (T : Type) (n : usize) (x : T), array T n.
+
+Axiom array_index_usize : forall (T : Type) (n : usize) (x : array T n) (i : usize), result T.
+Axiom array_update_usize : forall (T : Type) (n : usize) (x : array T n) (i : usize) (nx : T), result (array T n).
+
+(*** Slice *)
+Definition slice T := { l: list T | Z.of_nat (length l) <= usize_max}.
+
+Axiom slice_len : forall (T : Type) (s : slice T), usize.
+Axiom slice_index_usize : forall (T : Type) (x : slice T) (i : usize), result T.
+Axiom slice_update_usize : forall (T : Type) (x : slice T) (i : usize) (nx : T), result (slice T).
+
+(*** Subslices *)
+
+Axiom array_to_slice : forall (T : Type) (n : usize) (x : array T n), result (slice T).
+Axiom array_from_slice : forall (T : Type) (n : usize) (x : array T n) (s : slice T), result (array T n).
+
+Axiom array_subslice: forall (T : Type) (n : usize) (x : array T n) (r : core_ops_range_Range usize), result (slice T).
+Axiom array_update_subslice: forall (T : Type) (n : usize) (x : array T n) (r : core_ops_range_Range usize) (ns : slice T), result (array T n).
+
+Axiom slice_subslice: forall (T : Type) (x : slice T) (r : core_ops_range_Range usize), result (slice T).
+Axiom slice_update_subslice: forall (T : Type) (x : slice T) (r : core_ops_range_Range usize) (ns : slice T), result (slice T).
+
+(*** Vectors *)
+
+Definition alloc_vec_Vec T := { l: list T | Z.of_nat (length l) <= usize_max }.
+
+Definition alloc_vec_Vec_to_list {T: Type} (v: alloc_vec_Vec T) : list T := proj1_sig v.
+
+Definition alloc_vec_Vec_length {T: Type} (v: alloc_vec_Vec T) : Z := Z.of_nat (length (alloc_vec_Vec_to_list v)).
+
+Definition alloc_vec_Vec_new (T: Type) : alloc_vec_Vec T := (exist _ [] le_0_usize_max).
+
+Lemma alloc_vec_Vec_len_in_usize {T} (v: alloc_vec_Vec T) : usize_min <= alloc_vec_Vec_length v <= usize_max.
+Proof.
+  unfold alloc_vec_Vec_length, usize_min.
+  split.
+  - lia.
+  - apply (proj2_sig v).
+Qed.
+
+Definition alloc_vec_Vec_len (T: Type) (v: alloc_vec_Vec T) : usize :=
+  exist _ (alloc_vec_Vec_length v) (alloc_vec_Vec_len_in_usize v).
+
+Fixpoint list_update {A} (l: list A) (n: nat) (a: A)
+  : list A :=
+  match l with
+  | []     => []
+  | x :: t => match n with
+    | 0%nat => a :: t
+    | S m => x :: (list_update t m a)
+end end.
+
+Definition alloc_vec_Vec_bind {A B} (v: alloc_vec_Vec A) (f: list A -> result (list B)) : result (alloc_vec_Vec B) :=
+  l <- f (alloc_vec_Vec_to_list v) ;
+  match sumbool_of_bool (scalar_le_max Usize (Z.of_nat (length l))) with
+  | left H => Return (exist _ l (scalar_le_max_valid _ _ H))
+  | right _ => Fail_ Failure
+  end.
+
+(* The **forward** function shouldn't be used *)
+Definition alloc_vec_Vec_push_fwd (T: Type) (v: alloc_vec_Vec T) (x: T) : unit := tt.
+
+Definition alloc_vec_Vec_push (T: Type) (v: alloc_vec_Vec T) (x: T) : result (alloc_vec_Vec T) :=
+  alloc_vec_Vec_bind v (fun l => Return (l ++ [x])).
+
+(* The **forward** function shouldn't be used *)
+Definition alloc_vec_Vec_insert_fwd (T: Type) (v: alloc_vec_Vec T) (i: usize) (x: T) : result unit :=
+  if to_Z i <? alloc_vec_Vec_length v then Return tt else Fail_ Failure.
+
+Definition alloc_vec_Vec_insert (T: Type) (v: alloc_vec_Vec T) (i: usize) (x: T) : result (alloc_vec_Vec T) :=
+  alloc_vec_Vec_bind v (fun l =>
+    if to_Z i <? Z.of_nat (length l)
+    then Return (list_update l (usize_to_nat i) x)
+    else Fail_ Failure).
+
+(* Helper *)
+Axiom alloc_vec_Vec_index_usize : forall {T : Type} (v : alloc_vec_Vec T) (i : usize), result T.
+
+(* Helper *)
+Axiom alloc_vec_Vec_update_usize : forall {T : Type} (v : alloc_vec_Vec T) (i : usize) (x : T), result (alloc_vec_Vec T).
+
+(* Trait declaration: [core::slice::index::private_slice_index::Sealed] *)
+Definition core_slice_index_private_slice_index_Sealed (self : Type) := unit.
+
+(* Trait declaration: [core::slice::index::SliceIndex] *)
+Record core_slice_index_SliceIndex (Self T : Type) := mk_core_slice_index_SliceIndex {
+  core_slice_index_SliceIndex_sealedInst : core_slice_index_private_slice_index_Sealed Self;
+  core_slice_index_SliceIndex_Output : Type;
+  core_slice_index_SliceIndex_get : Self -> T -> result (option core_slice_index_SliceIndex_Output);
+  core_slice_index_SliceIndex_get_mut : Self -> T -> result (option core_slice_index_SliceIndex_Output);
+  core_slice_index_SliceIndex_get_mut_back : Self -> T -> option core_slice_index_SliceIndex_Output -> result T;
+  core_slice_index_SliceIndex_get_unchecked : Self -> const_raw_ptr T -> result (const_raw_ptr core_slice_index_SliceIndex_Output);
+  core_slice_index_SliceIndex_get_unchecked_mut : Self -> mut_raw_ptr T -> result (mut_raw_ptr core_slice_index_SliceIndex_Output);
+  core_slice_index_SliceIndex_index : Self -> T -> result core_slice_index_SliceIndex_Output;
+  core_slice_index_SliceIndex_index_mut : Self -> T -> result core_slice_index_SliceIndex_Output;
+  core_slice_index_SliceIndex_index_mut_back : Self -> T -> core_slice_index_SliceIndex_Output -> result T;
+}.
+Arguments mk_core_slice_index_SliceIndex {_ _}.
+Arguments core_slice_index_SliceIndex_sealedInst {_ _}.
+Arguments core_slice_index_SliceIndex_Output {_ _}.
+Arguments core_slice_index_SliceIndex_get {_ _}.
+Arguments core_slice_index_SliceIndex_get_mut {_ _}.
+Arguments core_slice_index_SliceIndex_get_mut_back {_ _}.
+Arguments core_slice_index_SliceIndex_get_unchecked {_ _}.
+Arguments core_slice_index_SliceIndex_get_unchecked_mut {_ _}.
+Arguments core_slice_index_SliceIndex_index {_ _}.
+Arguments core_slice_index_SliceIndex_index_mut {_ _}.
+Arguments core_slice_index_SliceIndex_index_mut_back {_ _}.
+
+(* [core::slice::index::[T]::index]: forward function *)
+Definition core_slice_index_Slice_index
+  (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T))
+  (s : slice T) (i : Idx) : result inst.(core_slice_index_SliceIndex_Output) :=
+  x <- inst.(core_slice_index_SliceIndex_get) i s;
+  match x with
+  | None => Fail_ Failure
+  | Some x => Return x
+  end.
+
+(* [core::slice::index::Range:::get]: forward function *)
+Axiom core_slice_index_RangeUsize_get : forall (T : Type) (i : core_ops_range_Range usize) (s : slice T), result (option (slice T)).
+
+(* [core::slice::index::Range::get_mut]: forward function *)
+Axiom core_slice_index_RangeUsize_get_mut :
+  forall (T : Type), core_ops_range_Range usize -> slice T -> result (option (slice T)).
+
+(* [core::slice::index::Range::get_mut]: backward function 0 *)
+Axiom core_slice_index_RangeUsize_get_mut_back :
+  forall (T : Type), core_ops_range_Range usize -> slice T -> option (slice T) -> result (slice T).
+
+(* [core::slice::index::Range::get_unchecked]: forward function *)
+Definition core_slice_index_RangeUsize_get_unchecked
+  (T : Type) :
+  core_ops_range_Range usize -> const_raw_ptr (slice T) -> result (const_raw_ptr (slice T)) :=
+  (* Don't know what the model should be - for now we always fail to make
+     sure code which uses it fails *)
+  fun _ _ => Fail_ Failure.
+
+(* [core::slice::index::Range::get_unchecked_mut]: forward function *)
+Definition core_slice_index_RangeUsize_get_unchecked_mut
+  (T : Type) :
+  core_ops_range_Range usize -> mut_raw_ptr (slice T) -> result (mut_raw_ptr (slice T)) :=
+  (* Don't know what the model should be - for now we always fail to make
+    sure code which uses it fails *)
+  fun _ _ => Fail_ Failure.
+
+(* [core::slice::index::Range::index]: forward function *)
+Axiom core_slice_index_RangeUsize_index :
+  forall (T : Type), core_ops_range_Range usize -> slice T -> result (slice T).
+
+(* [core::slice::index::Range::index_mut]: forward function *)
+Axiom core_slice_index_RangeUsize_index_mut :
+  forall (T : Type), core_ops_range_Range usize -> slice T -> result (slice T).
+
+(* [core::slice::index::Range::index_mut]: backward function 0 *)
+Axiom core_slice_index_RangeUsize_index_mut_back :
+  forall (T : Type), core_ops_range_Range usize -> slice T -> slice T -> result (slice T).
+
+(* [core::slice::index::[T]::index_mut]: forward function *)
+Axiom core_slice_index_Slice_index_mut :
+  forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T)),
+  slice T -> Idx -> result inst.(core_slice_index_SliceIndex_Output).
+
+(* [core::slice::index::[T]::index_mut]: backward function 0 *)
+Axiom core_slice_index_Slice_index_mut_back :
+  forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T)),
+  slice T -> Idx -> inst.(core_slice_index_SliceIndex_Output) -> result (slice T).
+
+(* [core::array::[T; N]::index]: forward function *)
+Axiom core_array_Array_index :
+  forall (T Idx : Type) (N : usize) (inst : core_ops_index_Index (slice T) Idx)
+  (a : array T N) (i : Idx), result inst.(core_ops_index_Index_Output).
+
+(* [core::array::[T; N]::index_mut]: forward function *)
+Axiom core_array_Array_index_mut :
+  forall (T Idx : Type) (N : usize) (inst : core_ops_index_IndexMut (slice T) Idx)
+  (a : array T N) (i : Idx), result inst.(core_ops_index_IndexMut_indexInst).(core_ops_index_Index_Output).
+
+(* [core::array::[T; N]::index_mut]: backward function 0 *)
+Axiom core_array_Array_index_mut_back :
+  forall (T Idx : Type) (N : usize) (inst : core_ops_index_IndexMut (slice T) Idx)
+  (a : array T N) (i : Idx) (x : inst.(core_ops_index_IndexMut_indexInst).(core_ops_index_Index_Output)), result (array T N).
+
+(* Trait implementation: [core::slice::index::private_slice_index::Range] *)
+Definition core_slice_index_private_slice_index_SealedRangeUsizeInst
+  : core_slice_index_private_slice_index_Sealed (core_ops_range_Range usize) := tt.
+
+(* Trait implementation: [core::slice::index::Range] *)
+Definition core_slice_index_SliceIndexRangeUsizeSliceTInst (T : Type) :
+  core_slice_index_SliceIndex (core_ops_range_Range usize) (slice T) := {|
+  core_slice_index_SliceIndex_sealedInst := core_slice_index_private_slice_index_SealedRangeUsizeInst;
+  core_slice_index_SliceIndex_Output := slice T;
+  core_slice_index_SliceIndex_get := core_slice_index_RangeUsize_get T;
+  core_slice_index_SliceIndex_get_mut := core_slice_index_RangeUsize_get_mut T;
+  core_slice_index_SliceIndex_get_mut_back := core_slice_index_RangeUsize_get_mut_back T;
+  core_slice_index_SliceIndex_get_unchecked := core_slice_index_RangeUsize_get_unchecked T;
+  core_slice_index_SliceIndex_get_unchecked_mut := core_slice_index_RangeUsize_get_unchecked_mut T;
+  core_slice_index_SliceIndex_index := core_slice_index_RangeUsize_index T;
+  core_slice_index_SliceIndex_index_mut := core_slice_index_RangeUsize_index_mut T;
+  core_slice_index_SliceIndex_index_mut_back := core_slice_index_RangeUsize_index_mut_back T;
+|}.
+
+(* Trait implementation: [core::slice::index::[T]] *)
+Definition core_ops_index_IndexSliceTIInst (T Idx : Type)
+  (inst : core_slice_index_SliceIndex Idx (slice T)) :
+  core_ops_index_Index (slice T) Idx := {|
+  core_ops_index_Index_Output := inst.(core_slice_index_SliceIndex_Output);
+  core_ops_index_Index_index := core_slice_index_Slice_index T Idx inst;
+|}.
+
+(* Trait implementation: [core::slice::index::[T]] *)
+Definition core_ops_index_IndexMutSliceTIInst (T Idx : Type)
+  (inst : core_slice_index_SliceIndex Idx (slice T)) :
+  core_ops_index_IndexMut (slice T) Idx := {|
+  core_ops_index_IndexMut_indexInst := core_ops_index_IndexSliceTIInst T Idx inst;
+  core_ops_index_IndexMut_index_mut := core_slice_index_Slice_index_mut T Idx inst;
+  core_ops_index_IndexMut_index_mut_back := core_slice_index_Slice_index_mut_back T Idx inst;
+|}.
+
+(* Trait implementation: [core::array::[T; N]] *)
+Definition core_ops_index_IndexArrayInst (T Idx : Type) (N : usize)
+  (inst : core_ops_index_Index (slice T) Idx) :
+  core_ops_index_Index (array T N) Idx := {|
+  core_ops_index_Index_Output := inst.(core_ops_index_Index_Output);
+  core_ops_index_Index_index := core_array_Array_index T Idx N inst;
+|}.
+
+(* Trait implementation: [core::array::[T; N]] *)
+Definition core_ops_index_IndexMutArrayInst (T Idx : Type) (N : usize)
+  (inst : core_ops_index_IndexMut (slice T) Idx) :
+  core_ops_index_IndexMut (array T N) Idx := {|
+  core_ops_index_IndexMut_indexInst := core_ops_index_IndexArrayInst T Idx N inst.(core_ops_index_IndexMut_indexInst);
+  core_ops_index_IndexMut_index_mut := core_array_Array_index_mut T Idx N inst;
+  core_ops_index_IndexMut_index_mut_back := core_array_Array_index_mut_back T Idx N inst;
+|}.
+
+(* [core::slice::index::usize::get]: forward function *)
+Axiom core_slice_index_usize_get : forall (T : Type), usize -> slice T -> result (option T).
+
+(* [core::slice::index::usize::get_mut]: forward function *)
+Axiom core_slice_index_usize_get_mut : forall (T : Type), usize -> slice T -> result (option T).
+
+(* [core::slice::index::usize::get_mut]: backward function 0 *)
+Axiom core_slice_index_usize_get_mut_back :
+  forall (T : Type), usize -> slice T -> option T -> result (slice T).
+
+(* [core::slice::index::usize::get_unchecked]: forward function *)
+Axiom core_slice_index_usize_get_unchecked :
+  forall (T : Type), usize -> const_raw_ptr (slice T) -> result (const_raw_ptr T).
+
+(* [core::slice::index::usize::get_unchecked_mut]: forward function *)
+Axiom core_slice_index_usize_get_unchecked_mut :
+  forall (T : Type), usize -> mut_raw_ptr (slice T) -> result (mut_raw_ptr T).
+
+(* [core::slice::index::usize::index]: forward function *)
+Axiom core_slice_index_usize_index : forall (T : Type), usize -> slice T -> result T.
+
+(* [core::slice::index::usize::index_mut]: forward function *)
+Axiom core_slice_index_usize_index_mut : forall (T : Type), usize -> slice T -> result T.
+
+(* [core::slice::index::usize::index_mut]: backward function 0 *)
+Axiom core_slice_index_usize_index_mut_back :
+  forall (T : Type), usize -> slice T -> T -> result (slice T).
+
+(* Trait implementation: [core::slice::index::private_slice_index::usize] *)
+Definition core_slice_index_private_slice_index_SealedUsizeInst
+  : core_slice_index_private_slice_index_Sealed usize := tt.
+
+(* Trait implementation: [core::slice::index::usize] *)
+Definition core_slice_index_SliceIndexUsizeSliceTInst (T : Type) :
+  core_slice_index_SliceIndex usize (slice T) := {|
+  core_slice_index_SliceIndex_sealedInst := core_slice_index_private_slice_index_SealedUsizeInst;
+  core_slice_index_SliceIndex_Output := T;
+  core_slice_index_SliceIndex_get := core_slice_index_usize_get T;
+  core_slice_index_SliceIndex_get_mut := core_slice_index_usize_get_mut T;
+  core_slice_index_SliceIndex_get_mut_back := core_slice_index_usize_get_mut_back T;
+  core_slice_index_SliceIndex_get_unchecked := core_slice_index_usize_get_unchecked T;
+  core_slice_index_SliceIndex_get_unchecked_mut := core_slice_index_usize_get_unchecked_mut T;
+  core_slice_index_SliceIndex_index := core_slice_index_usize_index T;
+  core_slice_index_SliceIndex_index_mut := core_slice_index_usize_index_mut T;
+  core_slice_index_SliceIndex_index_mut_back := core_slice_index_usize_index_mut_back T;
+|}.
+
+(* [alloc::vec::Vec::index]: forward function *)
+Axiom alloc_vec_Vec_index : forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T))
+  (Self : alloc_vec_Vec T) (i : Idx), result inst.(core_slice_index_SliceIndex_Output).
+
+(* [alloc::vec::Vec::index_mut]: forward function *)
+Axiom alloc_vec_Vec_index_mut : forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T))
+  (Self : alloc_vec_Vec T) (i : Idx), result inst.(core_slice_index_SliceIndex_Output).
+
+(* [alloc::vec::Vec::index_mut]: backward function 0 *)
+Axiom alloc_vec_Vec_index_mut_back :
+  forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T))
+  (Self : alloc_vec_Vec T) (i : Idx) (x : inst.(core_slice_index_SliceIndex_Output)), result (alloc_vec_Vec T).
+
+(* Trait implementation: [alloc::vec::Vec] *)
+Definition alloc_vec_Vec_coreopsindexIndexInst (T Idx : Type)
+  (inst : core_slice_index_SliceIndex Idx (slice T)) :
+  core_ops_index_Index (alloc_vec_Vec T) Idx := {|
+  core_ops_index_Index_Output := inst.(core_slice_index_SliceIndex_Output);
+  core_ops_index_Index_index := alloc_vec_Vec_index T Idx inst;
+|}.
+
+(* Trait implementation: [alloc::vec::Vec] *)
+Definition alloc_vec_Vec_coreopsindexIndexMutInst (T Idx : Type)
+  (inst : core_slice_index_SliceIndex Idx (slice T)) :
+  core_ops_index_IndexMut (alloc_vec_Vec T) Idx := {|
+  core_ops_index_IndexMut_indexInst := alloc_vec_Vec_coreopsindexIndexInst T Idx inst;
+  core_ops_index_IndexMut_index_mut := alloc_vec_Vec_index_mut T Idx inst;
+  core_ops_index_IndexMut_index_mut_back := alloc_vec_Vec_index_mut_back T Idx inst;
+|}.
+
+(*** Theorems *)
+
+Axiom alloc_vec_Vec_index_eq : forall {a : Type} (v : alloc_vec_Vec a) (i : usize) (x : a),
+  alloc_vec_Vec_index a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i =
+    alloc_vec_Vec_index_usize v i.
+
+Axiom alloc_vec_Vec_index_mut_eq : forall {a : Type} (v : alloc_vec_Vec a) (i : usize) (x : a),
+  alloc_vec_Vec_index_mut a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i =
+    alloc_vec_Vec_index_usize v i.
+
+Axiom alloc_vec_Vec_index_mut_back_eq : forall {a : Type} (v : alloc_vec_Vec a) (i : usize) (x : a),
+  alloc_vec_Vec_index_mut_back a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i x =
+    alloc_vec_Vec_update_usize v i x.
+
+End Primitives.
diff --git a/tests/coq/traits/Traits.v b/tests/coq/traits/Traits.v
new file mode 100644
index 00000000..549a7116
--- /dev/null
+++ b/tests/coq/traits/Traits.v
@@ -0,0 +1,609 @@
+(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
+(** [traits] *)
+Require Import Primitives.
+Import Primitives.
+Require Import Coq.ZArith.ZArith.
+Require Import List.
+Import ListNotations.
+Local Open Scope Primitives_scope.
+Module Traits.
+
+(** Trait declaration: [traits::BoolTrait]
+    Source: 'src/traits.rs', lines 1:0-1:19 *)
+Record BoolTrait_t (Self : Type) := mkBoolTrait_t {
+  BoolTrait_t_get_bool : Self -> result bool;
+}.
+
+Arguments mkBoolTrait_t { _ }.
+Arguments BoolTrait_t_get_bool { _ }.
+
+(** [traits::{bool}::get_bool]: forward function
+    Source: 'src/traits.rs', lines 12:4-12:30 *)
+Definition bool_get_bool (self : bool) : result bool :=
+  Return self.
+
+(** Trait implementation: [traits::{bool}]
+    Source: 'src/traits.rs', lines 11:0-11:23 *)
+Definition traits_BoolTraitBoolInst : BoolTrait_t bool := {|
+  BoolTrait_t_get_bool := bool_get_bool;
+|}.
+
+(** [traits::BoolTrait::ret_true]: forward function
+    Source: 'src/traits.rs', lines 6:4-6:30 *)
+Definition boolTrait_ret_true
+  {Self : Type} (self_clause : BoolTrait_t Self) (self : Self) : result bool :=
+  Return true
+.
+
+(** [traits::test_bool_trait_bool]: forward function
+    Source: 'src/traits.rs', lines 17:0-17:44 *)
+Definition test_bool_trait_bool (x : bool) : result bool :=
+  b <- bool_get_bool x;
+  if b then boolTrait_ret_true traits_BoolTraitBoolInst x else Return false
+.
+
+(** [traits::{core::option::Option<T>#1}::get_bool]: forward function
+    Source: 'src/traits.rs', lines 23:4-23:30 *)
+Definition option_get_bool (T : Type) (self : option T) : result bool :=
+  match self with | None => Return false | Some t => Return true end
+.
+
+(** Trait implementation: [traits::{core::option::Option<T>#1}]
+    Source: 'src/traits.rs', lines 22:0-22:31 *)
+Definition traits_BoolTraitcoreoptionOptionTInst (T : Type) : BoolTrait_t
+  (option T) := {|
+  BoolTrait_t_get_bool := option_get_bool T;
+|}.
+
+(** [traits::test_bool_trait_option]: forward function
+    Source: 'src/traits.rs', lines 31:0-31:54 *)
+Definition test_bool_trait_option (T : Type) (x : option T) : result bool :=
+  b <- option_get_bool T x;
+  if b
+  then boolTrait_ret_true (traits_BoolTraitcoreoptionOptionTInst T) x
+  else Return false
+.
+
+(** [traits::test_bool_trait]: forward function
+    Source: 'src/traits.rs', lines 35:0-35:50 *)
+Definition test_bool_trait
+  (T : Type) (boolTraitTInst : BoolTrait_t T) (x : T) : result bool :=
+  boolTraitTInst.(BoolTrait_t_get_bool) x
+.
+
+(** Trait declaration: [traits::ToU64]
+    Source: 'src/traits.rs', lines 39:0-39:15 *)
+Record ToU64_t (Self : Type) := mkToU64_t {
+  ToU64_t_to_u64 : Self -> result u64;
+}.
+
+Arguments mkToU64_t { _ }.
+Arguments ToU64_t_to_u64 { _ }.
+
+(** [traits::{u64#2}::to_u64]: forward function
+    Source: 'src/traits.rs', lines 44:4-44:26 *)
+Definition u64_to_u64 (self : u64) : result u64 :=
+  Return self.
+
+(** Trait implementation: [traits::{u64#2}]
+    Source: 'src/traits.rs', lines 43:0-43:18 *)
+Definition traits_ToU64U64Inst : ToU64_t u64 := {|
+  ToU64_t_to_u64 := u64_to_u64;
+|}.
+
+(** [traits::{(A, A)#3}::to_u64]: forward function
+    Source: 'src/traits.rs', lines 50:4-50:26 *)
+Definition pair_to_u64
+  (A : Type) (toU64AInst : ToU64_t A) (self : (A * A)) : result u64 :=
+  let (t, t0) := self in
+  i <- toU64AInst.(ToU64_t_to_u64) t;
+  i0 <- toU64AInst.(ToU64_t_to_u64) t0;
+  u64_add i i0
+.
+
+(** Trait implementation: [traits::{(A, A)#3}]
+    Source: 'src/traits.rs', lines 49:0-49:31 *)
+Definition traits_ToU64TupleAAInst (A : Type) (toU64AInst : ToU64_t A) :
+  ToU64_t (A * A) := {|
+  ToU64_t_to_u64 := pair_to_u64 A toU64AInst;
+|}.
+
+(** [traits::f]: forward function
+    Source: 'src/traits.rs', lines 55:0-55:36 *)
+Definition f (T : Type) (toU64TInst : ToU64_t T) (x : (T * T)) : result u64 :=
+  pair_to_u64 T toU64TInst x
+.
+
+(** [traits::g]: forward function
+    Source: 'src/traits.rs', lines 59:0-61:18 *)
+Definition g
+  (T : Type) (toU64TupleTTInst : ToU64_t (T * T)) (x : (T * T)) : result u64 :=
+  toU64TupleTTInst.(ToU64_t_to_u64) x
+.
+
+(** [traits::h0]: forward function
+    Source: 'src/traits.rs', lines 66:0-66:24 *)
+Definition h0 (x : u64) : result u64 :=
+  u64_to_u64 x.
+
+(** [traits::Wrapper]
+    Source: 'src/traits.rs', lines 70:0-70:21 *)
+Record Wrapper_t (T : Type) := mkWrapper_t { wrapper_x : T; }.
+
+Arguments mkWrapper_t { _ }.
+Arguments wrapper_x { _ }.
+
+(** [traits::{traits::Wrapper<T>#4}::to_u64]: forward function
+    Source: 'src/traits.rs', lines 75:4-75:26 *)
+Definition wrapper_to_u64
+  (T : Type) (toU64TInst : ToU64_t T) (self : Wrapper_t T) : result u64 :=
+  toU64TInst.(ToU64_t_to_u64) self.(wrapper_x)
+.
+
+(** Trait implementation: [traits::{traits::Wrapper<T>#4}]
+    Source: 'src/traits.rs', lines 74:0-74:35 *)
+Definition traits_ToU64traitsWrapperTInst (T : Type) (toU64TInst : ToU64_t T) :
+  ToU64_t (Wrapper_t T) := {|
+  ToU64_t_to_u64 := wrapper_to_u64 T toU64TInst;
+|}.
+
+(** [traits::h1]: forward function
+    Source: 'src/traits.rs', lines 80:0-80:33 *)
+Definition h1 (x : Wrapper_t u64) : result u64 :=
+  wrapper_to_u64 u64 traits_ToU64U64Inst x
+.
+
+(** [traits::h2]: forward function
+    Source: 'src/traits.rs', lines 84:0-84:41 *)
+Definition h2
+  (T : Type) (toU64TInst : ToU64_t T) (x : Wrapper_t T) : result u64 :=
+  wrapper_to_u64 T toU64TInst x
+.
+
+(** Trait declaration: [traits::ToType]
+    Source: 'src/traits.rs', lines 88:0-88:19 *)
+Record ToType_t (Self T : Type) := mkToType_t {
+  ToType_t_to_type : Self -> result T;
+}.
+
+Arguments mkToType_t { _ _ }.
+Arguments ToType_t_to_type { _ _ }.
+
+(** [traits::{u64#5}::to_type]: forward function
+    Source: 'src/traits.rs', lines 93:4-93:28 *)
+Definition u64_to_type (self : u64) : result bool :=
+  Return (self s> 0%u64).
+
+(** Trait implementation: [traits::{u64#5}]
+    Source: 'src/traits.rs', lines 92:0-92:25 *)
+Definition traits_ToTypeU64BoolInst : ToType_t u64 bool := {|
+  ToType_t_to_type := u64_to_type;
+|}.
+
+(** Trait declaration: [traits::OfType]
+    Source: 'src/traits.rs', lines 98:0-98:16 *)
+Record OfType_t (Self : Type) := mkOfType_t {
+  OfType_t_of_type : forall (T : Type) (toTypeTSelfInst : ToType_t T Self), T
+    -> result Self;
+}.
+
+Arguments mkOfType_t { _ }.
+Arguments OfType_t_of_type { _ }.
+
+(** [traits::h3]: forward function
+    Source: 'src/traits.rs', lines 104:0-104:50 *)
+Definition h3
+  (T1 T2 : Type) (ofTypeT1Inst : OfType_t T1) (toTypeT2T1Inst : ToType_t T2 T1)
+  (y : T2) :
+  result T1
+  :=
+  ofTypeT1Inst.(OfType_t_of_type) T2 toTypeT2T1Inst y
+.
+
+(** Trait declaration: [traits::OfTypeBis]
+    Source: 'src/traits.rs', lines 109:0-109:36 *)
+Record OfTypeBis_t (Self T : Type) := mkOfTypeBis_t {
+  OfTypeBis_tOfTypeBis_t_ToTypeTSelfInst : ToType_t T Self;
+  OfTypeBis_t_of_type : T -> result Self;
+}.
+
+Arguments mkOfTypeBis_t { _ _ }.
+Arguments OfTypeBis_tOfTypeBis_t_ToTypeTSelfInst { _ _ }.
+Arguments OfTypeBis_t_of_type { _ _ }.
+
+(** [traits::h4]: forward function
+    Source: 'src/traits.rs', lines 118:0-118:57 *)
+Definition h4
+  (T1 T2 : Type) (ofTypeBisT1T2Inst : OfTypeBis_t T1 T2) (toTypeT2T1Inst :
+  ToType_t T2 T1) (y : T2) :
+  result T1
+  :=
+  ofTypeBisT1T2Inst.(OfTypeBis_t_of_type) y
+.
+
+(** [traits::TestType]
+    Source: 'src/traits.rs', lines 122:0-122:22 *)
+Record TestType_t (T : Type) := mkTestType_t { testType_0 : T; }.
+
+Arguments mkTestType_t { _ }.
+Arguments testType_0 { _ }.
+
+(** [traits::{traits::TestType<T>#6}::test::TestType1]
+    Source: 'src/traits.rs', lines 127:8-127:24 *)
+Record TestType_test_TestType1_t :=
+mkTestType_test_TestType1_t {
+  testType_test_TestType1_0 : u64;
+}
+.
+
+(** Trait declaration: [traits::{traits::TestType<T>#6}::test::TestTrait]
+    Source: 'src/traits.rs', lines 128:8-128:23 *)
+Record TestType_test_TestTrait_t (Self : Type) := mkTestType_test_TestTrait_t {
+  TestType_test_TestTrait_t_test : Self -> result bool;
+}.
+
+Arguments mkTestType_test_TestTrait_t { _ }.
+Arguments TestType_test_TestTrait_t_test { _ }.
+
+(** [traits::{traits::TestType<T>#6}::test::{traits::{traits::TestType<T>#6}::test::TestType1}::test]: forward function
+    Source: 'src/traits.rs', lines 139:12-139:34 *)
+Definition testType_test_TestType1_test
+  (self : TestType_test_TestType1_t) : result bool :=
+  Return (self.(testType_test_TestType1_0) s> 1%u64)
+.
+
+(** Trait implementation: [traits::{traits::TestType<T>#6}::test::{traits::{traits::TestType<T>#6}::test::TestType1}]
+    Source: 'src/traits.rs', lines 138:8-138:36 *)
+Definition traits_TestType_test_TestTraittraitstraitsTestTypeTtestTestType1Inst
+  : TestType_test_TestTrait_t TestType_test_TestType1_t := {|
+  TestType_test_TestTrait_t_test := testType_test_TestType1_test;
+|}.
+
+(** [traits::{traits::TestType<T>#6}::test]: forward function
+    Source: 'src/traits.rs', lines 126:4-126:36 *)
+Definition testType_test
+  (T : Type) (toU64TInst : ToU64_t T) (self : TestType_t T) (x : T) :
+  result bool
+  :=
+  x0 <- toU64TInst.(ToU64_t_to_u64) x;
+  if x0 s> 0%u64
+  then testType_test_TestType1_test {| testType_test_TestType1_0 := 0%u64 |}
+  else Return false
+.
+
+(** [traits::BoolWrapper]
+    Source: 'src/traits.rs', lines 150:0-150:22 *)
+Record BoolWrapper_t := mkBoolWrapper_t { boolWrapper_0 : bool; }.
+
+(** [traits::{traits::BoolWrapper#7}::to_type]: forward function
+    Source: 'src/traits.rs', lines 156:4-156:25 *)
+Definition boolWrapper_to_type
+  (T : Type) (toTypeBoolTInst : ToType_t bool T) (self : BoolWrapper_t) :
+  result T
+  :=
+  toTypeBoolTInst.(ToType_t_to_type) self.(boolWrapper_0)
+.
+
+(** Trait implementation: [traits::{traits::BoolWrapper#7}]
+    Source: 'src/traits.rs', lines 152:0-152:33 *)
+Definition traits_ToTypetraitsBoolWrapperTInst (T : Type) (toTypeBoolTInst :
+  ToType_t bool T) : ToType_t BoolWrapper_t T := {|
+  ToType_t_to_type := boolWrapper_to_type T toTypeBoolTInst;
+|}.
+
+(** [traits::WithConstTy::LEN2]
+    Source: 'src/traits.rs', lines 164:4-164:21 *)
+Definition with_const_ty_len2_body : result usize := Return 32%usize.
+Definition with_const_ty_len2_c : usize := with_const_ty_len2_body%global.
+
+(** Trait declaration: [traits::WithConstTy]
+    Source: 'src/traits.rs', lines 161:0-161:39 *)
+Record WithConstTy_t (Self : Type) (LEN : usize) := mkWithConstTy_t {
+  WithConstTy_tWithConstTy_t_LEN1 : usize;
+  WithConstTy_tWithConstTy_t_LEN2 : usize;
+  WithConstTy_tWithConstTy_t_V : Type;
+  WithConstTy_tWithConstTy_t_W : Type;
+  WithConstTy_tWithConstTy_t_W_clause_0 : ToU64_t WithConstTy_tWithConstTy_t_W;
+  WithConstTy_t_f : WithConstTy_tWithConstTy_t_W -> array u8 LEN -> result
+    WithConstTy_tWithConstTy_t_W;
+}.
+
+Arguments mkWithConstTy_t { _ _ }.
+Arguments WithConstTy_tWithConstTy_t_LEN1 { _ _ }.
+Arguments WithConstTy_tWithConstTy_t_LEN2 { _ _ }.
+Arguments WithConstTy_tWithConstTy_t_V { _ _ }.
+Arguments WithConstTy_tWithConstTy_t_W { _ _ }.
+Arguments WithConstTy_tWithConstTy_t_W_clause_0 { _ _ }.
+Arguments WithConstTy_t_f { _ _ }.
+
+(** [traits::{bool#8}::LEN1]
+    Source: 'src/traits.rs', lines 175:4-175:21 *)
+Definition bool_len1_body : result usize := Return 12%usize.
+Definition bool_len1_c : usize := bool_len1_body%global.
+
+(** [traits::{bool#8}::f]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ())
+    Source: 'src/traits.rs', lines 180:4-180:39 *)
+Definition bool_f (i : u64) (a : array u8 32%usize) : result u64 :=
+  Return i.
+
+(** Trait implementation: [traits::{bool#8}]
+    Source: 'src/traits.rs', lines 174:0-174:29 *)
+Definition traits_WithConstTyBool32Inst : WithConstTy_t bool 32%usize := {|
+  WithConstTy_tWithConstTy_t_LEN1 := bool_len1_c;
+  WithConstTy_tWithConstTy_t_LEN2 := with_const_ty_len2_c;
+  WithConstTy_tWithConstTy_t_V := u8;
+  WithConstTy_tWithConstTy_t_W := u64;
+  WithConstTy_tWithConstTy_t_W_clause_0 := traits_ToU64U64Inst;
+  WithConstTy_t_f := bool_f;
+|}.
+
+(** [traits::use_with_const_ty1]: forward function
+    Source: 'src/traits.rs', lines 183:0-183:75 *)
+Definition use_with_const_ty1
+  (H : Type) (LEN : usize) (withConstTyHLENInst : WithConstTy_t H LEN) :
+  result usize
+  :=
+  let i := withConstTyHLENInst.(WithConstTy_tWithConstTy_t_LEN1) in Return i
+.
+
+(** [traits::use_with_const_ty2]: forward function
+    Source: 'src/traits.rs', lines 187:0-187:73 *)
+Definition use_with_const_ty2
+  (H : Type) (LEN : usize) (withConstTyHLENInst : WithConstTy_t H LEN)
+  (w : withConstTyHLENInst.(WithConstTy_tWithConstTy_t_W)) :
+  result unit
+  :=
+  Return tt
+.
+
+(** [traits::use_with_const_ty3]: forward function
+    Source: 'src/traits.rs', lines 189:0-189:80 *)
+Definition use_with_const_ty3
+  (H : Type) (LEN : usize) (withConstTyHLENInst : WithConstTy_t H LEN)
+  (x : withConstTyHLENInst.(WithConstTy_tWithConstTy_t_W)) :
+  result u64
+  :=
+  withConstTyHLENInst.(WithConstTy_tWithConstTy_t_W_clause_0).(ToU64_t_to_u64)
+    x
+.
+
+(** [traits::test_where1]: forward function
+    Source: 'src/traits.rs', lines 193:0-193:40 *)
+Definition test_where1 (T : Type) (_x : T) : result unit :=
+  Return tt.
+
+(** [traits::test_where2]: forward function
+    Source: 'src/traits.rs', lines 194:0-194:57 *)
+Definition test_where2
+  (T : Type) (withConstTyT32Inst : WithConstTy_t T 32%usize) (_x : u32) :
+  result unit
+  :=
+  Return tt
+.
+
+(** Trait declaration: [traits::ParentTrait0]
+    Source: 'src/traits.rs', lines 200:0-200:22 *)
+Record ParentTrait0_t (Self : Type) := mkParentTrait0_t {
+  ParentTrait0_tParentTrait0_t_W : Type;
+  ParentTrait0_t_get_name : Self -> result string;
+  ParentTrait0_t_get_w : Self -> result ParentTrait0_tParentTrait0_t_W;
+}.
+
+Arguments mkParentTrait0_t { _ }.
+Arguments ParentTrait0_tParentTrait0_t_W { _ }.
+Arguments ParentTrait0_t_get_name { _ }.
+Arguments ParentTrait0_t_get_w { _ }.
+
+(** Trait declaration: [traits::ParentTrait1]
+    Source: 'src/traits.rs', lines 205:0-205:22 *)
+Record ParentTrait1_t (Self : Type) := mkParentTrait1_t{}.
+
+Arguments mkParentTrait1_t { _ }.
+
+(** Trait declaration: [traits::ChildTrait]
+    Source: 'src/traits.rs', lines 206:0-206:49 *)
+Record ChildTrait_t (Self : Type) := mkChildTrait_t {
+  ChildTrait_tChildTrait_t_ParentTrait0SelfInst : ParentTrait0_t Self;
+  ChildTrait_tChildTrait_t_ParentTrait1SelfInst : ParentTrait1_t Self;
+}.
+
+Arguments mkChildTrait_t { _ }.
+Arguments ChildTrait_tChildTrait_t_ParentTrait0SelfInst { _ }.
+Arguments ChildTrait_tChildTrait_t_ParentTrait1SelfInst { _ }.
+
+(** [traits::test_child_trait1]: forward function
+    Source: 'src/traits.rs', lines 209:0-209:56 *)
+Definition test_child_trait1
+  (T : Type) (childTraitTInst : ChildTrait_t T) (x : T) : result string :=
+  childTraitTInst.(ChildTrait_tChildTrait_t_ParentTrait0SelfInst).(ParentTrait0_t_get_name)
+    x
+.
+
+(** [traits::test_child_trait2]: forward function
+    Source: 'src/traits.rs', lines 213:0-213:54 *)
+Definition test_child_trait2
+  (T : Type) (childTraitTInst : ChildTrait_t T) (x : T) :
+  result
+    childTraitTInst.(ChildTrait_tChildTrait_t_ParentTrait0SelfInst).(ParentTrait0_tParentTrait0_t_W)
+  :=
+  childTraitTInst.(ChildTrait_tChildTrait_t_ParentTrait0SelfInst).(ParentTrait0_t_get_w)
+    x
+.
+
+(** [traits::order1]: forward function
+    Source: 'src/traits.rs', lines 219:0-219:59 *)
+Definition order1
+  (T U : Type) (parentTrait0TInst : ParentTrait0_t T) (parentTrait0UInst :
+  ParentTrait0_t U) :
+  result unit
+  :=
+  Return tt
+.
+
+(** Trait declaration: [traits::ChildTrait1]
+    Source: 'src/traits.rs', lines 222:0-222:35 *)
+Record ChildTrait1_t (Self : Type) := mkChildTrait1_t {
+  ChildTrait1_tChildTrait1_t_ParentTrait1SelfInst : ParentTrait1_t Self;
+}.
+
+Arguments mkChildTrait1_t { _ }.
+Arguments ChildTrait1_tChildTrait1_t_ParentTrait1SelfInst { _ }.
+
+(** Trait implementation: [traits::{usize#9}]
+    Source: 'src/traits.rs', lines 224:0-224:27 *)
+Definition traits_ParentTrait1UsizeInst : ParentTrait1_t usize
+  := mkParentTrait1_t.
+
+(** Trait implementation: [traits::{usize#10}]
+    Source: 'src/traits.rs', lines 225:0-225:26 *)
+Definition traits_ChildTrait1UsizeInst : ChildTrait1_t usize := {|
+  ChildTrait1_tChildTrait1_t_ParentTrait1SelfInst :=
+    traits_ParentTrait1UsizeInst;
+|}.
+
+(** Trait declaration: [traits::Iterator]
+    Source: 'src/traits.rs', lines 229:0-229:18 *)
+Record Iterator_t (Self : Type) := mkIterator_t {
+  Iterator_tIterator_t_Item : Type;
+}.
+
+Arguments mkIterator_t { _ }.
+Arguments Iterator_tIterator_t_Item { _ }.
+
+(** Trait declaration: [traits::IntoIterator]
+    Source: 'src/traits.rs', lines 233:0-233:22 *)
+Record IntoIterator_t (Self : Type) := mkIntoIterator_t {
+  IntoIterator_tIntoIterator_t_Item : Type;
+  IntoIterator_tIntoIterator_t_IntoIter : Type;
+  IntoIterator_tIntoIterator_t_IntoIter_clause_0 : Iterator_t
+    IntoIterator_tIntoIterator_t_IntoIter;
+  IntoIterator_t_into_iter : Self -> result
+    IntoIterator_tIntoIterator_t_IntoIter;
+}.
+
+Arguments mkIntoIterator_t { _ }.
+Arguments IntoIterator_tIntoIterator_t_Item { _ }.
+Arguments IntoIterator_tIntoIterator_t_IntoIter { _ }.
+Arguments IntoIterator_tIntoIterator_t_IntoIter_clause_0 { _ }.
+Arguments IntoIterator_t_into_iter { _ }.
+
+(** Trait declaration: [traits::FromResidual]
+    Source: 'src/traits.rs', lines 250:0-250:21 *)
+Record FromResidual_t (Self T : Type) := mkFromResidual_t{}.
+
+Arguments mkFromResidual_t { _ _ }.
+
+(** Trait declaration: [traits::Try]
+    Source: 'src/traits.rs', lines 246:0-246:48 *)
+Record Try_t (Self : Type) := mkTry_t {
+  Try_tTry_t_Residual : Type;
+  Try_tTry_t_FromResidualSelftraitsTrySelfResidualInst : FromResidual_t Self
+    Try_tTry_t_Residual;
+}.
+
+Arguments mkTry_t { _ }.
+Arguments Try_tTry_t_Residual { _ }.
+Arguments Try_tTry_t_FromResidualSelftraitsTrySelfResidualInst { _ }.
+
+(** Trait declaration: [traits::WithTarget]
+    Source: 'src/traits.rs', lines 252:0-252:20 *)
+Record WithTarget_t (Self : Type) := mkWithTarget_t {
+  WithTarget_tWithTarget_t_Target : Type;
+}.
+
+Arguments mkWithTarget_t { _ }.
+Arguments WithTarget_tWithTarget_t_Target { _ }.
+
+(** Trait declaration: [traits::ParentTrait2]
+    Source: 'src/traits.rs', lines 256:0-256:22 *)
+Record ParentTrait2_t (Self : Type) := mkParentTrait2_t {
+  ParentTrait2_tParentTrait2_t_U : Type;
+  ParentTrait2_tParentTrait2_t_U_clause_0 : WithTarget_t
+    ParentTrait2_tParentTrait2_t_U;
+}.
+
+Arguments mkParentTrait2_t { _ }.
+Arguments ParentTrait2_tParentTrait2_t_U { _ }.
+Arguments ParentTrait2_tParentTrait2_t_U_clause_0 { _ }.
+
+(** Trait declaration: [traits::ChildTrait2]
+    Source: 'src/traits.rs', lines 260:0-260:35 *)
+Record ChildTrait2_t (Self : Type) := mkChildTrait2_t {
+  ChildTrait2_tChildTrait2_t_ParentTrait2SelfInst : ParentTrait2_t Self;
+  ChildTrait2_t_convert :
+    (ChildTrait2_tChildTrait2_t_ParentTrait2SelfInst).(ParentTrait2_tParentTrait2_t_U)
+    -> result
+    (ChildTrait2_tChildTrait2_t_ParentTrait2SelfInst).(ParentTrait2_tParentTrait2_t_U_clause_0).(WithTarget_tWithTarget_t_Target);
+}.
+
+Arguments mkChildTrait2_t { _ }.
+Arguments ChildTrait2_tChildTrait2_t_ParentTrait2SelfInst { _ }.
+Arguments ChildTrait2_t_convert { _ }.
+
+(** Trait implementation: [traits::{u32#11}]
+    Source: 'src/traits.rs', lines 264:0-264:23 *)
+Definition traits_WithTargetU32Inst : WithTarget_t u32 := {|
+  WithTarget_tWithTarget_t_Target := u32;
+|}.
+
+(** Trait implementation: [traits::{u32#12}]
+    Source: 'src/traits.rs', lines 268:0-268:25 *)
+Definition traits_ParentTrait2U32Inst : ParentTrait2_t u32 := {|
+  ParentTrait2_tParentTrait2_t_U := u32;
+  ParentTrait2_tParentTrait2_t_U_clause_0 := traits_WithTargetU32Inst;
+|}.
+
+(** [traits::{u32#13}::convert]: forward function
+    Source: 'src/traits.rs', lines 273:4-273:29 *)
+Definition u32_convert (x : u32) : result u32 :=
+  Return x.
+
+(** Trait implementation: [traits::{u32#13}]
+    Source: 'src/traits.rs', lines 272:0-272:24 *)
+Definition traits_ChildTrait2U32Inst : ChildTrait2_t u32 := {|
+  ChildTrait2_tChildTrait2_t_ParentTrait2SelfInst :=
+    traits_ParentTrait2U32Inst;
+  ChildTrait2_t_convert := u32_convert;
+|}.
+
+(** Trait declaration: [traits::CFnOnce]
+    Source: 'src/traits.rs', lines 286:0-286:23 *)
+Record CFnOnce_t (Self Args : Type) := mkCFnOnce_t {
+  CFnOnce_tCFnOnce_t_Output : Type;
+  CFnOnce_t_call_once : Self -> Args -> result CFnOnce_tCFnOnce_t_Output;
+}.
+
+Arguments mkCFnOnce_t { _ _ }.
+Arguments CFnOnce_tCFnOnce_t_Output { _ _ }.
+Arguments CFnOnce_t_call_once { _ _ }.
+
+(** Trait declaration: [traits::CFnMut]
+    Source: 'src/traits.rs', lines 292:0-292:37 *)
+Record CFnMut_t (Self Args : Type) := mkCFnMut_t {
+  CFnMut_tCFnMut_t_CFnOnceSelfArgsInst : CFnOnce_t Self Args;
+  CFnMut_t_call_mut : Self -> Args -> result
+    (CFnMut_tCFnMut_t_CFnOnceSelfArgsInst).(CFnOnce_tCFnOnce_t_Output);
+  CFnMut_t_call_mut_back : Self -> Args ->
+    (CFnMut_tCFnMut_t_CFnOnceSelfArgsInst).(CFnOnce_tCFnOnce_t_Output) ->
+    result Self;
+}.
+
+Arguments mkCFnMut_t { _ _ }.
+Arguments CFnMut_tCFnMut_t_CFnOnceSelfArgsInst { _ _ }.
+Arguments CFnMut_t_call_mut { _ _ }.
+Arguments CFnMut_t_call_mut_back { _ _ }.
+
+(** Trait declaration: [traits::CFn]
+    Source: 'src/traits.rs', lines 296:0-296:33 *)
+Record CFn_t (Self Args : Type) := mkCFn_t {
+  CFn_tCFn_t_CFnMutSelfArgsInst : CFnMut_t Self Args;
+  CFn_t_call_mut : Self -> Args -> result
+    (CFn_tCFn_t_CFnMutSelfArgsInst).(CFnMut_tCFnMut_t_CFnOnceSelfArgsInst).(CFnOnce_tCFnOnce_t_Output);
+}.
+
+Arguments mkCFn_t { _ _ }.
+Arguments CFn_tCFn_t_CFnMutSelfArgsInst { _ _ }.
+Arguments CFn_t_call_mut { _ _ }.
+
+End Traits.
diff --git a/tests/coq/traits/_CoqProject b/tests/coq/traits/_CoqProject
new file mode 100644
index 00000000..5b6199fc
--- /dev/null
+++ b/tests/coq/traits/_CoqProject
@@ -0,0 +1,7 @@
+# This file was automatically generated - see ../Makefile
+-R . Lib
+-arg -w
+-arg all
+
+Traits.v
+Primitives.v