Regenerate the Coq test files

3 files changed, 546 insertions, 265 deletions

diff --git a/tests/coq/array/Array_Funs.v b/tests/coq/array/Array_Funs.v
index 6ff3066a..9980a6e8 100644
--- a/tests/coq/array/Array_Funs.v
+++ b/tests/coq/array/Array_Funs.v
@@ -10,16 +10,21 @@ Require Export Array_Types.
 Import Array_Types.
 Module Array_Funs.
 
+(** [array::incr]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ()) *)
+Definition incr (x : u32) : result u32 :=
+  u32_add x 1%u32.
+
 (** [array::array_to_shared_slice_]: forward function *)
-Definition array_to_shared_slice__fwd
+Definition array_to_shared_slice_
   (T : Type) (s : array T 32%usize) : result (slice T) :=
-  array_to_slice_shared T 32%usize s
+  array_to_slice T 32%usize s
 .
 
 (** [array::array_to_mut_slice_]: forward function *)
-Definition array_to_mut_slice__fwd
+Definition array_to_mut_slice_
   (T : Type) (s : array T 32%usize) : result (slice T) :=
-  array_to_slice_mut_fwd T 32%usize s
+  array_to_slice T 32%usize s
 .
 
 (** [array::array_to_mut_slice_]: backward function 0 *)
@@ -27,58 +32,44 @@ 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_from_slice 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
+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 *)
-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
+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 *)
-Definition shared_slice_len_fwd (T : Type) (s : slice T) : result usize :=
+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 *)
-Definition index_array_shared_fwd
+Definition index_array_shared
   (T : Type) (s : array T 32%usize) (i : usize) : result T :=
-  array_index_shared T 32%usize s i
+  array_index_usize 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
+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 *)
-Definition index_array_copy_fwd (x : array u32 32%usize) : result u32 :=
-  array_index_shared u32 32%usize x 0%usize
+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 *)
-Definition index_mut_array_fwd
+Definition index_mut_array
   (T : Type) (s : array T 32%usize) (i : usize) : result T :=
-  array_index_mut_fwd T 32%usize s i
+  array_index_usize T 32%usize s i
 .
 
 (** [array::index_mut_array]: backward function 0 *)
@@ -86,298 +77,314 @@ 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_update_usize 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
+Definition index_slice (T : Type) (s : slice T) (i : usize) : result T :=
+  slice_index_usize 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
+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 *)
 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
+  slice_update_usize 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)
+Definition slice_subslice_shared_
+  (n : nat) (x : slice u32) (y : usize) (z : usize) : result (slice u32) :=
+  core_slice_index_Slice_index u32 (core_ops_range_Range usize)
+    (core_slice_index_Range_coresliceindexSliceIndexInst u32) x
+    {| core_ops_range_Range_start := y; core_ops_range_Range_end_ := 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)
+Definition slice_subslice_mut_
+  (n : nat) (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_Range_coresliceindexSliceIndexInst u32) x
+    {| core_ops_range_Range_start := y; core_ops_range_Range_end_ := z |}
 .
 
 (** [array::slice_subslice_mut_]: backward function 0 *)
 Definition slice_subslice_mut__back
-  (x : slice u32) (y : usize) (z : usize) (ret : slice u32) :
+  (n : nat) (x : slice u32) (y : usize) (z : usize) (ret : slice u32) :
   result (slice u32)
   :=
-  slice_subslice_mut_back u32 x (mk_range y z) ret
+  core_slice_index_Slice_index_mut_back u32 (core_ops_range_Range usize)
+    (core_slice_index_Range_coresliceindexSliceIndexInst u32) x
+    {| core_ops_range_Range_start := y; core_ops_range_Range_end_ := z |} ret
 .
 
 (** [array::array_to_slice_shared_]: forward function *)
-Definition array_to_slice_shared__fwd
+Definition array_to_slice_shared_
   (x : array u32 32%usize) : result (slice u32) :=
-  array_to_slice_shared u32 32%usize x
+  array_to_slice 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
+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 *)
 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_from_slice 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)
+Definition array_subslice_shared_
+  (n : nat) (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_slice_index_Slice_coreopsindexIndexInst u32 (core_ops_range_Range
+    usize) (core_slice_index_Range_coresliceindexSliceIndexInst u32)) x
+    {| core_ops_range_Range_start := y; core_ops_range_Range_end_ := 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)
+Definition array_subslice_mut_
+  (n : nat) (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_slice_index_Slice_coreopsindexIndexMutInst u32 (core_ops_range_Range
+    usize) (core_slice_index_Range_coresliceindexSliceIndexInst u32)) x
+    {| core_ops_range_Range_start := y; core_ops_range_Range_end_ := 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) :
+  (n : nat) (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
+  core_array_Array_index_mut_back u32 (core_ops_range_Range usize) 32%usize
+    (core_slice_index_Slice_coreopsindexIndexMutInst u32 (core_ops_range_Range
+    usize) (core_slice_index_Range_coresliceindexSliceIndexInst u32)) x
+    {| core_ops_range_Range_start := y; core_ops_range_Range_end_ := 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
+Definition index_slice_0 (T : Type) (s : slice T) : result T :=
+  slice_index_usize 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
+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 *)
-Definition index_index_array_fwd
+Definition index_index_array
   (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
+  a <- array_index_usize (array u32 32%usize) 32%usize s i;
+  array_index_usize u32 32%usize a j
 .
 
-(** [array::const_gen_ret]: forward function *)
-Definition const_gen_ret_fwd (N : usize) : result usize :=
-  Return N.
-
 (** [array::update_update_array]: forward function *)
-Definition update_update_array_fwd
+Definition update_update_array
   (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;
+  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 *)
-Definition array_local_deep_copy_fwd (x : array u32 32%usize) : result unit :=
+Definition array_local_deep_copy (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 :=
+Definition take_array (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 :=
+Definition take_array_borrow (a : array u32 2%usize) : result unit :=
   Return tt
 .
 
 (** [array::take_slice]: forward function *)
-Definition take_slice_fwd (s : slice u32) : result unit :=
+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 ()) *)
-Definition take_mut_slice_fwd_back (s : slice u32) : result (slice u32) :=
-  Return s
-.
+Definition take_mut_slice (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;
+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 *)
-Definition index_array_fwd (x : array u32 2%usize) : result u32 :=
-  array_index_shared u32 2%usize x 0%usize
+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 *)
-Definition index_array_borrow_fwd (x : array u32 2%usize) : result u32 :=
-  array_index_shared u32 2%usize x 0%usize
+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 *)
-Definition index_slice_u32_0_fwd (x : slice u32) : result u32 :=
-  slice_index_shared u32 x 0%usize
+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 *)
-Definition index_mut_slice_u32_0_fwd (x : slice u32) : result u32 :=
-  slice_index_shared u32 x 0%usize
+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 *)
 Definition index_mut_slice_u32_0_back (x : slice u32) : result (slice u32) :=
-  _ <- slice_index_shared u32 x 0%usize; Return x
+  _ <- slice_index_usize 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 ]);
+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_fwd (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
+  i2 <- index_array_borrow (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;
+  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_mut_fwd u32 2%usize (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
-  i6 <- index_mut_slice_u32_0_fwd s0;
+  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_to_slice_mut_back u32 2%usize (mk_array u32 2%usize [ 0%u32; 0%u32 ])
-      s1;
+  _ <- array_from_slice 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
+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 ()) *)
-Definition update_array_mut_borrow_fwd_back
+Definition update_array_mut_borrow
   (x : array u32 2%usize) : result (array u32 2%usize) :=
-  array_index_mut_back u32 2%usize x 0%usize 1%u32
+  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 ()) *)
-Definition update_mut_slice_fwd_back (x : slice u32) : result (slice u32) :=
-  slice_index_mut_back u32 x 0%usize 1%u32
+Definition update_mut_slice (x : slice u32) : result (slice u32) :=
+  slice_update_usize 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;
+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 *)
-Definition range_all_fwd : result unit :=
+Definition range_all (n : nat) : 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;
+    core_array_Array_index_mut u32 (core_ops_range_Range usize) 4%usize
+      (core_slice_index_Slice_coreopsindexIndexMutInst u32
+      (core_ops_range_Range usize)
+      (core_slice_index_Range_coresliceindexSliceIndexInst 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;
   _ <-
-    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;
+    core_array_Array_index_mut_back u32 (core_ops_range_Range usize) 4%usize
+      (core_slice_index_Slice_coreopsindexIndexMutInst u32
+      (core_ops_range_Range usize)
+      (core_slice_index_Range_coresliceindexSliceIndexInst 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 *)
-Definition deref_array_borrow_fwd (x : array u32 2%usize) : result u32 :=
-  array_index_shared u32 2%usize x 0%usize
+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 *)
-Definition deref_array_mut_borrow_fwd (x : array u32 2%usize) : result u32 :=
-  array_index_shared u32 2%usize x 0%usize
+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 *)
 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_index_usize 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 :=
+Definition take_array_t (a : array AB_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
+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 *)
-Fixpoint sum_loop_fwd
-  (n : nat) (s : slice u32) (sum : u32) (i : usize) : result u32 :=
+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_shared u32 s i;
-      sum0 <- u32_add sum i1;
+      i1 <- slice_index_usize u32 s i;
+      sum1 <- u32_add sum0 i1;
       i2 <- usize_add i 1%usize;
-      sum_loop_fwd n0 s sum0 i2)
-    else Return sum
+      sum_loop n0 s sum1 i2)
+    else Return sum0
   end
 .
 
 (** [array::sum]: forward function *)
-Definition sum_fwd (n : nat) (s : slice u32) : result u32 :=
-  sum_loop_fwd n s 0%u32 0%usize
+Definition sum (n : nat) (s : slice u32) : result u32 :=
+  sum_loop 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) :
+Fixpoint sum2_loop
+  (n : nat) (s : slice u32) (s2 : slice u32) (sum0 : u32) (i : usize) :
   result u32
   :=
   match n with
@@ -386,69 +393,64 @@ Fixpoint sum2_loop_fwd
     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;
+      i1 <- slice_index_usize u32 s i;
+      i2 <- slice_index_usize u32 s2 i;
       i3 <- u32_add i1 i2;
-      sum0 <- u32_add sum i3;
+      sum1 <- u32_add sum0 i3;
       i4 <- usize_add i 1%usize;
-      sum2_loop_fwd n0 s s2 sum0 i4)
-    else Return sum
+      sum2_loop n0 s s2 sum1 i4)
+    else Return sum0
   end
 .
 
 (** [array::sum2]: forward function *)
-Definition sum2_fwd (n : nat) (s : slice u32) (s2 : slice u32) : result u32 :=
+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_fwd n s s2 0%u32 0%usize
+  if negb (i s= i0) then Fail_ Failure else sum2_loop 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;
+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 *)
-Definition f1_fwd : result unit :=
+Definition f1 : result unit :=
   _ <-
-    array_index_mut_back u32 2%usize (mk_array u32 2%usize [ 1%u32; 2%u32 ])
+    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 *)
-Definition f2_fwd (i : u32) : result unit :=
+Definition f2 (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)
+Definition f4
+  (n : nat) (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_slice_index_Slice_coreopsindexIndexInst u32 (core_ops_range_Range
+    usize) (core_slice_index_Range_coresliceindexSliceIndexInst u32)) x
+    {| core_ops_range_Range_start := y; core_ops_range_Range_end_ := z |}
 .
 
 (** [array::f3]: forward function *)
-Definition f3_fwd (n : nat) : result u32 :=
+Definition f3 (n : nat) : result u32 :=
   i <-
-    array_index_shared u32 2%usize (mk_array u32 2%usize [ 1%u32; 2%u32 ])
+    array_index_usize 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
+  _ <- 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 n b 16%usize 18%usize;
+  sum2 n s s0
 .
 
 (** [array::SZ] *)
@@ -456,24 +458,18 @@ Definition sz_body : result usize := Return 32%usize.
 Definition sz_c : usize := sz_body%global.
 
 (** [array::f5]: forward function *)
-Definition f5_fwd (x : array u32 32%usize) : result u32 :=
-  array_index_shared u32 32%usize x 0%usize
+Definition f5 (x : array u32 32%usize) : result u32 :=
+  array_index_usize u32 32%usize x 0%usize
 .
 
 (** [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 ]);
+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_to_slice_mut_back u32 2%usize (mk_array u32 2%usize [ 0%u32; 0%u32 ])
-      s1;
+  _ <- 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_to_slice_mut_back u32 2%usize (mk_array u32 2%usize [ 0%u32; 0%u32 ])
-      s2;
+  _ <- array_from_slice u32 2%usize (mk_array u32 2%usize [ 0%u32; 0%u32 ]) s2;
   Return tt
 .
 
diff --git a/tests/coq/array/Array_Types.v b/tests/coq/array/Array_Types.v
index 7be6dc9b..a13d64e6 100644
--- a/tests/coq/array/Array_Types.v
+++ b/tests/coq/array/Array_Types.v
@@ -8,7 +8,7 @@ Import ListNotations.
 Local Open Scope Primitives_scope.
 Module Array_Types.
 
-(** [array::T] *)
-Inductive T_t := | TA : T_t | TB : T_t.
+(** [array::AB] *)
+Inductive AB_t := | AB_A : AB_t | AB_B : AB_t.
 
 End Array_Types .
diff --git a/tests/coq/array/Primitives.v b/tests/coq/array/Primitives.v
index 8d6c9c8d..85e38f01 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 *)
 
@@ -408,12 +410,75 @@ Definition core_i64_max   := i64_max %i64.
 Definition core_i128_max  := i64_max %i128.
 Axiom core_isize_max : isize. (** TODO *)
 
-(*** Range *)
-Record range (T : Type) := mk_range {
-  start: T;
-  end_: T;
+(*** 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_range {_}.
+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}.
@@ -433,51 +498,50 @@ 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: 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 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 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 :=
@@ -488,50 +552,271 @@ 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) (x : T), 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_Range_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_Range_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_Range_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_Range_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_Range_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_Range_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_Range_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_Range_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::[T]] *)
+Definition core_slice_index_Slice_coreopsindexIndexInst (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::private_slice_index::Range] *)
+Definition core_slice_index_private_slice_index_Range_coresliceindexprivate_slice_indexSealedInst
+  : core_slice_index_private_slice_index_Sealed (core_ops_range_Range usize) := tt.
+
+(* Trait implementation: [core::slice::index::Range] *)
+Definition core_slice_index_Range_coresliceindexSliceIndexInst (T : Type) :
+  core_slice_index_SliceIndex (core_ops_range_Range usize) (slice T) := {|
+  core_slice_index_SliceIndex_sealedInst := core_slice_index_private_slice_index_Range_coresliceindexprivate_slice_indexSealedInst;
+  core_slice_index_SliceIndex_Output := slice T;
+  core_slice_index_SliceIndex_get := core_slice_index_Range_get T;
+  core_slice_index_SliceIndex_get_mut := core_slice_index_Range_get_mut T;
+  core_slice_index_SliceIndex_get_mut_back := core_slice_index_Range_get_mut_back T;
+  core_slice_index_SliceIndex_get_unchecked := core_slice_index_Range_get_unchecked T;
+  core_slice_index_SliceIndex_get_unchecked_mut := core_slice_index_Range_get_unchecked_mut T;
+  core_slice_index_SliceIndex_index := core_slice_index_Range_index T;
+  core_slice_index_SliceIndex_index_mut := core_slice_index_Range_index_mut T;
+  core_slice_index_SliceIndex_index_mut_back := core_slice_index_Range_index_mut_back T;
+|}.
+
+(* Trait implementation: [core::slice::index::[T]] *)
+Definition core_slice_index_Slice_coreopsindexIndexMutInst (T Idx : Type)
+  (inst : core_slice_index_SliceIndex Idx (slice T)) :
+  core_ops_index_IndexMut (slice T) Idx := {|
+  core_ops_index_IndexMut_indexInst := core_slice_index_Slice_coreopsindexIndexInst 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_array_Array_coreopsindexIndexInst (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_array_Array_coreopsindexIndexMutInst (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_array_Array_coreopsindexIndexInst 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_usize_coresliceindexprivate_slice_indexSealedInst
+  : core_slice_index_private_slice_index_Sealed usize := tt.
+
+(* Trait implementation: [core::slice::index::usize] *)
+Definition core_slice_index_usize_coresliceindexSliceIndexInst (T : Type) :
+  core_slice_index_SliceIndex usize (slice T) := {|
+  core_slice_index_SliceIndex_sealedInst := core_slice_index_private_slice_index_usize_coresliceindexprivate_slice_indexSealedInst;
+  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_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_usize_coresliceindexSliceIndexInst a) v i x =
+    alloc_vec_Vec_update_usize v i x.
 
 End Primitives.