Regenerate the test files and add the fstar-split tests

22 files changed, 1731 insertions, 2666 deletions

diff --git a/tests/coq/array/Array.v b/tests/coq/array/Array.v
index 1f2cc0e0..faa0e92c 100644
--- a/tests/coq/array/Array.v
+++ b/tests/coq/array/Array.v
@@ -12,108 +12,98 @@ Module Array.
     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 ())
+(** [array::incr]:
     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
+(** [array::array_to_shared_slice_]:
     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
+(** [array::array_to_mut_slice_]:
     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)
+  (T : Type) (s : array T 32%usize) :
+  result ((slice T) * (slice T -> result (array T 32%usize)))
   :=
-  array_from_slice T 32%usize s ret
+  p <- array_to_slice_mut T 32%usize s;
+  let (s1, to_slice_mut_back) := p in
+  let back := fun (ret : slice T) => to_slice_mut_back ret in
+  Return (s1, back)
 .
 
-(** [array::array_len]: forward function
+(** [array::array_len]:
     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
+  s1 <- array_to_slice T 32%usize s; let i := slice_len T s1 in Return i
 .
 
-(** [array::shared_array_len]: forward function
+(** [array::shared_array_len]:
     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
+  s1 <- array_to_slice T 32%usize s; let i := slice_len T s1 in Return i
 .
 
-(** [array::shared_slice_len]: forward function
+(** [array::shared_slice_len]:
     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
+(** [array::index_array_shared]:
     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
+(** [array::index_array_u32]:
     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
+(** [array::index_array_copy]:
     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
+(** [array::index_mut_array]:
     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)
+  (T : Type) (s : array T 32%usize) (i : usize) :
+  result (T * (T -> result (array T 32%usize)))
   :=
-  array_update_usize T 32%usize s i ret
+  p <- array_index_mut_usize T 32%usize s i;
+  let (t, index_mut_back) := p in
+  let back := fun (ret : T) => index_mut_back ret in
+  Return (t, back)
 .
 
-(** [array::index_slice]: forward function
+(** [array::index_slice]:
     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
+(** [array::index_mut_slice]:
     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
+Definition index_mut_slice
+  (T : Type) (s : slice T) (i : usize) :
+  result (T * (T -> result (slice T)))
+  :=
+  p <- slice_index_mut_usize T s i;
+  let (t, index_mut_back) := p in
+  let back := fun (ret : T) => index_mut_back ret in
+  Return (t, back)
 .
 
-(** [array::slice_subslice_shared_]: forward function
+(** [array::slice_subslice_shared_]:
     Source: 'src/array.rs', lines 64:0-64:70 *)
 Definition slice_subslice_shared_
   (x : slice u32) (y : usize) (z : usize) : result (slice u32) :=
@@ -122,47 +112,41 @@ Definition slice_subslice_shared_
     {| core_ops_range_Range_start := y; core_ops_range_Range_end_ := z |}
 .
 
-(** [array::slice_subslice_mut_]: forward function
+(** [array::slice_subslice_mut_]:
     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)
+  (x : slice u32) (y : usize) (z : usize) :
+  result ((slice u32) * (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
+  p <-
+    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 |};
+  let (s, index_mut_back) := p in
+  let back := fun (ret : slice u32) => index_mut_back ret in
+  Return (s, back)
 .
 
-(** [array::array_to_slice_shared_]: forward function
+(** [array::array_to_slice_shared_]:
     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
+(** [array::array_to_slice_mut_]:
     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
+Definition array_to_slice_mut_
+  (x : array u32 32%usize) :
+  result ((slice u32) * (slice u32 -> result (array u32 32%usize)))
+  :=
+  p <- array_to_slice_mut u32 32%usize x;
+  let (s, to_slice_mut_back) := p in
+  let back := fun (ret : slice u32) => to_slice_mut_back ret in
+  Return (s, back)
 .
 
-(** [array::array_subslice_shared_]: forward function
+(** [array::array_subslice_shared_]:
     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) :=
@@ -172,41 +156,35 @@ Definition array_subslice_shared_
     {| core_ops_range_Range_start := y; core_ops_range_Range_end_ := z |}
 .
 
-(** [array::array_subslice_mut_]: forward function
+(** [array::array_subslice_mut_]:
     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)
+  (x : array u32 32%usize) (y : usize) (z : usize) :
+  result ((slice u32) * (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
+  p <-
+    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 |};
+  let (s, index_mut_back) := p in
+  let back := fun (ret : slice u32) => index_mut_back ret in
+  Return (s, back)
 .
 
-(** [array::index_slice_0]: forward function
+(** [array::index_slice_0]:
     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
+(** [array::index_array_0]:
     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
+(** [array::index_index_array]:
     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) :
@@ -216,157 +194,164 @@ Definition index_index_array
   array_index_usize u32 32%usize a j
 .
 
-(** [array::update_update_array]: forward function
+(** [array::update_update_array]:
     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;
+  p <- array_index_mut_usize (array u32 32%usize) 32%usize s i;
+  let (a, index_mut_back) := p in
+  p1 <- array_index_mut_usize u32 32%usize a j;
+  let (_, index_mut_back1) := p1 in
+  a1 <- index_mut_back1 0%u32;
+  _ <- index_mut_back a1;
   Return tt
 .
 
-(** [array::array_local_deep_copy]: forward function
+(** [array::array_local_deep_copy]:
     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
+(** [array::take_array]:
     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
+(** [array::take_array_borrow]:
     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
+(** [array::take_slice]:
     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 ())
+(** [array::take_mut_slice]:
     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
+(** [array::const_array]:
     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
+(** [array::const_slice]:
     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
+(** [array::take_all]:
     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 (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;
+  p <- array_to_slice_mut u32 2%usize (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
+  let (s1, to_slice_mut_back) := p in
+  s2 <- take_mut_slice s1;
+  _ <- to_slice_mut_back s2;
   Return tt
 .
 
-(** [array::index_array]: forward function
+(** [array::index_array]:
     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
+(** [array::index_array_borrow]:
     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
+(** [array::index_slice_u32_0]:
     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
+(** [array::index_mut_slice_u32_0]:
     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
+Definition index_mut_slice_u32_0
+  (x : slice u32) : result (u32 * (slice u32)) :=
+  i <- slice_index_usize u32 x 0%usize; Return (i, x)
 .
 
-(** [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
+(** [array::index_all]:
     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;
+  i1 <- index_array (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
+  i2 <- u32_add i i1;
+  i3 <- index_array_borrow (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
+  i4 <- u32_add i2 i3;
   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
+  i5 <- index_slice_u32_0 s;
+  i6 <- u32_add i4 i5;
+  p <- array_to_slice_mut u32 2%usize (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
+  let (s1, to_slice_mut_back) := p in
+  p1 <- index_mut_slice_u32_0 s1;
+  let (i7, s2) := p1 in
+  i8 <- u32_add i6 i7;
+  _ <- to_slice_mut_back s2;
+  Return i8
+.
+
+(** [array::update_array]:
     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
+  p <- array_index_mut_usize u32 2%usize x 0%usize;
+  let (_, index_mut_back) := p in
+  _ <- index_mut_back 1%u32;
+  Return tt
 .
 
-(** [array::update_array_mut_borrow]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+(** [array::update_array_mut_borrow]:
     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
+  p <- array_index_mut_usize u32 2%usize x 0%usize;
+  let (_, index_mut_back) := p in
+  index_mut_back 1%u32
 .
 
-(** [array::update_mut_slice]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+(** [array::update_mut_slice]:
     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
+  p <- slice_index_mut_usize u32 x 0%usize;
+  let (_, index_mut_back) := p in
+  index_mut_back 1%u32
 .
 
-(** [array::update_all]: forward function
+(** [array::update_all]:
     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;
+  _ <- update_array (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
+  a <- update_array_mut_borrow (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
+  p <- array_to_slice_mut u32 2%usize a;
+  let (s, to_slice_mut_back) := p in
+  s1 <- update_mut_slice s;
+  _ <- to_slice_mut_back s1;
   Return tt
 .
 
-(** [array::range_all]: forward function
+(** [array::range_all]:
     Source: 'src/array.rs', lines 205:0-205:18 *)
 Definition range_all : result unit :=
-  s <-
+  p <-
     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))
@@ -375,127 +360,119 @@ Definition range_all : result unit :=
         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;
+  let (s, index_mut_back) := p in
+  s1 <- update_mut_slice s;
+  _ <- index_mut_back s1;
   Return tt
 .
 
-(** [array::deref_array_borrow]: forward function
+(** [array::deref_array_borrow]:
     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
+(** [array::deref_array_mut_borrow]:
     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
+Definition deref_array_mut_borrow
+  (x : array u32 2%usize) : result (u32 * (array u32 2%usize)) :=
+  i <- array_index_usize u32 2%usize x 0%usize; Return (i, x)
 .
 
-(** [array::take_array_t]: forward function
+(** [array::take_array_t]:
     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
+(** [array::non_copyable_array]:
     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
+(** [array::sum]: loop 0:
     Source: 'src/array.rs', lines 242:0-250:1 *)
 Fixpoint sum_loop
-  (n : nat) (s : slice u32) (sum0 : u32) (i : usize) : result u32 :=
+  (n : nat) (s : slice u32) (sum1 : u32) (i : usize) : result u32 :=
   match n with
   | O => Fail_ OutOfFuel
-  | S n0 =>
-    let i0 := slice_len u32 s in
-    if i s< i0
+  | S n1 =>
+    let i1 := slice_len u32 s in
+    if i s< i1
     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
+      i2 <- slice_index_usize u32 s i;
+      sum3 <- u32_add sum1 i2;
+      i3 <- usize_add i 1%usize;
+      sum_loop n1 s sum3 i3)
+    else Return sum1
   end
 .
 
-(** [array::sum]: forward function
+(** [array::sum]:
     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
+(** [array::sum2]: loop 0:
     Source: 'src/array.rs', lines 252:0-261:1 *)
 Fixpoint sum2_loop
-  (n : nat) (s : slice u32) (s2 : slice u32) (sum0 : u32) (i : usize) :
+  (n : nat) (s : slice u32) (s2 : slice u32) (sum1 : u32) (i : usize) :
   result u32
   :=
   match n with
   | O => Fail_ OutOfFuel
-  | S n0 =>
-    let i0 := slice_len u32 s in
-    if i s< i0
+  | S n1 =>
+    let i1 := slice_len u32 s in
+    if i s< i1
     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
+      i2 <- slice_index_usize u32 s i;
+      i3 <- slice_index_usize u32 s2 i;
+      i4 <- u32_add i2 i3;
+      sum3 <- u32_add sum1 i4;
+      i5 <- usize_add i 1%usize;
+      sum2_loop n1 s s2 sum3 i5)
+    else Return sum1
   end
 .
 
-(** [array::sum2]: forward function
+(** [array::sum2]:
     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
+  let i1 := slice_len u32 s2 in
+  if negb (i s= i1) then Fail_ Failure else sum2_loop n s s2 0%u32 0%usize
 .
 
-(** [array::f0]: forward function
+(** [array::f0]:
     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;
+  p <- array_to_slice_mut u32 2%usize (mk_array u32 2%usize [ 1%u32; 2%u32 ]);
+  let (s, to_slice_mut_back) := p in
+  p1 <- slice_index_mut_usize u32 s 0%usize;
+  let (_, index_mut_back) := p1 in
+  s1 <- index_mut_back 1%u32;
+  _ <- to_slice_mut_back s1;
   Return tt
 .
 
-(** [array::f1]: forward function
+(** [array::f1]:
     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;
+  p <-
+    array_index_mut_usize u32 2%usize (mk_array u32 2%usize [ 1%u32; 2%u32 ])
+      0%usize;
+  let (_, index_mut_back) := p in
+  _ <- index_mut_back 1%u32;
   Return tt
 .
 
-(** [array::f2]: forward function
+(** [array::f2]:
     Source: 'src/array.rs', lines 273:0-273:17 *)
 Definition f2 (i : u32) : result unit :=
   Return tt.
 
-(** [array::f4]: forward function
+(** [array::f4]:
     Source: 'src/array.rs', lines 282:0-282:54 *)
 Definition f4
   (x : array u32 32%usize) (y : usize) (z : usize) : result (slice u32) :=
@@ -505,7 +482,7 @@ Definition f4
     {| core_ops_range_Range_start := y; core_ops_range_Range_end_ := z |}
 .
 
-(** [array::f3]: forward function
+(** [array::f3]:
     Source: 'src/array.rs', lines 275:0-275:18 *)
 Definition f3 (n : nat) : result u32 :=
   i <-
@@ -514,8 +491,8 @@ Definition f3 (n : nat) : result u32 :=
   _ <- 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
+  s1 <- f4 b 16%usize 18%usize;
+  sum2 n s s1
 .
 
 (** [array::SZ]
@@ -523,21 +500,25 @@ Definition f3 (n : nat) : result u32 :=
 Definition sz_body : result usize := Return 32%usize.
 Definition sz_c : usize := sz_body%global.
 
-(** [array::f5]: forward function
+(** [array::f5]:
     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
+(** [array::ite]:
     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;
+  p <- array_to_slice_mut u32 2%usize (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
+  let (s, to_slice_mut_back) := p in
+  p1 <- index_mut_slice_u32_0 s;
+  let (_, s1) := p1 in
+  p2 <- array_to_slice_mut u32 2%usize (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
+  let (s2, to_slice_mut_back1) := p2 in
+  p3 <- index_mut_slice_u32_0 s2;
+  let (_, s3) := p3 in
+  _ <- to_slice_mut_back1 s3;
+  _ <- to_slice_mut_back s1;
   Return tt
 .
 
diff --git a/tests/coq/array/Primitives.v b/tests/coq/array/Primitives.v
index 84280b96..990e27e4 100644
--- a/tests/coq/array/Primitives.v
+++ b/tests/coq/array/Primitives.v
@@ -67,8 +67,7 @@ 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 .
+Definition core_mem_replace (a : Type) (x : a) (y : a) : a * a := (x, x) .
 
 Record mut_raw_ptr (T : Type) := { mut_raw_ptr_v : T }.
 Record const_raw_ptr (T : Type) := { const_raw_ptr_v : T }.
@@ -504,13 +503,15 @@ 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;
+  core_ops_index_IndexMut_index_mut :
+    Self ->
+    Idx ->
+    result (core_ops_index_IndexMut_indexInst.(core_ops_index_Index_Output) *
+            (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 {
@@ -524,13 +525,14 @@ 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;
+  core_ops_deref_DerefMut_deref_mut :
+    Self ->
+    result (core_ops_deref_DerefMut_derefInst.(core_ops_deref_Deref_target) *
+            (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;
@@ -543,8 +545,8 @@ 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.
+Definition alloc_boxed_Box_deref_mut (T : Type) (x : T) : result (T * (T -> result T)) :=
+  Return (x, fun x => Return x).
 
 (* Trait instance *)
 Definition alloc_boxed_Box_coreopsDerefInst (Self : Type) : core_ops_deref_Deref Self := {|
@@ -556,7 +558,6 @@ Definition alloc_boxed_Box_coreopsDerefInst (Self : Type) : core_ops_deref_Deref
 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;
 |}.
 
 
@@ -584,6 +585,13 @@ 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).
 
+Definition array_index_mut_usize (T : Type) (n : usize) (a : array T n) (i : usize) :
+  result (T * (T -> result (array T n))) :=
+  match array_index_usize T n a i with
+  | Fail_ e => Fail_ e
+  | Return x => Return (x, array_update_usize T n a i)
+  end.
+
 (*** Slice *)
 Definition slice T := { l: list T | Z.of_nat (length l) <= usize_max}.
 
@@ -591,11 +599,25 @@ 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).
 
+Definition slice_index_mut_usize (T : Type) (s : slice T) (i : usize) :
+  result (T * (T -> result (slice T))) :=
+  match slice_index_usize T s i with
+  | Fail_ e => Fail_ e
+  | Return x => Return (x, slice_update_usize T s i)
+  end.
+
 (*** 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).
 
+Definition array_to_slice_mut (T : Type) (n : usize) (a : array T n) :
+  result (slice T * (slice T -> result (array T n))) :=
+  match array_to_slice T n a with
+  | Fail_ e => Fail_ e
+  | Return x => Return (x, array_from_slice T n a)
+  end.
+
 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).
 
@@ -639,16 +661,9 @@ Definition alloc_vec_Vec_bind {A B} (v: alloc_vec_Vec A) (f: list A -> result (l
   | 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)
@@ -661,6 +676,14 @@ Axiom alloc_vec_Vec_index_usize : forall {T : Type} (v : alloc_vec_Vec T) (i : u
 (* Helper *)
 Axiom alloc_vec_Vec_update_usize : forall {T : Type} (v : alloc_vec_Vec T) (i : usize) (x : T), result (alloc_vec_Vec T).
 
+Definition alloc_vec_Vec_index_mut_usize {T : Type} (v: alloc_vec_Vec T) (i: usize) :
+  result (T * (T -> result (alloc_vec_Vec T))) :=
+  match alloc_vec_Vec_index_usize v i with
+  | Return x =>
+    Return (x, alloc_vec_Vec_update_usize v i)
+  | Fail_ e => Fail_ e
+  end.
+
 (* Trait declaration: [core::slice::index::private_slice_index::Sealed] *)
 Definition core_slice_index_private_slice_index_Sealed (self : Type) := unit.
 
@@ -669,25 +692,23 @@ Record core_slice_index_SliceIndex (Self T : Type) := mk_core_slice_index_SliceI
   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_mut :
+    Self -> T -> result (option core_slice_index_SliceIndex_Output * (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;
+  core_slice_index_SliceIndex_index_mut :
+    Self -> T -> result (core_slice_index_SliceIndex_Output * (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
@@ -704,11 +725,9 @@ Axiom core_slice_index_RangeUsize_get : forall (T : Type) (i : core_ops_range_Ra
 
 (* [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).
+  forall (T : Type),
+    core_ops_range_Range usize -> slice T ->
+    result (option (slice T) * (option (slice T) -> result (slice T))).
 
 (* [core::slice::index::Range::get_unchecked]: forward function *)
 Definition core_slice_index_RangeUsize_get_unchecked
@@ -732,21 +751,14 @@ Axiom core_slice_index_RangeUsize_index :
 
 (* [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).
+  forall (T : Type), core_ops_range_Range usize -> slice T -> result (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).
+  slice T -> Idx ->
+  result (inst.(core_slice_index_SliceIndex_Output) *
+          (inst.(core_slice_index_SliceIndex_Output) -> result (slice T))).
 
 (* [core::array::[T; N]::index]: forward function *)
 Axiom core_array_Array_index :
@@ -756,12 +768,9 @@ Axiom core_array_Array_index :
 (* [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).
+  (a : array T N) (i : Idx),
+  result (inst.(core_ops_index_IndexMut_indexInst).(core_ops_index_Index_Output) *
+          (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
@@ -774,12 +783,10 @@ Definition core_slice_index_SliceIndexRangeUsizeSliceTInst (T : Type) :
   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]] *)
@@ -796,7 +803,6 @@ Definition core_ops_index_IndexMutSliceTIInst (T Idx : Type)
   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]] *)
@@ -813,18 +819,14 @@ Definition core_ops_index_IndexMutArrayInst (T Idx : Type) (N : usize)
   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).
+Axiom core_slice_index_usize_get_mut :
+  forall (T : Type), usize -> slice T -> result (option T * (option T -> result (slice T))).
 
 (* [core::slice::index::usize::get_unchecked]: forward function *)
 Axiom core_slice_index_usize_get_unchecked :
@@ -838,11 +840,8 @@ Axiom core_slice_index_usize_get_unchecked_mut :
 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).
+Axiom core_slice_index_usize_index_mut :
+  forall (T : Type), usize -> slice T -> result (T * (T -> result (slice T))).
 
 (* Trait implementation: [core::slice::index::private_slice_index::usize] *)
 Definition core_slice_index_private_slice_index_SealedUsizeInst
@@ -855,12 +854,10 @@ Definition core_slice_index_SliceIndexUsizeSliceTInst (T : Type) :
   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 *)
@@ -869,12 +866,9 @@ Axiom alloc_vec_Vec_index : forall (T Idx : Type) (inst : core_slice_index_Slice
 
 (* [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).
+  (Self : alloc_vec_Vec T) (i : Idx),
+  result (inst.(core_slice_index_SliceIndex_Output) *
+          (inst.(core_slice_index_SliceIndex_Output) -> result (alloc_vec_Vec T))).
 
 (* Trait implementation: [alloc::vec::Vec] *)
 Definition alloc_vec_Vec_coreopsindexIndexInst (T Idx : Type)
@@ -890,7 +884,6 @@ Definition alloc_vec_Vec_coreopsindexIndexMutInst (T Idx : Type)
   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 *)
@@ -901,10 +894,6 @@ Axiom alloc_vec_Vec_index_eq : forall {a : Type} (v : alloc_vec_Vec a) (i : usiz
 
 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.
+    alloc_vec_Vec_index_mut_usize v i.
 
 End Primitives.
diff --git a/tests/coq/betree/BetreeMain_Funs.v b/tests/coq/betree/BetreeMain_Funs.v
index a5dd4230..516bc7b7 100644
--- a/tests/coq/betree/BetreeMain_Funs.v
+++ b/tests/coq/betree/BetreeMain_Funs.v
@@ -12,7 +12,7 @@ Require Import BetreeMain_FunsExternal.
 Include BetreeMain_FunsExternal.
 Module BetreeMain_Funs.
 
-(** [betree_main::betree::load_internal_node]: forward function
+(** [betree_main::betree::load_internal_node]:
     Source: 'src/betree.rs', lines 36:0-36:52 *)
 Definition betree_load_internal_node
   (id : u64) (st : state) :
@@ -21,70 +21,57 @@ Definition betree_load_internal_node
   betree_utils_load_internal_node id st
 .
 
-(** [betree_main::betree::store_internal_node]: forward function
+(** [betree_main::betree::store_internal_node]:
     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 id content st;
-  let (st0, _) := p in
-  Return (st0, tt)
+  let (st1, _) := p in
+  Return (st1, tt)
 .
 
-(** [betree_main::betree::load_leaf_node]: forward function
+(** [betree_main::betree::load_leaf_node]:
     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
+(** [betree_main::betree::store_leaf_node]:
     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 id content st;
-  let (st0, _) := p in
-  Return (st0, tt)
+  let (st1, _) := p in
+  Return (st1, tt)
 .
 
-(** [betree_main::betree::fresh_node_id]: forward function
+(** [betree_main::betree::fresh_node_id]:
     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
+Definition betree_fresh_node_id (counter : u64) : result (u64 * u64) :=
+  counter1 <- u64_add counter 1%u64; Return (counter, counter1)
 .
 
-(** [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::{betree_main::betree::NodeIdCounter}::new]: forward function
+(** [betree_main::betree::{betree_main::betree::NodeIdCounter}::new]:
     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::{betree_main::betree::NodeIdCounter}::fresh_id]: forward function
+(** [betree_main::betree::{betree_main::betree::NodeIdCounter}::fresh_id]:
     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::{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 :=
+  (self : betree_NodeIdCounter_t) : result (u64 * betree_NodeIdCounter_t) :=
   i <- u64_add self.(betree_NodeIdCounter_next_node_id) 1%u64;
-  Return {| betree_NodeIdCounter_next_node_id := i |}
+  Return (self.(betree_NodeIdCounter_next_node_id),
+    {| betree_NodeIdCounter_next_node_id := i |})
 .
 
-(** [betree_main::betree::upsert_update]: forward function
+(** [betree_main::betree::upsert_update]:
     Source: 'src/betree.rs', lines 234:0-234:70 *)
 Definition betree_upsert_update
   (prev : option u64) (st : betree_UpsertFunState_t) : result u64 :=
@@ -92,49 +79,49 @@ Definition betree_upsert_update
   | None =>
     match st with
     | Betree_UpsertFunState_Add v => Return v
-    | Betree_UpsertFunState_Sub i => Return 0%u64
+    | Betree_UpsertFunState_Sub _ => Return 0%u64
     end
-  | Some prev0 =>
+  | Some prev1 =>
     match st with
     | 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
+      margin <- u64_sub core_u64_max prev1;
+      if margin s>= v then u64_add prev1 v else Return core_u64_max
     | Betree_UpsertFunState_Sub v =>
-      if prev0 s>= v then u64_sub prev0 v else Return 0%u64
+      if prev1 s>= v then u64_sub prev1 v else Return 0%u64
     end
   end
 .
 
-(** [betree_main::betree::{betree_main::betree::List<T>#1}::len]: forward function
+(** [betree_main::betree::{betree_main::betree::List<T>#1}::len]:
     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 =>
+  | S n1 =>
     match self with
-    | Betree_List_Cons t tl => i <- betree_List_len T n0 tl; u64_add 1%u64 i
+    | Betree_List_Cons _ tl => i <- betree_List_len T n1 tl; u64_add 1%u64 i
     | Betree_List_Nil => Return 0%u64
     end
   end
 .
 
-(** [betree_main::betree::{betree_main::betree::List<T>#1}::split_at]: forward function
+(** [betree_main::betree::{betree_main::betree::List<T>#1}::split_at]:
     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) :
+  (T : Type) (n : nat) (self : betree_List_t T) (n1 : u64) :
   result ((betree_List_t T) * (betree_List_t T))
   :=
   match n with
   | O => Fail_ OutOfFuel
-  | S n1 =>
-    if n0 s= 0%u64
+  | S n2 =>
+    if n1 s= 0%u64
     then Return (Betree_List_Nil, self)
     else
       match self with
       | Betree_List_Cons hd tl =>
-        i <- u64_sub n0 1%u64;
-        p <- betree_List_split_at T n1 tl i;
+        i <- u64_sub n1 1%u64;
+        p <- betree_List_split_at T n2 tl i;
         let (ls0, ls1) := p in
         let l := ls0 in
         Return (Betree_List_Cons hd l, ls1)
@@ -143,58 +130,46 @@ Fixpoint betree_List_split_at
   end
 .
 
-(** [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 ())
+(** [betree_main::betree::{betree_main::betree::List<T>#1}::push_front]:
     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 (tl, _) := core_mem_replace (betree_List_t T) self Betree_List_Nil in
   let l := tl in
   Return (Betree_List_Cons x l)
 .
 
-(** [betree_main::betree::{betree_main::betree::List<T>#1}::pop_front]: forward function
+(** [betree_main::betree::{betree_main::betree::List<T>#1}::pop_front]:
     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
+  (T : Type) (self : betree_List_t T) : result (T * (betree_List_t T)) :=
+  let (ls, _) := core_mem_replace (betree_List_t T) self Betree_List_Nil in
   match ls with
-  | Betree_List_Cons x tl => Return x
+  | Betree_List_Cons x tl => Return (x, tl)
   | Betree_List_Nil => Fail_ Failure
   end
 .
 
-(** [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
-  | Betree_List_Cons x tl => Return tl
-  | Betree_List_Nil => Fail_ Failure
-  end
-.
-
-(** [betree_main::betree::{betree_main::betree::List<T>#1}::hd]: forward function
+(** [betree_main::betree::{betree_main::betree::List<T>#1}::hd]:
     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
-  | Betree_List_Cons hd l => Return hd
+  | Betree_List_Cons hd _ => Return hd
   | Betree_List_Nil => Fail_ Failure
   end
 .
 
-(** [betree_main::betree::{betree_main::betree::List<(u64, T)>#2}::head_has_key]: forward function
+(** [betree_main::betree::{betree_main::betree::List<(u64, T)>#2}::head_has_key]:
     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
-  | Betree_List_Cons hd l => let (i, _) := hd in Return (i s= key)
+  | Betree_List_Cons hd _ => let (i, _) := hd in Return (i s= key)
   | Betree_List_Nil => Return false
   end
 .
 
-(** [betree_main::betree::{betree_main::betree::List<(u64, T)>#2}::partition_at_pivot]: forward function
+(** [betree_main::betree::{betree_main::betree::List<(u64, T)>#2}::partition_at_pivot]:
     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) :
@@ -202,14 +177,14 @@ Fixpoint betree_ListTupleU64T_partition_at_pivot
   :=
   match n with
   | O => Fail_ OutOfFuel
-  | S n0 =>
+  | S n1 =>
     match self with
     | Betree_List_Cons hd tl =>
       let (i, t) := hd in
       if i s>= pivot
       then Return (Betree_List_Nil, Betree_List_Cons (i, t) tl)
       else (
-        p <- betree_ListTupleU64T_partition_at_pivot T n0 tl pivot;
+        p <- betree_ListTupleU64T_partition_at_pivot T n1 tl pivot;
         let (ls0, ls1) := p in
         let l := ls0 in
         Return (Betree_List_Cons (i, t) l, ls1))
@@ -218,107 +193,76 @@ Fixpoint betree_ListTupleU64T_partition_at_pivot
   end
 .
 
-(** [betree_main::betree::{betree_main::betree::Leaf#3}::split]: forward function
+(** [betree_main::betree::{betree_main::betree::Leaf#3}::split]:
     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 * betree_NodeIdCounter_t))
   :=
   p <-
     betree_List_split_at (u64 * u64) n content
       params.(betree_Params_split_size);
   let (content0, content1) := p in
-  p0 <- betree_List_hd (u64 * u64) content1;
-  let (pivot, _) := p0 in
-  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 id1 content1 st0;
-  let (st1, _) := p2 in
-  let n0 := Betree_Node_Leaf
+  p1 <- betree_List_hd (u64 * u64) content1;
+  let (pivot, _) := p1 in
+  p2 <- betree_NodeIdCounter_fresh_id node_id_cnt;
+  let (id0, nic) := p2 in
+  p3 <- betree_NodeIdCounter_fresh_id nic;
+  let (id1, nic1) := p3 in
+  p4 <- betree_store_leaf_node id0 content0 st;
+  let (st1, _) := p4 in
+  p5 <- betree_store_leaf_node id1 content1 st1;
+  let (st2, _) := p5 in
+  let n1 := Betree_Node_Leaf
     {|
       betree_Leaf_id := id0;
       betree_Leaf_size := params.(betree_Params_split_size)
     |} in
-  let n1 := Betree_Node_Leaf
+  let n2 := Betree_Node_Leaf
     {|
       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 (st2, (mkbetree_Internal_t self.(betree_Leaf_id) pivot n1 n2, nic1))
 .
 
-(** [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_NodeIdCounter_t
-  :=
-  p <-
-    betree_List_split_at (u64 * u64) n content
-      params.(betree_Params_split_size);
-  let (content0, content1) := p in
-  _ <- 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 id1 content1 st0;
-  betree_NodeIdCounter_fresh_id_back node_id_cnt0
-.
-
-(** [betree_main::betree::{betree_main::betree::Node#5}::lookup_first_message_for_key]: forward function
+(** [betree_main::betree::{betree_main::betree::Node#5}::lookup_first_message_for_key]:
     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))
+  result ((betree_List_t (u64 * betree_Message_t)) * (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
-    | Betree_List_Cons x next_msgs =>
-      let (i, m) := x in
-      if i s>= key
-      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::{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 =>
+  | S n1 =>
     match msgs with
     | Betree_List_Cons x next_msgs =>
       let (i, m) := x in
       if i s>= key
-      then Return ret
+      then
+        let back_'a :=
+          fun (ret : betree_List_t (u64 * betree_Message_t)) => Return ret in
+        Return (Betree_List_Cons (i, m) next_msgs, back_'a)
       else (
-        next_msgs0 <-
-          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
+        p <- betree_Node_lookup_first_message_for_key n1 key next_msgs;
+        let (l, lookup_first_message_for_key_back) := p in
+        let back_'a :=
+          fun (ret : betree_List_t (u64 * betree_Message_t)) =>
+            next_msgs1 <- lookup_first_message_for_key_back ret;
+            Return (Betree_List_Cons (i, m) next_msgs1) in
+        Return (l, back_'a))
+    | Betree_List_Nil =>
+      let back_'a :=
+        fun (ret : betree_List_t (u64 * betree_Message_t)) => Return ret in
+      Return (Betree_List_Nil, back_'a)
     end
   end
 .
 
-(** [betree_main::betree::{betree_main::betree::Node#5}::lookup_in_bindings]: forward function
+(** [betree_main::betree::{betree_main::betree::Node#5}::lookup_in_bindings]:
     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)) :
@@ -326,263 +270,146 @@ Fixpoint betree_Node_lookup_in_bindings
   :=
   match n with
   | O => Fail_ OutOfFuel
-  | S n0 =>
+  | S n1 =>
     match bindings with
     | Betree_List_Cons hd tl =>
-      let (i, i0) := hd in
+      let (i, i1) := hd in
       if i s= key
-      then Return (Some i0)
+      then Return (Some i1)
       else
         if i s> key
         then Return None
-        else betree_Node_lookup_in_bindings n0 key tl
+        else betree_Node_lookup_in_bindings n1 key tl
     | Betree_List_Nil => Return None
     end
   end
 .
 
-(** [betree_main::betree::{betree_main::betree::Node#5}::apply_upserts]: forward function
+(** [betree_main::betree::{betree_main::betree::Node#5}::apply_upserts]:
     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)
+  result (state * (u64 * (betree_List_t (u64 * betree_Message_t))))
   :=
   match n with
   | O => Fail_ OutOfFuel
-  | S n0 =>
+  | S n1 =>
     b <- betree_ListTupleU64T_head_has_key betree_Message_t msgs key;
     if b
     then (
-      msg <- betree_List_pop_front (u64 * betree_Message_t) msgs;
+      p <- betree_List_pop_front (u64 * betree_Message_t) msgs;
+      let (msg, l) := p in
       let (_, m) := msg in
       match m with
-      | Betree_Message_Insert i => Fail_ Failure
+      | Betree_Message_Insert _ => 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
+        betree_Node_apply_upserts n1 l (Some v) key st
       end)
     else (
       p <- core_option_Option_unwrap u64 prev st;
-      let (st0, v) := p in
-      _ <-
+      let (st1, v) := p in
+      l <-
         betree_List_push_front (u64 * betree_Message_t) msgs (key,
           Betree_Message_Insert v);
-      Return (st0, v))
-  end
-.
-
-(** [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))
-  :=
-  match n with
-  | O => Fail_ OutOfFuel
-  | S n0 =>
-    b <- betree_ListTupleU64T_head_has_key betree_Message_t msgs key;
-    if b
-    then (
-      msg <- betree_List_pop_front (u64 * betree_Message_t) msgs;
-      let (_, m) := msg in
-      match m with
-      | 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 u64 prev st;
-      let (_, v) := p in
-      betree_List_push_front (u64 * betree_Message_t) msgs (key,
-        Betree_Message_Insert v))
+      Return (st1, (v, l)))
   end
 .
 
-(** [betree_main::betree::{betree_main::betree::Internal#4}::lookup_in_children]: forward function
+(** [betree_main::betree::{betree_main::betree::Internal#4}::lookup_in_children]:
     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 n0 self.(betree_Internal_left) key st
-    else betree_Node_lookup n0 self.(betree_Internal_right) key st
-  end
-
-(** [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
+  result (state * ((option u64) * betree_Internal_t))
   :=
   match n with
   | O => Fail_ OutOfFuel
-  | S n0 =>
+  | S n1 =>
     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)))
+      p <- betree_Node_lookup n1 self.(betree_Internal_left) key st;
+      let (st1, p1) := p in
+      let (o, n2) := p1 in
+      Return (st1, (o, mkbetree_Internal_t self.(betree_Internal_id)
+        self.(betree_Internal_pivot) n2 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))
+      p <- betree_Node_lookup n1 self.(betree_Internal_right) key st;
+      let (st1, p1) := p in
+      let (o, n2) := p1 in
+      Return (st1, (o, mkbetree_Internal_t self.(betree_Internal_id)
+        self.(betree_Internal_pivot) self.(betree_Internal_left) n2)))
   end
 
-(** [betree_main::betree::{betree_main::betree::Node#5}::lookup]: forward function
+(** [betree_main::betree::{betree_main::betree::Node#5}::lookup]:
     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))
+  result (state * ((option u64) * betree_Node_t))
   :=
   match n with
   | O => Fail_ OutOfFuel
-  | S n0 =>
-    match self with
-    | 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 n0 key msgs;
-      match pending with
-      | Betree_List_Cons p0 l =>
-        let (k, msg) := p0 in
-        if k s<> key
-        then (
-          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
-              (Betree_List_Cons (k, msg) l);
-          Return (st1, o))
-        else
-          match msg with
-          | Betree_Message_Insert v =>
-            _ <-
-              betree_Node_lookup_first_message_for_key_back n0 key msgs
-                (Betree_List_Cons (k, Betree_Message_Insert v) l);
-            Return (st0, Some v)
-          | Betree_Message_Delete =>
-            _ <-
-              betree_Node_lookup_first_message_for_key_back n0 key msgs
-                (Betree_List_Cons (k, Betree_Message_Delete) l);
-            Return (st0, None)
-          | Betree_Message_Upsert ufs =>
-            p1 <- betree_Internal_lookup_in_children n0 node key st0;
-            let (st1, v) := p1 in
-            p2 <-
-              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;
-            pending0 <-
-              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
-                pending0;
-            p3 <-
-              betree_store_internal_node node0.(betree_Internal_id) msgs0 st2;
-            let (st3, _) := p3 in
-            Return (st3, Some v0)
-          end
-      | 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
-            Betree_List_Nil;
-        Return (st1, o)
-      end
-    | Betree_Node_Leaf node =>
-      p <- betree_load_leaf_node node.(betree_Leaf_id) st;
-      let (st0, bindings) := p in
-      o <- betree_Node_lookup_in_bindings n0 key bindings;
-      Return (st0, o)
-    end
-  end
-
-(** [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 =>
+  | S n1 =>
     match self with
     | 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 n0 key msgs;
+      let (st1, msgs) := p in
+      p1 <- betree_Node_lookup_first_message_for_key n1 key msgs;
+      let (pending, lookup_first_message_for_key_back) := p1 in
       match pending with
-      | Betree_List_Cons p0 l =>
-        let (k, msg) := p0 in
+      | Betree_List_Cons p2 l =>
+        let (k, msg) := p2 in
         if k s<> key
         then (
-          _ <-
-            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))
+          p3 <- betree_Internal_lookup_in_children n1 node key st1;
+          let (st2, p4) := p3 in
+          let (o, i) := p4 in
+          _ <- lookup_first_message_for_key_back (Betree_List_Cons (k, msg) l);
+          Return (st2, (o, Betree_Node_Internal i)))
         else
           match msg with
           | Betree_Message_Insert v =>
             _ <-
-              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)
+              lookup_first_message_for_key_back (Betree_List_Cons (k,
+                Betree_Message_Insert v) l);
+            Return (st1, (Some v, Betree_Node_Internal node))
           | Betree_Message_Delete =>
             _ <-
-              betree_Node_lookup_first_message_for_key_back n0 key msgs
-                (Betree_List_Cons (k, Betree_Message_Delete) l);
-            Return (Betree_Node_Internal node)
+              lookup_first_message_for_key_back (Betree_List_Cons (k,
+                Betree_Message_Delete) l);
+            Return (st1, (None, 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 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;
-            pending0 <-
-              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
-                pending0;
-            _ <-
-              betree_store_internal_node node0.(betree_Internal_id) msgs0 st2;
-            Return (Betree_Node_Internal node0)
+            p3 <- betree_Internal_lookup_in_children n1 node key st1;
+            let (st2, p4) := p3 in
+            let (v, i) := p4 in
+            p5 <-
+              betree_Node_apply_upserts n1 (Betree_List_Cons (k,
+                Betree_Message_Upsert ufs) l) v key st2;
+            let (st3, p6) := p5 in
+            let (v1, l1) := p6 in
+            msgs1 <- lookup_first_message_for_key_back l1;
+            p7 <- betree_store_internal_node i.(betree_Internal_id) msgs1 st3;
+            let (st4, _) := p7 in
+            Return (st4, (Some v1, Betree_Node_Internal i))
           end
       | Betree_List_Nil =>
-        _ <-
-          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)
+        p2 <- betree_Internal_lookup_in_children n1 node key st1;
+        let (st2, p3) := p2 in
+        let (o, i) := p3 in
+        _ <- lookup_first_message_for_key_back Betree_List_Nil;
+        Return (st2, (o, Betree_Node_Internal i))
       end
     | Betree_Node_Leaf node =>
       p <- betree_load_leaf_node node.(betree_Leaf_id) st;
-      let (_, bindings) := p in
-      _ <- betree_Node_lookup_in_bindings n0 key bindings;
-      Return (Betree_Node_Leaf node)
+      let (st1, bindings) := p in
+      o <- betree_Node_lookup_in_bindings n1 key bindings;
+      Return (st1, (o, Betree_Node_Leaf node))
     end
   end
 .
 
-(** [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 ())
+(** [betree_main::betree::{betree_main::betree::Node#5}::filter_messages_for_key]:
     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)) :
@@ -590,127 +417,118 @@ Fixpoint betree_Node_filter_messages_for_key
   :=
   match n with
   | O => Fail_ OutOfFuel
-  | S n0 =>
+  | S n1 =>
     match msgs with
     | 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) (Betree_List_Cons
-            (k, m) l);
-        betree_Node_filter_messages_for_key n0 key msgs0)
+        p1 <-
+          betree_List_pop_front (u64 * betree_Message_t) (Betree_List_Cons (k,
+            m) l);
+        let (_, l1) := p1 in
+        betree_Node_filter_messages_for_key n1 key l1)
       else Return (Betree_List_Cons (k, m) l)
     | Betree_List_Nil => Return Betree_List_Nil
     end
   end
 .
 
-(** [betree_main::betree::{betree_main::betree::Node#5}::lookup_first_message_after_key]: forward function
+(** [betree_main::betree::{betree_main::betree::Node#5}::lookup_first_message_after_key]:
     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))
+  result ((betree_List_t (u64 * betree_Message_t)) * (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
-    | Betree_List_Cons p next_msgs =>
-      let (k, m) := p in
-      if k s= key
-      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::{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 =>
+  | S n1 =>
     match msgs with
     | 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 (Betree_List_Cons (k, m) next_msgs0))
-      else Return ret
-    | Betree_List_Nil => Return ret
+        p1 <- betree_Node_lookup_first_message_after_key n1 key next_msgs;
+        let (l, lookup_first_message_after_key_back) := p1 in
+        let back_'a :=
+          fun (ret : betree_List_t (u64 * betree_Message_t)) =>
+            next_msgs1 <- lookup_first_message_after_key_back ret;
+            Return (Betree_List_Cons (k, m) next_msgs1) in
+        Return (l, back_'a))
+      else
+        let back_'a :=
+          fun (ret : betree_List_t (u64 * betree_Message_t)) => Return ret in
+        Return (Betree_List_Cons (k, m) next_msgs, back_'a)
+    | Betree_List_Nil =>
+      let back_'a :=
+        fun (ret : betree_List_t (u64 * betree_Message_t)) => Return ret in
+      Return (Betree_List_Nil, back_'a)
     end
   end
 .
 
-(** [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 ())
+(** [betree_main::betree::{betree_main::betree::Node#5}::apply_to_internal]:
     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 n key msgs;
-  b <- betree_ListTupleU64T_head_has_key betree_Message_t msgs0 key;
+  p <- betree_Node_lookup_first_message_for_key n key msgs;
+  let (msgs1, lookup_first_message_for_key_back) := p in
+  b <- betree_ListTupleU64T_head_has_key betree_Message_t msgs1 key;
   if b
   then
     match new_msg with
     | Betree_Message_Insert i =>
-      msgs1 <- betree_Node_filter_messages_for_key n key msgs0;
-      msgs2 <-
-        betree_List_push_front (u64 * betree_Message_t) msgs1 (key,
+      l <- betree_Node_filter_messages_for_key n key msgs1;
+      l1 <-
+        betree_List_push_front (u64 * betree_Message_t) l (key,
           Betree_Message_Insert i);
-      betree_Node_lookup_first_message_for_key_back n key msgs msgs2
+      lookup_first_message_for_key_back l1
     | Betree_Message_Delete =>
-      msgs1 <- betree_Node_filter_messages_for_key n key msgs0;
-      msgs2 <-
-        betree_List_push_front (u64 * betree_Message_t) msgs1 (key,
+      l <- betree_Node_filter_messages_for_key n key msgs1;
+      l1 <-
+        betree_List_push_front (u64 * betree_Message_t) l (key,
           Betree_Message_Delete);
-      betree_Node_lookup_first_message_for_key_back n key msgs msgs2
+      lookup_first_message_for_key_back l1
     | Betree_Message_Upsert s =>
-      p <- betree_List_hd (u64 * betree_Message_t) msgs0;
-      let (_, m) := p in
+      p1 <- betree_List_hd (u64 * betree_Message_t) msgs1;
+      let (_, m) := p1 in
       match m with
       | 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 (u64 * betree_Message_t) msgs1 (key,
+        p2 <- betree_List_pop_front (u64 * betree_Message_t) msgs1;
+        let (_, l) := p2 in
+        l1 <-
+          betree_List_push_front (u64 * betree_Message_t) l (key,
             Betree_Message_Insert v);
-        betree_Node_lookup_first_message_for_key_back n key msgs msgs2
+        lookup_first_message_for_key_back l1
       | Betree_Message_Delete =>
+        p2 <- betree_List_pop_front (u64 * betree_Message_t) msgs1;
+        let (_, l) := p2 in
         v <- betree_upsert_update None s;
-        msgs1 <- betree_List_pop_front_back (u64 * betree_Message_t) msgs0;
-        msgs2 <-
-          betree_List_push_front (u64 * betree_Message_t) msgs1 (key,
+        l1 <-
+          betree_List_push_front (u64 * betree_Message_t) l (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 (u64 * betree_Message_t) msgs1 (key,
+        lookup_first_message_for_key_back l1
+      | Betree_Message_Upsert _ =>
+        p2 <- betree_Node_lookup_first_message_after_key n key msgs1;
+        let (msgs2, lookup_first_message_after_key_back) := p2 in
+        l <-
+          betree_List_push_front (u64 * betree_Message_t) msgs2 (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
+        msgs3 <- lookup_first_message_after_key_back l;
+        lookup_first_message_for_key_back msgs3
       end
     end
   else (
-    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)
+    l <- betree_List_push_front (u64 * betree_Message_t) msgs1 (key, new_msg);
+    lookup_first_message_for_key_back l)
 .
 
-(** [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 ())
+(** [betree_main::betree::{betree_main::betree::Node#5}::apply_messages_to_internal]:
     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))
@@ -719,104 +537,88 @@ Fixpoint betree_Node_apply_messages_to_internal
   :=
   match n with
   | O => Fail_ OutOfFuel
-  | S n0 =>
+  | S n1 =>
     match new_msgs with
     | Betree_List_Cons new_msg new_msgs_tl =>
       let (i, m) := new_msg in
-      msgs0 <- betree_Node_apply_to_internal n0 msgs i m;
-      betree_Node_apply_messages_to_internal n0 msgs0 new_msgs_tl
+      l <- betree_Node_apply_to_internal n1 msgs i m;
+      betree_Node_apply_messages_to_internal n1 l new_msgs_tl
     | Betree_List_Nil => Return msgs
     end
   end
 .
 
-(** [betree_main::betree::{betree_main::betree::Node#5}::lookup_mut_in_bindings]: forward function
+(** [betree_main::betree::{betree_main::betree::Node#5}::lookup_mut_in_bindings]:
     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
-    | Betree_List_Cons hd tl =>
-      let (i, i0) := hd in
-      if i s>= key
-      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::{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))
+  result ((betree_List_t (u64 * u64)) * (betree_List_t (u64 * u64) -> result
+    (betree_List_t (u64 * u64))))
   :=
   match n with
   | O => Fail_ OutOfFuel
-  | S n0 =>
+  | S n1 =>
     match bindings with
     | Betree_List_Cons hd tl =>
-      let (i, i0) := hd in
+      let (i, i1) := hd in
       if i s>= key
-      then Return ret
+      then
+        let back_'a := fun (ret : betree_List_t (u64 * u64)) => Return ret in
+        Return (Betree_List_Cons (i, i1) tl, back_'a)
       else (
-        tl0 <- betree_Node_lookup_mut_in_bindings_back n0 key tl ret;
-        Return (Betree_List_Cons (i, i0) tl0))
-    | Betree_List_Nil => Return ret
+        p <- betree_Node_lookup_mut_in_bindings n1 key tl;
+        let (l, lookup_mut_in_bindings_back) := p in
+        let back_'a :=
+          fun (ret : betree_List_t (u64 * u64)) =>
+            tl1 <- lookup_mut_in_bindings_back ret;
+            Return (Betree_List_Cons (i, i1) tl1) in
+        Return (l, back_'a))
+    | Betree_List_Nil =>
+      let back_'a := fun (ret : betree_List_t (u64 * u64)) => Return ret in
+      Return (Betree_List_Nil, back_'a)
     end
   end
 .
 
-(** [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 ())
+(** [betree_main::betree::{betree_main::betree::Node#5}::apply_to_leaf]:
     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 n key bindings;
-  b <- betree_ListTupleU64T_head_has_key u64 bindings0 key;
+  p <- betree_Node_lookup_mut_in_bindings n key bindings;
+  let (bindings1, lookup_mut_in_bindings_back) := p in
+  b <- betree_ListTupleU64T_head_has_key u64 bindings1 key;
   if b
   then (
-    hd <- betree_List_pop_front (u64 * u64) bindings0;
+    p1 <- betree_List_pop_front (u64 * u64) bindings1;
+    let (hd, l) := p1 in
     match new_msg with
     | 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
+      l1 <- betree_List_push_front (u64 * u64) l (key, v);
+      lookup_mut_in_bindings_back l1
+    | Betree_Message_Delete => lookup_mut_in_bindings_back l
     | Betree_Message_Upsert s =>
       let (_, i) := hd in
       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
+      l1 <- betree_List_push_front (u64 * u64) l (key, v);
+      lookup_mut_in_bindings_back l1
     end)
   else
     match new_msg with
     | 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
+      l <- betree_List_push_front (u64 * u64) bindings1 (key, v);
+      lookup_mut_in_bindings_back l
+    | Betree_Message_Delete => lookup_mut_in_bindings_back bindings1
     | 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
+      l <- betree_List_push_front (u64 * u64) bindings1 (key, v);
+      lookup_mut_in_bindings_back l
     end
 .
 
-(** [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 ())
+(** [betree_main::betree::{betree_main::betree::Node#5}::apply_messages_to_leaf]:
     Source: 'src/betree.rs', lines 444:4-447:5 *)
 Fixpoint betree_Node_apply_messages_to_leaf
   (n : nat) (bindings : betree_List_t (u64 * u64))
@@ -825,404 +627,230 @@ Fixpoint betree_Node_apply_messages_to_leaf
   :=
   match n with
   | O => Fail_ OutOfFuel
-  | S n0 =>
+  | S n1 =>
     match new_msgs with
     | Betree_List_Cons new_msg new_msgs_tl =>
       let (i, m) := new_msg in
-      bindings0 <- betree_Node_apply_to_leaf n0 bindings i m;
-      betree_Node_apply_messages_to_leaf n0 bindings0 new_msgs_tl
+      l <- betree_Node_apply_to_leaf n1 bindings i m;
+      betree_Node_apply_messages_to_leaf n1 l new_msgs_tl
     | Betree_List_Nil => Return bindings
     end
   end
 .
 
-(** [betree_main::betree::{betree_main::betree::Internal#4}::flush]: forward function
+(** [betree_main::betree::{betree_main::betree::Internal#4}::flush]:
     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)))
+  result (state * ((betree_List_t (u64 * betree_Message_t)) *
+    (betree_Internal_t * betree_NodeIdCounter_t)))
   :=
   match n with
   | O => Fail_ OutOfFuel
-  | S n0 =>
-    p <-
-      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 (u64 * betree_Message_t) n0 msgs_left;
-    if len_left s>= params.(betree_Params_min_flush_size)
-    then (
-      p0 <-
-        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
-          node_id_cnt msgs_left st;
-      let (_, node_id_cnt0) := p1 in
-      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 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)
-            params node_id_cnt0 msgs_right st0;
-        Return (st1, Betree_List_Nil))
-      else Return (st0, msgs_right))
-    else (
-      p0 <-
-        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
-          node_id_cnt msgs_right st;
-      Return (st0, msgs_left))
-  end
-
-(** [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 =>
+  | S n1 =>
     p <-
-      betree_ListTupleU64T_partition_at_pivot betree_Message_t n0 content
+      betree_ListTupleU64T_partition_at_pivot betree_Message_t n1 content
         self.(betree_Internal_pivot);
     let (msgs_left, msgs_right) := p in
-    len_left <- betree_List_len (u64 * betree_Message_t) n0 msgs_left;
+    len_left <- betree_List_len (u64 * betree_Message_t) n1 msgs_left;
     if len_left s>= params.(betree_Params_min_flush_size)
     then (
-      p0 <-
-        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 n1 self.(betree_Internal_left) params
           node_id_cnt msgs_left st;
-      let (n1, node_id_cnt0) := p1 in
-      len_right <- betree_List_len (u64 * betree_Message_t) n0 msgs_right;
+      let (st1, p2) := p1 in
+      let (n2, node_id_cnt1) := p2 in
+      len_right <- betree_List_len (u64 * betree_Message_t) n1 msgs_right;
       if len_right s>= params.(betree_Params_min_flush_size)
       then (
-        p2 <-
-          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))
+        p3 <-
+          betree_Node_apply_messages n1 self.(betree_Internal_right) params
+            node_id_cnt1 msgs_right st1;
+        let (st2, p4) := p3 in
+        let (n3, node_id_cnt2) := p4 in
+        Return (st2, (Betree_List_Nil, (mkbetree_Internal_t
+          self.(betree_Internal_id) self.(betree_Internal_pivot) n2 n3,
+          node_id_cnt2))))
       else
-        Return (mkbetree_Internal_t self.(betree_Internal_id)
-          self.(betree_Internal_pivot) n1 self.(betree_Internal_right),
-          node_id_cnt0))
+        Return (st1, (msgs_right, (mkbetree_Internal_t
+          self.(betree_Internal_id) self.(betree_Internal_pivot) n2
+          self.(betree_Internal_right), node_id_cnt1))))
     else (
-      p0 <-
-        betree_Node_apply_messages_back n0 self.(betree_Internal_right) params
+      p1 <-
+        betree_Node_apply_messages n1 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,
-        node_id_cnt0))
+      let (st1, p2) := p1 in
+      let (n2, node_id_cnt1) := p2 in
+      Return (st1, (msgs_left, (mkbetree_Internal_t self.(betree_Internal_id)
+        self.(betree_Internal_pivot) self.(betree_Internal_left) n2,
+        node_id_cnt1))))
   end
 
-(** [betree_main::betree::{betree_main::betree::Node#5}::apply_messages]: forward function
+(** [betree_main::betree::{betree_main::betree::Node#5}::apply_messages]:
     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)
+  result (state * (betree_Node_t * betree_NodeIdCounter_t))
   :=
   match n with
   | O => Fail_ OutOfFuel
-  | S n0 =>
+  | S n1 =>
     match self with
     | 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 n0 content msgs;
-      num_msgs <- betree_List_len (u64 * betree_Message_t) n0 content0;
+      let (st1, content) := p in
+      l <- betree_Node_apply_messages_to_internal n1 content msgs;
+      num_msgs <- betree_List_len (u64 * betree_Message_t) n1 l;
       if num_msgs s>= params.(betree_Params_min_flush_size)
       then (
-        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;
-        let (node0, _) := p1 in
-        p2 <-
-          betree_store_internal_node node0.(betree_Internal_id) content1 st1;
-        let (st2, _) := p2 in
-        Return (st2, tt))
+        p1 <- betree_Internal_flush n1 node params node_id_cnt l st1;
+        let (st2, p2) := p1 in
+        let (content1, p3) := p2 in
+        let (node1, node_id_cnt1) := p3 in
+        p4 <-
+          betree_store_internal_node node1.(betree_Internal_id) content1 st2;
+        let (st3, _) := p4 in
+        Return (st3, (Betree_Node_Internal node1, node_id_cnt1)))
       else (
-        p0 <-
-          betree_store_internal_node node.(betree_Internal_id) content0 st0;
-        let (st1, _) := p0 in
-        Return (st1, tt))
-    | 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 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 n0 node content0 params node_id_cnt st0;
-        let (st1, _) := p0 in
-        p1 <- betree_store_leaf_node node.(betree_Leaf_id) Betree_List_Nil st1;
+        p1 <- betree_store_internal_node node.(betree_Internal_id) l st1;
         let (st2, _) := p1 in
-        Return (st2, tt))
-      else (
-        p0 <- betree_store_leaf_node node.(betree_Leaf_id) content0 st0;
-        let (st1, _) := p0 in
-        Return (st1, tt))
-    end
-  end
-
-(** [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
-    | 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 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 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;
-        let (node0, node_id_cnt0) := p1 in
-        _ <-
-          betree_store_internal_node node0.(betree_Internal_id) content1 st1;
-        Return (Betree_Node_Internal node0, node_id_cnt0))
-      else (
-        _ <- betree_store_internal_node node.(betree_Internal_id) content0 st0;
-        Return (Betree_Node_Internal node, node_id_cnt))
+        Return (st2, (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 n0 content msgs;
-      len <- betree_List_len (u64 * u64) n0 content0;
+      let (st1, content) := p in
+      l <- betree_Node_apply_messages_to_leaf n1 content msgs;
+      len <- betree_List_len (u64 * u64) n1 l;
       i <- u64_mul 2%u64 params.(betree_Params_split_size);
       if len s>= i
       then (
-        p0 <- betree_Leaf_split n0 node content0 params node_id_cnt st0;
-        let (st1, new_node) := p0 in
-        _ <- 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 (Betree_Node_Internal new_node, node_id_cnt0))
+        p1 <- betree_Leaf_split n1 node l params node_id_cnt st1;
+        let (st2, p2) := p1 in
+        let (new_node, nic) := p2 in
+        p3 <- betree_store_leaf_node node.(betree_Leaf_id) Betree_List_Nil st2;
+        let (st3, _) := p3 in
+        Return (st3, (Betree_Node_Internal new_node, nic)))
       else (
-        _ <- betree_store_leaf_node node.(betree_Leaf_id) content0 st0;
-        Return (Betree_Node_Leaf
+        p1 <- betree_store_leaf_node node.(betree_Leaf_id) l st1;
+        let (st2, _) := p1 in
+        Return (st2, (Betree_Node_Leaf
           {| betree_Leaf_id := node.(betree_Leaf_id); betree_Leaf_size := len
-          |}, node_id_cnt))
+          |}, node_id_cnt)))
     end
   end
 .
 
-(** [betree_main::betree::{betree_main::betree::Node#5}::apply]: forward function
+(** [betree_main::betree::{betree_main::betree::Node#5}::apply]:
     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)
+  result (state * (betree_Node_t * betree_NodeIdCounter_t))
   :=
   let l := Betree_List_Nil in
   p <-
     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 (Betree_List_Cons
-      (key, new_msg) l) st;
-  Return (st0, tt)
-.
-
-(** [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 := Betree_List_Nil in
-  betree_Node_apply_messages_back n self params node_id_cnt (Betree_List_Cons
-    (key, new_msg) l) st
+  let (st1, p1) := p in
+  let (self1, node_id_cnt1) := p1 in
+  Return (st1, (self1, node_id_cnt1))
 .
 
-(** [betree_main::betree::{betree_main::betree::BeTree#6}::new]: forward function
+(** [betree_main::betree::{betree_main::betree::BeTree#6}::new]:
     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_BeTree_t)
   :=
   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_NodeIdCounter_fresh_id_back node_id_cnt;
-  Return (st0,
+  p <- betree_NodeIdCounter_fresh_id node_id_cnt;
+  let (id, nic) := p in
+  p1 <- betree_store_leaf_node id Betree_List_Nil st;
+  let (st1, _) := p1 in
+  Return (st1,
     {|
       betree_BeTree_params :=
         {|
           betree_Params_min_flush_size := min_flush_size;
           betree_Params_split_size := split_size
         |};
-      betree_BeTree_node_id_cnt := node_id_cnt0;
+      betree_BeTree_node_id_cnt := nic;
       betree_BeTree_root :=
         (Betree_Node_Leaf
           {| betree_Leaf_id := id; betree_Leaf_size := 0%u64 |})
     |})
 .
 
-(** [betree_main::betree::{betree_main::betree::BeTree#6}::apply]: forward function
+(** [betree_main::betree::{betree_main::betree::BeTree#6}::apply]:
     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)
+  result (state * betree_BeTree_t)
   :=
   p <-
     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_BeTree_root)
-      self.(betree_BeTree_params) self.(betree_BeTree_node_id_cnt) key msg st;
-  Return (st0, tt)
-.
-
-(** [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_BeTree_t
-  :=
-  p <-
-    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
+  let (st1, p1) := p in
+  let (n1, nic) := p1 in
+  Return (st1,
     {|
       betree_BeTree_params := self.(betree_BeTree_params);
       betree_BeTree_node_id_cnt := nic;
-      betree_BeTree_root := n0
-    |}
+      betree_BeTree_root := n1
+    |})
 .
 
-(** [betree_main::betree::{betree_main::betree::BeTree#6}::insert]: forward function
+(** [betree_main::betree::{betree_main::betree::BeTree#6}::insert]:
     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_BeTree_apply n self key (Betree_Message_Insert value) st;
-  let (st0, _) := p in
-  _ <- betree_BeTree_apply_back n self key (Betree_Message_Insert value) st;
-  Return (st0, tt)
-.
-
-(** [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
+  result (state * betree_BeTree_t)
   :=
-  betree_BeTree_apply_back n self key (Betree_Message_Insert value) st
+  betree_BeTree_apply n self key (Betree_Message_Insert value) st
 .
 
-(** [betree_main::betree::{betree_main::betree::BeTree#6}::delete]: forward function
+(** [betree_main::betree::{betree_main::betree::BeTree#6}::delete]:
     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_BeTree_apply n self key Betree_Message_Delete st;
-  let (st0, _) := p in
-  _ <- betree_BeTree_apply_back n self key Betree_Message_Delete st;
-  Return (st0, tt)
-.
-
-(** [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
+  result (state * betree_BeTree_t)
   :=
-  betree_BeTree_apply_back n self key Betree_Message_Delete st
+  betree_BeTree_apply n self key Betree_Message_Delete st
 .
 
-(** [betree_main::betree::{betree_main::betree::BeTree#6}::upsert]: forward function
+(** [betree_main::betree::{betree_main::betree::BeTree#6}::upsert]:
     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_BeTree_apply n self key (Betree_Message_Upsert upd) st;
-  let (st0, _) := p in
-  _ <- betree_BeTree_apply_back n self key (Betree_Message_Upsert upd) st;
-  Return (st0, tt)
-.
-
-(** [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
+  result (state * betree_BeTree_t)
   :=
-  betree_BeTree_apply_back n self key (Betree_Message_Upsert upd) st
+  betree_BeTree_apply n self key (Betree_Message_Upsert upd) st
 .
 
-(** [betree_main::betree::{betree_main::betree::BeTree#6}::lookup]: forward function
+(** [betree_main::betree::{betree_main::betree::BeTree#6}::lookup]:
     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 n self.(betree_BeTree_root) key st
-.
-
-(** [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
+  result (state * ((option u64) * betree_BeTree_t))
   :=
-  n0 <- betree_Node_lookup_back n self.(betree_BeTree_root) key st;
-  Return
+  p <- betree_Node_lookup n self.(betree_BeTree_root) key st;
+  let (st1, p1) := p in
+  let (o, n1) := p1 in
+  Return (st1, (o,
     {|
       betree_BeTree_params := self.(betree_BeTree_params);
       betree_BeTree_node_id_cnt := self.(betree_BeTree_node_id_cnt);
-      betree_BeTree_root := n0
-    |}
+      betree_BeTree_root := n1
+    |}))
 .
 
-(** [betree_main::main]: forward function
+(** [betree_main::main]:
     Source: 'src/betree_main.rs', lines 5:0-5:9 *)
 Definition main : result unit :=
   Return tt.
diff --git a/tests/coq/betree/BetreeMain_FunsExternal_Template.v b/tests/coq/betree/BetreeMain_FunsExternal_Template.v
index 36022a20..a9969448 100644
--- a/tests/coq/betree/BetreeMain_FunsExternal_Template.v
+++ b/tests/coq/betree/BetreeMain_FunsExternal_Template.v
@@ -11,13 +11,13 @@ Require Import BetreeMain_Types.
 Include BetreeMain_Types.
 Module BetreeMain_FunsExternal_Template.
 
-(** [betree_main::betree_utils::load_internal_node]: forward function
+(** [betree_main::betree_utils::load_internal_node]:
     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
+(** [betree_main::betree_utils::store_internal_node]:
     Source: 'src/betree_utils.rs', lines 115:0-115:71 *)
 Axiom betree_utils_store_internal_node
   :
@@ -25,19 +25,19 @@ Axiom betree_utils_store_internal_node
     unit)
 .
 
-(** [betree_main::betree_utils::load_leaf_node]: forward function
+(** [betree_main::betree_utils::load_leaf_node]:
     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
+(** [betree_main::betree_utils::store_leaf_node]:
     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
+(** [core::option::{core::option::Option<T>}::unwrap]:
     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)
diff --git a/tests/coq/betree/BetreeMain_Types.v b/tests/coq/betree/BetreeMain_Types.v
index 22989256..acbc2085 100644
--- a/tests/coq/betree/BetreeMain_Types.v
+++ b/tests/coq/betree/BetreeMain_Types.v
@@ -61,31 +61,31 @@ with betree_Node_t :=
 .
 
 Definition betree_Internal_id (x : betree_Internal_t) :=
-  match x with | mkbetree_Internal_t x0 _ _ _ => x0 end
+  match x with | mkbetree_Internal_t x1 _ _ _ => x1 end
 .
 
-Notation "x1 .(betree_Internal_id)" := (betree_Internal_id x1) (at level 9).
+Notation "x2 .(betree_Internal_id)" := (betree_Internal_id x2) (at level 9).
 
 Definition betree_Internal_pivot (x : betree_Internal_t) :=
-  match x with | mkbetree_Internal_t _ x0 _ _ => x0 end
+  match x with | mkbetree_Internal_t _ x1 _ _ => x1 end
 .
 
-Notation "x1 .(betree_Internal_pivot)" := (betree_Internal_pivot x1)
+Notation "x2 .(betree_Internal_pivot)" := (betree_Internal_pivot x2)
   (at level 9)
 .
 
 Definition betree_Internal_left (x : betree_Internal_t) :=
-  match x with | mkbetree_Internal_t _ _ x0 _ => x0 end
+  match x with | mkbetree_Internal_t _ _ x1 _ => x1 end
 .
 
-Notation "x1 .(betree_Internal_left)" := (betree_Internal_left x1) (at level 9)
+Notation "x2 .(betree_Internal_left)" := (betree_Internal_left x2) (at level 9)
 .
 
 Definition betree_Internal_right (x : betree_Internal_t) :=
-  match x with | mkbetree_Internal_t _ _ _ x0 => x0 end
+  match x with | mkbetree_Internal_t _ _ _ x1 => x1 end
 .
 
-Notation "x1 .(betree_Internal_right)" := (betree_Internal_right x1)
+Notation "x2 .(betree_Internal_right)" := (betree_Internal_right x2)
   (at level 9)
 .
 
diff --git a/tests/coq/betree/Primitives.v b/tests/coq/betree/Primitives.v
index 84280b96..990e27e4 100644
--- a/tests/coq/betree/Primitives.v
+++ b/tests/coq/betree/Primitives.v
@@ -67,8 +67,7 @@ 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 .
+Definition core_mem_replace (a : Type) (x : a) (y : a) : a * a := (x, x) .
 
 Record mut_raw_ptr (T : Type) := { mut_raw_ptr_v : T }.
 Record const_raw_ptr (T : Type) := { const_raw_ptr_v : T }.
@@ -504,13 +503,15 @@ 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;
+  core_ops_index_IndexMut_index_mut :
+    Self ->
+    Idx ->
+    result (core_ops_index_IndexMut_indexInst.(core_ops_index_Index_Output) *
+            (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 {
@@ -524,13 +525,14 @@ 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;
+  core_ops_deref_DerefMut_deref_mut :
+    Self ->
+    result (core_ops_deref_DerefMut_derefInst.(core_ops_deref_Deref_target) *
+            (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;
@@ -543,8 +545,8 @@ 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.
+Definition alloc_boxed_Box_deref_mut (T : Type) (x : T) : result (T * (T -> result T)) :=
+  Return (x, fun x => Return x).
 
 (* Trait instance *)
 Definition alloc_boxed_Box_coreopsDerefInst (Self : Type) : core_ops_deref_Deref Self := {|
@@ -556,7 +558,6 @@ Definition alloc_boxed_Box_coreopsDerefInst (Self : Type) : core_ops_deref_Deref
 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;
 |}.
 
 
@@ -584,6 +585,13 @@ 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).
 
+Definition array_index_mut_usize (T : Type) (n : usize) (a : array T n) (i : usize) :
+  result (T * (T -> result (array T n))) :=
+  match array_index_usize T n a i with
+  | Fail_ e => Fail_ e
+  | Return x => Return (x, array_update_usize T n a i)
+  end.
+
 (*** Slice *)
 Definition slice T := { l: list T | Z.of_nat (length l) <= usize_max}.
 
@@ -591,11 +599,25 @@ 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).
 
+Definition slice_index_mut_usize (T : Type) (s : slice T) (i : usize) :
+  result (T * (T -> result (slice T))) :=
+  match slice_index_usize T s i with
+  | Fail_ e => Fail_ e
+  | Return x => Return (x, slice_update_usize T s i)
+  end.
+
 (*** 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).
 
+Definition array_to_slice_mut (T : Type) (n : usize) (a : array T n) :
+  result (slice T * (slice T -> result (array T n))) :=
+  match array_to_slice T n a with
+  | Fail_ e => Fail_ e
+  | Return x => Return (x, array_from_slice T n a)
+  end.
+
 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).
 
@@ -639,16 +661,9 @@ Definition alloc_vec_Vec_bind {A B} (v: alloc_vec_Vec A) (f: list A -> result (l
   | 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)
@@ -661,6 +676,14 @@ Axiom alloc_vec_Vec_index_usize : forall {T : Type} (v : alloc_vec_Vec T) (i : u
 (* Helper *)
 Axiom alloc_vec_Vec_update_usize : forall {T : Type} (v : alloc_vec_Vec T) (i : usize) (x : T), result (alloc_vec_Vec T).
 
+Definition alloc_vec_Vec_index_mut_usize {T : Type} (v: alloc_vec_Vec T) (i: usize) :
+  result (T * (T -> result (alloc_vec_Vec T))) :=
+  match alloc_vec_Vec_index_usize v i with
+  | Return x =>
+    Return (x, alloc_vec_Vec_update_usize v i)
+  | Fail_ e => Fail_ e
+  end.
+
 (* Trait declaration: [core::slice::index::private_slice_index::Sealed] *)
 Definition core_slice_index_private_slice_index_Sealed (self : Type) := unit.
 
@@ -669,25 +692,23 @@ Record core_slice_index_SliceIndex (Self T : Type) := mk_core_slice_index_SliceI
   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_mut :
+    Self -> T -> result (option core_slice_index_SliceIndex_Output * (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;
+  core_slice_index_SliceIndex_index_mut :
+    Self -> T -> result (core_slice_index_SliceIndex_Output * (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
@@ -704,11 +725,9 @@ Axiom core_slice_index_RangeUsize_get : forall (T : Type) (i : core_ops_range_Ra
 
 (* [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).
+  forall (T : Type),
+    core_ops_range_Range usize -> slice T ->
+    result (option (slice T) * (option (slice T) -> result (slice T))).
 
 (* [core::slice::index::Range::get_unchecked]: forward function *)
 Definition core_slice_index_RangeUsize_get_unchecked
@@ -732,21 +751,14 @@ Axiom core_slice_index_RangeUsize_index :
 
 (* [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).
+  forall (T : Type), core_ops_range_Range usize -> slice T -> result (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).
+  slice T -> Idx ->
+  result (inst.(core_slice_index_SliceIndex_Output) *
+          (inst.(core_slice_index_SliceIndex_Output) -> result (slice T))).
 
 (* [core::array::[T; N]::index]: forward function *)
 Axiom core_array_Array_index :
@@ -756,12 +768,9 @@ Axiom core_array_Array_index :
 (* [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).
+  (a : array T N) (i : Idx),
+  result (inst.(core_ops_index_IndexMut_indexInst).(core_ops_index_Index_Output) *
+          (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
@@ -774,12 +783,10 @@ Definition core_slice_index_SliceIndexRangeUsizeSliceTInst (T : Type) :
   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]] *)
@@ -796,7 +803,6 @@ Definition core_ops_index_IndexMutSliceTIInst (T Idx : Type)
   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]] *)
@@ -813,18 +819,14 @@ Definition core_ops_index_IndexMutArrayInst (T Idx : Type) (N : usize)
   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).
+Axiom core_slice_index_usize_get_mut :
+  forall (T : Type), usize -> slice T -> result (option T * (option T -> result (slice T))).
 
 (* [core::slice::index::usize::get_unchecked]: forward function *)
 Axiom core_slice_index_usize_get_unchecked :
@@ -838,11 +840,8 @@ Axiom core_slice_index_usize_get_unchecked_mut :
 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).
+Axiom core_slice_index_usize_index_mut :
+  forall (T : Type), usize -> slice T -> result (T * (T -> result (slice T))).
 
 (* Trait implementation: [core::slice::index::private_slice_index::usize] *)
 Definition core_slice_index_private_slice_index_SealedUsizeInst
@@ -855,12 +854,10 @@ Definition core_slice_index_SliceIndexUsizeSliceTInst (T : Type) :
   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 *)
@@ -869,12 +866,9 @@ Axiom alloc_vec_Vec_index : forall (T Idx : Type) (inst : core_slice_index_Slice
 
 (* [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).
+  (Self : alloc_vec_Vec T) (i : Idx),
+  result (inst.(core_slice_index_SliceIndex_Output) *
+          (inst.(core_slice_index_SliceIndex_Output) -> result (alloc_vec_Vec T))).
 
 (* Trait implementation: [alloc::vec::Vec] *)
 Definition alloc_vec_Vec_coreopsindexIndexInst (T Idx : Type)
@@ -890,7 +884,6 @@ Definition alloc_vec_Vec_coreopsindexIndexMutInst (T Idx : Type)
   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 *)
@@ -901,10 +894,6 @@ Axiom alloc_vec_Vec_index_eq : forall {a : Type} (v : alloc_vec_Vec a) (i : usiz
 
 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.
+    alloc_vec_Vec_index_mut_usize v i.
 
 End Primitives.
diff --git a/tests/coq/hashmap/Hashmap_Funs.v b/tests/coq/hashmap/Hashmap_Funs.v
index 64de44a6..5cd9fe70 100644
--- a/tests/coq/hashmap/Hashmap_Funs.v
+++ b/tests/coq/hashmap/Hashmap_Funs.v
@@ -10,39 +10,39 @@ Require Import Hashmap_Types.
 Include Hashmap_Types.
 Module Hashmap_Funs.
 
-(** [hashmap::hash_key]: forward function
+(** [hashmap::hash_key]:
     Source: 'src/hashmap.rs', lines 27:0-27:32 *)
 Definition hash_key (k : usize) : result usize :=
   Return k.
 
-(** [hashmap::{hashmap::HashMap<T>}::allocate_slots]: loop 0: forward function
+(** [hashmap::{hashmap::HashMap<T>}::allocate_slots]: loop 0:
     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) :
+  (T : Type) (n : nat) (slots : alloc_vec_Vec (List_t T)) (n1 : usize) :
   result (alloc_vec_Vec (List_t T))
   :=
   match n with
   | O => Fail_ OutOfFuel
-  | S n1 =>
-    if n0 s> 0%usize
+  | S n2 =>
+    if n1 s> 0%usize
     then (
-      slots0 <- alloc_vec_Vec_push (List_t T) slots List_Nil;
-      n2 <- usize_sub n0 1%usize;
-      hashMap_allocate_slots_loop T n1 slots0 n2)
+      v <- alloc_vec_Vec_push (List_t T) slots List_Nil;
+      n3 <- usize_sub n1 1%usize;
+      hashMap_allocate_slots_loop T n2 v n3)
     else Return slots
   end
 .
 
-(** [hashmap::{hashmap::HashMap<T>}::allocate_slots]: forward function
+(** [hashmap::{hashmap::HashMap<T>}::allocate_slots]:
     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) :
+  (T : Type) (n : nat) (slots : alloc_vec_Vec (List_t T)) (n1 : usize) :
   result (alloc_vec_Vec (List_t T))
   :=
-  hashMap_allocate_slots_loop T n slots n0
+  hashMap_allocate_slots_loop T n slots n1
 .
 
-(** [hashmap::{hashmap::HashMap<T>}::new_with_capacity]: forward function
+(** [hashmap::{hashmap::HashMap<T>}::new_with_capacity]:
     Source: 'src/hashmap.rs', lines 59:4-63:13 *)
 Definition hashMap_new_with_capacity
   (T : Type) (n : nat) (capacity : usize) (max_load_dividend : usize)
@@ -52,24 +52,23 @@ Definition hashMap_new_with_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;
+  i1 <- usize_div i max_load_divisor;
   Return
     {|
       hashMap_num_entries := 0%usize;
       hashMap_max_load_factor := (max_load_dividend, max_load_divisor);
-      hashMap_max_load := i0;
+      hashMap_max_load := i1;
       hashMap_slots := slots
     |}
 .
 
-(** [hashmap::{hashmap::HashMap<T>}::new]: forward function
+(** [hashmap::{hashmap::HashMap<T>}::new]:
     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::HashMap<T>}::clear]: loop 0: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+(** [hashmap::{hashmap::HashMap<T>}::clear]: loop 0:
     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) :
@@ -77,101 +76,73 @@ Fixpoint hashMap_clear_loop
   :=
   match n with
   | O => Fail_ OutOfFuel
-  | S n0 =>
-    let i0 := alloc_vec_Vec_len (List_t T) slots in
-    if i s< i0
+  | S n1 =>
+    let i1 := alloc_vec_Vec_len (List_t T) slots in
+    if i s< i1
     then (
-      i1 <- usize_add i 1%usize;
-      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)
+      p <-
+        alloc_vec_Vec_index_mut (List_t T) usize
+          (core_slice_index_SliceIndexUsizeSliceTInst (List_t T)) slots i;
+      let (_, index_mut_back) := p in
+      i2 <- usize_add i 1%usize;
+      slots1 <- index_mut_back List_Nil;
+      hashMap_clear_loop T n1 slots1 i2)
     else Return slots
   end
 .
 
-(** [hashmap::{hashmap::HashMap<T>}::clear]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+(** [hashmap::{hashmap::HashMap<T>}::clear]:
     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;
+  back <- hashMap_clear_loop T n self.(hashMap_slots) 0%usize;
   Return
     {|
       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_slots := back
     |}
 .
 
-(** [hashmap::{hashmap::HashMap<T>}::len]: forward function
+(** [hashmap::{hashmap::HashMap<T>}::len]:
     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::HashMap<T>}::insert_in_list]: loop 0: forward function
+(** [hashmap::{hashmap::HashMap<T>}::insert_in_list]: loop 0:
     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
+  result (bool * (List_t T))
   :=
   match n with
   | O => Fail_ OutOfFuel
-  | S n0 =>
+  | S n1 =>
     match ls with
     | List_Cons ckey cvalue tl =>
       if ckey s= key
-      then Return false
-      else hashMap_insert_in_list_loop T n0 key value tl
-    | List_Nil => Return true
+      then Return (false, List_Cons ckey value tl)
+      else (
+        p <- hashMap_insert_in_list_loop T n1 key value tl;
+        let (b, back) := p in
+        Return (b, List_Cons ckey cvalue back))
+    | List_Nil => let l := List_Nil in Return (true, List_Cons key value l)
     end
   end
 .
 
-(** [hashmap::{hashmap::HashMap<T>}::insert_in_list]: forward function
+(** [hashmap::{hashmap::HashMap<T>}::insert_in_list]:
     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
+  result (bool * (List_t T))
   :=
   hashMap_insert_in_list_loop T n key value ls
 .
 
-(** [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)
-  :=
-  match n with
-  | O => Fail_ OutOfFuel
-  | S n0 =>
-    match ls with
-    | List_Cons ckey cvalue tl =>
-      if ckey s= key
-      then Return (List_Cons ckey value tl)
-      else (
-        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::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)
-  :=
-  hashMap_insert_in_list_loop_back T n key value ls
-.
-
-(** [hashmap::{hashmap::HashMap<T>}::insert_no_resize]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+(** [hashmap::{hashmap::HashMap<T>}::insert_no_resize]:
     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) :
@@ -180,32 +151,26 @@ Definition hashMap_insert_no_resize
   hash <- hash_key key;
   let i := alloc_vec_Vec_len (List_t T) self.(hashMap_slots) in
   hash_mod <- usize_rem hash i;
-  l <-
+  p <-
     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;
+  let (l, index_mut_back) := p in
+  p1 <- hashMap_insert_in_list T n key value l;
+  let (inserted, l1) := p1 in
   if inserted
   then (
-    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;
+    i1 <- usize_add self.(hashMap_num_entries) 1%usize;
+    v <- index_mut_back l1;
     Return
       {|
-        hashMap_num_entries := i0;
+        hashMap_num_entries := i1;
         hashMap_max_load_factor := self.(hashMap_max_load_factor);
         hashMap_max_load := self.(hashMap_max_load);
         hashMap_slots := v
       |})
   else (
-    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;
+    v <- index_mut_back l1;
     Return
       {|
         hashMap_num_entries := self.(hashMap_num_entries);
@@ -215,8 +180,7 @@ Definition hashMap_insert_no_resize
       |})
 .
 
-(** [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 ())
+(** [hashmap::{hashmap::HashMap<T>}::move_elements_from_list]: loop 0:
     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) :
@@ -224,18 +188,17 @@ Fixpoint hashMap_move_elements_from_list_loop
   :=
   match n with
   | O => Fail_ OutOfFuel
-  | S n0 =>
+  | S n1 =>
     match ls with
     | 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
+      hm <- hashMap_insert_no_resize T n1 ntable k v;
+      hashMap_move_elements_from_list_loop T n1 hm tl
     | List_Nil => Return ntable
     end
   end
 .
 
-(** [hashmap::{hashmap::HashMap<T>}::move_elements_from_list]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+(** [hashmap::{hashmap::HashMap<T>}::move_elements_from_list]:
     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) :
@@ -244,8 +207,7 @@ Definition hashMap_move_elements_from_list
   hashMap_move_elements_from_list_loop T n ntable ls
 .
 
-(** [hashmap::{hashmap::HashMap<T>}::move_elements]: loop 0: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+(** [hashmap::{hashmap::HashMap<T>}::move_elements]: loop 0:
     Source: 'src/hashmap.rs', lines 171:4-180:5 *)
 Fixpoint hashMap_move_elements_loop
   (T : Type) (n : nat) (ntable : HashMap_t T)
@@ -254,108 +216,105 @@ Fixpoint hashMap_move_elements_loop
   :=
   match n with
   | O => Fail_ OutOfFuel
-  | S n0 =>
-    let i0 := alloc_vec_Vec_len (List_t T) slots in
-    if i s< i0
+  | S n1 =>
+    let i1 := alloc_vec_Vec_len (List_t T) slots in
+    if i s< i1
     then (
-      l <-
+      p <-
         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 := 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)
+      let (l, index_mut_back) := p in
+      let (ls, l1) := core_mem_replace (List_t T) l List_Nil in
+      hm <- hashMap_move_elements_from_list T n1 ntable ls;
+      i2 <- usize_add i 1%usize;
+      slots1 <- index_mut_back l1;
+      back_'a <- hashMap_move_elements_loop T n1 hm slots1 i2;
+      let (hm1, v) := back_'a in
+      Return (hm1, v))
     else Return (ntable, slots)
   end
 .
 
-(** [hashmap::{hashmap::HashMap<T>}::move_elements]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+(** [hashmap::{hashmap::HashMap<T>}::move_elements]:
     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)))
   :=
-  hashMap_move_elements_loop T n ntable slots i
+  back_'a <- hashMap_move_elements_loop T n ntable slots i;
+  let (hm, v) := back_'a in
+  Return (hm, v)
 .
 
-(** [hashmap::{hashmap::HashMap<T>}::try_resize]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+(** [hashmap::{hashmap::HashMap<T>}::try_resize]:
     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.(hashMap_max_load_factor) in
-  i1 <- usize_div n1 i;
-  if capacity s<= i1
+  let (i, i1) := self.(hashMap_max_load_factor) in
+  i2 <- usize_div n1 i;
+  if capacity s<= i2
   then (
-    i2 <- usize_mul capacity 2%usize;
-    ntable <- hashMap_new_with_capacity T n i2 i i0;
+    i3 <- usize_mul capacity 2%usize;
+    ntable <- hashMap_new_with_capacity T n i3 i i1;
     p <- hashMap_move_elements T n ntable self.(hashMap_slots) 0%usize;
-    let (ntable0, _) := p in
+    let (ntable1, _) := p in
     Return
       {|
         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)
+        hashMap_max_load_factor := (i, i1);
+        hashMap_max_load := ntable1.(hashMap_max_load);
+        hashMap_slots := ntable1.(hashMap_slots)
       |})
   else
     Return
       {|
         hashMap_num_entries := self.(hashMap_num_entries);
-        hashMap_max_load_factor := (i, i0);
+        hashMap_max_load_factor := (i, i1);
         hashMap_max_load := self.(hashMap_max_load);
         hashMap_slots := self.(hashMap_slots)
       |}
 .
 
-(** [hashmap::{hashmap::HashMap<T>}::insert]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+(** [hashmap::{hashmap::HashMap<T>}::insert]:
     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 <- 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
+  hm <- hashMap_insert_no_resize T n self key value;
+  i <- hashMap_len T hm;
+  if i s> hm.(hashMap_max_load) then hashMap_try_resize T n hm else Return hm
 .
 
-(** [hashmap::{hashmap::HashMap<T>}::contains_key_in_list]: loop 0: forward function
+(** [hashmap::{hashmap::HashMap<T>}::contains_key_in_list]: loop 0:
     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 =>
+  | S n1 =>
     match ls with
-    | List_Cons ckey t tl =>
+    | List_Cons ckey _ tl =>
       if ckey s= key
       then Return true
-      else hashMap_contains_key_in_list_loop T n0 key tl
+      else hashMap_contains_key_in_list_loop T n1 key tl
     | List_Nil => Return false
     end
   end
 .
 
-(** [hashmap::{hashmap::HashMap<T>}::contains_key_in_list]: forward function
+(** [hashmap::{hashmap::HashMap<T>}::contains_key_in_list]:
     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 :=
   hashMap_contains_key_in_list_loop T n key ls
 .
 
-(** [hashmap::{hashmap::HashMap<T>}::contains_key]: forward function
+(** [hashmap::{hashmap::HashMap<T>}::contains_key]:
     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 :=
@@ -369,31 +328,31 @@ Definition hashMap_contains_key
   hashMap_contains_key_in_list T n key l
 .
 
-(** [hashmap::{hashmap::HashMap<T>}::get_in_list]: loop 0: forward function
+(** [hashmap::{hashmap::HashMap<T>}::get_in_list]: loop 0:
     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 =>
+  | S n1 =>
     match ls with
     | List_Cons ckey cvalue tl =>
       if ckey s= key
       then Return cvalue
-      else hashMap_get_in_list_loop T n0 key tl
+      else hashMap_get_in_list_loop T n1 key tl
     | List_Nil => Fail_ Failure
     end
   end
 .
 
-(** [hashmap::{hashmap::HashMap<T>}::get_in_list]: forward function
+(** [hashmap::{hashmap::HashMap<T>}::get_in_list]:
     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 :=
   hashMap_get_in_list_loop T n key ls
 .
 
-(** [hashmap::{hashmap::HashMap<T>}::get]: forward function
+(** [hashmap::{hashmap::HashMap<T>}::get]:
     Source: 'src/hashmap.rs', lines 239:4-239:55 *)
 Definition hashMap_get
   (T : Type) (n : nat) (self : HashMap_t T) (key : usize) : result T :=
@@ -407,264 +366,188 @@ Definition hashMap_get
   hashMap_get_in_list T n key l
 .
 
-(** [hashmap::{hashmap::HashMap<T>}::get_mut_in_list]: loop 0: forward function
+(** [hashmap::{hashmap::HashMap<T>}::get_mut_in_list]: loop 0:
     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
-    | List_Cons ckey cvalue tl =>
-      if ckey s= key
-      then Return cvalue
-      else hashMap_get_mut_in_list_loop T n0 tl key
-    | List_Nil => Fail_ Failure
-    end
-  end
-.
-
-(** [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 :=
-  hashMap_get_mut_in_list_loop T n ls key
-.
-
-(** [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)
+  (T : Type) (n : nat) (ls : List_t T) (key : usize) :
+  result (T * (T -> result (List_t T)))
   :=
   match n with
   | O => Fail_ OutOfFuel
-  | S n0 =>
+  | S n1 =>
     match ls with
     | List_Cons ckey cvalue tl =>
       if ckey s= key
-      then Return (List_Cons ckey ret tl)
+      then
+        let back_'a := fun (ret : T) => Return (List_Cons ckey ret tl) in
+        Return (cvalue, back_'a)
       else (
-        tl0 <- hashMap_get_mut_in_list_loop_back T n0 tl key ret;
-        Return (List_Cons ckey cvalue tl0))
+        p <- hashMap_get_mut_in_list_loop T n1 tl key;
+        let (t, back_'a) := p in
+        let back_'a1 :=
+          fun (ret : T) =>
+            tl1 <- back_'a ret; Return (List_Cons ckey cvalue tl1) in
+        Return (t, back_'a1))
     | List_Nil => Fail_ Failure
     end
   end
 .
 
-(** [hashmap::{hashmap::HashMap<T>}::get_mut_in_list]: backward function 0
+(** [hashmap::{hashmap::HashMap<T>}::get_mut_in_list]:
     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)
+Definition hashMap_get_mut_in_list
+  (T : Type) (n : nat) (ls : List_t T) (key : usize) :
+  result (T * (T -> result (List_t T)))
   :=
-  hashMap_get_mut_in_list_loop_back T n ls key ret
+  p <- hashMap_get_mut_in_list_loop T n ls key;
+  let (t, back_'a) := p in
+  let back_'a1 := fun (ret : T) => back_'a ret in
+  Return (t, back_'a1)
 .
 
-(** [hashmap::{hashmap::HashMap<T>}::get_mut]: forward function
+(** [hashmap::{hashmap::HashMap<T>}::get_mut]:
     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 <-
-    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)
+  (T : Type) (n : nat) (self : HashMap_t T) (key : usize) :
+  result (T * (T -> result (HashMap_t 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 <-
+  p <-
     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
-    {|
-      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::HashMap<T>}::remove_from_list]: loop 0: forward function
+  let (l, index_mut_back) := p in
+  p1 <- hashMap_get_mut_in_list T n l key;
+  let (t, get_mut_in_list_back) := p1 in
+  let back_'a :=
+    fun (ret : T) =>
+      l1 <- get_mut_in_list_back ret;
+      v <- index_mut_back l1;
+      Return
+        {|
+          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
+        |} in
+  Return (t, back_'a)
+.
+
+(** [hashmap::{hashmap::HashMap<T>}::remove_from_list]: loop 0:
     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) :=
+  (T : Type) (n : nat) (key : usize) (ls : List_t T) :
+  result ((option T) * (List_t T))
+  :=
   match n with
   | O => Fail_ OutOfFuel
-  | S n0 =>
+  | S n1 =>
     match ls with
     | List_Cons ckey t tl =>
       if ckey s= key
       then
-        let mv_ls := core_mem_replace (List_t T) (List_Cons ckey t tl) List_Nil
-          in
+        let (mv_ls, _) :=
+          core_mem_replace (List_t T) (List_Cons ckey t tl) List_Nil in
         match mv_ls with
-        | List_Cons i cvalue tl0 => Return (Some cvalue)
+        | List_Cons _ cvalue tl1 => Return (Some cvalue, tl1)
         | List_Nil => Fail_ Failure
         end
-      else hashMap_remove_from_list_loop T n0 key tl
-    | List_Nil => Return None
+      else (
+        p <- hashMap_remove_from_list_loop T n1 key tl;
+        let (o, back) := p in
+        Return (o, List_Cons ckey t back))
+    | List_Nil => Return (None, List_Nil)
     end
   end
 .
 
-(** [hashmap::{hashmap::HashMap<T>}::remove_from_list]: forward function
+(** [hashmap::{hashmap::HashMap<T>}::remove_from_list]:
     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) :=
+  (T : Type) (n : nat) (key : usize) (ls : List_t T) :
+  result ((option T) * (List_t T))
+  :=
   hashMap_remove_from_list_loop T n key ls
 .
 
-(** [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
-    | List_Cons ckey t tl =>
-      if ckey s= key
-      then
-        let mv_ls := core_mem_replace (List_t T) (List_Cons ckey t tl) List_Nil
-          in
-        match mv_ls with
-        | List_Cons i cvalue tl0 => Return tl0
-        | List_Nil => Fail_ Failure
-        end
-      else (
-        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::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) :=
-  hashMap_remove_from_list_loop_back T n key ls
-.
-
-(** [hashmap::{hashmap::HashMap<T>}::remove]: forward function
+(** [hashmap::{hashmap::HashMap<T>}::remove]:
     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 key;
-  let i := alloc_vec_Vec_len (List_t T) self.(hashMap_slots) in
-  hash_mod <- usize_rem hash i;
-  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.(hashMap_num_entries) 1%usize; Return (Some x0)
-  end
-.
-
-(** [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)
+  result ((option T) * (HashMap_t 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 <-
+  p <-
     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;
+  let (l, index_mut_back) := p in
+  p1 <- hashMap_remove_from_list T n key l;
+  let (x, l1) := p1 in
   match x with
   | None =>
-    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
+    v <- index_mut_back l1;
+    Return (None,
       {|
         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.(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
+      |})
+  | Some x1 =>
+    i1 <- usize_sub self.(hashMap_num_entries) 1%usize;
+    v <- index_mut_back l1;
+    Return (Some x1,
       {|
-        hashMap_num_entries := i0;
+        hashMap_num_entries := i1;
         hashMap_max_load_factor := self.(hashMap_max_load_factor);
         hashMap_max_load := self.(hashMap_max_load);
         hashMap_slots := v
-      |}
+      |})
   end
 .
 
-(** [hashmap::test1]: forward function
+(** [hashmap::test1]:
     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;
+  hm1 <- hashMap_insert u64 n hm 0%usize 42%u64;
+  hm2 <- hashMap_insert u64 n hm1 128%usize 18%u64;
+  hm3 <- hashMap_insert u64 n hm2 1024%usize 138%u64;
+  hm4 <- hashMap_insert u64 n hm3 1056%usize 256%u64;
+  i <- hashMap_get u64 n hm4 128%usize;
   if negb (i s= 18%u64)
   then Fail_ Failure
   else (
-    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)
+    p <- hashMap_get_mut u64 n hm4 1024%usize;
+    let (_, get_mut_back) := p in
+    hm5 <- get_mut_back 56%u64;
+    i1 <- hashMap_get u64 n hm5 1024%usize;
+    if negb (i1 s= 56%u64)
     then Fail_ Failure
     else (
-      x <- hashMap_remove u64 n hm4 1024%usize;
+      p1 <- hashMap_remove u64 n hm5 1024%usize;
+      let (x, hm6) := p1 in
       match x with
       | None => Fail_ Failure
-      | Some x0 =>
-        if negb (x0 s= 56%u64)
+      | Some x1 =>
+        if negb (x1 s= 56%u64)
         then Fail_ Failure
         else (
-          hm5 <- hashMap_remove_back u64 n hm4 1024%usize;
-          i1 <- hashMap_get u64 n hm5 0%usize;
-          if negb (i1 s= 42%u64)
+          i2 <- hashMap_get u64 n hm6 0%usize;
+          if negb (i2 s= 42%u64)
           then Fail_ Failure
           else (
-            i2 <- hashMap_get u64 n hm5 128%usize;
-            if negb (i2 s= 18%u64)
+            i3 <- hashMap_get u64 n hm6 128%usize;
+            if negb (i3 s= 18%u64)
             then Fail_ Failure
             else (
-              i3 <- hashMap_get u64 n hm5 1056%usize;
-              if negb (i3 s= 256%u64) then Fail_ Failure else Return tt)))
+              i4 <- hashMap_get u64 n hm6 1056%usize;
+              if negb (i4 s= 256%u64) then Fail_ Failure else Return tt)))
       end))
 .
 
diff --git a/tests/coq/hashmap/Primitives.v b/tests/coq/hashmap/Primitives.v
index 84280b96..990e27e4 100644
--- a/tests/coq/hashmap/Primitives.v
+++ b/tests/coq/hashmap/Primitives.v
@@ -67,8 +67,7 @@ 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 .
+Definition core_mem_replace (a : Type) (x : a) (y : a) : a * a := (x, x) .
 
 Record mut_raw_ptr (T : Type) := { mut_raw_ptr_v : T }.
 Record const_raw_ptr (T : Type) := { const_raw_ptr_v : T }.
@@ -504,13 +503,15 @@ 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;
+  core_ops_index_IndexMut_index_mut :
+    Self ->
+    Idx ->
+    result (core_ops_index_IndexMut_indexInst.(core_ops_index_Index_Output) *
+            (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 {
@@ -524,13 +525,14 @@ 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;
+  core_ops_deref_DerefMut_deref_mut :
+    Self ->
+    result (core_ops_deref_DerefMut_derefInst.(core_ops_deref_Deref_target) *
+            (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;
@@ -543,8 +545,8 @@ 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.
+Definition alloc_boxed_Box_deref_mut (T : Type) (x : T) : result (T * (T -> result T)) :=
+  Return (x, fun x => Return x).
 
 (* Trait instance *)
 Definition alloc_boxed_Box_coreopsDerefInst (Self : Type) : core_ops_deref_Deref Self := {|
@@ -556,7 +558,6 @@ Definition alloc_boxed_Box_coreopsDerefInst (Self : Type) : core_ops_deref_Deref
 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;
 |}.
 
 
@@ -584,6 +585,13 @@ 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).
 
+Definition array_index_mut_usize (T : Type) (n : usize) (a : array T n) (i : usize) :
+  result (T * (T -> result (array T n))) :=
+  match array_index_usize T n a i with
+  | Fail_ e => Fail_ e
+  | Return x => Return (x, array_update_usize T n a i)
+  end.
+
 (*** Slice *)
 Definition slice T := { l: list T | Z.of_nat (length l) <= usize_max}.
 
@@ -591,11 +599,25 @@ 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).
 
+Definition slice_index_mut_usize (T : Type) (s : slice T) (i : usize) :
+  result (T * (T -> result (slice T))) :=
+  match slice_index_usize T s i with
+  | Fail_ e => Fail_ e
+  | Return x => Return (x, slice_update_usize T s i)
+  end.
+
 (*** 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).
 
+Definition array_to_slice_mut (T : Type) (n : usize) (a : array T n) :
+  result (slice T * (slice T -> result (array T n))) :=
+  match array_to_slice T n a with
+  | Fail_ e => Fail_ e
+  | Return x => Return (x, array_from_slice T n a)
+  end.
+
 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).
 
@@ -639,16 +661,9 @@ Definition alloc_vec_Vec_bind {A B} (v: alloc_vec_Vec A) (f: list A -> result (l
   | 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)
@@ -661,6 +676,14 @@ Axiom alloc_vec_Vec_index_usize : forall {T : Type} (v : alloc_vec_Vec T) (i : u
 (* Helper *)
 Axiom alloc_vec_Vec_update_usize : forall {T : Type} (v : alloc_vec_Vec T) (i : usize) (x : T), result (alloc_vec_Vec T).
 
+Definition alloc_vec_Vec_index_mut_usize {T : Type} (v: alloc_vec_Vec T) (i: usize) :
+  result (T * (T -> result (alloc_vec_Vec T))) :=
+  match alloc_vec_Vec_index_usize v i with
+  | Return x =>
+    Return (x, alloc_vec_Vec_update_usize v i)
+  | Fail_ e => Fail_ e
+  end.
+
 (* Trait declaration: [core::slice::index::private_slice_index::Sealed] *)
 Definition core_slice_index_private_slice_index_Sealed (self : Type) := unit.
 
@@ -669,25 +692,23 @@ Record core_slice_index_SliceIndex (Self T : Type) := mk_core_slice_index_SliceI
   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_mut :
+    Self -> T -> result (option core_slice_index_SliceIndex_Output * (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;
+  core_slice_index_SliceIndex_index_mut :
+    Self -> T -> result (core_slice_index_SliceIndex_Output * (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
@@ -704,11 +725,9 @@ Axiom core_slice_index_RangeUsize_get : forall (T : Type) (i : core_ops_range_Ra
 
 (* [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).
+  forall (T : Type),
+    core_ops_range_Range usize -> slice T ->
+    result (option (slice T) * (option (slice T) -> result (slice T))).
 
 (* [core::slice::index::Range::get_unchecked]: forward function *)
 Definition core_slice_index_RangeUsize_get_unchecked
@@ -732,21 +751,14 @@ Axiom core_slice_index_RangeUsize_index :
 
 (* [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).
+  forall (T : Type), core_ops_range_Range usize -> slice T -> result (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).
+  slice T -> Idx ->
+  result (inst.(core_slice_index_SliceIndex_Output) *
+          (inst.(core_slice_index_SliceIndex_Output) -> result (slice T))).
 
 (* [core::array::[T; N]::index]: forward function *)
 Axiom core_array_Array_index :
@@ -756,12 +768,9 @@ Axiom core_array_Array_index :
 (* [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).
+  (a : array T N) (i : Idx),
+  result (inst.(core_ops_index_IndexMut_indexInst).(core_ops_index_Index_Output) *
+          (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
@@ -774,12 +783,10 @@ Definition core_slice_index_SliceIndexRangeUsizeSliceTInst (T : Type) :
   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]] *)
@@ -796,7 +803,6 @@ Definition core_ops_index_IndexMutSliceTIInst (T Idx : Type)
   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]] *)
@@ -813,18 +819,14 @@ Definition core_ops_index_IndexMutArrayInst (T Idx : Type) (N : usize)
   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).
+Axiom core_slice_index_usize_get_mut :
+  forall (T : Type), usize -> slice T -> result (option T * (option T -> result (slice T))).
 
 (* [core::slice::index::usize::get_unchecked]: forward function *)
 Axiom core_slice_index_usize_get_unchecked :
@@ -838,11 +840,8 @@ Axiom core_slice_index_usize_get_unchecked_mut :
 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).
+Axiom core_slice_index_usize_index_mut :
+  forall (T : Type), usize -> slice T -> result (T * (T -> result (slice T))).
 
 (* Trait implementation: [core::slice::index::private_slice_index::usize] *)
 Definition core_slice_index_private_slice_index_SealedUsizeInst
@@ -855,12 +854,10 @@ Definition core_slice_index_SliceIndexUsizeSliceTInst (T : Type) :
   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 *)
@@ -869,12 +866,9 @@ Axiom alloc_vec_Vec_index : forall (T Idx : Type) (inst : core_slice_index_Slice
 
 (* [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).
+  (Self : alloc_vec_Vec T) (i : Idx),
+  result (inst.(core_slice_index_SliceIndex_Output) *
+          (inst.(core_slice_index_SliceIndex_Output) -> result (alloc_vec_Vec T))).
 
 (* Trait implementation: [alloc::vec::Vec] *)
 Definition alloc_vec_Vec_coreopsindexIndexInst (T Idx : Type)
@@ -890,7 +884,6 @@ Definition alloc_vec_Vec_coreopsindexIndexMutInst (T Idx : Type)
   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 *)
@@ -901,10 +894,6 @@ Axiom alloc_vec_Vec_index_eq : forall {a : Type} (v : alloc_vec_Vec a) (i : usiz
 
 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.
+    alloc_vec_Vec_index_mut_usize v i.
 
 End Primitives.
diff --git a/tests/coq/hashmap_on_disk/HashmapMain_Funs.v b/tests/coq/hashmap_on_disk/HashmapMain_Funs.v
index faba0afe..b74fa61a 100644
--- a/tests/coq/hashmap_on_disk/HashmapMain_Funs.v
+++ b/tests/coq/hashmap_on_disk/HashmapMain_Funs.v
@@ -12,41 +12,41 @@ Require Import HashmapMain_FunsExternal.
 Include HashmapMain_FunsExternal.
 Module HashmapMain_Funs.
 
-(** [hashmap_main::hashmap::hash_key]: forward function
+(** [hashmap_main::hashmap::hash_key]:
     Source: 'src/hashmap.rs', lines 27:0-27:32 *)
 Definition hashmap_hash_key (k : usize) : result usize :=
   Return k.
 
-(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::allocate_slots]: loop 0: forward function
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::allocate_slots]: loop 0:
     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)
+  (T : Type) (n : nat) (slots : alloc_vec_Vec (hashmap_List_t T)) (n1 : usize)
   :
   result (alloc_vec_Vec (hashmap_List_t T))
   :=
   match n with
   | O => Fail_ OutOfFuel
-  | S n1 =>
-    if n0 s> 0%usize
+  | S n2 =>
+    if n1 s> 0%usize
     then (
-      slots0 <- alloc_vec_Vec_push (hashmap_List_t T) slots Hashmap_List_Nil;
-      n2 <- usize_sub n0 1%usize;
-      hashmap_HashMap_allocate_slots_loop T n1 slots0 n2)
+      v <- alloc_vec_Vec_push (hashmap_List_t T) slots Hashmap_List_Nil;
+      n3 <- usize_sub n1 1%usize;
+      hashmap_HashMap_allocate_slots_loop T n2 v n3)
     else Return slots
   end
 .
 
-(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::allocate_slots]: forward function
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::allocate_slots]:
     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)
+  (T : Type) (n : nat) (slots : alloc_vec_Vec (hashmap_List_t T)) (n1 : usize)
   :
   result (alloc_vec_Vec (hashmap_List_t T))
   :=
-  hashmap_HashMap_allocate_slots_loop T n slots n0
+  hashmap_HashMap_allocate_slots_loop T n slots n1
 .
 
-(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::new_with_capacity]: forward function
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::new_with_capacity]:
     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)
@@ -56,25 +56,24 @@ Definition hashmap_HashMap_new_with_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;
+  i1 <- usize_div i max_load_divisor;
   Return
     {|
       hashmap_HashMap_num_entries := 0%usize;
       hashmap_HashMap_max_load_factor := (max_load_dividend, max_load_divisor);
-      hashmap_HashMap_max_load := i0;
+      hashmap_HashMap_max_load := i1;
       hashmap_HashMap_slots := slots
     |}
 .
 
-(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::new]: forward function
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::new]:
     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_main::hashmap::HashMap<T>}::clear]: loop 0: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::clear]: loop 0:
     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) :
@@ -82,105 +81,78 @@ Fixpoint hashmap_HashMap_clear_loop
   :=
   match n with
   | O => Fail_ OutOfFuel
-  | S n0 =>
-    let i0 := alloc_vec_Vec_len (hashmap_List_t T) slots in
-    if i s< i0
+  | S n1 =>
+    let i1 := alloc_vec_Vec_len (hashmap_List_t T) slots in
+    if i s< i1
     then (
-      i1 <- usize_add i 1%usize;
-      slots0 <-
-        alloc_vec_Vec_index_mut_back (hashmap_List_t T) usize
+      p <-
+        alloc_vec_Vec_index_mut (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)
+          i;
+      let (_, index_mut_back) := p in
+      i2 <- usize_add i 1%usize;
+      slots1 <- index_mut_back Hashmap_List_Nil;
+      hashmap_HashMap_clear_loop T n1 slots1 i2)
     else Return slots
   end
 .
 
-(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::clear]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::clear]:
     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_HashMap_clear_loop T n self.(hashmap_HashMap_slots) 0%usize;
+  back <- hashmap_HashMap_clear_loop T n self.(hashmap_HashMap_slots) 0%usize;
   Return
     {|
       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_HashMap_slots := back
     |}
 .
 
-(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::len]: forward function
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::len]:
     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_main::hashmap::HashMap<T>}::insert_in_list]: loop 0: forward function
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::insert_in_list]: loop 0:
     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
+  result (bool * (hashmap_List_t T))
   :=
   match n with
   | O => Fail_ OutOfFuel
-  | S n0 =>
-    match ls with
-    | Hashmap_List_Cons ckey cvalue tl =>
-      if ckey s= key
-      then Return false
-      else hashmap_HashMap_insert_in_list_loop T n0 key value tl
-    | Hashmap_List_Nil => Return true
-    end
-  end
-.
-
-(** [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_HashMap_insert_in_list_loop T n key value ls
-.
-
-(** [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 =>
+  | S n1 =>
     match ls with
     | Hashmap_List_Cons ckey cvalue tl =>
       if ckey s= key
-      then Return (Hashmap_List_Cons ckey value tl)
+      then Return (false, Hashmap_List_Cons ckey value tl)
       else (
-        tl0 <- hashmap_HashMap_insert_in_list_loop_back T n0 key value tl;
-        Return (Hashmap_List_Cons ckey cvalue tl0))
+        p <- hashmap_HashMap_insert_in_list_loop T n1 key value tl;
+        let (b, back) := p in
+        Return (b, Hashmap_List_Cons ckey cvalue back))
     | Hashmap_List_Nil =>
-      let l := Hashmap_List_Nil in Return (Hashmap_List_Cons key value l)
+      let l := Hashmap_List_Nil in Return (true, Hashmap_List_Cons key value l)
     end
   end
 .
 
-(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::insert_in_list]: backward function 0
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::insert_in_list]:
     Source: 'src/hashmap.rs', lines 97:4-97:71 *)
-Definition hashmap_HashMap_insert_in_list_back
+Definition hashmap_HashMap_insert_in_list
   (T : Type) (n : nat) (key : usize) (value : T) (ls : hashmap_List_t T) :
-  result (hashmap_List_t T)
+  result (bool * (hashmap_List_t T))
   :=
-  hashmap_HashMap_insert_in_list_loop_back T n key value ls
+  hashmap_HashMap_insert_in_list_loop T n key value ls
 .
 
-(** [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 ())
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::insert_no_resize]:
     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) :
@@ -189,33 +161,27 @@ Definition hashmap_HashMap_insert_no_resize
   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 <-
+  p <-
     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;
+  let (l, index_mut_back) := p in
+  p1 <- hashmap_HashMap_insert_in_list T n key value l;
+  let (inserted, l1) := p1 in
   if inserted
   then (
-    i0 <- usize_add self.(hashmap_HashMap_num_entries) 1%usize;
-    l0 <- hashmap_HashMap_insert_in_list_back T n key value l;
-    v <-
-      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;
+    i1 <- usize_add self.(hashmap_HashMap_num_entries) 1%usize;
+    v <- index_mut_back l1;
     Return
       {|
-        hashmap_HashMap_num_entries := i0;
+        hashmap_HashMap_num_entries := i1;
         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_HashMap_insert_in_list_back T n key value l;
-    v <-
-      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;
+    v <- index_mut_back l1;
     Return
       {|
         hashmap_HashMap_num_entries := self.(hashmap_HashMap_num_entries);
@@ -226,8 +192,7 @@ Definition hashmap_HashMap_insert_no_resize
       |})
 .
 
-(** [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 ())
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::move_elements_from_list]: loop 0:
     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) :
@@ -235,18 +200,17 @@ Fixpoint hashmap_HashMap_move_elements_from_list_loop
   :=
   match n with
   | O => Fail_ OutOfFuel
-  | S n0 =>
+  | S n1 =>
     match ls with
     | 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
+      hm <- hashmap_HashMap_insert_no_resize T n1 ntable k v;
+      hashmap_HashMap_move_elements_from_list_loop T n1 hm tl
     | Hashmap_List_Nil => Return ntable
     end
   end
 .
 
-(** [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 ())
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::move_elements_from_list]:
     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) :
@@ -255,8 +219,7 @@ Definition hashmap_HashMap_move_elements_from_list
   hashmap_HashMap_move_elements_from_list_loop T n ntable ls
 .
 
-(** [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 ())
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::move_elements]: loop 0:
     Source: 'src/hashmap.rs', lines 171:4-180:5 *)
 Fixpoint hashmap_HashMap_move_elements_loop
   (T : Type) (n : nat) (ntable : hashmap_HashMap_t T)
@@ -265,40 +228,39 @@ Fixpoint hashmap_HashMap_move_elements_loop
   :=
   match n with
   | O => Fail_ OutOfFuel
-  | S n0 =>
-    let i0 := alloc_vec_Vec_len (hashmap_List_t T) slots in
-    if i s< i0
+  | S n1 =>
+    let i1 := alloc_vec_Vec_len (hashmap_List_t T) slots in
+    if i s< i1
     then (
-      l <-
+      p <-
         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 := 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)
+      let (l, index_mut_back) := p in
+      let (ls, l1) := core_mem_replace (hashmap_List_t T) l Hashmap_List_Nil in
+      hm <- hashmap_HashMap_move_elements_from_list T n1 ntable ls;
+      i2 <- usize_add i 1%usize;
+      slots1 <- index_mut_back l1;
+      back_'a <- hashmap_HashMap_move_elements_loop T n1 hm slots1 i2;
+      let (hm1, v) := back_'a in
+      Return (hm1, v))
     else Return (ntable, slots)
   end
 .
 
-(** [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 ())
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::move_elements]:
     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_HashMap_move_elements_loop T n ntable slots i
+  back_'a <- hashmap_HashMap_move_elements_loop T n ntable slots i;
+  let (hm, v) := back_'a in
+  Return (hm, v)
 .
 
-(** [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 ())
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::try_resize]:
     Source: 'src/hashmap.rs', lines 140:4-140:28 *)
 Definition hashmap_HashMap_try_resize
   (T : Type) (n : nat) (self : hashmap_HashMap_t T) :
@@ -308,72 +270,71 @@ Definition hashmap_HashMap_try_resize
   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_HashMap_max_load_factor) in
-  i1 <- usize_div n1 i;
-  if capacity s<= i1
+  let (i, i1) := self.(hashmap_HashMap_max_load_factor) in
+  i2 <- usize_div n1 i;
+  if capacity s<= i2
   then (
-    i2 <- usize_mul capacity 2%usize;
-    ntable <- hashmap_HashMap_new_with_capacity T n i2 i i0;
+    i3 <- usize_mul capacity 2%usize;
+    ntable <- hashmap_HashMap_new_with_capacity T n i3 i i1;
     p <-
       hashmap_HashMap_move_elements T n ntable self.(hashmap_HashMap_slots)
         0%usize;
-    let (ntable0, _) := p in
+    let (ntable1, _) := p in
     Return
       {|
         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)
+        hashmap_HashMap_max_load_factor := (i, i1);
+        hashmap_HashMap_max_load := ntable1.(hashmap_HashMap_max_load);
+        hashmap_HashMap_slots := ntable1.(hashmap_HashMap_slots)
       |})
   else
     Return
       {|
         hashmap_HashMap_num_entries := self.(hashmap_HashMap_num_entries);
-        hashmap_HashMap_max_load_factor := (i, i0);
+        hashmap_HashMap_max_load_factor := (i, i1);
         hashmap_HashMap_max_load := self.(hashmap_HashMap_max_load);
         hashmap_HashMap_slots := self.(hashmap_HashMap_slots)
       |}
 .
 
-(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::insert]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::insert]:
     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_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
+  hm <- hashmap_HashMap_insert_no_resize T n self key value;
+  i <- hashmap_HashMap_len T hm;
+  if i s> hm.(hashmap_HashMap_max_load)
+  then hashmap_HashMap_try_resize T n hm
+  else Return hm
 .
 
-(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::contains_key_in_list]: loop 0: forward function
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::contains_key_in_list]: loop 0:
     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 =>
+  | S n1 =>
     match ls with
-    | Hashmap_List_Cons ckey t tl =>
+    | Hashmap_List_Cons ckey _ tl =>
       if ckey s= key
       then Return true
-      else hashmap_HashMap_contains_key_in_list_loop T n0 key tl
+      else hashmap_HashMap_contains_key_in_list_loop T n1 key tl
     | Hashmap_List_Nil => Return false
     end
   end
 .
 
-(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::contains_key_in_list]: forward function
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::contains_key_in_list]:
     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_main::hashmap::HashMap<T>}::contains_key]: forward function
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::contains_key]:
     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) :
@@ -389,31 +350,31 @@ Definition hashmap_HashMap_contains_key
   hashmap_HashMap_contains_key_in_list T n key l
 .
 
-(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_in_list]: loop 0: forward function
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_in_list]: loop 0:
     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 =>
+  | S n1 =>
     match ls with
     | Hashmap_List_Cons ckey cvalue tl =>
       if ckey s= key
       then Return cvalue
-      else hashmap_HashMap_get_in_list_loop T n0 key tl
+      else hashmap_HashMap_get_in_list_loop T n1 key tl
     | Hashmap_List_Nil => Fail_ Failure
     end
   end
 .
 
-(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_in_list]: forward function
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_in_list]:
     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_main::hashmap::HashMap<T>}::get]: forward function
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get]:
     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 :=
@@ -427,292 +388,209 @@ Definition hashmap_HashMap_get
   hashmap_HashMap_get_in_list T n key l
 .
 
-(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_mut_in_list]: loop 0: forward function
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_mut_in_list]: loop 0:
     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
-    | Hashmap_List_Cons ckey cvalue tl =>
-      if ckey s= key
-      then Return cvalue
-      else hashmap_HashMap_get_mut_in_list_loop T n0 tl key
-    | Hashmap_List_Nil => Fail_ Failure
-    end
-  end
-.
-
-(** [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_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)
+  (T : Type) (n : nat) (ls : hashmap_List_t T) (key : usize) :
+  result (T * (T -> result (hashmap_List_t T)))
   :=
   match n with
   | O => Fail_ OutOfFuel
-  | S n0 =>
+  | S n1 =>
     match ls with
     | Hashmap_List_Cons ckey cvalue tl =>
       if ckey s= key
-      then Return (Hashmap_List_Cons ckey ret tl)
+      then
+        let back_'a := fun (ret : T) => Return (Hashmap_List_Cons ckey ret tl)
+          in
+        Return (cvalue, back_'a)
       else (
-        tl0 <- hashmap_HashMap_get_mut_in_list_loop_back T n0 tl key ret;
-        Return (Hashmap_List_Cons ckey cvalue tl0))
+        p <- hashmap_HashMap_get_mut_in_list_loop T n1 tl key;
+        let (t, back_'a) := p in
+        let back_'a1 :=
+          fun (ret : T) =>
+            tl1 <- back_'a ret; Return (Hashmap_List_Cons ckey cvalue tl1) in
+        Return (t, back_'a1))
     | Hashmap_List_Nil => Fail_ Failure
     end
   end
 .
 
-(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_mut_in_list]: backward function 0
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_mut_in_list]:
     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)
+Definition hashmap_HashMap_get_mut_in_list
+  (T : Type) (n : nat) (ls : hashmap_List_t T) (key : usize) :
+  result (T * (T -> result (hashmap_List_t T)))
   :=
-  hashmap_HashMap_get_mut_in_list_loop_back T n ls key ret
+  p <- hashmap_HashMap_get_mut_in_list_loop T n ls key;
+  let (t, back_'a) := p in
+  let back_'a1 := fun (ret : T) => back_'a ret in
+  Return (t, back_'a1)
 .
 
-(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_mut]: forward function
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_mut]:
     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 <-
-    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_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)
+  (T : Type) (n : nat) (self : hashmap_HashMap_t T) (key : usize) :
+  result (T * (T -> result (hashmap_HashMap_t 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 <-
+  p <-
     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 <-
-    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_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_main::hashmap::HashMap<T>}::remove_from_list]: loop 0: forward function
+  let (l, index_mut_back) := p in
+  p1 <- hashmap_HashMap_get_mut_in_list T n l key;
+  let (t, get_mut_in_list_back) := p1 in
+  let back_'a :=
+    fun (ret : T) =>
+      l1 <- get_mut_in_list_back ret;
+      v <- index_mut_back l1;
+      Return
+        {|
+          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
+        |} in
+  Return (t, back_'a)
+.
+
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::remove_from_list]: loop 0:
     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)
+  result ((option T) * (hashmap_List_t T))
   :=
   match n with
   | O => Fail_ OutOfFuel
-  | S n0 =>
+  | S n1 =>
     match ls with
     | Hashmap_List_Cons ckey t tl =>
       if ckey s= key
       then
-        let mv_ls :=
+        let (mv_ls, _) :=
           core_mem_replace (hashmap_List_t T) (Hashmap_List_Cons ckey t tl)
             Hashmap_List_Nil in
         match mv_ls with
-        | Hashmap_List_Cons i cvalue tl0 => Return (Some cvalue)
+        | Hashmap_List_Cons _ cvalue tl1 => Return (Some cvalue, tl1)
         | Hashmap_List_Nil => Fail_ Failure
         end
-      else hashmap_HashMap_remove_from_list_loop T n0 key tl
-    | Hashmap_List_Nil => Return None
+      else (
+        p <- hashmap_HashMap_remove_from_list_loop T n1 key tl;
+        let (o, back) := p in
+        Return (o, Hashmap_List_Cons ckey t back))
+    | Hashmap_List_Nil => Return (None, Hashmap_List_Nil)
     end
   end
 .
 
-(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::remove_from_list]: forward function
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::remove_from_list]:
     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)
+  result ((option T) * (hashmap_List_t T))
   :=
   hashmap_HashMap_remove_from_list_loop T n key ls
 .
 
-(** [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
-    | Hashmap_List_Cons ckey t tl =>
-      if ckey s= key
-      then
-        let mv_ls :=
-          core_mem_replace (hashmap_List_t T) (Hashmap_List_Cons ckey t tl)
-            Hashmap_List_Nil in
-        match mv_ls with
-        | Hashmap_List_Cons i cvalue tl0 => Return tl0
-        | Hashmap_List_Nil => Fail_ Failure
-        end
-      else (
-        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_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_HashMap_remove_from_list_loop_back T n key ls
-.
-
-(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::remove]: forward function
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::remove]:
     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)
+  result ((option T) * (hashmap_HashMap_t 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 <-
+  p <-
     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_HashMap_num_entries) 1%usize; Return (Some x0)
-  end
-.
-
-(** [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 key;
-  let i := alloc_vec_Vec_len (hashmap_List_t T) self.(hashmap_HashMap_slots) in
-  hash_mod <- usize_rem hash i;
-  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;
+  let (l, index_mut_back) := p in
+  p1 <- hashmap_HashMap_remove_from_list T n key l;
+  let (x, l1) := p1 in
   match x with
   | None =>
-    l0 <- hashmap_HashMap_remove_from_list_back T n key l;
-    v <-
-      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
+    v <- index_mut_back l1;
+    Return (None,
       {|
         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_HashMap_num_entries) 1%usize;
-    l0 <- hashmap_HashMap_remove_from_list_back T n key l;
-    v <-
-      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
+      |})
+  | Some x1 =>
+    i1 <- usize_sub self.(hashmap_HashMap_num_entries) 1%usize;
+    v <- index_mut_back l1;
+    Return (Some x1,
       {|
-        hashmap_HashMap_num_entries := i0;
+        hashmap_HashMap_num_entries := i1;
         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
+(** [hashmap_main::hashmap::test1]:
     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;
+  hm1 <- hashmap_HashMap_insert u64 n hm 0%usize 42%u64;
+  hm2 <- hashmap_HashMap_insert u64 n hm1 128%usize 18%u64;
+  hm3 <- hashmap_HashMap_insert u64 n hm2 1024%usize 138%u64;
+  hm4 <- hashmap_HashMap_insert u64 n hm3 1056%usize 256%u64;
+  i <- hashmap_HashMap_get u64 n hm4 128%usize;
   if negb (i s= 18%u64)
   then Fail_ Failure
   else (
-    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)
+    p <- hashmap_HashMap_get_mut u64 n hm4 1024%usize;
+    let (_, get_mut_back) := p in
+    hm5 <- get_mut_back 56%u64;
+    i1 <- hashmap_HashMap_get u64 n hm5 1024%usize;
+    if negb (i1 s= 56%u64)
     then Fail_ Failure
     else (
-      x <- hashmap_HashMap_remove u64 n hm4 1024%usize;
+      p1 <- hashmap_HashMap_remove u64 n hm5 1024%usize;
+      let (x, hm6) := p1 in
       match x with
       | None => Fail_ Failure
-      | Some x0 =>
-        if negb (x0 s= 56%u64)
+      | Some x1 =>
+        if negb (x1 s= 56%u64)
         then Fail_ Failure
         else (
-          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)
+          i2 <- hashmap_HashMap_get u64 n hm6 0%usize;
+          if negb (i2 s= 42%u64)
           then Fail_ Failure
           else (
-            i2 <- hashmap_HashMap_get u64 n hm5 128%usize;
-            if negb (i2 s= 18%u64)
+            i3 <- hashmap_HashMap_get u64 n hm6 128%usize;
+            if negb (i3 s= 18%u64)
             then Fail_ Failure
             else (
-              i3 <- hashmap_HashMap_get u64 n hm5 1056%usize;
-              if negb (i3 s= 256%u64) then Fail_ Failure else Return tt)))
+              i4 <- hashmap_HashMap_get u64 n hm6 1056%usize;
+              if negb (i4 s= 256%u64) then Fail_ Failure else Return tt)))
       end))
 .
 
-(** [hashmap_main::insert_on_disk]: forward function
+(** [hashmap_main::insert_on_disk]:
     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 st;
-  let (st0, hm) := p in
-  hm0 <- hashmap_HashMap_insert u64 n hm key value;
-  p0 <- hashmap_utils_serialize hm0 st0;
-  let (st1, _) := p0 in
-  Return (st1, tt)
+  let (st1, hm) := p in
+  hm1 <- hashmap_HashMap_insert u64 n hm key value;
+  p1 <- hashmap_utils_serialize hm1 st1;
+  let (st2, _) := p1 in
+  Return (st2, tt)
 .
 
-(** [hashmap_main::main]: forward function
+(** [hashmap_main::main]:
     Source: 'src/hashmap_main.rs', lines 16:0-16:13 *)
 Definition main : result unit :=
   Return tt.
diff --git a/tests/coq/hashmap_on_disk/HashmapMain_FunsExternal_Template.v b/tests/coq/hashmap_on_disk/HashmapMain_FunsExternal_Template.v
index e10d02f6..fb2e052a 100644
--- a/tests/coq/hashmap_on_disk/HashmapMain_FunsExternal_Template.v
+++ b/tests/coq/hashmap_on_disk/HashmapMain_FunsExternal_Template.v
@@ -11,13 +11,13 @@ Require Import HashmapMain_Types.
 Include HashmapMain_Types.
 Module HashmapMain_FunsExternal_Template.
 
-(** [hashmap_main::hashmap_utils::deserialize]: forward function
+(** [hashmap_main::hashmap_utils::deserialize]:
     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
+(** [hashmap_main::hashmap_utils::serialize]:
     Source: 'src/hashmap_utils.rs', lines 5:0-5:42 *)
 Axiom hashmap_utils_serialize
   : hashmap_HashMap_t u64 -> state -> result (state * unit)
diff --git a/tests/coq/hashmap_on_disk/Primitives.v b/tests/coq/hashmap_on_disk/Primitives.v
index 84280b96..990e27e4 100644
--- a/tests/coq/hashmap_on_disk/Primitives.v
+++ b/tests/coq/hashmap_on_disk/Primitives.v
@@ -67,8 +67,7 @@ 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 .
+Definition core_mem_replace (a : Type) (x : a) (y : a) : a * a := (x, x) .
 
 Record mut_raw_ptr (T : Type) := { mut_raw_ptr_v : T }.
 Record const_raw_ptr (T : Type) := { const_raw_ptr_v : T }.
@@ -504,13 +503,15 @@ 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;
+  core_ops_index_IndexMut_index_mut :
+    Self ->
+    Idx ->
+    result (core_ops_index_IndexMut_indexInst.(core_ops_index_Index_Output) *
+            (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 {
@@ -524,13 +525,14 @@ 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;
+  core_ops_deref_DerefMut_deref_mut :
+    Self ->
+    result (core_ops_deref_DerefMut_derefInst.(core_ops_deref_Deref_target) *
+            (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;
@@ -543,8 +545,8 @@ 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.
+Definition alloc_boxed_Box_deref_mut (T : Type) (x : T) : result (T * (T -> result T)) :=
+  Return (x, fun x => Return x).
 
 (* Trait instance *)
 Definition alloc_boxed_Box_coreopsDerefInst (Self : Type) : core_ops_deref_Deref Self := {|
@@ -556,7 +558,6 @@ Definition alloc_boxed_Box_coreopsDerefInst (Self : Type) : core_ops_deref_Deref
 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;
 |}.
 
 
@@ -584,6 +585,13 @@ 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).
 
+Definition array_index_mut_usize (T : Type) (n : usize) (a : array T n) (i : usize) :
+  result (T * (T -> result (array T n))) :=
+  match array_index_usize T n a i with
+  | Fail_ e => Fail_ e
+  | Return x => Return (x, array_update_usize T n a i)
+  end.
+
 (*** Slice *)
 Definition slice T := { l: list T | Z.of_nat (length l) <= usize_max}.
 
@@ -591,11 +599,25 @@ 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).
 
+Definition slice_index_mut_usize (T : Type) (s : slice T) (i : usize) :
+  result (T * (T -> result (slice T))) :=
+  match slice_index_usize T s i with
+  | Fail_ e => Fail_ e
+  | Return x => Return (x, slice_update_usize T s i)
+  end.
+
 (*** 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).
 
+Definition array_to_slice_mut (T : Type) (n : usize) (a : array T n) :
+  result (slice T * (slice T -> result (array T n))) :=
+  match array_to_slice T n a with
+  | Fail_ e => Fail_ e
+  | Return x => Return (x, array_from_slice T n a)
+  end.
+
 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).
 
@@ -639,16 +661,9 @@ Definition alloc_vec_Vec_bind {A B} (v: alloc_vec_Vec A) (f: list A -> result (l
   | 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)
@@ -661,6 +676,14 @@ Axiom alloc_vec_Vec_index_usize : forall {T : Type} (v : alloc_vec_Vec T) (i : u
 (* Helper *)
 Axiom alloc_vec_Vec_update_usize : forall {T : Type} (v : alloc_vec_Vec T) (i : usize) (x : T), result (alloc_vec_Vec T).
 
+Definition alloc_vec_Vec_index_mut_usize {T : Type} (v: alloc_vec_Vec T) (i: usize) :
+  result (T * (T -> result (alloc_vec_Vec T))) :=
+  match alloc_vec_Vec_index_usize v i with
+  | Return x =>
+    Return (x, alloc_vec_Vec_update_usize v i)
+  | Fail_ e => Fail_ e
+  end.
+
 (* Trait declaration: [core::slice::index::private_slice_index::Sealed] *)
 Definition core_slice_index_private_slice_index_Sealed (self : Type) := unit.
 
@@ -669,25 +692,23 @@ Record core_slice_index_SliceIndex (Self T : Type) := mk_core_slice_index_SliceI
   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_mut :
+    Self -> T -> result (option core_slice_index_SliceIndex_Output * (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;
+  core_slice_index_SliceIndex_index_mut :
+    Self -> T -> result (core_slice_index_SliceIndex_Output * (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
@@ -704,11 +725,9 @@ Axiom core_slice_index_RangeUsize_get : forall (T : Type) (i : core_ops_range_Ra
 
 (* [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).
+  forall (T : Type),
+    core_ops_range_Range usize -> slice T ->
+    result (option (slice T) * (option (slice T) -> result (slice T))).
 
 (* [core::slice::index::Range::get_unchecked]: forward function *)
 Definition core_slice_index_RangeUsize_get_unchecked
@@ -732,21 +751,14 @@ Axiom core_slice_index_RangeUsize_index :
 
 (* [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).
+  forall (T : Type), core_ops_range_Range usize -> slice T -> result (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).
+  slice T -> Idx ->
+  result (inst.(core_slice_index_SliceIndex_Output) *
+          (inst.(core_slice_index_SliceIndex_Output) -> result (slice T))).
 
 (* [core::array::[T; N]::index]: forward function *)
 Axiom core_array_Array_index :
@@ -756,12 +768,9 @@ Axiom core_array_Array_index :
 (* [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).
+  (a : array T N) (i : Idx),
+  result (inst.(core_ops_index_IndexMut_indexInst).(core_ops_index_Index_Output) *
+          (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
@@ -774,12 +783,10 @@ Definition core_slice_index_SliceIndexRangeUsizeSliceTInst (T : Type) :
   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]] *)
@@ -796,7 +803,6 @@ Definition core_ops_index_IndexMutSliceTIInst (T Idx : Type)
   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]] *)
@@ -813,18 +819,14 @@ Definition core_ops_index_IndexMutArrayInst (T Idx : Type) (N : usize)
   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).
+Axiom core_slice_index_usize_get_mut :
+  forall (T : Type), usize -> slice T -> result (option T * (option T -> result (slice T))).
 
 (* [core::slice::index::usize::get_unchecked]: forward function *)
 Axiom core_slice_index_usize_get_unchecked :
@@ -838,11 +840,8 @@ Axiom core_slice_index_usize_get_unchecked_mut :
 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).
+Axiom core_slice_index_usize_index_mut :
+  forall (T : Type), usize -> slice T -> result (T * (T -> result (slice T))).
 
 (* Trait implementation: [core::slice::index::private_slice_index::usize] *)
 Definition core_slice_index_private_slice_index_SealedUsizeInst
@@ -855,12 +854,10 @@ Definition core_slice_index_SliceIndexUsizeSliceTInst (T : Type) :
   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 *)
@@ -869,12 +866,9 @@ Axiom alloc_vec_Vec_index : forall (T Idx : Type) (inst : core_slice_index_Slice
 
 (* [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).
+  (Self : alloc_vec_Vec T) (i : Idx),
+  result (inst.(core_slice_index_SliceIndex_Output) *
+          (inst.(core_slice_index_SliceIndex_Output) -> result (alloc_vec_Vec T))).
 
 (* Trait implementation: [alloc::vec::Vec] *)
 Definition alloc_vec_Vec_coreopsindexIndexInst (T Idx : Type)
@@ -890,7 +884,6 @@ Definition alloc_vec_Vec_coreopsindexIndexMutInst (T Idx : Type)
   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 *)
@@ -901,10 +894,6 @@ Axiom alloc_vec_Vec_index_eq : forall {a : Type} (v : alloc_vec_Vec a) (i : usiz
 
 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.
+    alloc_vec_Vec_index_mut_usize v i.
 
 End Primitives.
diff --git a/tests/coq/misc/Bitwise.v b/tests/coq/misc/Bitwise.v
index 94771b37..b04c95f2 100644
--- a/tests/coq/misc/Bitwise.v
+++ b/tests/coq/misc/Bitwise.v
@@ -8,29 +8,29 @@ Import ListNotations.
 Local Open Scope Primitives_scope.
 Module Bitwise.
 
-(** [bitwise::shift_u32]: forward function
+(** [bitwise::shift_u32]:
     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
+(** [bitwise::shift_i32]:
     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
+(** [bitwise::xor_u32]:
     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
+(** [bitwise::or_u32]:
     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
+(** [bitwise::and_u32]:
     Source: 'src/bitwise.rs', lines 25:0-25:37 *)
 Definition and_u32 (a : u32) (b : u32) : result u32 :=
   Return (u32_and a b).
diff --git a/tests/coq/misc/Constants.v b/tests/coq/misc/Constants.v
index ad899f25..0f33cbd6 100644
--- a/tests/coq/misc/Constants.v
+++ b/tests/coq/misc/Constants.v
@@ -23,7 +23,7 @@ Definition x1_c : u32 := x1_body%global.
 Definition x2_body : result u32 := Return 3%u32.
 Definition x2_c : u32 := x2_body%global.
 
-(** [constants::incr]: forward function
+(** [constants::incr]:
     Source: 'src/constants.rs', lines 17:0-17:32 *)
 Definition incr (n : u32) : result u32 :=
   u32_add n 1%u32.
@@ -33,7 +33,7 @@ Definition incr (n : u32) : result u32 :=
 Definition x3_body : result u32 := incr 32%u32.
 Definition x3_c : u32 := x3_body%global.
 
-(** [constants::mk_pair0]: forward function
+(** [constants::mk_pair0]:
     Source: 'src/constants.rs', lines 23:0-23:51 *)
 Definition mk_pair0 (x : u32) (y : u32) : result (u32 * u32) :=
   Return (x, y).
@@ -46,7 +46,7 @@ Arguments mkPair_t { _ _ }.
 Arguments pair_x { _ _ }.
 Arguments pair_y { _ _ }.
 
-(** [constants::mk_pair1]: forward function
+(** [constants::mk_pair1]:
     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 |}
@@ -81,7 +81,7 @@ Record Wrap_t (T : Type) := mkWrap_t { wrap_value : T; }.
 Arguments mkWrap_t { _ }.
 Arguments wrap_value { _ }.
 
-(** [constants::{constants::Wrap<T>}::new]: forward function
+(** [constants::{constants::Wrap<T>}::new]:
     Source: 'src/constants.rs', lines 54:4-54:41 *)
 Definition wrap_new (T : Type) (value : T) : result (Wrap_t T) :=
   Return {| wrap_value := value |}
@@ -92,7 +92,7 @@ Definition wrap_new (T : Type) (value : T) : result (Wrap_t T) :=
 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
+(** [constants::unwrap_y]:
     Source: 'src/constants.rs', lines 43:0-43:30 *)
 Definition unwrap_y : result i32 :=
   Return y_c.(wrap_value).
@@ -107,12 +107,12 @@ Definition yval_c : i32 := yval_body%global.
 Definition get_z1_z1_body : result i32 := Return 3%i32.
 Definition get_z1_z1_c : i32 := get_z1_z1_body%global.
 
-(** [constants::get_z1]: forward function
+(** [constants::get_z1]:
     Source: 'src/constants.rs', lines 61:0-61:28 *)
 Definition get_z1 : result i32 :=
   Return get_z1_z1_c.
 
-(** [constants::add]: forward function
+(** [constants::add]:
     Source: 'src/constants.rs', lines 66:0-66:39 *)
 Definition add (a : i32) (b : i32) : result i32 :=
   i32_add a b.
@@ -132,10 +132,10 @@ Definition q2_c : i32 := q2_body%global.
 Definition q3_body : result i32 := add q2_c 3%i32.
 Definition q3_c : i32 := q3_body%global.
 
-(** [constants::get_z2]: forward function
+(** [constants::get_z2]:
     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.
+  i <- get_z1; i1 <- add i q3_c; add q1_c i1.
 
 (** [constants::S1]
     Source: 'src/constants.rs', lines 80:0-80:18 *)
diff --git a/tests/coq/misc/External_Funs.v b/tests/coq/misc/External_Funs.v
index e9d39f66..049f5d39 100644
--- a/tests/coq/misc/External_Funs.v
+++ b/tests/coq/misc/External_Funs.v
@@ -12,44 +12,23 @@ Require Import External_FunsExternal.
 Include External_FunsExternal.
 Module External_Funs.
 
-(** [external::swap]: forward function
+(** [external::swap]:
     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 T x y st;
-  let (st0, _) := p in
-  p0 <- core_mem_swap_back0 T x y st st0;
-  let (st1, _) := p0 in
-  p1 <- core_mem_swap_back1 T x y st st1;
-  let (st2, _) := p1 in
-  Return (st2, tt)
+  (T : Type) (x : T) (y : T) (st : state) : result (state * (T * T)) :=
+  core_mem_swap T x y st
 .
 
-(** [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 T x y st;
-  let (st1, _) := p in
-  p0 <- core_mem_swap_back0 T x y st st1;
-  let (st2, x0) := p0 in
-  p1 <- core_mem_swap_back1 T x y st st2;
-  let (_, y0) := p1 in
-  Return (st0, (x0, y0))
-.
-
-(** [external::test_new_non_zero_u32]: forward function
+(** [external::test_new_non_zero_u32]:
     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
+  let (st1, o) := p in
+  core_option_Option_unwrap core_num_nonzero_NonZeroU32_t o st1
 .
 
-(** [external::test_vec]: forward function
+(** [external::test_vec]:
     Source: 'src/external.rs', lines 17:0-17:17 *)
 Definition test_vec : result unit :=
   let v := alloc_vec_Vec_new u32 in
@@ -60,59 +39,39 @@ Definition test_vec : result unit :=
 (** Unit test for [external::test_vec] *)
 Check (test_vec )%return.
 
-(** [external::custom_swap]: forward function
+(** [external::custom_swap]:
     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 T x y st;
-  let (st0, _) := p in
-  p0 <- core_mem_swap_back0 T x y st st0;
-  let (st1, x0) := p0 in
-  p1 <- core_mem_swap_back1 T x y st st1;
-  let (st2, _) := p1 in
-  Return (st2, x0)
-.
-
-(** [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))
+  (T : Type) (x : T) (y : T) (st : state) :
+  result (state * (T * (T -> state -> result (state * (T * T)))))
   :=
   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
-  p1 <- core_mem_swap_back1 T x y st st2;
-  let (_, y0) := p1 in
-  Return (st0, (ret, y0))
+  let (st1, p1) := p in
+  let (t, t1) := p1 in
+  let back_'a := fun (ret : T) (st2 : state) => Return (st2, (ret, t1)) in
+  Return (st1, (t, back_'a))
 .
 
-(** [external::test_custom_swap]: forward function
+(** [external::test_custom_swap]:
     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 u32 x y st; let (st0, _) := p in Return (st0, tt)
-.
-
-(** [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))
-  :=
-  custom_swap_back u32 x y st 1%u32 st0
+  (x : u32) (y : u32) (st : state) : result (state * (u32 * u32)) :=
+  p <- custom_swap u32 x y st;
+  let (st1, p1) := p in
+  let (_, custom_swap_back) := p1 in
+  p2 <- custom_swap_back 1%u32 st1;
+  let (_, p3) := p2 in
+  let (x1, y1) := p3 in
+  Return (st1, (x1, y1))
 .
 
-(** [external::test_swap_non_zero]: forward function
+(** [external::test_swap_non_zero]:
     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
-  let (x0, _) := p1 in
-  if x0 s= 0%u32 then Fail_ Failure else Return (st1, x0)
+  let (st1, p1) := p in
+  let (x1, _) := p1 in
+  if x1 s= 0%u32 then Fail_ Failure else Return (st1, x1)
 .
 
 End External_Funs.
diff --git a/tests/coq/misc/External_FunsExternal_Template.v b/tests/coq/misc/External_FunsExternal_Template.v
index 31e69c39..6773ac18 100644
--- a/tests/coq/misc/External_FunsExternal_Template.v
+++ b/tests/coq/misc/External_FunsExternal_Template.v
@@ -11,31 +11,19 @@ Require Import External_Types.
 Include External_Types.
 Module External_FunsExternal_Template.
 
-(** [core::mem::swap]: forward function
+(** [core::mem::swap]:
     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)
+  forall(T : Type), T -> T -> state -> result (state * (T * T))
 .
 
-(** [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
+(** [core::num::nonzero::{core::num::nonzero::NonZeroU32#14}::new]:
     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
+(** [core::option::{core::option::Option<T>}::unwrap]:
     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)
diff --git a/tests/coq/misc/Loops.v b/tests/coq/misc/Loops.v
index 83c249c1..313c2cfd 100644
--- a/tests/coq/misc/Loops.v
+++ b/tests/coq/misc/Loops.v
@@ -8,90 +8,90 @@ Import ListNotations.
 Local Open Scope Primitives_scope.
 Module Loops.
 
-(** [loops::sum]: loop 0: forward function
+(** [loops::sum]: loop 0:
     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 =>
+  | S n1 =>
     if i s< max
-    then (s0 <- u32_add s i; i0 <- u32_add i 1%u32; sum_loop n0 max i0 s0)
+    then (s1 <- u32_add s i; i1 <- u32_add i 1%u32; sum_loop n1 max i1 s1)
     else u32_mul s 2%u32
   end
 .
 
-(** [loops::sum]: forward function
+(** [loops::sum]:
     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
+(** [loops::sum_with_mut_borrows]: loop 0:
     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
-  | S n0 =>
+  | S n1 =>
     if mi s< max
     then (
-      ms0 <- u32_add ms mi;
-      mi0 <- u32_add mi 1%u32;
-      sum_with_mut_borrows_loop n0 max mi0 ms0)
+      ms1 <- u32_add ms mi;
+      mi1 <- u32_add mi 1%u32;
+      sum_with_mut_borrows_loop n1 max mi1 ms1)
     else u32_mul ms 2%u32
   end
 .
 
-(** [loops::sum_with_mut_borrows]: forward function
+(** [loops::sum_with_mut_borrows]:
     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
+(** [loops::sum_with_shared_borrows]: loop 0:
     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
-  | S n0 =>
+  | S n1 =>
     if i s< max
     then (
-      i0 <- u32_add i 1%u32;
-      s0 <- u32_add s i0;
-      sum_with_shared_borrows_loop n0 max i0 s0)
+      i1 <- u32_add i 1%u32;
+      s1 <- u32_add s i1;
+      sum_with_shared_borrows_loop n1 max i1 s1)
     else u32_mul s 2%u32
   end
 .
 
-(** [loops::sum_with_shared_borrows]: forward function
+(** [loops::sum_with_shared_borrows]:
     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 ())
+(** [loops::clear]: loop 0:
     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 := alloc_vec_Vec_len u32 v in
-    if i s< i0
+  | S n1 =>
+    let i1 := alloc_vec_Vec_len u32 v in
+    if i s< i1
     then (
-      i1 <- usize_add i 1%usize;
-      v0 <-
-        alloc_vec_Vec_index_mut_back u32 usize
-          (core_slice_index_SliceIndexUsizeSliceTInst u32) v i 0%u32;
-      clear_loop n0 v0 i1)
+      p <-
+        alloc_vec_Vec_index_mut u32 usize
+          (core_slice_index_SliceIndexUsizeSliceTInst u32) v i;
+      let (_, index_mut_back) := p in
+      i2 <- usize_add i 1%usize;
+      v1 <- index_mut_back 0%u32;
+      clear_loop n1 v1 i2)
     else Return v
   end
 .
 
-(** [loops::clear]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+(** [loops::clear]:
     Source: 'src/loops.rs', lines 52:0-52:30 *)
 Definition clear
   (n : nat) (v : alloc_vec_Vec u32) : result (alloc_vec_Vec u32) :=
@@ -108,181 +108,146 @@ Inductive List_t (T : Type) :=
 Arguments List_Cons { _ }.
 Arguments List_Nil { _ }.
 
-(** [loops::list_mem]: loop 0: forward function
+(** [loops::list_mem]: loop 0:
     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 =>
+  | S n1 =>
     match ls with
-    | List_Cons y tl => if y s= x then Return true else list_mem_loop n0 x tl
+    | List_Cons y tl => if y s= x then Return true else list_mem_loop n1 x tl
     | List_Nil => Return false
     end
   end
 .
 
-(** [loops::list_mem]: forward function
+(** [loops::list_mem]:
     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
+(** [loops::list_nth_mut_loop]: loop 0:
     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
-    | List_Cons x tl =>
-      if i s= 0%u32
-      then Return x
-      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
-    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 T n ls i
-.
-
-(** [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)
+  (T : Type) (n : nat) (ls : List_t T) (i : u32) :
+  result (T * (T -> result (List_t T)))
   :=
   match n with
   | O => Fail_ OutOfFuel
-  | S n0 =>
+  | S n1 =>
     match ls with
     | List_Cons x tl =>
       if i s= 0%u32
-      then Return (List_Cons ret tl)
+      then
+        let back := fun (ret : T) => Return (List_Cons ret tl) in
+        Return (x, back)
       else (
-        i0 <- u32_sub i 1%u32;
-        tl0 <- list_nth_mut_loop_loop_back T n0 tl i0 ret;
-        Return (List_Cons x tl0))
+        i1 <- u32_sub i 1%u32;
+        p <- list_nth_mut_loop_loop T n1 tl i1;
+        let (t, back) := p in
+        let back1 := fun (ret : T) => tl1 <- back ret; Return (List_Cons x tl1)
+          in
+        Return (t, back1))
     | List_Nil => Fail_ Failure
     end
   end
 .
 
-(** [loops::list_nth_mut_loop]: backward function 0
+(** [loops::list_nth_mut_loop]:
     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)
+Definition list_nth_mut_loop
+  (T : Type) (n : nat) (ls : List_t T) (i : u32) :
+  result (T * (T -> result (List_t T)))
   :=
-  list_nth_mut_loop_loop_back T n ls i ret
+  p <- list_nth_mut_loop_loop T n ls i;
+  let (t, back) := p in
+  let back1 := fun (ret : T) => back ret in
+  Return (t, back1)
 .
 
-(** [loops::list_nth_shared_loop]: loop 0: forward function
+(** [loops::list_nth_shared_loop]: loop 0:
     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 =>
+  | S n1 =>
     match ls with
     | List_Cons x tl =>
       if i s= 0%u32
       then Return x
-      else (i0 <- u32_sub i 1%u32; list_nth_shared_loop_loop T n0 tl i0)
+      else (i1 <- u32_sub i 1%u32; list_nth_shared_loop_loop T n1 tl i1)
     | List_Nil => Fail_ Failure
     end
   end
 .
 
-(** [loops::list_nth_shared_loop]: forward function
+(** [loops::list_nth_shared_loop]:
     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 T n ls i
 .
 
-(** [loops::get_elem_mut]: loop 0: forward function
+(** [loops::get_elem_mut]: loop 0:
     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
-    | 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
-    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
-    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)
+  (n : nat) (x : usize) (ls : List_t usize) :
+  result (usize * (usize -> result (List_t usize)))
   :=
   match n with
   | O => Fail_ OutOfFuel
-  | S n0 =>
+  | S n1 =>
     match ls with
     | List_Cons y tl =>
       if y s= x
-      then Return (List_Cons ret tl)
+      then
+        let back := fun (ret : usize) => Return (List_Cons ret tl) in
+        Return (y, back)
       else (
-        tl0 <- get_elem_mut_loop_back n0 x tl ret; Return (List_Cons y tl0))
+        p <- get_elem_mut_loop n1 x tl;
+        let (i, back) := p in
+        let back1 :=
+          fun (ret : usize) => tl1 <- back ret; Return (List_Cons y tl1) in
+        Return (i, back1))
     | List_Nil => Fail_ Failure
     end
   end
 .
 
-(** [loops::get_elem_mut]: backward function 0
+(** [loops::get_elem_mut]:
     Source: 'src/loops.rs', lines 103:0-103:73 *)
-Definition get_elem_mut_back
-  (n : nat) (slots : alloc_vec_Vec (List_t usize)) (x : usize) (ret : usize) :
-  result (alloc_vec_Vec (List_t usize))
+Definition get_elem_mut
+  (n : nat) (slots : alloc_vec_Vec (List_t usize)) (x : usize) :
+  result (usize * (usize -> result (alloc_vec_Vec (List_t usize))))
   :=
-  l <-
+  p <-
     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;
-  alloc_vec_Vec_index_mut_back (List_t usize) usize
-    (core_slice_index_SliceIndexUsizeSliceTInst (List_t usize)) slots 0%usize
-    l0
+  let (l, index_mut_back) := p in
+  p1 <- get_elem_mut_loop n x l;
+  let (i, back) := p1 in
+  let back1 := fun (ret : usize) => l1 <- back ret; index_mut_back l1 in
+  Return (i, back1)
 .
 
-(** [loops::get_elem_shared]: loop 0: forward function
+(** [loops::get_elem_shared]: loop 0:
     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 =>
+  | S n1 =>
     match ls with
     | List_Cons y tl =>
-      if y s= x then Return y else get_elem_shared_loop n0 x tl
+      if y s= x then Return y else get_elem_shared_loop n1 x tl
     | List_Nil => Fail_ Failure
     end
   end
 .
 
-(** [loops::get_elem_shared]: forward function
+(** [loops::get_elem_shared]:
     Source: 'src/loops.rs', lines 119:0-119:68 *)
 Definition get_elem_shared
   (n : nat) (slots : alloc_vec_Vec (List_t usize)) (x : usize) :
@@ -294,123 +259,114 @@ Definition get_elem_shared
   get_elem_shared_loop n x l
 .
 
-(** [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]:
     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
+Definition id_mut
+  (T : Type) (ls : List_t T) :
+  result ((List_t T) * (List_t T -> result (List_t T)))
+  :=
+  let back := fun (ret : List_t T) => Return ret in Return (ls, back)
 .
 
-(** [loops::id_shared]: forward function
+(** [loops::id_shared]:
     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
+(** [loops::list_nth_mut_loop_with_id]: loop 0:
     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
-    | 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 T n0 i0 tl)
-    | List_Nil => Fail_ Failure
-    end
-  end
-.
-
-(** [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 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
-    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)
+  (T : Type) (n : nat) (i : u32) (ls : List_t T) :
+  result (T * (T -> result (List_t T)))
   :=
   match n with
   | O => Fail_ OutOfFuel
-  | S n0 =>
+  | S n1 =>
     match ls with
     | List_Cons x tl =>
       if i s= 0%u32
-      then Return (List_Cons ret tl)
+      then
+        let back := fun (ret : T) => Return (List_Cons ret tl) in
+        Return (x, back)
       else (
-        i0 <- u32_sub i 1%u32;
-        tl0 <- list_nth_mut_loop_with_id_loop_back T n0 i0 tl ret;
-        Return (List_Cons x tl0))
+        i1 <- u32_sub i 1%u32;
+        p <- list_nth_mut_loop_with_id_loop T n1 i1 tl;
+        let (t, back) := p in
+        let back1 := fun (ret : T) => tl1 <- back ret; Return (List_Cons x tl1)
+          in
+        Return (t, back1))
     | List_Nil => Fail_ Failure
     end
   end
 .
 
-(** [loops::list_nth_mut_loop_with_id]: backward function 0
+(** [loops::list_nth_mut_loop_with_id]:
     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)
+Definition list_nth_mut_loop_with_id
+  (T : Type) (n : nat) (ls : List_t T) (i : u32) :
+  result (T * (T -> result (List_t T)))
   :=
-  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
+  p <- id_mut T ls;
+  let (ls1, id_mut_back) := p in
+  p1 <- list_nth_mut_loop_with_id_loop T n i ls1;
+  let (t, back) := p1 in
+  let back1 := fun (ret : T) => l <- back ret; id_mut_back l in
+  Return (t, back1)
 .
 
-(** [loops::list_nth_shared_loop_with_id]: loop 0: forward function
+(** [loops::list_nth_shared_loop_with_id]: loop 0:
     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 =>
+  | S n1 =>
     match ls with
     | 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 T n0 i0 tl)
+        i1 <- u32_sub i 1%u32; list_nth_shared_loop_with_id_loop T n1 i1 tl)
     | List_Nil => Fail_ Failure
     end
   end
 .
 
-(** [loops::list_nth_shared_loop_with_id]: forward function
+(** [loops::list_nth_shared_loop_with_id]:
     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 T ls; list_nth_shared_loop_with_id_loop T n i ls0
+  ls1 <- id_shared T ls; list_nth_shared_loop_with_id_loop T n i ls1
 .
 
-(** [loops::list_nth_mut_loop_pair]: loop 0: forward function
+(** [loops::list_nth_mut_loop_pair]: loop 0:
     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)
+  result ((T * T) * (T -> result (List_t T)) * (T -> result (List_t T)))
   :=
   match n with
   | O => Fail_ OutOfFuel
-  | S n0 =>
+  | S n1 =>
     match ls0 with
     | List_Cons x0 tl0 =>
       match ls1 with
       | List_Cons x1 tl1 =>
         if i s= 0%u32
-        then Return (x0, x1)
+        then
+          let back_'a := fun (ret : T) => Return (List_Cons ret tl0) in
+          let back_'b := fun (ret : T) => Return (List_Cons ret tl1) in
+          Return ((x0, x1), back_'a, back_'b)
         else (
-          i0 <- u32_sub i 1%u32; list_nth_mut_loop_pair_loop T n0 tl0 tl1 i0)
+          i1 <- u32_sub i 1%u32;
+          t <- list_nth_mut_loop_pair_loop T n1 tl0 tl1 i1;
+          let (p, back_'a, back_'b) := t in
+          let back_'a1 :=
+            fun (ret : T) => tl01 <- back_'a ret; Return (List_Cons x0 tl01) in
+          let back_'b1 :=
+            fun (ret : T) => tl11 <- back_'b ret; Return (List_Cons x1 tl11) in
+          Return (p, back_'a1, back_'b1))
       | List_Nil => Fail_ Failure
       end
     | List_Nil => Fail_ Failure
@@ -418,86 +374,20 @@ Fixpoint list_nth_mut_loop_pair_loop
   end
 .
 
-(** [loops::list_nth_mut_loop_pair]: forward function
+(** [loops::list_nth_mut_loop_pair]:
     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)
+  result ((T * T) * (T -> result (List_t T)) * (T -> result (List_t T)))
   :=
-  list_nth_mut_loop_pair_loop T n ls0 ls1 i
+  t <- list_nth_mut_loop_pair_loop T n ls0 ls1 i;
+  let (p, back_'a, back_'b) := t in
+  let back_'a1 := fun (ret : T) => back_'a ret in
+  let back_'b1 := fun (ret : T) => back_'b ret in
+  Return (p, back_'a1, back_'b1)
 .
 
-(** [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)
-  :=
-  match n with
-  | O => Fail_ OutOfFuel
-  | S n0 =>
-    match ls0 with
-    | List_Cons x0 tl0 =>
-      match ls1 with
-      | List_Cons x1 tl1 =>
-        if i s= 0%u32
-        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 (List_Cons x0 tl00))
-      | List_Nil => Fail_ Failure
-      end
-    | List_Nil => Fail_ Failure
-    end
-  end
-.
-
-(** [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)
-  :=
-  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
-    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)
-  :=
-  match n with
-  | O => Fail_ OutOfFuel
-  | S n0 =>
-    match ls0 with
-    | List_Cons x0 tl0 =>
-      match ls1 with
-      | List_Cons x1 tl1 =>
-        if i s= 0%u32
-        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 (List_Cons x1 tl10))
-      | List_Nil => Fail_ Failure
-      end
-    | List_Nil => Fail_ Failure
-    end
-  end
-.
-
-(** [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)
-  :=
-  list_nth_mut_loop_pair_loop_back'b T n ls0 ls1 i ret
-.
-
-(** [loops::list_nth_shared_loop_pair]: loop 0: forward function
+(** [loops::list_nth_shared_loop_pair]: loop 0:
     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) :
@@ -505,7 +395,7 @@ Fixpoint list_nth_shared_loop_pair_loop
   :=
   match n with
   | O => Fail_ OutOfFuel
-  | S n0 =>
+  | S n1 =>
     match ls0 with
     | List_Cons x0 tl0 =>
       match ls1 with
@@ -513,7 +403,7 @@ Fixpoint list_nth_shared_loop_pair_loop
         if i s= 0%u32
         then Return (x0, x1)
         else (
-          i0 <- u32_sub i 1%u32; list_nth_shared_loop_pair_loop T n0 tl0 tl1 i0)
+          i1 <- u32_sub i 1%u32; list_nth_shared_loop_pair_loop T n1 tl0 tl1 i1)
       | List_Nil => Fail_ Failure
       end
     | List_Nil => Fail_ Failure
@@ -521,7 +411,7 @@ Fixpoint list_nth_shared_loop_pair_loop
   end
 .
 
-(** [loops::list_nth_shared_loop_pair]: forward function
+(** [loops::list_nth_shared_loop_pair]:
     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) :
@@ -530,24 +420,36 @@ Definition list_nth_shared_loop_pair
   list_nth_shared_loop_pair_loop T n ls0 ls1 i
 .
 
-(** [loops::list_nth_mut_loop_pair_merge]: loop 0: forward function
+(** [loops::list_nth_mut_loop_pair_merge]: loop 0:
     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)
+  result ((T * T) * ((T * T) -> result ((List_t T) * (List_t T))))
   :=
   match n with
   | O => Fail_ OutOfFuel
-  | S n0 =>
+  | S n1 =>
     match ls0 with
     | List_Cons x0 tl0 =>
       match ls1 with
       | List_Cons x1 tl1 =>
         if i s= 0%u32
-        then Return (x0, x1)
+        then
+          let back_'a :=
+            fun (ret : (T * T)) =>
+              let (t, t1) := ret in Return (List_Cons t tl0, List_Cons t1 tl1)
+            in
+          Return ((x0, x1), back_'a)
         else (
-          i0 <- u32_sub i 1%u32;
-          list_nth_mut_loop_pair_merge_loop T n0 tl0 tl1 i0)
+          i1 <- u32_sub i 1%u32;
+          p <- list_nth_mut_loop_pair_merge_loop T n1 tl0 tl1 i1;
+          let (p1, back_'a) := p in
+          let back_'a1 :=
+            fun (ret : (T * T)) =>
+              p2 <- back_'a ret;
+              let (tl01, tl11) := p2 in
+              Return (List_Cons x0 tl01, List_Cons x1 tl11) in
+          Return (p1, back_'a1))
       | List_Nil => Fail_ Failure
       end
     | List_Nil => Fail_ Failure
@@ -555,54 +457,19 @@ Fixpoint list_nth_mut_loop_pair_merge_loop
   end
 .
 
-(** [loops::list_nth_mut_loop_pair_merge]: forward function
+(** [loops::list_nth_mut_loop_pair_merge]:
     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)
+  result ((T * T) * ((T * T) -> result ((List_t T) * (List_t T))))
   :=
-  list_nth_mut_loop_pair_merge_loop T n ls0 ls1 i
+  p <- list_nth_mut_loop_pair_merge_loop T n ls0 ls1 i;
+  let (p1, back_'a) := p in
+  let back_'a1 := fun (ret : (T * T)) => back_'a ret in
+  Return (p1, back_'a1)
 .
 
-(** [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)) :
-  result ((List_t T) * (List_t T))
-  :=
-  match n with
-  | O => Fail_ OutOfFuel
-  | S n0 =>
-    match ls0 with
-    | List_Cons x0 tl0 =>
-      match ls1 with
-      | List_Cons x1 tl1 =>
-        if i s= 0%u32
-        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 (List_Cons x0 tl00, List_Cons x1 tl10))
-      | List_Nil => Fail_ Failure
-      end
-    | List_Nil => Fail_ Failure
-    end
-  end
-.
-
-(** [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)) :
-  result ((List_t T) * (List_t T))
-  :=
-  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
+(** [loops::list_nth_shared_loop_pair_merge]: loop 0:
     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) :
@@ -610,7 +477,7 @@ Fixpoint list_nth_shared_loop_pair_merge_loop
   :=
   match n with
   | O => Fail_ OutOfFuel
-  | S n0 =>
+  | S n1 =>
     match ls0 with
     | List_Cons x0 tl0 =>
       match ls1 with
@@ -618,8 +485,8 @@ Fixpoint list_nth_shared_loop_pair_merge_loop
         if i s= 0%u32
         then Return (x0, x1)
         else (
-          i0 <- u32_sub i 1%u32;
-          list_nth_shared_loop_pair_merge_loop T n0 tl0 tl1 i0)
+          i1 <- u32_sub i 1%u32;
+          list_nth_shared_loop_pair_merge_loop T n1 tl0 tl1 i1)
       | List_Nil => Fail_ Failure
       end
     | List_Nil => Fail_ Failure
@@ -627,7 +494,7 @@ Fixpoint list_nth_shared_loop_pair_merge_loop
   end
 .
 
-(** [loops::list_nth_shared_loop_pair_merge]: forward function
+(** [loops::list_nth_shared_loop_pair_merge]:
     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) :
@@ -636,24 +503,30 @@ Definition list_nth_shared_loop_pair_merge
   list_nth_shared_loop_pair_merge_loop T n ls0 ls1 i
 .
 
-(** [loops::list_nth_mut_shared_loop_pair]: loop 0: forward function
+(** [loops::list_nth_mut_shared_loop_pair]: loop 0:
     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)
+  result ((T * T) * (T -> result (List_t T)))
   :=
   match n with
   | O => Fail_ OutOfFuel
-  | S n0 =>
+  | S n1 =>
     match ls0 with
     | List_Cons x0 tl0 =>
       match ls1 with
       | List_Cons x1 tl1 =>
         if i s= 0%u32
-        then Return (x0, x1)
+        then
+          let back_'a := fun (ret : T) => Return (List_Cons ret tl0) in
+          Return ((x0, x1), back_'a)
         else (
-          i0 <- u32_sub i 1%u32;
-          list_nth_mut_shared_loop_pair_loop T n0 tl0 tl1 i0)
+          i1 <- u32_sub i 1%u32;
+          p <- list_nth_mut_shared_loop_pair_loop T n1 tl0 tl1 i1;
+          let (p1, back_'a) := p in
+          let back_'a1 :=
+            fun (ret : T) => tl01 <- back_'a ret; Return (List_Cons x0 tl01) in
+          Return (p1, back_'a1))
       | List_Nil => Fail_ Failure
       end
     | List_Nil => Fail_ Failure
@@ -661,68 +534,42 @@ Fixpoint list_nth_mut_shared_loop_pair_loop
   end
 .
 
-(** [loops::list_nth_mut_shared_loop_pair]: forward function
+(** [loops::list_nth_mut_shared_loop_pair]:
     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)
+  result ((T * T) * (T -> result (List_t T)))
   :=
-  list_nth_mut_shared_loop_pair_loop T n ls0 ls1 i
+  p <- list_nth_mut_shared_loop_pair_loop T n ls0 ls1 i;
+  let (p1, back_'a) := p in
+  let back_'a1 := fun (ret : T) => back_'a ret in
+  Return (p1, back_'a1)
 .
 
-(** [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)
-  :=
-  match n with
-  | O => Fail_ OutOfFuel
-  | S n0 =>
-    match ls0 with
-    | List_Cons x0 tl0 =>
-      match ls1 with
-      | List_Cons x1 tl1 =>
-        if i s= 0%u32
-        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 (List_Cons x0 tl00))
-      | List_Nil => Fail_ Failure
-      end
-    | List_Nil => Fail_ Failure
-    end
-  end
-.
-
-(** [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)
-  :=
-  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
+(** [loops::list_nth_mut_shared_loop_pair_merge]: loop 0:
     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)
+  result ((T * T) * (T -> result (List_t T)))
   :=
   match n with
   | O => Fail_ OutOfFuel
-  | S n0 =>
+  | S n1 =>
     match ls0 with
     | List_Cons x0 tl0 =>
       match ls1 with
       | List_Cons x1 tl1 =>
         if i s= 0%u32
-        then Return (x0, x1)
+        then
+          let back_'a := fun (ret : T) => Return (List_Cons ret tl0) in
+          Return ((x0, x1), back_'a)
         else (
-          i0 <- u32_sub i 1%u32;
-          list_nth_mut_shared_loop_pair_merge_loop T n0 tl0 tl1 i0)
+          i1 <- u32_sub i 1%u32;
+          p <- list_nth_mut_shared_loop_pair_merge_loop T n1 tl0 tl1 i1;
+          let (p1, back_'a) := p in
+          let back_'a1 :=
+            fun (ret : T) => tl01 <- back_'a ret; Return (List_Cons x0 tl01) in
+          Return (p1, back_'a1))
       | List_Nil => Fail_ Failure
       end
     | List_Nil => Fail_ Failure
@@ -730,69 +577,42 @@ Fixpoint list_nth_mut_shared_loop_pair_merge_loop
   end
 .
 
-(** [loops::list_nth_mut_shared_loop_pair_merge]: forward function
+(** [loops::list_nth_mut_shared_loop_pair_merge]:
     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 T n ls0 ls1 i
-.
-
-(** [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)
-  :=
-  match n with
-  | O => Fail_ OutOfFuel
-  | S n0 =>
-    match ls0 with
-    | List_Cons x0 tl0 =>
-      match ls1 with
-      | List_Cons x1 tl1 =>
-        if i s= 0%u32
-        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 (List_Cons x0 tl00))
-      | List_Nil => Fail_ Failure
-      end
-    | List_Nil => Fail_ Failure
-    end
-  end
-.
-
-(** [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)
+  result ((T * T) * (T -> result (List_t T)))
   :=
-  list_nth_mut_shared_loop_pair_merge_loop_back T n ls0 ls1 i ret
+  p <- list_nth_mut_shared_loop_pair_merge_loop T n ls0 ls1 i;
+  let (p1, back_'a) := p in
+  let back_'a1 := fun (ret : T) => back_'a ret in
+  Return (p1, back_'a1)
 .
 
-(** [loops::list_nth_shared_mut_loop_pair]: loop 0: forward function
+(** [loops::list_nth_shared_mut_loop_pair]: loop 0:
     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)
+  result ((T * T) * (T -> result (List_t T)))
   :=
   match n with
   | O => Fail_ OutOfFuel
-  | S n0 =>
+  | S n1 =>
     match ls0 with
     | List_Cons x0 tl0 =>
       match ls1 with
       | List_Cons x1 tl1 =>
         if i s= 0%u32
-        then Return (x0, x1)
+        then
+          let back_'b := fun (ret : T) => Return (List_Cons ret tl1) in
+          Return ((x0, x1), back_'b)
         else (
-          i0 <- u32_sub i 1%u32;
-          list_nth_shared_mut_loop_pair_loop T n0 tl0 tl1 i0)
+          i1 <- u32_sub i 1%u32;
+          p <- list_nth_shared_mut_loop_pair_loop T n1 tl0 tl1 i1;
+          let (p1, back_'b) := p in
+          let back_'b1 :=
+            fun (ret : T) => tl11 <- back_'b ret; Return (List_Cons x1 tl11) in
+          Return (p1, back_'b1))
       | List_Nil => Fail_ Failure
       end
     | List_Nil => Fail_ Failure
@@ -800,68 +620,42 @@ Fixpoint list_nth_shared_mut_loop_pair_loop
   end
 .
 
-(** [loops::list_nth_shared_mut_loop_pair]: forward function
+(** [loops::list_nth_shared_mut_loop_pair]:
     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)
+  result ((T * T) * (T -> result (List_t T)))
   :=
-  list_nth_shared_mut_loop_pair_loop T n ls0 ls1 i
-.
-
-(** [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)
-  :=
-  match n with
-  | O => Fail_ OutOfFuel
-  | S n0 =>
-    match ls0 with
-    | List_Cons x0 tl0 =>
-      match ls1 with
-      | List_Cons x1 tl1 =>
-        if i s= 0%u32
-        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 (List_Cons x1 tl10))
-      | List_Nil => Fail_ Failure
-      end
-    | List_Nil => Fail_ Failure
-    end
-  end
+  p <- list_nth_shared_mut_loop_pair_loop T n ls0 ls1 i;
+  let (p1, back_'b) := p in
+  let back_'b1 := fun (ret : T) => back_'b ret in
+  Return (p1, back_'b1)
 .
 
-(** [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)
-  :=
-  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
+(** [loops::list_nth_shared_mut_loop_pair_merge]: loop 0:
     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)
+  result ((T * T) * (T -> result (List_t T)))
   :=
   match n with
   | O => Fail_ OutOfFuel
-  | S n0 =>
+  | S n1 =>
     match ls0 with
     | List_Cons x0 tl0 =>
       match ls1 with
       | List_Cons x1 tl1 =>
         if i s= 0%u32
-        then Return (x0, x1)
+        then
+          let back_'a := fun (ret : T) => Return (List_Cons ret tl1) in
+          Return ((x0, x1), back_'a)
         else (
-          i0 <- u32_sub i 1%u32;
-          list_nth_shared_mut_loop_pair_merge_loop T n0 tl0 tl1 i0)
+          i1 <- u32_sub i 1%u32;
+          p <- list_nth_shared_mut_loop_pair_merge_loop T n1 tl0 tl1 i1;
+          let (p1, back_'a) := p in
+          let back_'a1 :=
+            fun (ret : T) => tl11 <- back_'a ret; Return (List_Cons x1 tl11) in
+          Return (p1, back_'a1))
       | List_Nil => Fail_ Failure
       end
     | List_Nil => Fail_ Failure
@@ -869,49 +663,16 @@ Fixpoint list_nth_shared_mut_loop_pair_merge_loop
   end
 .
 
-(** [loops::list_nth_shared_mut_loop_pair_merge]: forward function
+(** [loops::list_nth_shared_mut_loop_pair_merge]:
     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 T n ls0 ls1 i
-.
-
-(** [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)
-  :=
-  match n with
-  | O => Fail_ OutOfFuel
-  | S n0 =>
-    match ls0 with
-    | List_Cons x0 tl0 =>
-      match ls1 with
-      | List_Cons x1 tl1 =>
-        if i s= 0%u32
-        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 (List_Cons x1 tl10))
-      | List_Nil => Fail_ Failure
-      end
-    | List_Nil => Fail_ Failure
-    end
-  end
-.
-
-(** [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)
+  result ((T * T) * (T -> result (List_t T)))
   :=
-  list_nth_shared_mut_loop_pair_merge_loop_back T n ls0 ls1 i ret
+  p <- list_nth_shared_mut_loop_pair_merge_loop T n ls0 ls1 i;
+  let (p1, back_'a) := p in
+  let back_'a1 := fun (ret : T) => back_'a ret in
+  Return (p1, back_'a1)
 .
 
 End Loops.
diff --git a/tests/coq/misc/Paper.v b/tests/coq/misc/Paper.v
index 6b110193..e46df0ce 100644
--- a/tests/coq/misc/Paper.v
+++ b/tests/coq/misc/Paper.v
@@ -8,44 +8,40 @@ Import ListNotations.
 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 ())
+(** [paper::ref_incr]:
     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
+(** [paper::test_incr]:
     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
+  i <- ref_incr 0%i32; if negb (i s= 1%i32) then Fail_ Failure else Return tt
 .
 
 (** Unit test for [paper::test_incr] *)
 Check (test_incr )%return.
 
-(** [paper::choose]: forward function
+(** [paper::choose]:
     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
+Definition choose
+  (T : Type) (b : bool) (x : T) (y : T) : result (T * (T -> result (T * T))) :=
+  if b
+  then let back_'a := fun (ret : T) => Return (ret, y) in Return (x, back_'a)
+  else let back_'a := fun (ret : T) => Return (x, ret) in Return (y, back_'a)
 .
 
-(** [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
+(** [paper::test_choose]:
     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)
+  p <- choose i32 true 0%i32 0%i32;
+  let (z, choose_back) := p in
+  z1 <- i32_add z 1%i32;
+  if negb (z1 s= 1%i32)
   then Fail_ Failure
   else (
-    p <- choose_back i32 true 0%i32 0%i32 z0;
-    let (x, y) := p in
+    p1 <- choose_back z1;
+    let (x, y) := p1 in
     if negb (x s= 1%i32)
     then Fail_ Failure
     else if negb (y s= 0%i32) then Fail_ Failure else Return tt)
@@ -64,35 +60,31 @@ Inductive List_t (T : Type) :=
 Arguments List_Cons { _ }.
 Arguments List_Nil { _ }.
 
-(** [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
-  | List_Cons x tl =>
-    if i s= 0%u32
-    then Return x
-    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]:
     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) :=
+Fixpoint list_nth_mut
+  (T : Type) (l : List_t T) (i : u32) :
+  result (T * (T -> result (List_t T)))
+  :=
   match l with
   | List_Cons x tl =>
     if i s= 0%u32
-    then Return (List_Cons ret tl)
+    then
+      let back_'a := fun (ret : T) => Return (List_Cons ret tl) in
+      Return (x, back_'a)
     else (
-      i0 <- u32_sub i 1%u32;
-      tl0 <- list_nth_mut_back T tl i0 ret;
-      Return (List_Cons x tl0))
+      i1 <- u32_sub i 1%u32;
+      p <- list_nth_mut T tl i1;
+      let (t, list_nth_mut_back) := p in
+      let back_'a :=
+        fun (ret : T) => tl1 <- list_nth_mut_back ret; Return (List_Cons x tl1)
+        in
+      Return (t, back_'a))
   | List_Nil => Fail_ Failure
   end
 .
 
-(** [paper::sum]: forward function
+(** [paper::sum]:
     Source: 'src/paper.rs', lines 57:0-57:32 *)
 Fixpoint sum (l : List_t i32) : result i32 :=
   match l with
@@ -101,31 +93,33 @@ Fixpoint sum (l : List_t i32) : result i32 :=
   end
 .
 
-(** [paper::test_nth]: forward function
+(** [paper::test_nth]:
     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 (List_Cons 1%i32 l1) 2%u32 x0;
-  i <- sum l2;
+  let l1 := List_Cons 3%i32 l in
+  let l2 := List_Cons 2%i32 l1 in
+  p <- list_nth_mut i32 (List_Cons 1%i32 l2) 2%u32;
+  let (x, list_nth_mut_back) := p in
+  x1 <- i32_add x 1%i32;
+  l3 <- list_nth_mut_back x1;
+  i <- sum l3;
   if negb (i s= 7%i32) then Fail_ Failure else Return tt
 .
 
 (** Unit test for [paper::test_nth] *)
 Check (test_nth )%return.
 
-(** [paper::call_choose]: forward function
+(** [paper::call_choose]:
     Source: 'src/paper.rs', lines 76:0-76:44 *)
 Definition call_choose (p : (u32 * u32)) : result u32 :=
   let (px, py) := p in
-  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
+  p1 <- choose u32 true px py;
+  let (pz, choose_back) := p1 in
+  pz1 <- u32_add pz 1%u32;
+  p2 <- choose_back pz1;
+  let (px1, _) := p2 in
+  Return px1
 .
 
 End Paper.
diff --git a/tests/coq/misc/PoloniusList.v b/tests/coq/misc/PoloniusList.v
index 2371b1cc..7e967855 100644
--- a/tests/coq/misc/PoloniusList.v
+++ b/tests/coq/misc/PoloniusList.v
@@ -18,26 +18,28 @@ Inductive List_t (T : Type) :=
 Arguments List_Cons { _ }.
 Arguments List_Nil { _ }.
 
-(** [polonius_list::get_list_at_x]: forward function
+(** [polonius_list::get_list_at_x]:
     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
-  | 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
-    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) :=
+Fixpoint get_list_at_x
+  (ls : List_t u32) (x : u32) :
+  result ((List_t u32) * (List_t u32 -> result (List_t u32)))
+  :=
   match ls with
   | List_Cons hd tl =>
     if hd s= x
-    then Return ret
-    else (tl0 <- get_list_at_x_back tl x ret; Return (List_Cons hd tl0))
-  | List_Nil => Return ret
+    then
+      let back_'a := fun (ret : List_t u32) => Return ret in
+      Return (List_Cons hd tl, back_'a)
+    else (
+      p <- get_list_at_x tl x;
+      let (l, get_list_at_x_back) := p in
+      let back_'a :=
+        fun (ret : List_t u32) =>
+          tl1 <- get_list_at_x_back ret; Return (List_Cons hd tl1) in
+      Return (l, back_'a))
+  | List_Nil =>
+    let back_'a := fun (ret : List_t u32) => Return ret in
+    Return (List_Nil, back_'a)
   end
 .
 
diff --git a/tests/coq/misc/Primitives.v b/tests/coq/misc/Primitives.v
index c0056073..990e27e4 100644
--- a/tests/coq/misc/Primitives.v
+++ b/tests/coq/misc/Primitives.v
@@ -67,7 +67,7 @@ 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 * (a -> a) := (x, fun x => x) .
+Definition core_mem_replace (a : Type) (x : a) (y : a) : a * a := (x, x) .
 
 Record mut_raw_ptr (T : Type) := { mut_raw_ptr_v : T }.
 Record const_raw_ptr (T : Type) := { const_raw_ptr_v : T }.
@@ -585,6 +585,13 @@ 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).
 
+Definition array_index_mut_usize (T : Type) (n : usize) (a : array T n) (i : usize) :
+  result (T * (T -> result (array T n))) :=
+  match array_index_usize T n a i with
+  | Fail_ e => Fail_ e
+  | Return x => Return (x, array_update_usize T n a i)
+  end.
+
 (*** Slice *)
 Definition slice T := { l: list T | Z.of_nat (length l) <= usize_max}.
 
@@ -592,11 +599,25 @@ 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).
 
+Definition slice_index_mut_usize (T : Type) (s : slice T) (i : usize) :
+  result (T * (T -> result (slice T))) :=
+  match slice_index_usize T s i with
+  | Fail_ e => Fail_ e
+  | Return x => Return (x, slice_update_usize T s i)
+  end.
+
 (*** 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).
 
+Definition array_to_slice_mut (T : Type) (n : usize) (a : array T n) :
+  result (slice T * (slice T -> result (array T n))) :=
+  match array_to_slice T n a with
+  | Fail_ e => Fail_ e
+  | Return x => Return (x, array_from_slice T n a)
+  end.
+
 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).
 
diff --git a/tests/coq/misc/_CoqProject b/tests/coq/misc/_CoqProject
index 869cdb4d..64cddedd 100644
--- a/tests/coq/misc/_CoqProject
+++ b/tests/coq/misc/_CoqProject
@@ -8,9 +8,9 @@ External_Types.v
 Primitives.v
 External_Funs.v
 External_TypesExternal.v
+Paper.v
 Constants.v
 PoloniusList.v
-Paper.v
 NoNestedBorrows.v
 External_FunsExternal.v
 Bitwise.v
diff --git a/tests/coq/traits/Primitives.v b/tests/coq/traits/Primitives.v
index 84280b96..990e27e4 100644
--- a/tests/coq/traits/Primitives.v
+++ b/tests/coq/traits/Primitives.v
@@ -67,8 +67,7 @@ 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 .
+Definition core_mem_replace (a : Type) (x : a) (y : a) : a * a := (x, x) .
 
 Record mut_raw_ptr (T : Type) := { mut_raw_ptr_v : T }.
 Record const_raw_ptr (T : Type) := { const_raw_ptr_v : T }.
@@ -504,13 +503,15 @@ 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;
+  core_ops_index_IndexMut_index_mut :
+    Self ->
+    Idx ->
+    result (core_ops_index_IndexMut_indexInst.(core_ops_index_Index_Output) *
+            (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 {
@@ -524,13 +525,14 @@ 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;
+  core_ops_deref_DerefMut_deref_mut :
+    Self ->
+    result (core_ops_deref_DerefMut_derefInst.(core_ops_deref_Deref_target) *
+            (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;
@@ -543,8 +545,8 @@ 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.
+Definition alloc_boxed_Box_deref_mut (T : Type) (x : T) : result (T * (T -> result T)) :=
+  Return (x, fun x => Return x).
 
 (* Trait instance *)
 Definition alloc_boxed_Box_coreopsDerefInst (Self : Type) : core_ops_deref_Deref Self := {|
@@ -556,7 +558,6 @@ Definition alloc_boxed_Box_coreopsDerefInst (Self : Type) : core_ops_deref_Deref
 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;
 |}.
 
 
@@ -584,6 +585,13 @@ 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).
 
+Definition array_index_mut_usize (T : Type) (n : usize) (a : array T n) (i : usize) :
+  result (T * (T -> result (array T n))) :=
+  match array_index_usize T n a i with
+  | Fail_ e => Fail_ e
+  | Return x => Return (x, array_update_usize T n a i)
+  end.
+
 (*** Slice *)
 Definition slice T := { l: list T | Z.of_nat (length l) <= usize_max}.
 
@@ -591,11 +599,25 @@ 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).
 
+Definition slice_index_mut_usize (T : Type) (s : slice T) (i : usize) :
+  result (T * (T -> result (slice T))) :=
+  match slice_index_usize T s i with
+  | Fail_ e => Fail_ e
+  | Return x => Return (x, slice_update_usize T s i)
+  end.
+
 (*** 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).
 
+Definition array_to_slice_mut (T : Type) (n : usize) (a : array T n) :
+  result (slice T * (slice T -> result (array T n))) :=
+  match array_to_slice T n a with
+  | Fail_ e => Fail_ e
+  | Return x => Return (x, array_from_slice T n a)
+  end.
+
 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).
 
@@ -639,16 +661,9 @@ Definition alloc_vec_Vec_bind {A B} (v: alloc_vec_Vec A) (f: list A -> result (l
   | 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)
@@ -661,6 +676,14 @@ Axiom alloc_vec_Vec_index_usize : forall {T : Type} (v : alloc_vec_Vec T) (i : u
 (* Helper *)
 Axiom alloc_vec_Vec_update_usize : forall {T : Type} (v : alloc_vec_Vec T) (i : usize) (x : T), result (alloc_vec_Vec T).
 
+Definition alloc_vec_Vec_index_mut_usize {T : Type} (v: alloc_vec_Vec T) (i: usize) :
+  result (T * (T -> result (alloc_vec_Vec T))) :=
+  match alloc_vec_Vec_index_usize v i with
+  | Return x =>
+    Return (x, alloc_vec_Vec_update_usize v i)
+  | Fail_ e => Fail_ e
+  end.
+
 (* Trait declaration: [core::slice::index::private_slice_index::Sealed] *)
 Definition core_slice_index_private_slice_index_Sealed (self : Type) := unit.
 
@@ -669,25 +692,23 @@ Record core_slice_index_SliceIndex (Self T : Type) := mk_core_slice_index_SliceI
   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_mut :
+    Self -> T -> result (option core_slice_index_SliceIndex_Output * (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;
+  core_slice_index_SliceIndex_index_mut :
+    Self -> T -> result (core_slice_index_SliceIndex_Output * (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
@@ -704,11 +725,9 @@ Axiom core_slice_index_RangeUsize_get : forall (T : Type) (i : core_ops_range_Ra
 
 (* [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).
+  forall (T : Type),
+    core_ops_range_Range usize -> slice T ->
+    result (option (slice T) * (option (slice T) -> result (slice T))).
 
 (* [core::slice::index::Range::get_unchecked]: forward function *)
 Definition core_slice_index_RangeUsize_get_unchecked
@@ -732,21 +751,14 @@ Axiom core_slice_index_RangeUsize_index :
 
 (* [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).
+  forall (T : Type), core_ops_range_Range usize -> slice T -> result (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).
+  slice T -> Idx ->
+  result (inst.(core_slice_index_SliceIndex_Output) *
+          (inst.(core_slice_index_SliceIndex_Output) -> result (slice T))).
 
 (* [core::array::[T; N]::index]: forward function *)
 Axiom core_array_Array_index :
@@ -756,12 +768,9 @@ Axiom core_array_Array_index :
 (* [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).
+  (a : array T N) (i : Idx),
+  result (inst.(core_ops_index_IndexMut_indexInst).(core_ops_index_Index_Output) *
+          (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
@@ -774,12 +783,10 @@ Definition core_slice_index_SliceIndexRangeUsizeSliceTInst (T : Type) :
   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]] *)
@@ -796,7 +803,6 @@ Definition core_ops_index_IndexMutSliceTIInst (T Idx : Type)
   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]] *)
@@ -813,18 +819,14 @@ Definition core_ops_index_IndexMutArrayInst (T Idx : Type) (N : usize)
   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).
+Axiom core_slice_index_usize_get_mut :
+  forall (T : Type), usize -> slice T -> result (option T * (option T -> result (slice T))).
 
 (* [core::slice::index::usize::get_unchecked]: forward function *)
 Axiom core_slice_index_usize_get_unchecked :
@@ -838,11 +840,8 @@ Axiom core_slice_index_usize_get_unchecked_mut :
 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).
+Axiom core_slice_index_usize_index_mut :
+  forall (T : Type), usize -> slice T -> result (T * (T -> result (slice T))).
 
 (* Trait implementation: [core::slice::index::private_slice_index::usize] *)
 Definition core_slice_index_private_slice_index_SealedUsizeInst
@@ -855,12 +854,10 @@ Definition core_slice_index_SliceIndexUsizeSliceTInst (T : Type) :
   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 *)
@@ -869,12 +866,9 @@ Axiom alloc_vec_Vec_index : forall (T Idx : Type) (inst : core_slice_index_Slice
 
 (* [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).
+  (Self : alloc_vec_Vec T) (i : Idx),
+  result (inst.(core_slice_index_SliceIndex_Output) *
+          (inst.(core_slice_index_SliceIndex_Output) -> result (alloc_vec_Vec T))).
 
 (* Trait implementation: [alloc::vec::Vec] *)
 Definition alloc_vec_Vec_coreopsindexIndexInst (T Idx : Type)
@@ -890,7 +884,6 @@ Definition alloc_vec_Vec_coreopsindexIndexMutInst (T Idx : Type)
   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 *)
@@ -901,10 +894,6 @@ Axiom alloc_vec_Vec_index_eq : forall {a : Type} (v : alloc_vec_Vec a) (i : usiz
 
 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.
+    alloc_vec_Vec_index_mut_usize v i.
 
 End Primitives.
diff --git a/tests/coq/traits/Traits.v b/tests/coq/traits/Traits.v
index 2448e8f3..7055e25d 100644
--- a/tests/coq/traits/Traits.v
+++ b/tests/coq/traits/Traits.v
@@ -17,7 +17,7 @@ Record BoolTrait_t (Self : Type) := mkBoolTrait_t {
 Arguments mkBoolTrait_t { _ }.
 Arguments BoolTrait_t_get_bool { _ }.
 
-(** [traits::{bool}::get_bool]: forward function
+(** [traits::{bool}::get_bool]:
     Source: 'src/traits.rs', lines 12:4-12:30 *)
 Definition bool_get_bool (self : bool) : result bool :=
   Return self.
@@ -28,24 +28,24 @@ Definition traits_BoolTraitBoolInst : BoolTrait_t bool := {|
   BoolTrait_t_get_bool := bool_get_bool;
 |}.
 
-(** [traits::BoolTrait::ret_true]: forward function
+(** [traits::BoolTrait::ret_true]:
     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
+(** [traits::test_bool_trait_bool]:
     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
+(** [traits::{core::option::Option<T>#1}::get_bool]:
     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
+  match self with | None => Return false | Some _ => Return true end
 .
 
 (** Trait implementation: [traits::{core::option::Option<T>#1}]
@@ -55,7 +55,7 @@ Definition traits_BoolTraitcoreoptionOptionTInst (T : Type) : BoolTrait_t
   BoolTrait_t_get_bool := option_get_bool T;
 |}.
 
-(** [traits::test_bool_trait_option]: forward function
+(** [traits::test_bool_trait_option]:
     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;
@@ -64,7 +64,7 @@ Definition test_bool_trait_option (T : Type) (x : option T) : result bool :=
   else Return false
 .
 
-(** [traits::test_bool_trait]: forward function
+(** [traits::test_bool_trait]:
     Source: 'src/traits.rs', lines 35:0-35:50 *)
 Definition test_bool_trait
   (T : Type) (boolTraitTInst : BoolTrait_t T) (x : T) : result bool :=
@@ -80,7 +80,7 @@ Record ToU64_t (Self : Type) := mkToU64_t {
 Arguments mkToU64_t { _ }.
 Arguments ToU64_t_to_u64 { _ }.
 
-(** [traits::{u64#2}::to_u64]: forward function
+(** [traits::{u64#2}::to_u64]:
     Source: 'src/traits.rs', lines 44:4-44:26 *)
 Definition u64_to_u64 (self : u64) : result u64 :=
   Return self.
@@ -91,14 +91,14 @@ Definition traits_ToU64U64Inst : ToU64_t u64 := {|
   ToU64_t_to_u64 := u64_to_u64;
 |}.
 
-(** [traits::{(A, A)#3}::to_u64]: forward function
+(** [traits::{(A, A)#3}::to_u64]:
     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
+  let (t, t1) := self in
   i <- toU64AInst.(ToU64_t_to_u64) t;
-  i0 <- toU64AInst.(ToU64_t_to_u64) t0;
-  u64_add i i0
+  i1 <- toU64AInst.(ToU64_t_to_u64) t1;
+  u64_add i i1
 .
 
 (** Trait implementation: [traits::{(A, A)#3}]
@@ -108,20 +108,20 @@ Definition traits_ToU64TupleAAInst (A : Type) (toU64AInst : ToU64_t A) :
   ToU64_t_to_u64 := pair_to_u64 A toU64AInst;
 |}.
 
-(** [traits::f]: forward function
+(** [traits::f]:
     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
+(** [traits::g]:
     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
+(** [traits::h0]:
     Source: 'src/traits.rs', lines 66:0-66:24 *)
 Definition h0 (x : u64) : result u64 :=
   u64_to_u64 x.
@@ -133,7 +133,7 @@ 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
+(** [traits::{traits::Wrapper<T>#4}::to_u64]:
     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 :=
@@ -147,13 +147,13 @@ Definition traits_ToU64traitsWrapperTInst (T : Type) (toU64TInst : ToU64_t T) :
   ToU64_t_to_u64 := wrapper_to_u64 T toU64TInst;
 |}.
 
-(** [traits::h1]: forward function
+(** [traits::h1]:
     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
+(** [traits::h2]:
     Source: 'src/traits.rs', lines 84:0-84:41 *)
 Definition h2
   (T : Type) (toU64TInst : ToU64_t T) (x : Wrapper_t T) : result u64 :=
@@ -169,7 +169,7 @@ Record ToType_t (Self T : Type) := mkToType_t {
 Arguments mkToType_t { _ _ }.
 Arguments ToType_t_to_type { _ _ }.
 
-(** [traits::{u64#5}::to_type]: forward function
+(** [traits::{u64#5}::to_type]:
     Source: 'src/traits.rs', lines 93:4-93:28 *)
 Definition u64_to_type (self : u64) : result bool :=
   Return (self s> 0%u64).
@@ -190,7 +190,7 @@ Record OfType_t (Self : Type) := mkOfType_t {
 Arguments mkOfType_t { _ }.
 Arguments OfType_t_of_type { _ }.
 
-(** [traits::h3]: forward function
+(** [traits::h3]:
     Source: 'src/traits.rs', lines 104:0-104:50 *)
 Definition h3
   (T1 T2 : Type) (ofTypeT1Inst : OfType_t T1) (toTypeT2T1Inst : ToType_t T2 T1)
@@ -211,7 +211,7 @@ Arguments mkOfTypeBis_t { _ _ }.
 Arguments OfTypeBis_tOfTypeBis_t_ToTypeTSelfInst { _ _ }.
 Arguments OfTypeBis_t_of_type { _ _ }.
 
-(** [traits::h4]: forward function
+(** [traits::h4]:
     Source: 'src/traits.rs', lines 118:0-118:57 *)
 Definition h4
   (T1 T2 : Type) (ofTypeBisT1T2Inst : OfTypeBis_t T1 T2) (toTypeT2T1Inst :
@@ -238,7 +238,7 @@ Record TestType_test_TestTrait_t (Self : Type) := mkTestType_test_TestTrait_t {
 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
+(** [traits::{traits::TestType<T>#6}::test::{traits::{traits::TestType<T>#6}::test::TestType1}::test]:
     Source: 'src/traits.rs', lines 139:12-139:34 *)
 Definition testType_test_TestType1_test
   (self : TestType_test_TestType1_t) : result bool :=
@@ -252,21 +252,21 @@ Definition traits_TestType_test_TestTraittraitstraitsTestTypeTtestTestType1Inst
   TestType_test_TestTrait_t_test := testType_test_TestType1_test;
 |}.
 
-(** [traits::{traits::TestType<T>#6}::test]: forward function
+(** [traits::{traits::TestType<T>#6}::test]:
     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 0%u64 else Return false
+  x1 <- toU64TInst.(ToU64_t_to_u64) x;
+  if x1 s> 0%u64 then testType_test_TestType1_test 0%u64 else Return false
 .
 
 (** [traits::BoolWrapper]
     Source: 'src/traits.rs', lines 150:0-150:22 *)
 Definition BoolWrapper_t : Type := bool.
 
-(** [traits::{traits::BoolWrapper#7}::to_type]: forward function
+(** [traits::{traits::BoolWrapper#7}::to_type]:
     Source: 'src/traits.rs', lines 156:4-156:25 *)
 Definition boolWrapper_to_type
   (T : Type) (toTypeBoolTInst : ToType_t bool T) (self : BoolWrapper_t) :
@@ -312,8 +312,7 @@ Arguments WithConstTy_t_f { _ _ }.
 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 ())
+(** [traits::{bool#8}::f]:
     Source: 'src/traits.rs', lines 180:4-180:39 *)
 Definition bool_f (i : u64) (a : array u8 32%usize) : result u64 :=
   Return i.
@@ -329,7 +328,7 @@ Definition traits_WithConstTyBool32Inst : WithConstTy_t bool 32%usize := {|
   WithConstTy_t_f := bool_f;
 |}.
 
-(** [traits::use_with_const_ty1]: forward function
+(** [traits::use_with_const_ty1]:
     Source: 'src/traits.rs', lines 183:0-183:75 *)
 Definition use_with_const_ty1
   (H : Type) (LEN : usize) (withConstTyHLENInst : WithConstTy_t H LEN) :
@@ -338,7 +337,7 @@ Definition use_with_const_ty1
   let i := withConstTyHLENInst.(WithConstTy_tWithConstTy_t_LEN1) in Return i
 .
 
-(** [traits::use_with_const_ty2]: forward function
+(** [traits::use_with_const_ty2]:
     Source: 'src/traits.rs', lines 187:0-187:73 *)
 Definition use_with_const_ty2
   (H : Type) (LEN : usize) (withConstTyHLENInst : WithConstTy_t H LEN)
@@ -348,7 +347,7 @@ Definition use_with_const_ty2
   Return tt
 .
 
-(** [traits::use_with_const_ty3]: forward function
+(** [traits::use_with_const_ty3]:
     Source: 'src/traits.rs', lines 189:0-189:80 *)
 Definition use_with_const_ty3
   (H : Type) (LEN : usize) (withConstTyHLENInst : WithConstTy_t H LEN)
@@ -359,12 +358,12 @@ Definition use_with_const_ty3
     x
 .
 
-(** [traits::test_where1]: forward function
+(** [traits::test_where1]:
     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
+(** [traits::test_where2]:
     Source: 'src/traits.rs', lines 194:0-194:57 *)
 Definition test_where2
   (T : Type) (withConstTyT32Inst : WithConstTy_t T 32%usize) (_x : u32) :
@@ -403,16 +402,25 @@ 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 *)
+(** [traits::test_parent_trait0]:
+    Source: 'src/traits.rs', lines 208:0-208:57 *)
+Definition test_parent_trait0
+  (T : Type) (parentTrait0TInst : ParentTrait0_t T) (x : T) :
+  result parentTrait0TInst.(ParentTrait0_tParentTrait0_t_W)
+  :=
+  parentTrait0TInst.(ParentTrait0_t_get_w) x
+.
+
+(** [traits::test_child_trait1]:
+    Source: 'src/traits.rs', lines 213:0-213:56 *)
 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 *)
+(** [traits::test_child_trait2]:
+    Source: 'src/traits.rs', lines 217:0-217:54 *)
 Definition test_child_trait2
   (T : Type) (childTraitTInst : ChildTrait_t T) (x : T) :
   result
@@ -422,8 +430,8 @@ Definition test_child_trait2
     x
 .
 
-(** [traits::order1]: forward function
-    Source: 'src/traits.rs', lines 219:0-219:59 *)
+(** [traits::order1]:
+    Source: 'src/traits.rs', lines 223:0-223:59 *)
 Definition order1
   (T U : Type) (parentTrait0TInst : ParentTrait0_t T) (parentTrait0UInst :
   ParentTrait0_t U) :
@@ -433,7 +441,7 @@ Definition order1
 .
 
 (** Trait declaration: [traits::ChildTrait1]
-    Source: 'src/traits.rs', lines 222:0-222:35 *)
+    Source: 'src/traits.rs', lines 226:0-226:35 *)
 Record ChildTrait1_t (Self : Type) := mkChildTrait1_t {
   ChildTrait1_tChildTrait1_t_ParentTrait1SelfInst : ParentTrait1_t Self;
 }.
@@ -442,19 +450,19 @@ Arguments mkChildTrait1_t { _ }.
 Arguments ChildTrait1_tChildTrait1_t_ParentTrait1SelfInst { _ }.
 
 (** Trait implementation: [traits::{usize#9}]
-    Source: 'src/traits.rs', lines 224:0-224:27 *)
+    Source: 'src/traits.rs', lines 228:0-228:27 *)
 Definition traits_ParentTrait1UsizeInst : ParentTrait1_t usize
   := mkParentTrait1_t.
 
 (** Trait implementation: [traits::{usize#10}]
-    Source: 'src/traits.rs', lines 225:0-225:26 *)
+    Source: 'src/traits.rs', lines 229:0-229:26 *)
 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 *)
+    Source: 'src/traits.rs', lines 233:0-233:18 *)
 Record Iterator_t (Self : Type) := mkIterator_t {
   Iterator_tIterator_t_Item : Type;
 }.
@@ -463,7 +471,7 @@ Arguments mkIterator_t { _ }.
 Arguments Iterator_tIterator_t_Item { _ }.
 
 (** Trait declaration: [traits::IntoIterator]
-    Source: 'src/traits.rs', lines 233:0-233:22 *)
+    Source: 'src/traits.rs', lines 237:0-237:22 *)
 Record IntoIterator_t (Self : Type) := mkIntoIterator_t {
   IntoIterator_tIntoIterator_t_Item : Type;
   IntoIterator_tIntoIterator_t_IntoIter : Type;
@@ -480,13 +488,13 @@ 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 *)
+    Source: 'src/traits.rs', lines 254:0-254:21 *)
 Record FromResidual_t (Self T : Type) := mkFromResidual_t{}.
 
 Arguments mkFromResidual_t { _ _ }.
 
 (** Trait declaration: [traits::Try]
-    Source: 'src/traits.rs', lines 246:0-246:48 *)
+    Source: 'src/traits.rs', lines 250:0-250:48 *)
 Record Try_t (Self : Type) := mkTry_t {
   Try_tTry_t_Residual : Type;
   Try_tTry_t_FromResidualSelftraitsTrySelfResidualInst : FromResidual_t Self
@@ -498,7 +506,7 @@ Arguments Try_tTry_t_Residual { _ }.
 Arguments Try_tTry_t_FromResidualSelftraitsTrySelfResidualInst { _ }.
 
 (** Trait declaration: [traits::WithTarget]
-    Source: 'src/traits.rs', lines 252:0-252:20 *)
+    Source: 'src/traits.rs', lines 256:0-256:20 *)
 Record WithTarget_t (Self : Type) := mkWithTarget_t {
   WithTarget_tWithTarget_t_Target : Type;
 }.
@@ -507,7 +515,7 @@ Arguments mkWithTarget_t { _ }.
 Arguments WithTarget_tWithTarget_t_Target { _ }.
 
 (** Trait declaration: [traits::ParentTrait2]
-    Source: 'src/traits.rs', lines 256:0-256:22 *)
+    Source: 'src/traits.rs', lines 260:0-260:22 *)
 Record ParentTrait2_t (Self : Type) := mkParentTrait2_t {
   ParentTrait2_tParentTrait2_t_U : Type;
   ParentTrait2_tParentTrait2_t_U_clause_0 : WithTarget_t
@@ -519,7 +527,7 @@ 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 *)
+    Source: 'src/traits.rs', lines 264:0-264:35 *)
 Record ChildTrait2_t (Self : Type) := mkChildTrait2_t {
   ChildTrait2_tChildTrait2_t_ParentTrait2SelfInst : ParentTrait2_t Self;
   ChildTrait2_t_convert :
@@ -533,25 +541,25 @@ Arguments ChildTrait2_tChildTrait2_t_ParentTrait2SelfInst { _ }.
 Arguments ChildTrait2_t_convert { _ }.
 
 (** Trait implementation: [traits::{u32#11}]
-    Source: 'src/traits.rs', lines 264:0-264:23 *)
+    Source: 'src/traits.rs', lines 268:0-268:23 *)
 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 *)
+    Source: 'src/traits.rs', lines 272:0-272:25 *)
 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 *)
+(** [traits::{u32#13}::convert]:
+    Source: 'src/traits.rs', lines 277:4-277:29 *)
 Definition u32_convert (x : u32) : result u32 :=
   Return x.
 
 (** Trait implementation: [traits::{u32#13}]
-    Source: 'src/traits.rs', lines 272:0-272:24 *)
+    Source: 'src/traits.rs', lines 276:0-276:24 *)
 Definition traits_ChildTrait2U32Inst : ChildTrait2_t u32 := {|
   ChildTrait2_tChildTrait2_t_ParentTrait2SelfInst :=
     traits_ParentTrait2U32Inst;
@@ -559,7 +567,7 @@ Definition traits_ChildTrait2U32Inst : ChildTrait2_t u32 := {|
 |}.
 
 (** Trait declaration: [traits::CFnOnce]
-    Source: 'src/traits.rs', lines 286:0-286:23 *)
+    Source: 'src/traits.rs', lines 290:0-290:23 *)
 Record CFnOnce_t (Self Args : Type) := mkCFnOnce_t {
   CFnOnce_tCFnOnce_t_Output : Type;
   CFnOnce_t_call_once : Self -> Args -> result CFnOnce_tCFnOnce_t_Output;
@@ -570,31 +578,48 @@ Arguments CFnOnce_tCFnOnce_t_Output { _ _ }.
 Arguments CFnOnce_t_call_once { _ _ }.
 
 (** Trait declaration: [traits::CFnMut]
-    Source: 'src/traits.rs', lines 292:0-292:37 *)
+    Source: 'src/traits.rs', lines 296:0-296:37 *)
 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;
+    ((CFnMut_tCFnMut_t_CFnOnceSelfArgsInst).(CFnOnce_tCFnOnce_t_Output) *
+    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 *)
+    Source: 'src/traits.rs', lines 300:0-300:33 *)
 Record CFn_t (Self Args : Type) := mkCFn_t {
   CFn_tCFn_t_CFnMutSelfArgsInst : CFnMut_t Self Args;
-  CFn_t_call_mut : Self -> Args -> result
+  CFn_t_call : 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 { _ _ }.
+Arguments CFn_t_call { _ _ }.
+
+(** Trait declaration: [traits::GetTrait]
+    Source: 'src/traits.rs', lines 304:0-304:18 *)
+Record GetTrait_t (Self : Type) := mkGetTrait_t {
+  GetTrait_tGetTrait_t_W : Type;
+  GetTrait_t_get_w : Self -> result GetTrait_tGetTrait_t_W;
+}.
+
+Arguments mkGetTrait_t { _ }.
+Arguments GetTrait_tGetTrait_t_W { _ }.
+Arguments GetTrait_t_get_w { _ }.
+
+(** [traits::test_get_trait]:
+    Source: 'src/traits.rs', lines 309:0-309:49 *)
+Definition test_get_trait
+  (T : Type) (getTraitTInst : GetTrait_t T) (x : T) :
+  result getTraitTInst.(GetTrait_tGetTrait_t_W)
+  :=
+  getTraitTInst.(GetTrait_t_get_w) x
+.
 
 End Traits.