Annotate the bound vars in the lambdas for Coq

2 files changed, 231 insertions, 273 deletions

diff --git a/tests/coq/misc/NoNestedBorrows.v b/tests/coq/misc/NoNestedBorrows.v
index 65164ac5..081c65c3 100644
--- a/tests/coq/misc/NoNestedBorrows.v
+++ b/tests/coq/misc/NoNestedBorrows.v
@@ -54,97 +54,97 @@ Inductive Sum_t (T1 T2 : Type) :=
 Arguments Sum_Left { _ _ }.
 Arguments Sum_Right { _ _ }.
 
-(** [no_nested_borrows::neg_test]: forward function
+(** [no_nested_borrows::neg_test]:
     Source: 'src/no_nested_borrows.rs', lines 48:0-48:30 *)
 Definition neg_test (x : i32) : result i32 :=
   i32_neg x.
 
-(** [no_nested_borrows::add_u32]: forward function
+(** [no_nested_borrows::add_u32]:
     Source: 'src/no_nested_borrows.rs', lines 54:0-54:37 *)
 Definition add_u32 (x : u32) (y : u32) : result u32 :=
   u32_add x y.
 
-(** [no_nested_borrows::subs_u32]: forward function
+(** [no_nested_borrows::subs_u32]:
     Source: 'src/no_nested_borrows.rs', lines 60:0-60:38 *)
 Definition subs_u32 (x : u32) (y : u32) : result u32 :=
   u32_sub x y.
 
-(** [no_nested_borrows::div_u32]: forward function
+(** [no_nested_borrows::div_u32]:
     Source: 'src/no_nested_borrows.rs', lines 66:0-66:37 *)
 Definition div_u32 (x : u32) (y : u32) : result u32 :=
   u32_div x y.
 
-(** [no_nested_borrows::div_u32_const]: forward function
+(** [no_nested_borrows::div_u32_const]:
     Source: 'src/no_nested_borrows.rs', lines 73:0-73:35 *)
 Definition div_u32_const (x : u32) : result u32 :=
   u32_div x 2%u32.
 
-(** [no_nested_borrows::rem_u32]: forward function
+(** [no_nested_borrows::rem_u32]:
     Source: 'src/no_nested_borrows.rs', lines 78:0-78:37 *)
 Definition rem_u32 (x : u32) (y : u32) : result u32 :=
   u32_rem x y.
 
-(** [no_nested_borrows::mul_u32]: forward function
+(** [no_nested_borrows::mul_u32]:
     Source: 'src/no_nested_borrows.rs', lines 82:0-82:37 *)
 Definition mul_u32 (x : u32) (y : u32) : result u32 :=
   u32_mul x y.
 
-(** [no_nested_borrows::add_i32]: forward function
+(** [no_nested_borrows::add_i32]:
     Source: 'src/no_nested_borrows.rs', lines 88:0-88:37 *)
 Definition add_i32 (x : i32) (y : i32) : result i32 :=
   i32_add x y.
 
-(** [no_nested_borrows::subs_i32]: forward function
+(** [no_nested_borrows::subs_i32]:
     Source: 'src/no_nested_borrows.rs', lines 92:0-92:38 *)
 Definition subs_i32 (x : i32) (y : i32) : result i32 :=
   i32_sub x y.
 
-(** [no_nested_borrows::div_i32]: forward function
+(** [no_nested_borrows::div_i32]:
     Source: 'src/no_nested_borrows.rs', lines 96:0-96:37 *)
 Definition div_i32 (x : i32) (y : i32) : result i32 :=
   i32_div x y.
 
-(** [no_nested_borrows::div_i32_const]: forward function
+(** [no_nested_borrows::div_i32_const]:
     Source: 'src/no_nested_borrows.rs', lines 100:0-100:35 *)
 Definition div_i32_const (x : i32) : result i32 :=
   i32_div x 2%i32.
 
-(** [no_nested_borrows::rem_i32]: forward function
+(** [no_nested_borrows::rem_i32]:
     Source: 'src/no_nested_borrows.rs', lines 104:0-104:37 *)
 Definition rem_i32 (x : i32) (y : i32) : result i32 :=
   i32_rem x y.
 
-(** [no_nested_borrows::mul_i32]: forward function
+(** [no_nested_borrows::mul_i32]:
     Source: 'src/no_nested_borrows.rs', lines 108:0-108:37 *)
 Definition mul_i32 (x : i32) (y : i32) : result i32 :=
   i32_mul x y.
 
-(** [no_nested_borrows::mix_arith_u32]: forward function
+(** [no_nested_borrows::mix_arith_u32]:
     Source: 'src/no_nested_borrows.rs', lines 112:0-112:51 *)
 Definition mix_arith_u32 (x : u32) (y : u32) (z : u32) : result u32 :=
   i <- u32_add x y;
-  i0 <- u32_div x y;
-  i1 <- u32_mul i i0;
-  i2 <- u32_rem z y;
-  i3 <- u32_sub x i2;
-  i4 <- u32_add i1 i3;
-  i5 <- u32_add x y;
-  i6 <- u32_add i5 z;
-  u32_rem i4 i6
+  i1 <- u32_div x y;
+  i2 <- u32_mul i i1;
+  i3 <- u32_rem z y;
+  i4 <- u32_sub x i3;
+  i5 <- u32_add i2 i4;
+  i6 <- u32_add x y;
+  i7 <- u32_add i6 z;
+  u32_rem i5 i7
 .
 
-(** [no_nested_borrows::mix_arith_i32]: forward function
+(** [no_nested_borrows::mix_arith_i32]:
     Source: 'src/no_nested_borrows.rs', lines 116:0-116:51 *)
 Definition mix_arith_i32 (x : i32) (y : i32) (z : i32) : result i32 :=
   i <- i32_add x y;
-  i0 <- i32_div x y;
-  i1 <- i32_mul i i0;
-  i2 <- i32_rem z y;
-  i3 <- i32_sub x i2;
-  i4 <- i32_add i1 i3;
-  i5 <- i32_add x y;
-  i6 <- i32_add i5 z;
-  i32_rem i4 i6
+  i1 <- i32_div x y;
+  i2 <- i32_mul i i1;
+  i3 <- i32_rem z y;
+  i4 <- i32_sub x i3;
+  i5 <- i32_add i2 i4;
+  i6 <- i32_add x y;
+  i7 <- i32_add i6 z;
+  i32_rem i5 i7
 .
 
 (** [no_nested_borrows::CONST0]
@@ -157,22 +157,22 @@ Definition const0_c : usize := const0_body%global.
 Definition const1_body : result usize := usize_mul 2%usize 2%usize.
 Definition const1_c : usize := const1_body%global.
 
-(** [no_nested_borrows::cast_u32_to_i32]: forward function
+(** [no_nested_borrows::cast_u32_to_i32]:
     Source: 'src/no_nested_borrows.rs', lines 128:0-128:37 *)
 Definition cast_u32_to_i32 (x : u32) : result i32 :=
   scalar_cast U32 I32 x.
 
-(** [no_nested_borrows::cast_bool_to_i32]: forward function
+(** [no_nested_borrows::cast_bool_to_i32]:
     Source: 'src/no_nested_borrows.rs', lines 132:0-132:39 *)
 Definition cast_bool_to_i32 (x : bool) : result i32 :=
   scalar_cast_bool I32 x.
 
-(** [no_nested_borrows::cast_bool_to_bool]: forward function
+(** [no_nested_borrows::cast_bool_to_bool]:
     Source: 'src/no_nested_borrows.rs', lines 137:0-137:41 *)
 Definition cast_bool_to_bool (x : bool) : result bool :=
   Return x.
 
-(** [no_nested_borrows::test2]: forward function
+(** [no_nested_borrows::test2]:
     Source: 'src/no_nested_borrows.rs', lines 142:0-142:14 *)
 Definition test2 : result unit :=
   _ <- u32_add 23%u32 44%u32; Return tt.
@@ -180,13 +180,13 @@ Definition test2 : result unit :=
 (** Unit test for [no_nested_borrows::test2] *)
 Check (test2 )%return.
 
-(** [no_nested_borrows::get_max]: forward function
+(** [no_nested_borrows::get_max]:
     Source: 'src/no_nested_borrows.rs', lines 154:0-154:37 *)
 Definition get_max (x : u32) (y : u32) : result u32 :=
   if x s>= y then Return x else Return y
 .
 
-(** [no_nested_borrows::test3]: forward function
+(** [no_nested_borrows::test3]:
     Source: 'src/no_nested_borrows.rs', lines 162:0-162:14 *)
 Definition test3 : result unit :=
   x <- get_max 4%u32 3%u32;
@@ -198,7 +198,7 @@ Definition test3 : result unit :=
 (** Unit test for [no_nested_borrows::test3] *)
 Check (test3 )%return.
 
-(** [no_nested_borrows::test_neg1]: forward function
+(** [no_nested_borrows::test_neg1]:
     Source: 'src/no_nested_borrows.rs', lines 169:0-169:18 *)
 Definition test_neg1 : result unit :=
   y <- i32_neg 3%i32; if negb (y s= (-3)%i32) then Fail_ Failure else Return tt
@@ -207,7 +207,7 @@ Definition test_neg1 : result unit :=
 (** Unit test for [no_nested_borrows::test_neg1] *)
 Check (test_neg1 )%return.
 
-(** [no_nested_borrows::refs_test1]: forward function
+(** [no_nested_borrows::refs_test1]:
     Source: 'src/no_nested_borrows.rs', lines 176:0-176:19 *)
 Definition refs_test1 : result unit :=
   if negb (1%i32 s= 1%i32) then Fail_ Failure else Return tt
@@ -216,7 +216,7 @@ Definition refs_test1 : result unit :=
 (** Unit test for [no_nested_borrows::refs_test1] *)
 Check (refs_test1 )%return.
 
-(** [no_nested_borrows::refs_test2]: forward function
+(** [no_nested_borrows::refs_test2]:
     Source: 'src/no_nested_borrows.rs', lines 187:0-187:19 *)
 Definition refs_test2 : result unit :=
   if negb (2%i32 s= 2%i32)
@@ -233,7 +233,7 @@ Definition refs_test2 : result unit :=
 (** Unit test for [no_nested_borrows::refs_test2] *)
 Check (refs_test2 )%return.
 
-(** [no_nested_borrows::test_list1]: forward function
+(** [no_nested_borrows::test_list1]:
     Source: 'src/no_nested_borrows.rs', lines 203:0-203:19 *)
 Definition test_list1 : result unit :=
   Return tt.
@@ -241,36 +241,38 @@ Definition test_list1 : result unit :=
 (** Unit test for [no_nested_borrows::test_list1] *)
 Check (test_list1 )%return.
 
-(** [no_nested_borrows::test_box1]: forward function
+(** [no_nested_borrows::test_box1]:
     Source: 'src/no_nested_borrows.rs', lines 208:0-208:18 *)
 Definition test_box1 : result unit :=
   let b := 0%i32 in
-  b0 <- alloc_boxed_Box_deref_mut_back i32 b 1%i32;
-  x <- alloc_boxed_Box_deref i32 b0;
+  p <- alloc_boxed_Box_deref_mut i32 b;
+  let (_, deref_mut_back) := p in
+  b1 <- deref_mut_back 1%i32;
+  x <- alloc_boxed_Box_deref i32 b1;
   if negb (x s= 1%i32) then Fail_ Failure else Return tt
 .
 
 (** Unit test for [no_nested_borrows::test_box1] *)
 Check (test_box1 )%return.
 
-(** [no_nested_borrows::copy_int]: forward function
+(** [no_nested_borrows::copy_int]:
     Source: 'src/no_nested_borrows.rs', lines 218:0-218:30 *)
 Definition copy_int (x : i32) : result i32 :=
   Return x.
 
-(** [no_nested_borrows::test_unreachable]: forward function
+(** [no_nested_borrows::test_unreachable]:
     Source: 'src/no_nested_borrows.rs', lines 224:0-224:32 *)
 Definition test_unreachable (b : bool) : result unit :=
   if b then Fail_ Failure else Return tt
 .
 
-(** [no_nested_borrows::test_panic]: forward function
+(** [no_nested_borrows::test_panic]:
     Source: 'src/no_nested_borrows.rs', lines 232:0-232:26 *)
 Definition test_panic (b : bool) : result unit :=
   if b then Fail_ Failure else Return tt
 .
 
-(** [no_nested_borrows::test_copy_int]: forward function
+(** [no_nested_borrows::test_copy_int]:
     Source: 'src/no_nested_borrows.rs', lines 239:0-239:22 *)
 Definition test_copy_int : result unit :=
   y <- copy_int 0%i32; if negb (0%i32 s= y) then Fail_ Failure else Return tt
@@ -279,13 +281,13 @@ Definition test_copy_int : result unit :=
 (** Unit test for [no_nested_borrows::test_copy_int] *)
 Check (test_copy_int )%return.
 
-(** [no_nested_borrows::is_cons]: forward function
+(** [no_nested_borrows::is_cons]:
     Source: 'src/no_nested_borrows.rs', lines 246:0-246:38 *)
 Definition is_cons (T : Type) (l : List_t T) : result bool :=
-  match l with | List_Cons t l0 => Return true | List_Nil => Return false end
+  match l with | List_Cons _ _ => Return true | List_Nil => Return false end
 .
 
-(** [no_nested_borrows::test_is_cons]: forward function
+(** [no_nested_borrows::test_is_cons]:
     Source: 'src/no_nested_borrows.rs', lines 253:0-253:21 *)
 Definition test_is_cons : result unit :=
   let l := List_Nil in
@@ -296,7 +298,7 @@ Definition test_is_cons : result unit :=
 (** Unit test for [no_nested_borrows::test_is_cons] *)
 Check (test_is_cons )%return.
 
-(** [no_nested_borrows::split_list]: forward function
+(** [no_nested_borrows::split_list]:
     Source: 'src/no_nested_borrows.rs', lines 259:0-259:48 *)
 Definition split_list (T : Type) (l : List_t T) : result (T * (List_t T)) :=
   match l with
@@ -305,7 +307,7 @@ Definition split_list (T : Type) (l : List_t T) : result (T * (List_t T)) :=
   end
 .
 
-(** [no_nested_borrows::test_split_list]: forward function
+(** [no_nested_borrows::test_split_list]:
     Source: 'src/no_nested_borrows.rs', lines 267:0-267:24 *)
 Definition test_split_list : result unit :=
   let l := List_Nil in
@@ -317,29 +319,26 @@ Definition test_split_list : result unit :=
 (** Unit test for [no_nested_borrows::test_split_list] *)
 Check (test_split_list )%return.
 
-(** [no_nested_borrows::choose]: forward function
+(** [no_nested_borrows::choose]:
     Source: 'src/no_nested_borrows.rs', lines 274:0-274:70 *)
-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)
 .
 
-(** [no_nested_borrows::choose]: backward function 0
-    Source: 'src/no_nested_borrows.rs', lines 274:0-274:70 *)
-Definition choose_back
-  (T : Type) (b : bool) (x : T) (y : T) (ret : T) : result (T * T) :=
-  if b then Return (ret, y) else Return (x, ret)
-.
-
-(** [no_nested_borrows::choose_test]: forward function
+(** [no_nested_borrows::choose_test]:
     Source: 'src/no_nested_borrows.rs', lines 282:0-282:20 *)
 Definition choose_test : result unit :=
-  z <- choose i32 true 0%i32 0%i32;
-  z0 <- i32_add z 1%i32;
-  if negb (z0 s= 1%i32)
+  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)
@@ -348,7 +347,7 @@ Definition choose_test : result unit :=
 (** Unit test for [no_nested_borrows::choose_test] *)
 Check (choose_test )%return.
 
-(** [no_nested_borrows::test_char]: forward function
+(** [no_nested_borrows::test_char]:
     Source: 'src/no_nested_borrows.rs', lines 294:0-294:26 *)
 Definition test_char : result char :=
   Return (char_of_byte Coq.Init.Byte.x61).
@@ -372,56 +371,52 @@ Arguments Tree_Node { _ }.
 Arguments NodeElem_Cons { _ }.
 Arguments NodeElem_Nil { _ }.
 
-(** [no_nested_borrows::list_length]: forward function
+(** [no_nested_borrows::list_length]:
     Source: 'src/no_nested_borrows.rs', lines 339:0-339:48 *)
 Fixpoint list_length (T : Type) (l : List_t T) : result u32 :=
   match l with
-  | List_Cons t l1 => i <- list_length T l1; u32_add 1%u32 i
+  | List_Cons _ l1 => i <- list_length T l1; u32_add 1%u32 i
   | List_Nil => Return 0%u32
   end
 .
 
-(** [no_nested_borrows::list_nth_shared]: forward function
+(** [no_nested_borrows::list_nth_shared]:
     Source: 'src/no_nested_borrows.rs', lines 347:0-347:62 *)
 Fixpoint list_nth_shared (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_shared T tl i0)
+    else (i1 <- u32_sub i 1%u32; list_nth_shared T tl i1)
   | List_Nil => Fail_ Failure
   end
 .
 
-(** [no_nested_borrows::list_nth_mut]: forward function
+(** [no_nested_borrows::list_nth_mut]:
     Source: 'src/no_nested_borrows.rs', lines 363:0-363:67 *)
-Fixpoint list_nth_mut (T : Type) (l : List_t T) (i : u32) : result 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 x
-    else (i0 <- u32_sub i 1%u32; list_nth_mut T tl i0)
-  | List_Nil => Fail_ Failure
-  end
-.
-
-(** [no_nested_borrows::list_nth_mut]: backward function 0
-    Source: 'src/no_nested_borrows.rs', lines 363:0-363:67 *)
-Fixpoint list_nth_mut_back
-  (T : Type) (l : List_t T) (i : u32) (ret : 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
 .
 
-(** [no_nested_borrows::list_rev_aux]: forward function
+(** [no_nested_borrows::list_rev_aux]:
     Source: 'src/no_nested_borrows.rs', lines 379:0-379:63 *)
 Fixpoint list_rev_aux
   (T : Type) (li : List_t T) (lo : List_t T) : result (List_t T) :=
@@ -431,116 +426,97 @@ Fixpoint list_rev_aux
   end
 .
 
-(** [no_nested_borrows::list_rev]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+(** [no_nested_borrows::list_rev]:
     Source: 'src/no_nested_borrows.rs', lines 393:0-393:42 *)
 Definition list_rev (T : Type) (l : List_t T) : result (List_t T) :=
-  let li := core_mem_replace (List_t T) l List_Nil in
+  let (li, _) := core_mem_replace (List_t T) l List_Nil in
   list_rev_aux T li List_Nil
 .
 
-(** [no_nested_borrows::test_list_functions]: forward function
+(** [no_nested_borrows::test_list_functions]:
     Source: 'src/no_nested_borrows.rs', lines 398:0-398:28 *)
 Definition test_list_functions : result unit :=
   let l := List_Nil in
-  let l0 := List_Cons 2%i32 l in
-  let l1 := List_Cons 1%i32 l0 in
-  i <- list_length i32 (List_Cons 0%i32 l1);
+  let l1 := List_Cons 2%i32 l in
+  let l2 := List_Cons 1%i32 l1 in
+  i <- list_length i32 (List_Cons 0%i32 l2);
   if negb (i s= 3%u32)
   then Fail_ Failure
   else (
-    i0 <- list_nth_shared i32 (List_Cons 0%i32 l1) 0%u32;
-    if negb (i0 s= 0%i32)
+    i1 <- list_nth_shared i32 (List_Cons 0%i32 l2) 0%u32;
+    if negb (i1 s= 0%i32)
     then Fail_ Failure
     else (
-      i1 <- list_nth_shared i32 (List_Cons 0%i32 l1) 1%u32;
-      if negb (i1 s= 1%i32)
+      i2 <- list_nth_shared i32 (List_Cons 0%i32 l2) 1%u32;
+      if negb (i2 s= 1%i32)
       then Fail_ Failure
       else (
-        i2 <- list_nth_shared i32 (List_Cons 0%i32 l1) 2%u32;
-        if negb (i2 s= 2%i32)
+        i3 <- list_nth_shared i32 (List_Cons 0%i32 l2) 2%u32;
+        if negb (i3 s= 2%i32)
         then Fail_ Failure
         else (
-          ls <- list_nth_mut_back i32 (List_Cons 0%i32 l1) 1%u32 3%i32;
-          i3 <- list_nth_shared i32 ls 0%u32;
-          if negb (i3 s= 0%i32)
+          p <- list_nth_mut i32 (List_Cons 0%i32 l2) 1%u32;
+          let (_, list_nth_mut_back) := p in
+          ls <- list_nth_mut_back 3%i32;
+          i4 <- list_nth_shared i32 ls 0%u32;
+          if negb (i4 s= 0%i32)
           then Fail_ Failure
           else (
-            i4 <- list_nth_shared i32 ls 1%u32;
-            if negb (i4 s= 3%i32)
+            i5 <- list_nth_shared i32 ls 1%u32;
+            if negb (i5 s= 3%i32)
             then Fail_ Failure
             else (
-              i5 <- list_nth_shared i32 ls 2%u32;
-              if negb (i5 s= 2%i32) then Fail_ Failure else Return tt))))))
+              i6 <- list_nth_shared i32 ls 2%u32;
+              if negb (i6 s= 2%i32) then Fail_ Failure else Return tt))))))
 .
 
 (** Unit test for [no_nested_borrows::test_list_functions] *)
 Check (test_list_functions )%return.
 
-(** [no_nested_borrows::id_mut_pair1]: forward function
+(** [no_nested_borrows::id_mut_pair1]:
     Source: 'src/no_nested_borrows.rs', lines 414:0-414:89 *)
-Definition id_mut_pair1 (T1 T2 : Type) (x : T1) (y : T2) : result (T1 * T2) :=
-  Return (x, y)
-.
-
-(** [no_nested_borrows::id_mut_pair1]: backward function 0
-    Source: 'src/no_nested_borrows.rs', lines 414:0-414:89 *)
-Definition id_mut_pair1_back
-  (T1 T2 : Type) (x : T1) (y : T2) (ret : (T1 * T2)) : result (T1 * T2) :=
-  let (t, t0) := ret in Return (t, t0)
-.
-
-(** [no_nested_borrows::id_mut_pair2]: forward function
-    Source: 'src/no_nested_borrows.rs', lines 418:0-418:88 *)
-Definition id_mut_pair2 (T1 T2 : Type) (p : (T1 * T2)) : result (T1 * T2) :=
-  let (t, t0) := p in Return (t, t0)
+Definition id_mut_pair1
+  (T1 T2 : Type) (x : T1) (y : T2) :
+  result ((T1 * T2) * ((T1 * T2) -> result (T1 * T2)))
+  :=
+  let back_'a := fun (ret : (T1 * T2)) => let (t, t1) := ret in Return (t, t1)
+    in
+  Return ((x, y), back_'a)
 .
 
-(** [no_nested_borrows::id_mut_pair2]: backward function 0
+(** [no_nested_borrows::id_mut_pair2]:
     Source: 'src/no_nested_borrows.rs', lines 418:0-418:88 *)
-Definition id_mut_pair2_back
-  (T1 T2 : Type) (p : (T1 * T2)) (ret : (T1 * T2)) : result (T1 * T2) :=
-  let (t, t0) := ret in Return (t, t0)
+Definition id_mut_pair2
+  (T1 T2 : Type) (p : (T1 * T2)) :
+  result ((T1 * T2) * ((T1 * T2) -> result (T1 * T2)))
+  :=
+  let (t, t1) := p in
+  let back_'a :=
+    fun (ret : (T1 * T2)) => let (t2, t3) := ret in Return (t2, t3) in
+  Return ((t, t1), back_'a)
 .
 
-(** [no_nested_borrows::id_mut_pair3]: forward function
+(** [no_nested_borrows::id_mut_pair3]:
     Source: 'src/no_nested_borrows.rs', lines 422:0-422:93 *)
-Definition id_mut_pair3 (T1 T2 : Type) (x : T1) (y : T2) : result (T1 * T2) :=
-  Return (x, y)
-.
-
-(** [no_nested_borrows::id_mut_pair3]: backward function 0
-    Source: 'src/no_nested_borrows.rs', lines 422:0-422:93 *)
-Definition id_mut_pair3_back'a
-  (T1 T2 : Type) (x : T1) (y : T2) (ret : T1) : result T1 :=
-  Return ret
-.
-
-(** [no_nested_borrows::id_mut_pair3]: backward function 1
-    Source: 'src/no_nested_borrows.rs', lines 422:0-422:93 *)
-Definition id_mut_pair3_back'b
-  (T1 T2 : Type) (x : T1) (y : T2) (ret : T2) : result T2 :=
-  Return ret
-.
-
-(** [no_nested_borrows::id_mut_pair4]: forward function
-    Source: 'src/no_nested_borrows.rs', lines 426:0-426:92 *)
-Definition id_mut_pair4 (T1 T2 : Type) (p : (T1 * T2)) : result (T1 * T2) :=
-  let (t, t0) := p in Return (t, t0)
+Definition id_mut_pair3
+  (T1 T2 : Type) (x : T1) (y : T2) :
+  result ((T1 * T2) * (T1 -> result T1) * (T2 -> result T2))
+  :=
+  let back_'a := fun (ret : T1) => Return ret in
+  let back_'b := fun (ret : T2) => Return ret in
+  Return ((x, y), back_'a, back_'b)
 .
 
-(** [no_nested_borrows::id_mut_pair4]: backward function 0
+(** [no_nested_borrows::id_mut_pair4]:
     Source: 'src/no_nested_borrows.rs', lines 426:0-426:92 *)
-Definition id_mut_pair4_back'a
-  (T1 T2 : Type) (p : (T1 * T2)) (ret : T1) : result T1 :=
-  Return ret
-.
-
-(** [no_nested_borrows::id_mut_pair4]: backward function 1
-    Source: 'src/no_nested_borrows.rs', lines 426:0-426:92 *)
-Definition id_mut_pair4_back'b
-  (T1 T2 : Type) (p : (T1 * T2)) (ret : T2) : result T2 :=
-  Return ret
+Definition id_mut_pair4
+  (T1 T2 : Type) (p : (T1 * T2)) :
+  result ((T1 * T2) * (T1 -> result T1) * (T2 -> result T2))
+  :=
+  let (t, t1) := p in
+  let back_'a := fun (ret : T1) => Return ret in
+  let back_'b := fun (ret : T2) => Return ret in
+  Return ((t, t1), back_'a, back_'b)
 .
 
 (** [no_nested_borrows::StructWithTuple]
@@ -554,19 +530,19 @@ mkStructWithTuple_t {
 Arguments mkStructWithTuple_t { _ _ }.
 Arguments structWithTuple_p { _ _ }.
 
-(** [no_nested_borrows::new_tuple1]: forward function
+(** [no_nested_borrows::new_tuple1]:
     Source: 'src/no_nested_borrows.rs', lines 437:0-437:48 *)
 Definition new_tuple1 : result (StructWithTuple_t u32 u32) :=
   Return {| structWithTuple_p := (1%u32, 2%u32) |}
 .
 
-(** [no_nested_borrows::new_tuple2]: forward function
+(** [no_nested_borrows::new_tuple2]:
     Source: 'src/no_nested_borrows.rs', lines 441:0-441:48 *)
 Definition new_tuple2 : result (StructWithTuple_t i16 i16) :=
   Return {| structWithTuple_p := (1%i16, 2%i16) |}
 .
 
-(** [no_nested_borrows::new_tuple3]: forward function
+(** [no_nested_borrows::new_tuple3]:
     Source: 'src/no_nested_borrows.rs', lines 445:0-445:48 *)
 Definition new_tuple3 : result (StructWithTuple_t u64 i64) :=
   Return {| structWithTuple_p := (1%u64, 2%i64) |}
@@ -583,13 +559,13 @@ mkStructWithPair_t {
 Arguments mkStructWithPair_t { _ _ }.
 Arguments structWithPair_p { _ _ }.
 
-(** [no_nested_borrows::new_pair1]: forward function
+(** [no_nested_borrows::new_pair1]:
     Source: 'src/no_nested_borrows.rs', lines 454:0-454:46 *)
 Definition new_pair1 : result (StructWithPair_t u32 u32) :=
   Return {| structWithPair_p := {| pair_x := 1%u32; pair_y := 2%u32 |} |}
 .
 
-(** [no_nested_borrows::test_constants]: forward function
+(** [no_nested_borrows::test_constants]:
     Source: 'src/no_nested_borrows.rs', lines 462:0-462:23 *)
 Definition test_constants : result unit :=
   swt <- new_tuple1;
@@ -597,14 +573,14 @@ Definition test_constants : result unit :=
   if negb (i s= 1%u32)
   then Fail_ Failure
   else (
-    swt0 <- new_tuple2;
-    let (i0, _) := swt0.(structWithTuple_p) in
-    if negb (i0 s= 1%i16)
+    swt1 <- new_tuple2;
+    let (i1, _) := swt1.(structWithTuple_p) in
+    if negb (i1 s= 1%i16)
     then Fail_ Failure
     else (
-      swt1 <- new_tuple3;
-      let (i1, _) := swt1.(structWithTuple_p) in
-      if negb (i1 s= 1%u64)
+      swt2 <- new_tuple3;
+      let (i2, _) := swt2.(structWithTuple_p) in
+      if negb (i2 s= 1%u64)
       then Fail_ Failure
       else (
         swp <- new_pair1;
@@ -616,7 +592,7 @@ Definition test_constants : result unit :=
 (** Unit test for [no_nested_borrows::test_constants] *)
 Check (test_constants )%return.
 
-(** [no_nested_borrows::test_weird_borrows1]: forward function
+(** [no_nested_borrows::test_weird_borrows1]:
     Source: 'src/no_nested_borrows.rs', lines 471:0-471:28 *)
 Definition test_weird_borrows1 : result unit :=
   Return tt.
@@ -624,65 +600,79 @@ Definition test_weird_borrows1 : result unit :=
 (** Unit test for [no_nested_borrows::test_weird_borrows1] *)
 Check (test_weird_borrows1 )%return.
 
-(** [no_nested_borrows::test_mem_replace]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+(** [no_nested_borrows::test_mem_replace]:
     Source: 'src/no_nested_borrows.rs', lines 481:0-481:37 *)
 Definition test_mem_replace (px : u32) : result u32 :=
-  let y := core_mem_replace u32 px 1%u32 in
+  let (y, _) := core_mem_replace u32 px 1%u32 in
   if negb (y s= 0%u32) then Fail_ Failure else Return 2%u32
 .
 
-(** [no_nested_borrows::test_shared_borrow_bool1]: forward function
+(** [no_nested_borrows::test_shared_borrow_bool1]:
     Source: 'src/no_nested_borrows.rs', lines 488:0-488:47 *)
 Definition test_shared_borrow_bool1 (b : bool) : result u32 :=
   if b then Return 0%u32 else Return 1%u32
 .
 
-(** [no_nested_borrows::test_shared_borrow_bool2]: forward function
+(** [no_nested_borrows::test_shared_borrow_bool2]:
     Source: 'src/no_nested_borrows.rs', lines 501:0-501:40 *)
 Definition test_shared_borrow_bool2 : result u32 :=
   Return 0%u32.
 
-(** [no_nested_borrows::test_shared_borrow_enum1]: forward function
+(** [no_nested_borrows::test_shared_borrow_enum1]:
     Source: 'src/no_nested_borrows.rs', lines 516:0-516:52 *)
 Definition test_shared_borrow_enum1 (l : List_t u32) : result u32 :=
-  match l with | List_Cons i l0 => Return 1%u32 | List_Nil => Return 0%u32 end
+  match l with | List_Cons _ _ => Return 1%u32 | List_Nil => Return 0%u32 end
 .
 
-(** [no_nested_borrows::test_shared_borrow_enum2]: forward function
+(** [no_nested_borrows::test_shared_borrow_enum2]:
     Source: 'src/no_nested_borrows.rs', lines 528:0-528:40 *)
 Definition test_shared_borrow_enum2 : result u32 :=
   Return 0%u32.
 
-(** [no_nested_borrows::Tuple]
+(** [no_nested_borrows::incr]:
     Source: 'src/no_nested_borrows.rs', lines 539:0-539:24 *)
+Definition incr (x : u32) : result u32 :=
+  u32_add x 1%u32.
+
+(** [no_nested_borrows::call_incr]:
+    Source: 'src/no_nested_borrows.rs', lines 543:0-543:35 *)
+Definition call_incr (x : u32) : result u32 :=
+  incr x.
+
+(** [no_nested_borrows::read_then_incr]:
+    Source: 'src/no_nested_borrows.rs', lines 548:0-548:41 *)
+Definition read_then_incr (x : u32) : result (u32 * u32) :=
+  x1 <- u32_add x 1%u32; Return (x, x1)
+.
+
+(** [no_nested_borrows::Tuple]
+    Source: 'src/no_nested_borrows.rs', lines 554:0-554:24 *)
 Definition Tuple_t (T1 T2 : Type) : Type := T1 * T2.
 
-(** [no_nested_borrows::use_tuple_struct]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
-    Source: 'src/no_nested_borrows.rs', lines 541:0-541:48 *)
+(** [no_nested_borrows::use_tuple_struct]:
+    Source: 'src/no_nested_borrows.rs', lines 556:0-556:48 *)
 Definition use_tuple_struct (x : Tuple_t u32 u32) : result (Tuple_t u32 u32) :=
   let (_, i) := x in Return (1%u32, i)
 .
 
-(** [no_nested_borrows::create_tuple_struct]: forward function
-    Source: 'src/no_nested_borrows.rs', lines 545:0-545:61 *)
+(** [no_nested_borrows::create_tuple_struct]:
+    Source: 'src/no_nested_borrows.rs', lines 560:0-560:61 *)
 Definition create_tuple_struct
   (x : u32) (y : u64) : result (Tuple_t u32 u64) :=
   Return (x, y)
 .
 
 (** [no_nested_borrows::IdType]
-    Source: 'src/no_nested_borrows.rs', lines 550:0-550:20 *)
+    Source: 'src/no_nested_borrows.rs', lines 565:0-565:20 *)
 Definition IdType_t (T : Type) : Type := T.
 
-(** [no_nested_borrows::use_id_type]: forward function
-    Source: 'src/no_nested_borrows.rs', lines 552:0-552:40 *)
+(** [no_nested_borrows::use_id_type]:
+    Source: 'src/no_nested_borrows.rs', lines 567:0-567:40 *)
 Definition use_id_type (T : Type) (x : IdType_t T) : result T :=
   Return x.
 
-(** [no_nested_borrows::create_id_type]: forward function
-    Source: 'src/no_nested_borrows.rs', lines 556:0-556:43 *)
+(** [no_nested_borrows::create_id_type]:
+    Source: 'src/no_nested_borrows.rs', lines 571:0-571:43 *)
 Definition create_id_type (T : Type) (x : T) : result (IdType_t T) :=
   Return x.
 
diff --git a/tests/coq/misc/Primitives.v b/tests/coq/misc/Primitives.v
index 84280b96..c0056073 100644
--- a/tests/coq/misc/Primitives.v
+++ b/tests/coq/misc/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 -> a) := (x, fun 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;
 |}.
 
 
@@ -639,16 +640,9 @@ 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 +655,14 @@ 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 +671,23 @@ 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 +704,9 @@ 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 +730,14 @@ 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 +747,9 @@ 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 +762,10 @@ 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 +782,6 @@ 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 +798,14 @@ 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 +819,8 @@ 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 +833,10 @@ 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 +845,9 @@ 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 +863,6 @@ 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 +873,6 @@ 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.