Regenerate some of the NoNestedBorrows tests

3 files changed, 474 insertions, 546 deletions

diff --git a/tests/fstar/misc/NoNestedBorrows.fst b/tests/fstar/misc/NoNestedBorrows.fst
index 1386b02c..0fd0c1dc 100644
--- a/tests/fstar/misc/NoNestedBorrows.fst
+++ b/tests/fstar/misc/NoNestedBorrows.fst
@@ -37,96 +37,96 @@ type sum_t (t1 t2 : Type0) =
 | Sum_Left : t1 -> sum_t t1 t2
 | Sum_Right : t2 -> sum_t t1 t2
 
-(** [no_nested_borrows::neg_test]: forward function
+(** [no_nested_borrows::neg_test]:
     Source: 'src/no_nested_borrows.rs', lines 48:0-48:30 *)
 let 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 *)
 let 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 *)
 let 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 *)
 let 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 *)
 let div_u32_const (x : u32) : result u32 =
   u32_div x 2
 
-(** [no_nested_borrows::rem_u32]: forward function
+(** [no_nested_borrows::rem_u32]:
     Source: 'src/no_nested_borrows.rs', lines 78:0-78:37 *)
 let 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 *)
 let 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 *)
 let 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 *)
 let 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 *)
 let 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 *)
 let div_i32_const (x : i32) : result i32 =
   i32_div x 2
 
-(** [no_nested_borrows::rem_i32]: forward function
+(** [no_nested_borrows::rem_i32]:
     Source: 'src/no_nested_borrows.rs', lines 104:0-104:37 *)
 let 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 *)
 let 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 *)
 let mix_arith_u32 (x : u32) (y : u32) (z : u32) : result u32 =
   let* i = u32_add x y in
-  let* i0 = u32_div x y in
-  let* i1 = u32_mul i i0 in
-  let* i2 = u32_rem z y in
-  let* i3 = u32_sub x i2 in
-  let* i4 = u32_add i1 i3 in
-  let* i5 = u32_add x y in
-  let* i6 = u32_add i5 z in
-  u32_rem i4 i6
-
-(** [no_nested_borrows::mix_arith_i32]: forward function
+  let* i1 = u32_div x y in
+  let* i2 = u32_mul i i1 in
+  let* i3 = u32_rem z y in
+  let* i4 = u32_sub x i3 in
+  let* i5 = u32_add i2 i4 in
+  let* i6 = u32_add x y in
+  let* i7 = u32_add i6 z in
+  u32_rem i5 i7
+
+(** [no_nested_borrows::mix_arith_i32]:
     Source: 'src/no_nested_borrows.rs', lines 116:0-116:51 *)
 let mix_arith_i32 (x : i32) (y : i32) (z : i32) : result i32 =
   let* i = i32_add x y in
-  let* i0 = i32_div x y in
-  let* i1 = i32_mul i i0 in
-  let* i2 = i32_rem z y in
-  let* i3 = i32_sub x i2 in
-  let* i4 = i32_add i1 i3 in
-  let* i5 = i32_add x y in
-  let* i6 = i32_add i5 z in
-  i32_rem i4 i6
+  let* i1 = i32_div x y in
+  let* i2 = i32_mul i i1 in
+  let* i3 = i32_rem z y in
+  let* i4 = i32_sub x i3 in
+  let* i5 = i32_add i2 i4 in
+  let* i6 = i32_add x y in
+  let* i7 = i32_add i6 z in
+  i32_rem i5 i7
 
 (** [no_nested_borrows::CONST0]
     Source: 'src/no_nested_borrows.rs', lines 125:0-125:23 *)
@@ -138,22 +138,22 @@ let const0_c : usize = eval_global const0_body
 let const1_body : result usize = usize_mul 2 2
 let const1_c : usize = eval_global const1_body
 
-(** [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 *)
 let 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 *)
 let 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 *)
 let 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 *)
 let test2 : result unit =
   let* _ = u32_add 23 44 in Return ()
@@ -161,12 +161,12 @@ let test2 : result unit =
 (** Unit test for [no_nested_borrows::test2] *)
 let _ = assert_norm (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 *)
 let get_max (x : u32) (y : u32) : result u32 =
   if x >= 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 *)
 let test3 : result unit =
   let* x = get_max 4 3 in
@@ -177,7 +177,7 @@ let test3 : result unit =
 (** Unit test for [no_nested_borrows::test3] *)
 let _ = assert_norm (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 *)
 let test_neg1 : result unit =
   let* y = i32_neg 3 in if not (y = -3) then Fail Failure else Return ()
@@ -185,7 +185,7 @@ let test_neg1 : result unit =
 (** Unit test for [no_nested_borrows::test_neg1] *)
 let _ = assert_norm (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 *)
 let refs_test1 : result unit =
   if not (1 = 1) then Fail Failure else Return ()
@@ -193,7 +193,7 @@ let refs_test1 : result unit =
 (** Unit test for [no_nested_borrows::refs_test1] *)
 let _ = assert_norm (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 *)
 let refs_test2 : result unit =
   if not (2 = 2)
@@ -209,7 +209,7 @@ let refs_test2 : result unit =
 (** Unit test for [no_nested_borrows::refs_test2] *)
 let _ = assert_norm (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 *)
 let test_list1 : result unit =
   Return ()
@@ -217,33 +217,34 @@ let test_list1 : result unit =
 (** Unit test for [no_nested_borrows::test_list1] *)
 let _ = assert_norm (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 *)
 let test_box1 : result unit =
   let b = 0 in
-  let* b0 = alloc_boxed_Box_deref_mut_back i32 b 1 in
-  let* x = alloc_boxed_Box_deref i32 b0 in
+  let* (_, deref_mut_back) = alloc_boxed_Box_deref_mut i32 b in
+  let* b1 = deref_mut_back 1 in
+  let* x = alloc_boxed_Box_deref i32 b1 in
   if not (x = 1) then Fail Failure else Return ()
 
 (** Unit test for [no_nested_borrows::test_box1] *)
 let _ = assert_norm (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 *)
 let 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 *)
 let test_unreachable (b : bool) : result unit =
   if b then Fail Failure else Return ()
 
-(** [no_nested_borrows::test_panic]: forward function
+(** [no_nested_borrows::test_panic]:
     Source: 'src/no_nested_borrows.rs', lines 232:0-232:26 *)
 let test_panic (b : bool) : result unit =
   if b then Fail Failure else Return ()
 
-(** [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 *)
 let test_copy_int : result unit =
   let* y = copy_int 0 in if not (0 = y) then Fail Failure else Return ()
@@ -251,15 +252,15 @@ let test_copy_int : result unit =
 (** Unit test for [no_nested_borrows::test_copy_int] *)
 let _ = assert_norm (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 *)
 let is_cons (t : Type0) (l : list_t t) : result bool =
   begin match l with
-  | List_Cons x l0 -> Return true
+  | 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 *)
 let test_is_cons : result unit =
   let l = List_Nil in
@@ -269,7 +270,7 @@ let test_is_cons : result unit =
 (** Unit test for [no_nested_borrows::test_is_cons] *)
 let _ = assert_norm (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 *)
 let split_list (t : Type0) (l : list_t t) : result (t & (list_t t)) =
   begin match l with
@@ -277,7 +278,7 @@ let split_list (t : Type0) (l : list_t t) : result (t & (list_t t)) =
   | List_Nil -> Fail Failure
   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 *)
 let test_split_list : result unit =
   let l = List_Nil in
@@ -288,26 +289,23 @@ let test_split_list : result unit =
 (** Unit test for [no_nested_borrows::test_split_list] *)
 let _ = assert_norm (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 *)
-let choose (t : Type0) (b : bool) (x : t) (y : t) : result t =
-  if b then Return x else Return y
+let choose
+  (t : Type0) (b : bool) (x : t) (y : t) : result (t & (t -> result (t & t))) =
+  if b
+  then let back_'a = fun ret -> Return (ret, y) in Return (x, back_'a)
+  else let back_'a = fun ret -> 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 *)
-let choose_back
-  (t : Type0) (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 *)
 let choose_test : result unit =
-  let* z = choose i32 true 0 0 in
-  let* z0 = i32_add z 1 in
-  if not (z0 = 1)
+  let* (z, choose_back) = choose i32 true 0 0 in
+  let* z1 = i32_add z 1 in
+  if not (z1 = 1)
   then Fail Failure
   else
-    let* (x, y) = choose_back i32 true 0 0 z0 in
+    let* (x, y) = choose_back z1 in
     if not (x = 1)
     then Fail Failure
     else if not (y = 0) then Fail Failure else Return ()
@@ -315,7 +313,7 @@ let choose_test : result unit =
 (** Unit test for [no_nested_borrows::choose_test] *)
 let _ = assert_norm (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 *)
 let test_char : result char =
   Return 'a'
@@ -332,50 +330,47 @@ and nodeElem_t (t : Type0) =
 | NodeElem_Cons : tree_t t -> nodeElem_t t -> nodeElem_t t
 | NodeElem_Nil : nodeElem_t t
 
-(** [no_nested_borrows::list_length]: forward function
+(** [no_nested_borrows::list_length]:
     Source: 'src/no_nested_borrows.rs', lines 339:0-339:48 *)
 let rec list_length (t : Type0) (l : list_t t) : result u32 =
   begin match l with
-  | List_Cons x l1 -> let* i = list_length t l1 in u32_add 1 i
+  | List_Cons _ l1 -> let* i = list_length t l1 in u32_add 1 i
   | List_Nil -> Return 0
   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 *)
 let rec list_nth_shared (t : Type0) (l : list_t t) (i : u32) : result t =
   begin match l with
   | List_Cons x tl ->
     if i = 0
     then Return x
-    else let* i0 = u32_sub i 1 in list_nth_shared t tl i0
-  | List_Nil -> Fail Failure
-  end
-
-(** [no_nested_borrows::list_nth_mut]: forward function
-    Source: 'src/no_nested_borrows.rs', lines 363:0-363:67 *)
-let rec list_nth_mut (t : Type0) (l : list_t t) (i : u32) : result t =
-  begin match l with
-  | List_Cons x tl ->
-    if i = 0 then Return x else let* i0 = u32_sub i 1 in list_nth_mut t tl i0
+    else let* i1 = u32_sub i 1 in list_nth_shared t tl i1
   | List_Nil -> Fail Failure
   end
 
-(** [no_nested_borrows::list_nth_mut]: backward function 0
+(** [no_nested_borrows::list_nth_mut]:
     Source: 'src/no_nested_borrows.rs', lines 363:0-363:67 *)
-let rec list_nth_mut_back
-  (t : Type0) (l : list_t t) (i : u32) (ret : t) : result (list_t t) =
+let rec list_nth_mut
+  (t : Type0) (l : list_t t) (i : u32) :
+  result (t & (t -> result (list_t t)))
+  =
   begin match l with
   | List_Cons x tl ->
     if i = 0
-    then Return (List_Cons ret tl)
+    then
+      let back_'a = fun ret -> Return (List_Cons ret tl) in Return (x, back_'a)
     else
-      let* i0 = u32_sub i 1 in
-      let* tl0 = list_nth_mut_back t tl i0 ret in
-      Return (List_Cons x tl0)
+      let* i1 = u32_sub i 1 in
+      let* (x1, list_nth_mut_back) = list_nth_mut t tl i1 in
+      let back_'a =
+        fun ret -> let* tl1 = list_nth_mut_back ret in Return (List_Cons x tl1)
+        in
+      Return (x1, 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 *)
 let rec list_rev_aux
   (t : Type0) (li : list_t t) (lo : list_t t) : result (list_t t) =
@@ -384,120 +379,105 @@ let rec list_rev_aux
   | List_Nil -> Return lo
   end
 
-(** [no_nested_borrows::list_rev]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+(** [no_nested_borrows::list_rev]:
     Source: 'src/no_nested_borrows.rs', lines 393:0-393:42 *)
 let list_rev (t : Type0) (l : list_t t) : result (list_t t) =
-  let li = core_mem_replace (list_t t) l List_Nil in list_rev_aux t li List_Nil
+  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 *)
 let test_list_functions : result unit =
   let l = List_Nil in
-  let l0 = List_Cons 2 l in
-  let l1 = List_Cons 1 l0 in
-  let* i = list_length i32 (List_Cons 0 l1) in
+  let l1 = List_Cons 2 l in
+  let l2 = List_Cons 1 l1 in
+  let* i = list_length i32 (List_Cons 0 l2) in
   if not (i = 3)
   then Fail Failure
   else
-    let* i0 = list_nth_shared i32 (List_Cons 0 l1) 0 in
-    if not (i0 = 0)
+    let* i1 = list_nth_shared i32 (List_Cons 0 l2) 0 in
+    if not (i1 = 0)
     then Fail Failure
     else
-      let* i1 = list_nth_shared i32 (List_Cons 0 l1) 1 in
-      if not (i1 = 1)
+      let* i2 = list_nth_shared i32 (List_Cons 0 l2) 1 in
+      if not (i2 = 1)
       then Fail Failure
       else
-        let* i2 = list_nth_shared i32 (List_Cons 0 l1) 2 in
-        if not (i2 = 2)
+        let* i3 = list_nth_shared i32 (List_Cons 0 l2) 2 in
+        if not (i3 = 2)
         then Fail Failure
         else
-          let* ls = list_nth_mut_back i32 (List_Cons 0 l1) 1 3 in
-          let* i3 = list_nth_shared i32 ls 0 in
-          if not (i3 = 0)
+          let* (_, list_nth_mut_back) = list_nth_mut i32 (List_Cons 0 l2) 1 in
+          let* ls = list_nth_mut_back 3 in
+          let* i4 = list_nth_shared i32 ls 0 in
+          if not (i4 = 0)
           then Fail Failure
           else
-            let* i4 = list_nth_shared i32 ls 1 in
-            if not (i4 = 3)
+            let* i5 = list_nth_shared i32 ls 1 in
+            if not (i5 = 3)
             then Fail Failure
             else
-              let* i5 = list_nth_shared i32 ls 2 in
-              if not (i5 = 2) then Fail Failure else Return ()
+              let* i6 = list_nth_shared i32 ls 2 in
+              if not (i6 = 2) then Fail Failure else Return ()
 
 (** Unit test for [no_nested_borrows::test_list_functions] *)
 let _ = assert_norm (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 *)
-let id_mut_pair1 (t1 t2 : Type0) (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 *)
-let id_mut_pair1_back
-  (t1 t2 : Type0) (x : t1) (y : t2) (ret : (t1 & t2)) : result (t1 & t2) =
-  let (x0, x1) = ret in Return (x0, x1)
-
-(** [no_nested_borrows::id_mut_pair2]: forward function
+let id_mut_pair1
+  (t1 t2 : Type0) (x : t1) (y : t2) :
+  result ((t1 & t2) & ((t1 & t2) -> result (t1 & t2)))
+  =
+  let back_'a = fun ret -> let (x1, x2) = ret in Return (x1, x2) in
+  Return ((x, y), back_'a)
+
+(** [no_nested_borrows::id_mut_pair2]:
     Source: 'src/no_nested_borrows.rs', lines 418:0-418:88 *)
-let id_mut_pair2 (t1 t2 : Type0) (p : (t1 & t2)) : result (t1 & t2) =
-  let (x, x0) = p in Return (x, x0)
-
-(** [no_nested_borrows::id_mut_pair2]: backward function 0
-    Source: 'src/no_nested_borrows.rs', lines 418:0-418:88 *)
-let id_mut_pair2_back
-  (t1 t2 : Type0) (p : (t1 & t2)) (ret : (t1 & t2)) : result (t1 & t2) =
-  let (x, x0) = ret in Return (x, x0)
-
-(** [no_nested_borrows::id_mut_pair3]: forward function
+let id_mut_pair2
+  (t1 t2 : Type0) (p : (t1 & t2)) :
+  result ((t1 & t2) & ((t1 & t2) -> result (t1 & t2)))
+  =
+  let (x, x1) = p in
+  let back_'a = fun ret -> let (x2, x3) = ret in Return (x2, x3) in
+  Return ((x, x1), back_'a)
+
+(** [no_nested_borrows::id_mut_pair3]:
     Source: 'src/no_nested_borrows.rs', lines 422:0-422:93 *)
-let id_mut_pair3 (t1 t2 : Type0) (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 *)
-let id_mut_pair3_back'a
-  (t1 t2 : Type0) (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 *)
-let id_mut_pair3_back'b
-  (t1 t2 : Type0) (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 *)
-let id_mut_pair4 (t1 t2 : Type0) (p : (t1 & t2)) : result (t1 & t2) =
-  let (x, x0) = p in Return (x, x0)
-
-(** [no_nested_borrows::id_mut_pair4]: backward function 0
+let id_mut_pair3
+  (t1 t2 : Type0) (x : t1) (y : t2) :
+  result ((t1 & t2) & (t1 -> result t1) & (t2 -> result t2))
+  =
+  let back_'a = fun ret -> Return ret in
+  let back_'b = fun ret -> Return ret in
+  Return ((x, y), back_'a, back_'b)
+
+(** [no_nested_borrows::id_mut_pair4]:
     Source: 'src/no_nested_borrows.rs', lines 426:0-426:92 *)
-let id_mut_pair4_back'a
-  (t1 t2 : Type0) (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 *)
-let id_mut_pair4_back'b
-  (t1 t2 : Type0) (p : (t1 & t2)) (ret : t2) : result t2 =
-  Return ret
+let id_mut_pair4
+  (t1 t2 : Type0) (p : (t1 & t2)) :
+  result ((t1 & t2) & (t1 -> result t1) & (t2 -> result t2))
+  =
+  let (x, x1) = p in
+  let back_'a = fun ret -> Return ret in
+  let back_'b = fun ret -> Return ret in
+  Return ((x, x1), back_'a, back_'b)
 
 (** [no_nested_borrows::StructWithTuple]
     Source: 'src/no_nested_borrows.rs', lines 433:0-433:34 *)
 type structWithTuple_t (t1 t2 : Type0) = { p : (t1 & t2); }
 
-(** [no_nested_borrows::new_tuple1]: forward function
+(** [no_nested_borrows::new_tuple1]:
     Source: 'src/no_nested_borrows.rs', lines 437:0-437:48 *)
 let new_tuple1 : result (structWithTuple_t u32 u32) =
   Return { p = (1, 2) }
 
-(** [no_nested_borrows::new_tuple2]: forward function
+(** [no_nested_borrows::new_tuple2]:
     Source: 'src/no_nested_borrows.rs', lines 441:0-441:48 *)
 let new_tuple2 : result (structWithTuple_t i16 i16) =
   Return { p = (1, 2) }
 
-(** [no_nested_borrows::new_tuple3]: forward function
+(** [no_nested_borrows::new_tuple3]:
     Source: 'src/no_nested_borrows.rs', lines 445:0-445:48 *)
 let new_tuple3 : result (structWithTuple_t u64 i64) =
   Return { p = (1, 2) }
@@ -506,12 +486,12 @@ let new_tuple3 : result (structWithTuple_t u64 i64) =
     Source: 'src/no_nested_borrows.rs', lines 450:0-450:33 *)
 type structWithPair_t (t1 t2 : Type0) = { p : pair_t t1 t2; }
 
-(** [no_nested_borrows::new_pair1]: forward function
+(** [no_nested_borrows::new_pair1]:
     Source: 'src/no_nested_borrows.rs', lines 454:0-454:46 *)
 let new_pair1 : result (structWithPair_t u32 u32) =
   Return { p = { x = 1; y = 2 } }
 
-(** [no_nested_borrows::test_constants]: forward function
+(** [no_nested_borrows::test_constants]:
     Source: 'src/no_nested_borrows.rs', lines 462:0-462:23 *)
 let test_constants : result unit =
   let* swt = new_tuple1 in
@@ -519,14 +499,14 @@ let test_constants : result unit =
   if not (i = 1)
   then Fail Failure
   else
-    let* swt0 = new_tuple2 in
-    let (i0, _) = swt0.p in
-    if not (i0 = 1)
+    let* swt1 = new_tuple2 in
+    let (i1, _) = swt1.p in
+    if not (i1 = 1)
     then Fail Failure
     else
-      let* swt1 = new_tuple3 in
-      let (i1, _) = swt1.p in
-      if not (i1 = 1)
+      let* swt2 = new_tuple3 in
+      let (i2, _) = swt2.p in
+      if not (i2 = 1)
       then Fail Failure
       else
         let* swp = new_pair1 in
@@ -535,7 +515,7 @@ let test_constants : result unit =
 (** Unit test for [no_nested_borrows::test_constants] *)
 let _ = assert_norm (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 *)
 let test_weird_borrows1 : result unit =
   Return ()
@@ -543,59 +523,72 @@ let test_weird_borrows1 : result unit =
 (** Unit test for [no_nested_borrows::test_weird_borrows1] *)
 let _ = assert_norm (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 *)
 let test_mem_replace (px : u32) : result u32 =
-  let y = core_mem_replace u32 px 1 in
+  let (y, _) = core_mem_replace u32 px 1 in
   if not (y = 0) then Fail Failure else Return 2
 
-(** [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 *)
 let test_shared_borrow_bool1 (b : bool) : result u32 =
   if b then Return 0 else Return 1
 
-(** [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 *)
 let test_shared_borrow_bool2 : result u32 =
   Return 0
 
-(** [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 *)
 let test_shared_borrow_enum1 (l : list_t u32) : result u32 =
-  begin match l with | List_Cons i l0 -> Return 1 | List_Nil -> Return 0 end
+  begin match l with | List_Cons _ _ -> Return 1 | List_Nil -> Return 0 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 *)
 let test_shared_borrow_enum2 : result u32 =
   Return 0
 
-(** [no_nested_borrows::Tuple]
+(** [no_nested_borrows::incr]:
     Source: 'src/no_nested_borrows.rs', lines 539:0-539:24 *)
+let incr (x : u32) : result u32 =
+  u32_add x 1
+
+(** [no_nested_borrows::call_incr]:
+    Source: 'src/no_nested_borrows.rs', lines 543:0-543:35 *)
+let 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 *)
+let read_then_incr (x : u32) : result (u32 & u32) =
+  let* x1 = u32_add x 1 in Return (x, x1)
+
+(** [no_nested_borrows::Tuple]
+    Source: 'src/no_nested_borrows.rs', lines 554:0-554:24 *)
 type tuple_t (t1 t2 : Type0) = 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 *)
 let use_tuple_struct (x : tuple_t u32 u32) : result (tuple_t u32 u32) =
   let (_, i) = x in Return (1, 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 *)
 let 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 *)
 type idType_t (t : Type0) = 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 *)
 let use_id_type (t : Type0) (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 *)
 let create_id_type (t : Type0) (x : t) : result (idType_t t) =
   Return x
 
diff --git a/tests/fstar/misc/Primitives.fst b/tests/fstar/misc/Primitives.fst
index a3ffbde4..6b8dbeb7 100644
--- a/tests/fstar/misc/Primitives.fst
+++ b/tests/fstar/misc/Primitives.fst
@@ -55,8 +55,7 @@ type string = string
 let is_zero (n: nat) : bool = n = 0
 let decrease (n: nat{n > 0}) : nat = n - 1
 
-let core_mem_replace (a : Type0) (x : a) (y : a) : a = x
-let core_mem_replace_back (a : Type0) (x : a) (y : a) : a = y
+let core_mem_replace (a : Type0) (x : a) (y : a) : a & (a -> a) = (x, (fun x -> x))
 
 // We don't really use raw pointers for now
 type mut_raw_ptr (t : Type0) = { v : t }
@@ -477,8 +476,7 @@ noeq type core_ops_index_Index (self idx : Type0) = {
 // Trait declaration: [core::ops::index::IndexMut]
 noeq type core_ops_index_IndexMut (self idx : Type0) = {
   indexInst : core_ops_index_Index self idx;
-  index_mut : self → idx → result indexInst.output;
-  index_mut_back : self → idx → indexInst.output → result self;
+  index_mut : self → idx → result (indexInst.output & (indexInst.output → result self));
 }
 
 // Trait declaration [core::ops::deref::Deref]
@@ -490,8 +488,7 @@ noeq type core_ops_deref_Deref (self : Type0) = {
 // Trait declaration [core::ops::deref::DerefMut]
 noeq type core_ops_deref_DerefMut (self : Type0) = {
   derefInst : core_ops_deref_Deref self;
-  deref_mut : self → result derefInst.target;
-  deref_mut_back : self → derefInst.target → result self;
+  deref_mut : self → result (derefInst.target & (derefInst.target → result self));
 }
 
 type core_ops_range_Range (a : Type0) = {
@@ -502,8 +499,8 @@ type core_ops_range_Range (a : Type0) = {
 (*** [alloc] *)
 
 let alloc_boxed_Box_deref (t : Type0) (x : t) : result t = Return x
-let alloc_boxed_Box_deref_mut (t : Type0) (x : t) : result t = Return x
-let alloc_boxed_Box_deref_mut_back (t : Type) (_ : t) (x : t) : result t = Return x
+let alloc_boxed_Box_deref_mut (t : Type0) (x : t) : result (t & (t -> result t)) =
+  Return (x, (fun x -> Return x))
 
 // Trait instance
 let alloc_boxed_Box_coreopsDerefInst (self : Type0) : core_ops_deref_Deref self = {
@@ -515,7 +512,6 @@ let alloc_boxed_Box_coreopsDerefInst (self : Type0) : core_ops_deref_Deref self
 let alloc_boxed_Box_coreopsDerefMutInst (self : Type0) : core_ops_deref_DerefMut self = {
   derefInst = alloc_boxed_Box_coreopsDerefInst self;
   deref_mut = alloc_boxed_Box_deref_mut self;
-  deref_mut_back = alloc_boxed_Box_deref_mut_back self;
 }
 
 (*** Array *)
@@ -588,8 +584,13 @@ let alloc_vec_Vec_index_usize (#a : Type0) (v : alloc_vec_Vec a) (i : usize) : r
 let alloc_vec_Vec_update_usize (#a : Type0) (v : alloc_vec_Vec a) (i : usize) (x : a) : result (alloc_vec_Vec a) =
   if i < length v then Return (list_update v i x) else Fail Failure
 
-// The **forward** function shouldn't be used
-let alloc_vec_Vec_push_fwd (a  : Type0) (v : alloc_vec_Vec a) (x : a) : unit = ()
+let alloc_vec_Vec_index_mut_usize (#a : Type0) (v: alloc_vec_Vec a) (i: usize) :
+  result (a & (a → result (alloc_vec_Vec a))) =
+  match alloc_vec_Vec_index_usize v i with
+  | Return x ->
+    Return (x, alloc_vec_Vec_update_usize v i)
+  | Fail e -> Fail e
+
 let alloc_vec_Vec_push (a  : Type0) (v : alloc_vec_Vec a) (x : a) :
   Pure (result (alloc_vec_Vec a))
   (requires True)
@@ -605,9 +606,6 @@ let alloc_vec_Vec_push (a  : Type0) (v : alloc_vec_Vec a) (x : a) :
     end
   else Fail Failure
 
-// The **forward** function shouldn't be used
-let alloc_vec_Vec_insert_fwd (a : Type0) (v : alloc_vec_Vec a) (i : usize) (x : a) : result unit =
-  if i < length v then Return () else Fail Failure
 let alloc_vec_Vec_insert (a : Type0) (v : alloc_vec_Vec a) (i : usize) (x : a) : result (alloc_vec_Vec a) =
   if i < length v then Return (list_update v i x) else Fail Failure
 
@@ -619,13 +617,11 @@ noeq type core_slice_index_SliceIndex (self t : Type0) = {
   sealedInst : core_slice_index_private_slice_index_Sealed self;
   output : Type0;
   get : self → t → result (option output);
-  get_mut : self → t → result (option output);
-  get_mut_back : self → t → option output → result t;
+  get_mut : self → t → result (option output & (option output -> result t));
   get_unchecked : self → const_raw_ptr t → result (const_raw_ptr output);
   get_unchecked_mut : self → mut_raw_ptr t → result (mut_raw_ptr output);
   index : self → t → result output;
-  index_mut : self → t → result output;
-  index_mut_back : self → t → output → result t;
+  index_mut : self → t → result (output & (output -> result t));
 }
 
 // [core::slice::index::[T]::index]: forward function
@@ -643,14 +639,8 @@ let core_slice_index_RangeUsize_get (t : Type0) (i : core_ops_range_Range usize)
   admit () // TODO
 
 // [core::slice::index::Range::get_mut]: forward function
-let core_slice_index_RangeUsize_get_mut
-  (t : Type0) : core_ops_range_Range usize → slice t → result (option (slice t)) =
-  admit () // TODO
-
-// [core::slice::index::Range::get_mut]: backward function 0
-let core_slice_index_RangeUsize_get_mut_back
-  (t : Type0) :
-  core_ops_range_Range usize → slice t → option (slice t) → result (slice t) =
+let core_slice_index_RangeUsize_get_mut (t : Type0) :
+  core_ops_range_Range usize → slice t → result (option (slice t) & (option (slice t) -> result (slice t))) =
   admit () // TODO
 
 // [core::slice::index::Range::get_unchecked]: forward function
@@ -675,27 +665,16 @@ let core_slice_index_RangeUsize_index
   admit () // TODO
 
 // [core::slice::index::Range::index_mut]: forward function
-let core_slice_index_RangeUsize_index_mut
-  (t : Type0) : core_ops_range_Range usize → slice t → result (slice t) =
-  admit () // TODO
-
-// [core::slice::index::Range::index_mut]: backward function 0
-let core_slice_index_RangeUsize_index_mut_back
-  (t : Type0) : core_ops_range_Range usize → slice t → slice t → result (slice t) =
+let core_slice_index_RangeUsize_index_mut (t : Type0) :
+  core_ops_range_Range usize → slice t → result (slice t & (slice t -> result (slice t))) =
   admit () // TODO
 
 // [core::slice::index::[T]::index_mut]: forward function
 let core_slice_index_Slice_index_mut
   (t idx : Type0) (inst : core_slice_index_SliceIndex idx (slice t)) :
-  slice t → idx → result inst.output =
+  slice t → idx → result (inst.output & (inst.output -> result (slice t))) =
   admit () // 
 
-// [core::slice::index::[T]::index_mut]: backward function 0
-let core_slice_index_Slice_index_mut_back
-  (t idx : Type0) (inst : core_slice_index_SliceIndex idx (slice t)) :
-  slice t → idx → inst.output → result (slice t) =
-  admit () // TODO
-
 // [core::array::[T; N]::index]: forward function
 let core_array_Array_index
   (t idx : Type0) (n : usize) (inst : core_ops_index_Index (slice t) idx)
@@ -705,13 +684,8 @@ let core_array_Array_index
 // [core::array::[T; N]::index_mut]: forward function
 let core_array_Array_index_mut
   (t idx : Type0) (n : usize) (inst : core_ops_index_IndexMut (slice t) idx)
-  (a : array t n) (i : idx) : result inst.indexInst.output =
-  admit () // TODO
-
-// [core::array::[T; N]::index_mut]: backward function 0
-let core_array_Array_index_mut_back
-  (t idx : Type0) (n : usize) (inst : core_ops_index_IndexMut (slice t) idx)
-  (a : array t n) (i : idx) (x : inst.indexInst.output) : result (array t n) =
+  (a : array t n) (i : idx) :
+  result (inst.indexInst.output & (inst.indexInst.output -> result (array t n))) =
   admit () // TODO
 
 // Trait implementation: [core::slice::index::private_slice_index::Range]
@@ -725,12 +699,10 @@ let core_slice_index_SliceIndexRangeUsizeSliceTInst (t : Type0) :
   output = slice t;
   get = core_slice_index_RangeUsize_get t;
   get_mut = core_slice_index_RangeUsize_get_mut t;
-  get_mut_back = core_slice_index_RangeUsize_get_mut_back t;
   get_unchecked = core_slice_index_RangeUsize_get_unchecked t;
   get_unchecked_mut = core_slice_index_RangeUsize_get_unchecked_mut t;
   index = core_slice_index_RangeUsize_index t;
   index_mut = core_slice_index_RangeUsize_index_mut t;
-  index_mut_back = core_slice_index_RangeUsize_index_mut_back t;
 }
 
 // Trait implementation: [core::slice::index::[T]]
@@ -747,7 +719,6 @@ let core_ops_index_IndexMutSliceTIInst (t idx : Type0)
   core_ops_index_IndexMut (slice t) idx = {
   indexInst = core_ops_index_IndexSliceTIInst t idx inst;
   index_mut = core_slice_index_Slice_index_mut t idx inst;
-  index_mut_back = core_slice_index_Slice_index_mut_back t idx inst;
 }
 
 // Trait implementation: [core::array::[T; N]]
@@ -764,7 +735,6 @@ let core_ops_index_IndexMutArrayIInst (t idx : Type0) (n : usize)
   core_ops_index_IndexMut (array t n) idx = {
   indexInst = core_ops_index_IndexArrayInst t idx n inst.indexInst;
   index_mut = core_array_Array_index_mut t idx n inst;
-  index_mut_back = core_array_Array_index_mut_back t idx n inst;
 }
 
 // [core::slice::index::usize::get]: forward function
@@ -773,13 +743,8 @@ let core_slice_index_usize_get
   admit () // TODO
 
 // [core::slice::index::usize::get_mut]: forward function
-let core_slice_index_usize_get_mut
-  (t : Type0) : usize → slice t → result (option t) =
-  admit () // TODO
-
-// [core::slice::index::usize::get_mut]: backward function 0
-let core_slice_index_usize_get_mut_back
-  (t : Type0) : usize → slice t → option t → result (slice t) =
+let core_slice_index_usize_get_mut (t : Type0) :
+  usize → slice t → result (option t & (option t -> result (slice t))) =
   admit () // TODO
 
 // [core::slice::index::usize::get_unchecked]: forward function
@@ -797,12 +762,8 @@ let core_slice_index_usize_index (t : Type0) : usize → slice t → result t =
   admit () // TODO
 
 // [core::slice::index::usize::index_mut]: forward function
-let core_slice_index_usize_index_mut (t : Type0) : usize → slice t → result t =
-  admit () // TODO
-
-// [core::slice::index::usize::index_mut]: backward function 0
-let core_slice_index_usize_index_mut_back
-  (t : Type0) : usize → slice t → t → result (slice t) =
+let core_slice_index_usize_index_mut (t : Type0) :
+  usize → slice t → result (t & (t -> result (slice t))) =
   admit () // TODO
 
 // Trait implementation: [core::slice::index::private_slice_index::usize]
@@ -816,12 +777,10 @@ let core_slice_index_SliceIndexUsizeSliceTInst (t : Type0) :
   output = t;
   get = core_slice_index_usize_get t;
   get_mut = core_slice_index_usize_get_mut t;
-  get_mut_back = core_slice_index_usize_get_mut_back t;
   get_unchecked = core_slice_index_usize_get_unchecked t;
   get_unchecked_mut = core_slice_index_usize_get_unchecked_mut t;
   index = core_slice_index_usize_index t;
   index_mut = core_slice_index_usize_index_mut t;
-  index_mut_back = core_slice_index_usize_index_mut_back t;
 }
 
 // [alloc::vec::Vec::index]: forward function
@@ -831,13 +790,8 @@ let alloc_vec_Vec_index (t idx : Type0) (inst : core_slice_index_SliceIndex idx
 
 // [alloc::vec::Vec::index_mut]: forward function
 let alloc_vec_Vec_index_mut (t idx : Type0) (inst : core_slice_index_SliceIndex idx (slice t))
-  (self : alloc_vec_Vec t) (i : idx) : result inst.output =
-  admit () // TODO
-
-// [alloc::vec::Vec::index_mut]: backward function 0
-let alloc_vec_Vec_index_mut_back
-  (t idx : Type0) (inst : core_slice_index_SliceIndex idx (slice t))
-  (self : alloc_vec_Vec t) (i : idx) (x : inst.output) : result (alloc_vec_Vec t) =
+  (self : alloc_vec_Vec t) (i : idx) :
+  result (inst.output & (inst.output -> result (alloc_vec_Vec t))) =
   admit () // TODO
 
 // Trait implementation: [alloc::vec::Vec]
@@ -854,7 +808,6 @@ let alloc_vec_Vec_coreopsindexIndexMutInst (t idx : Type0)
   core_ops_index_IndexMut (alloc_vec_Vec t) idx = {
   indexInst = alloc_vec_Vec_coreopsindexIndexInst t idx inst;
   index_mut = alloc_vec_Vec_index_mut t idx inst;
-  index_mut_back = alloc_vec_Vec_index_mut_back t idx inst;
 }
 
 (*** Theorems *)
@@ -870,15 +823,7 @@ let alloc_vec_Vec_index_eq (#a : Type0) (v : alloc_vec_Vec a) (i : usize) :
 let alloc_vec_Vec_index_mut_eq (#a : Type0) (v : alloc_vec_Vec a) (i : usize) :
   Lemma (
     alloc_vec_Vec_index_mut a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i ==
-      alloc_vec_Vec_index_usize v i)
+      alloc_vec_Vec_index_mut_usize v i)
   [SMTPat (alloc_vec_Vec_index_mut a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i)]
   =
   admit()
-
-let alloc_vec_Vec_index_mut_back_eq (#a : Type0) (v : alloc_vec_Vec a) (i : usize) (x : a) :
-  Lemma (
-    alloc_vec_Vec_index_mut_back a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i x ==
-      alloc_vec_Vec_update_usize v i x)
-  [SMTPat (alloc_vec_Vec_index_mut_back a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i x)]
-  =
-  admit()
diff --git a/tests/lean/NoNestedBorrows.lean b/tests/lean/NoNestedBorrows.lean
index 0bce3a64..cb0aac10 100644
--- a/tests/lean/NoNestedBorrows.lean
+++ b/tests/lean/NoNestedBorrows.lean
@@ -43,98 +43,98 @@ inductive Sum (T1 T2 : Type) :=
 | Left : T1 → Sum T1 T2
 | Right : T2 → Sum T1 T2
 
-/- [no_nested_borrows::neg_test]: forward function
+/- [no_nested_borrows::neg_test]:
    Source: 'src/no_nested_borrows.rs', lines 48:0-48:30 -/
 def neg_test (x : I32) : Result I32 :=
   - x
 
-/- [no_nested_borrows::add_u32]: forward function
+/- [no_nested_borrows::add_u32]:
    Source: 'src/no_nested_borrows.rs', lines 54:0-54:37 -/
 def add_u32 (x : U32) (y : U32) : Result U32 :=
   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 -/
 def subs_u32 (x : U32) (y : U32) : Result U32 :=
   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 -/
 def div_u32 (x : U32) (y : U32) : Result U32 :=
   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 -/
 def div_u32_const (x : U32) : Result U32 :=
   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 -/
 def rem_u32 (x : U32) (y : U32) : Result U32 :=
   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 -/
 def mul_u32 (x : U32) (y : U32) : Result U32 :=
   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 -/
 def add_i32 (x : I32) (y : I32) : Result I32 :=
   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 -/
 def subs_i32 (x : I32) (y : I32) : Result I32 :=
   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 -/
 def div_i32 (x : I32) (y : I32) : Result I32 :=
   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 -/
 def div_i32_const (x : I32) : Result I32 :=
   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 -/
 def rem_i32 (x : I32) (y : I32) : Result I32 :=
   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 -/
 def mul_i32 (x : I32) (y : I32) : Result I32 :=
   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 -/
 def mix_arith_u32 (x : U32) (y : U32) (z : U32) : Result U32 :=
   do
-    let i ← x + y
-    let i0 ← x / y
-    let i1 ← i * i0
-    let i2 ← z % y
-    let i3 ← x - i2
-    let i4 ← i1 + i3
-    let i5 ← x + y
-    let i6 ← i5 + z
-    i4 % i6
-
-/- [no_nested_borrows::mix_arith_i32]: forward function
+  let i ← x + y
+  let i1 ← x / y
+  let i2 ← i * i1
+  let i3 ← z % y
+  let i4 ← x - i3
+  let i5 ← i2 + i4
+  let i6 ← x + y
+  let i7 ← i6 + z
+  i5 % i7
+
+/- [no_nested_borrows::mix_arith_i32]:
    Source: 'src/no_nested_borrows.rs', lines 116:0-116:51 -/
 def mix_arith_i32 (x : I32) (y : I32) (z : I32) : Result I32 :=
   do
-    let i ← x + y
-    let i0 ← x / y
-    let i1 ← i * i0
-    let i2 ← z % y
-    let i3 ← x - i2
-    let i4 ← i1 + i3
-    let i5 ← x + y
-    let i6 ← i5 + z
-    i4 % i6
+  let i ← x + y
+  let i1 ← x / y
+  let i2 ← i * i1
+  let i3 ← z % y
+  let i4 ← x - i3
+  let i5 ← i2 + i4
+  let i6 ← x + y
+  let i7 ← i6 + z
+  i5 % i7
 
 /- [no_nested_borrows::CONST0]
    Source: 'src/no_nested_borrows.rs', lines 125:0-125:23 -/
@@ -146,65 +146,65 @@ def const0_c : Usize := eval_global const0_body (by simp)
 def const1_body : Result Usize := 2#usize * 2#usize
 def const1_c : Usize := eval_global const1_body (by simp)
 
-/- [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 -/
 def cast_u32_to_i32 (x : U32) : Result I32 :=
   Scalar.cast .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 -/
 def 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 -/
 def cast_bool_to_bool (x : Bool) : Result Bool :=
   Result.ret x
 
-/- [no_nested_borrows::test2]: forward function
+/- [no_nested_borrows::test2]:
    Source: 'src/no_nested_borrows.rs', lines 142:0-142:14 -/
 def test2 : Result Unit :=
   do
-    let _ ← 23#u32 + 44#u32
-    Result.ret ()
+  let _ ← 23#u32 + 44#u32
+  Result.ret ()
 
 /- Unit test for [no_nested_borrows::test2] -/
 #assert (test2 == Result.ret ())
 
-/- [no_nested_borrows::get_max]: forward function
+/- [no_nested_borrows::get_max]:
    Source: 'src/no_nested_borrows.rs', lines 154:0-154:37 -/
 def get_max (x : U32) (y : U32) : Result U32 :=
   if x >= y
   then Result.ret x
   else Result.ret y
 
-/- [no_nested_borrows::test3]: forward function
+/- [no_nested_borrows::test3]:
    Source: 'src/no_nested_borrows.rs', lines 162:0-162:14 -/
 def test3 : Result Unit :=
   do
-    let x ← get_max 4#u32 3#u32
-    let y ← get_max 10#u32 11#u32
-    let z ← x + y
-    if not (z = 15#u32)
-    then Result.fail .panic
-    else Result.ret ()
+  let x ← get_max 4#u32 3#u32
+  let y ← get_max 10#u32 11#u32
+  let z ← x + y
+  if not (z = 15#u32)
+  then Result.fail .panic
+  else Result.ret ()
 
 /- Unit test for [no_nested_borrows::test3] -/
 #assert (test3 == Result.ret ())
 
-/- [no_nested_borrows::test_neg1]: forward function
+/- [no_nested_borrows::test_neg1]:
    Source: 'src/no_nested_borrows.rs', lines 169:0-169:18 -/
 def test_neg1 : Result Unit :=
   do
-    let y ← - 3#i32
-    if not (y = (-(3:Int))#i32)
-    then Result.fail .panic
-    else Result.ret ()
+  let y ← - 3#i32
+  if not (y = (-(3:Int))#i32)
+  then Result.fail .panic
+  else Result.ret ()
 
 /- Unit test for [no_nested_borrows::test_neg1] -/
 #assert (test_neg1 == Result.ret ())
 
-/- [no_nested_borrows::refs_test1]: forward function
+/- [no_nested_borrows::refs_test1]:
    Source: 'src/no_nested_borrows.rs', lines 176:0-176:19 -/
 def refs_test1 : Result Unit :=
   if not (1#i32 = 1#i32)
@@ -214,7 +214,7 @@ def refs_test1 : Result Unit :=
 /- Unit test for [no_nested_borrows::refs_test1] -/
 #assert (refs_test1 == Result.ret ())
 
-/- [no_nested_borrows::refs_test2]: forward function
+/- [no_nested_borrows::refs_test2]:
    Source: 'src/no_nested_borrows.rs', lines 187:0-187:19 -/
 def refs_test2 : Result Unit :=
   if not (2#i32 = 2#i32)
@@ -232,7 +232,7 @@ def refs_test2 : Result Unit :=
 /- Unit test for [no_nested_borrows::refs_test2] -/
 #assert (refs_test2 == Result.ret ())
 
-/- [no_nested_borrows::test_list1]: forward function
+/- [no_nested_borrows::test_list1]:
    Source: 'src/no_nested_borrows.rs', lines 203:0-203:19 -/
 def test_list1 : Result Unit :=
   Result.ret ()
@@ -240,128 +240,126 @@ def test_list1 : Result Unit :=
 /- Unit test for [no_nested_borrows::test_list1] -/
 #assert (test_list1 == Result.ret ())
 
-/- [no_nested_borrows::test_box1]: forward function
+/- [no_nested_borrows::test_box1]:
    Source: 'src/no_nested_borrows.rs', lines 208:0-208:18 -/
 def test_box1 : Result Unit :=
   do
-    let b := 0#i32
-    let b0 ← alloc.boxed.Box.deref_mut_back I32 b 1#i32
-    let x ← alloc.boxed.Box.deref I32 b0
-    if not (x = 1#i32)
-    then Result.fail .panic
-    else Result.ret ()
+  let b := 0#i32
+  let (_, deref_mut_back) ← alloc.boxed.Box.deref_mut I32 b
+  let b1 ← deref_mut_back 1#i32
+  let x ← alloc.boxed.Box.deref I32 b1
+  if not (x = 1#i32)
+  then Result.fail .panic
+  else Result.ret ()
 
 /- Unit test for [no_nested_borrows::test_box1] -/
 #assert (test_box1 == Result.ret ())
 
-/- [no_nested_borrows::copy_int]: forward function
+/- [no_nested_borrows::copy_int]:
    Source: 'src/no_nested_borrows.rs', lines 218:0-218:30 -/
 def copy_int (x : I32) : Result I32 :=
   Result.ret x
 
-/- [no_nested_borrows::test_unreachable]: forward function
+/- [no_nested_borrows::test_unreachable]:
    Source: 'src/no_nested_borrows.rs', lines 224:0-224:32 -/
 def test_unreachable (b : Bool) : Result Unit :=
   if b
   then Result.fail .panic
   else Result.ret ()
 
-/- [no_nested_borrows::test_panic]: forward function
+/- [no_nested_borrows::test_panic]:
    Source: 'src/no_nested_borrows.rs', lines 232:0-232:26 -/
 def test_panic (b : Bool) : Result Unit :=
   if b
   then Result.fail .panic
   else Result.ret ()
 
-/- [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 -/
 def test_copy_int : Result Unit :=
   do
-    let y ← copy_int 0#i32
-    if not (0#i32 = y)
-    then Result.fail .panic
-    else Result.ret ()
+  let y ← copy_int 0#i32
+  if not (0#i32 = y)
+  then Result.fail .panic
+  else Result.ret ()
 
 /- Unit test for [no_nested_borrows::test_copy_int] -/
 #assert (test_copy_int == Result.ret ())
 
-/- [no_nested_borrows::is_cons]: forward function
+/- [no_nested_borrows::is_cons]:
    Source: 'src/no_nested_borrows.rs', lines 246:0-246:38 -/
 def is_cons (T : Type) (l : List T) : Result Bool :=
   match l with
-  | List.Cons t l0 => Result.ret true
+  | List.Cons _ _ => Result.ret true
   | List.Nil => Result.ret false
 
-/- [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 -/
 def test_is_cons : Result Unit :=
   do
-    let l := List.Nil
-    let b ← is_cons I32 (List.Cons 0#i32 l)
-    if not b
-    then Result.fail .panic
-    else Result.ret ()
+  let l := List.Nil
+  let b ← is_cons I32 (List.Cons 0#i32 l)
+  if not b
+  then Result.fail .panic
+  else Result.ret ()
 
 /- Unit test for [no_nested_borrows::test_is_cons] -/
 #assert (test_is_cons == Result.ret ())
 
-/- [no_nested_borrows::split_list]: forward function
+/- [no_nested_borrows::split_list]:
    Source: 'src/no_nested_borrows.rs', lines 259:0-259:48 -/
 def split_list (T : Type) (l : List T) : Result (T × (List T)) :=
   match l with
   | List.Cons hd tl => Result.ret (hd, tl)
   | List.Nil => Result.fail .panic
 
-/- [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 -/
 def test_split_list : Result Unit :=
   do
-    let l := List.Nil
-    let p ← split_list I32 (List.Cons 0#i32 l)
-    let (hd, _) := p
-    if not (hd = 0#i32)
-    then Result.fail .panic
-    else Result.ret ()
+  let l := List.Nil
+  let p ← split_list I32 (List.Cons 0#i32 l)
+  let (hd, _) := p
+  if not (hd = 0#i32)
+  then Result.fail .panic
+  else Result.ret ()
 
 /- Unit test for [no_nested_borrows::test_split_list] -/
 #assert (test_split_list == Result.ret ())
 
-/- [no_nested_borrows::choose]: forward function
+/- [no_nested_borrows::choose]:
    Source: 'src/no_nested_borrows.rs', lines 274:0-274:70 -/
-def choose (T : Type) (b : Bool) (x : T) (y : T) : Result T :=
+def choose
+  (T : Type) (b : Bool) (x : T) (y : T) :
+  Result (T × (T → Result (T × T)))
+  :=
   if b
-  then Result.ret x
-  else Result.ret y
+  then let back_'a := fun ret => Result.ret (ret, y)
+       Result.ret (x, back_'a)
+  else let back_'a := fun ret => Result.ret (x, ret)
+       Result.ret (y, back_'a)
 
-/- [no_nested_borrows::choose]: backward function 0
-   Source: 'src/no_nested_borrows.rs', lines 274:0-274:70 -/
-def choose_back
-  (T : Type) (b : Bool) (x : T) (y : T) (ret : T) : Result (T × T) :=
-  if b
-  then Result.ret (ret, y)
-  else Result.ret (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 -/
 def choose_test : Result Unit :=
   do
-    let z ← choose I32 true 0#i32 0#i32
-    let z0 ← z + 1#i32
-    if not (z0 = 1#i32)
+  let (z, choose_back) ← choose I32 true 0#i32 0#i32
+  let z1 ← z + 1#i32
+  if not (z1 = 1#i32)
+  then Result.fail .panic
+  else
+    do
+    let (x, y) ← choose_back z1
+    if not (x = 1#i32)
     then Result.fail .panic
-    else
-      do
-        let (x, y) ← choose_back I32 true 0#i32 0#i32 z0
-        if not (x = 1#i32)
-        then Result.fail .panic
-        else if not (y = 0#i32)
-             then Result.fail .panic
-             else Result.ret ()
+    else if not (y = 0#i32)
+         then Result.fail .panic
+         else Result.ret ()
 
 /- Unit test for [no_nested_borrows::choose_test] -/
 #assert (choose_test == Result.ret ())
 
-/- [no_nested_borrows::test_char]: forward function
+/- [no_nested_borrows::test_char]:
    Source: 'src/no_nested_borrows.rs', lines 294:0-294:26 -/
 def test_char : Result Char :=
   Result.ret 'a'
@@ -382,16 +380,16 @@ inductive NodeElem (T : Type) :=
 
 end
 
-/- [no_nested_borrows::list_length]: forward function
+/- [no_nested_borrows::list_length]:
    Source: 'src/no_nested_borrows.rs', lines 339:0-339:48 -/
 divergent def list_length (T : Type) (l : List T) : Result U32 :=
   match l with
-  | List.Cons t l1 => do
-                        let i ← list_length T l1
-                        1#u32 + i
+  | List.Cons _ l1 => do
+                      let i ← list_length T l1
+                      1#u32 + i
   | List.Nil => Result.ret 0#u32
 
-/- [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 -/
 divergent def list_nth_shared (T : Type) (l : List T) (i : U32) : Result T :=
   match l with
@@ -399,38 +397,33 @@ divergent def list_nth_shared (T : Type) (l : List T) (i : U32) : Result T :=
     if i = 0#u32
     then Result.ret x
     else do
-           let i0 ← i - 1#u32
-           list_nth_shared T tl i0
-  | List.Nil => Result.fail .panic
-
-/- [no_nested_borrows::list_nth_mut]: forward function
-   Source: 'src/no_nested_borrows.rs', lines 363:0-363:67 -/
-divergent def list_nth_mut (T : Type) (l : List T) (i : U32) : Result T :=
-  match l with
-  | List.Cons x tl =>
-    if i = 0#u32
-    then Result.ret x
-    else do
-           let i0 ← i - 1#u32
-           list_nth_mut T tl i0
+         let i1 ← i - 1#u32
+         list_nth_shared T tl i1
   | List.Nil => Result.fail .panic
 
-/- [no_nested_borrows::list_nth_mut]: backward function 0
+/- [no_nested_borrows::list_nth_mut]:
    Source: 'src/no_nested_borrows.rs', lines 363:0-363:67 -/
-divergent def list_nth_mut_back
-  (T : Type) (l : List T) (i : U32) (ret : T) : Result (List T) :=
+divergent def list_nth_mut
+  (T : Type) (l : List T) (i : U32) : Result (T × (T → Result (List T))) :=
   match l with
   | List.Cons x tl =>
     if i = 0#u32
-    then Result.ret (List.Cons ret tl)
+    then
+      let back_'a := fun ret => Result.ret (List.Cons ret tl)
+      Result.ret (x, back_'a)
     else
       do
-        let i0 ← i - 1#u32
-        let tl0 ← list_nth_mut_back T tl i0 ret
-        Result.ret (List.Cons x tl0)
+      let i1 ← i - 1#u32
+      let (t, list_nth_mut_back) ← list_nth_mut T tl i1
+      let back_'a :=
+        fun ret =>
+          do
+          let tl1 ← list_nth_mut_back ret
+          Result.ret (List.Cons x tl1)
+      Result.ret (t, back_'a)
   | List.Nil => Result.fail .panic
 
-/- [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 -/
 divergent def list_rev_aux
   (T : Type) (li : List T) (lo : List T) : Result (List T) :=
@@ -438,136 +431,118 @@ divergent def list_rev_aux
   | List.Cons hd tl => list_rev_aux T tl (List.Cons hd lo)
   | List.Nil => Result.ret lo
 
-/- [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 -/
 def list_rev (T : Type) (l : List T) : Result (List T) :=
-  let li := core.mem.replace (List T) l List.Nil
+  let (li, _) := core.mem.replace (List T) l List.Nil
   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 -/
 def test_list_functions : Result Unit :=
   do
-    let l := List.Nil
-    let l0 := List.Cons 2#i32 l
-    let l1 := List.Cons 1#i32 l0
-    let i ← list_length I32 (List.Cons 0#i32 l1)
-    if not (i = 3#u32)
+  let l := List.Nil
+  let l1 := List.Cons 2#i32 l
+  let l2 := List.Cons 1#i32 l1
+  let i ← list_length I32 (List.Cons 0#i32 l2)
+  if not (i = 3#u32)
+  then Result.fail .panic
+  else
+    do
+    let i1 ← list_nth_shared I32 (List.Cons 0#i32 l2) 0#u32
+    if not (i1 = 0#i32)
     then Result.fail .panic
     else
       do
-        let i0 ← list_nth_shared I32 (List.Cons 0#i32 l1) 0#u32
-        if not (i0 = 0#i32)
+      let i2 ← list_nth_shared I32 (List.Cons 0#i32 l2) 1#u32
+      if not (i2 = 1#i32)
+      then Result.fail .panic
+      else
+        do
+        let i3 ← list_nth_shared I32 (List.Cons 0#i32 l2) 2#u32
+        if not (i3 = 2#i32)
         then Result.fail .panic
         else
           do
-            let i1 ← list_nth_shared I32 (List.Cons 0#i32 l1) 1#u32
-            if not (i1 = 1#i32)
+          let (_, list_nth_mut_back) ←
+            list_nth_mut I32 (List.Cons 0#i32 l2) 1#u32
+          let ls ← list_nth_mut_back 3#i32
+          let i4 ← list_nth_shared I32 ls 0#u32
+          if not (i4 = 0#i32)
+          then Result.fail .panic
+          else
+            do
+            let i5 ← list_nth_shared I32 ls 1#u32
+            if not (i5 = 3#i32)
             then Result.fail .panic
             else
               do
-                let i2 ← list_nth_shared I32 (List.Cons 0#i32 l1) 2#u32
-                if not (i2 = 2#i32)
-                then Result.fail .panic
-                else
-                  do
-                    let ls ←
-                      list_nth_mut_back I32 (List.Cons 0#i32 l1) 1#u32 3#i32
-                    let i3 ← list_nth_shared I32 ls 0#u32
-                    if not (i3 = 0#i32)
-                    then Result.fail .panic
-                    else
-                      do
-                        let i4 ← list_nth_shared I32 ls 1#u32
-                        if not (i4 = 3#i32)
-                        then Result.fail .panic
-                        else
-                          do
-                            let i5 ← list_nth_shared I32 ls 2#u32
-                            if not (i5 = 2#i32)
-                            then Result.fail .panic
-                            else Result.ret ()
+              let i6 ← list_nth_shared I32 ls 2#u32
+              if not (i6 = 2#i32)
+              then Result.fail .panic
+              else Result.ret ()
 
 /- Unit test for [no_nested_borrows::test_list_functions] -/
 #assert (test_list_functions == Result.ret ())
 
-/- [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 -/
-def id_mut_pair1 (T1 T2 : Type) (x : T1) (y : T2) : Result (T1 × T2) :=
-  Result.ret (x, y)
-
-/- [no_nested_borrows::id_mut_pair1]: backward function 0
-   Source: 'src/no_nested_borrows.rs', lines 414:0-414:89 -/
-def id_mut_pair1_back
-  (T1 T2 : Type) (x : T1) (y : T2) (ret : (T1 × T2)) : Result (T1 × T2) :=
-  let (t, t0) := ret
-  Result.ret (t, t0)
-
-/- [no_nested_borrows::id_mut_pair2]: forward function
+def id_mut_pair1
+  (T1 T2 : Type) (x : T1) (y : T2) :
+  Result ((T1 × T2) × ((T1 × T2) → Result (T1 × T2)))
+  :=
+  let back_'a := fun ret => let (t, t1) := ret
+                            Result.ret (t, t1)
+  Result.ret ((x, y), back_'a)
+
+/- [no_nested_borrows::id_mut_pair2]:
    Source: 'src/no_nested_borrows.rs', lines 418:0-418:88 -/
-def id_mut_pair2 (T1 T2 : Type) (p : (T1 × T2)) : Result (T1 × T2) :=
-  let (t, t0) := p
-  Result.ret (t, t0)
-
-/- [no_nested_borrows::id_mut_pair2]: backward function 0
-   Source: 'src/no_nested_borrows.rs', lines 418:0-418:88 -/
-def id_mut_pair2_back
-  (T1 T2 : Type) (p : (T1 × T2)) (ret : (T1 × T2)) : Result (T1 × T2) :=
-  let (t, t0) := ret
-  Result.ret (t, t0)
-
-/- [no_nested_borrows::id_mut_pair3]: forward function
+def id_mut_pair2
+  (T1 T2 : Type) (p : (T1 × T2)) :
+  Result ((T1 × T2) × ((T1 × T2) → Result (T1 × T2)))
+  :=
+  let (t, t1) := p
+  let back_'a := fun ret => let (t2, t3) := ret
+                            Result.ret (t2, t3)
+  Result.ret ((t, t1), back_'a)
+
+/- [no_nested_borrows::id_mut_pair3]:
    Source: 'src/no_nested_borrows.rs', lines 422:0-422:93 -/
-def id_mut_pair3 (T1 T2 : Type) (x : T1) (y : T2) : Result (T1 × T2) :=
-  Result.ret (x, y)
-
-/- [no_nested_borrows::id_mut_pair3]: backward function 0
-   Source: 'src/no_nested_borrows.rs', lines 422:0-422:93 -/
-def id_mut_pair3_back'a
-  (T1 T2 : Type) (x : T1) (y : T2) (ret : T1) : Result T1 :=
-  Result.ret ret
-
-/- [no_nested_borrows::id_mut_pair3]: backward function 1
-   Source: 'src/no_nested_borrows.rs', lines 422:0-422:93 -/
-def id_mut_pair3_back'b
-  (T1 T2 : Type) (x : T1) (y : T2) (ret : T2) : Result T2 :=
-  Result.ret ret
-
-/- [no_nested_borrows::id_mut_pair4]: forward function
+def id_mut_pair3
+  (T1 T2 : Type) (x : T1) (y : T2) :
+  Result ((T1 × T2) × (T1 → Result T1) × (T2 → Result T2))
+  :=
+  let back_'a := fun ret => Result.ret ret
+  let back_'b := fun ret => Result.ret ret
+  Result.ret ((x, y), back_'a, back_'b)
+
+/- [no_nested_borrows::id_mut_pair4]:
    Source: 'src/no_nested_borrows.rs', lines 426:0-426:92 -/
-def id_mut_pair4 (T1 T2 : Type) (p : (T1 × T2)) : Result (T1 × T2) :=
-  let (t, t0) := p
-  Result.ret (t, t0)
-
-/- [no_nested_borrows::id_mut_pair4]: backward function 0
-   Source: 'src/no_nested_borrows.rs', lines 426:0-426:92 -/
-def id_mut_pair4_back'a
-  (T1 T2 : Type) (p : (T1 × T2)) (ret : T1) : Result T1 :=
-  Result.ret ret
-
-/- [no_nested_borrows::id_mut_pair4]: backward function 1
-   Source: 'src/no_nested_borrows.rs', lines 426:0-426:92 -/
-def id_mut_pair4_back'b
-  (T1 T2 : Type) (p : (T1 × T2)) (ret : T2) : Result T2 :=
-  Result.ret ret
+def id_mut_pair4
+  (T1 T2 : Type) (p : (T1 × T2)) :
+  Result ((T1 × T2) × (T1 → Result T1) × (T2 → Result T2))
+  :=
+  let (t, t1) := p
+  let back_'a := fun ret => Result.ret ret
+  let back_'b := fun ret => Result.ret ret
+  Result.ret ((t, t1), back_'a, back_'b)
 
 /- [no_nested_borrows::StructWithTuple]
    Source: 'src/no_nested_borrows.rs', lines 433:0-433:34 -/
 structure StructWithTuple (T1 T2 : Type) where
   p : (T1 × T2)
 
-/- [no_nested_borrows::new_tuple1]: forward function
+/- [no_nested_borrows::new_tuple1]:
    Source: 'src/no_nested_borrows.rs', lines 437:0-437:48 -/
 def new_tuple1 : Result (StructWithTuple U32 U32) :=
   Result.ret { 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 -/
 def new_tuple2 : Result (StructWithTuple I16 I16) :=
   Result.ret { 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 -/
 def new_tuple3 : Result (StructWithTuple U64 I64) :=
   Result.ret { p := (1#u64, 2#i64) }
@@ -577,42 +552,42 @@ def new_tuple3 : Result (StructWithTuple U64 I64) :=
 structure StructWithPair (T1 T2 : Type) where
   p : Pair T1 T2
 
-/- [no_nested_borrows::new_pair1]: forward function
+/- [no_nested_borrows::new_pair1]:
    Source: 'src/no_nested_borrows.rs', lines 454:0-454:46 -/
 def new_pair1 : Result (StructWithPair U32 U32) :=
   Result.ret { p := { x := 1#u32, 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 -/
 def test_constants : Result Unit :=
   do
-    let swt ← new_tuple1
-    let (i, _) := swt.p
-    if not (i = 1#u32)
+  let swt ← new_tuple1
+  let (i, _) := swt.p
+  if not (i = 1#u32)
+  then Result.fail .panic
+  else
+    do
+    let swt1 ← new_tuple2
+    let (i1, _) := swt1.p
+    if not (i1 = 1#i16)
     then Result.fail .panic
     else
       do
-        let swt0 ← new_tuple2
-        let (i0, _) := swt0.p
-        if not (i0 = 1#i16)
+      let swt2 ← new_tuple3
+      let (i2, _) := swt2.p
+      if not (i2 = 1#u64)
+      then Result.fail .panic
+      else
+        do
+        let swp ← new_pair1
+        if not (swp.p.x = 1#u32)
         then Result.fail .panic
-        else
-          do
-            let swt1 ← new_tuple3
-            let (i1, _) := swt1.p
-            if not (i1 = 1#u64)
-            then Result.fail .panic
-            else
-              do
-                let swp ← new_pair1
-                if not (swp.p.x = 1#u32)
-                then Result.fail .panic
-                else Result.ret ()
+        else Result.ret ()
 
 /- Unit test for [no_nested_borrows::test_constants] -/
 #assert (test_constants == Result.ret ())
 
-/- [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 -/
 def test_weird_borrows1 : Result Unit :=
   Result.ret ()
@@ -620,65 +595,80 @@ def test_weird_borrows1 : Result Unit :=
 /- Unit test for [no_nested_borrows::test_weird_borrows1] -/
 #assert (test_weird_borrows1 == Result.ret ())
 
-/- [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 -/
 def test_mem_replace (px : U32) : Result U32 :=
-  let y := core.mem.replace U32 px 1#u32
+  let (y, _) := core.mem.replace U32 px 1#u32
   if not (y = 0#u32)
   then Result.fail .panic
   else Result.ret 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 -/
 def test_shared_borrow_bool1 (b : Bool) : Result U32 :=
   if b
   then Result.ret 0#u32
   else Result.ret 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 -/
 def test_shared_borrow_bool2 : Result U32 :=
   Result.ret 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 -/
 def test_shared_borrow_enum1 (l : List U32) : Result U32 :=
   match l with
-  | List.Cons i l0 => Result.ret 1#u32
+  | List.Cons _ _ => Result.ret 1#u32
   | List.Nil => Result.ret 0#u32
 
-/- [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 -/
 def test_shared_borrow_enum2 : Result U32 :=
   Result.ret 0#u32
 
-/- [no_nested_borrows::Tuple]
+/- [no_nested_borrows::incr]:
    Source: 'src/no_nested_borrows.rs', lines 539:0-539:24 -/
+def incr (x : U32) : Result U32 :=
+  x + 1#u32
+
+/- [no_nested_borrows::call_incr]:
+   Source: 'src/no_nested_borrows.rs', lines 543:0-543:35 -/
+def 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 -/
+def read_then_incr (x : U32) : Result (U32 × U32) :=
+  do
+  let x1 ← x + 1#u32
+  Result.ret (x, x1)
+
+/- [no_nested_borrows::Tuple]
+   Source: 'src/no_nested_borrows.rs', lines 554:0-554:24 -/
 def Tuple (T1 T2 : 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 -/
 def use_tuple_struct (x : Tuple U32 U32) : Result (Tuple U32 U32) :=
   Result.ret (1#u32, x.1)
 
-/- [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 -/
 def create_tuple_struct (x : U32) (y : U64) : Result (Tuple U32 U64) :=
   Result.ret (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 -/
 @[reducible] def IdType (T : 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 -/
 def use_id_type (T : Type) (x : IdType T) : Result T :=
   Result.ret 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 -/
 def create_id_type (T : Type) (x : T) : Result (IdType T) :=
   Result.ret x