Regenerate the test files and add the fstar-split tests

4 files changed, 202 insertions, 3794 deletions

diff --git a/tests/fstar/hashmap/Hashmap.Funs.fst b/tests/fstar/hashmap/Hashmap.Funs.fst
index e6cd1411..9fc5d8a0 100644
--- a/tests/fstar/hashmap/Hashmap.Funs.fst
+++ b/tests/fstar/hashmap/Hashmap.Funs.fst
@@ -7,12 +7,12 @@ include Hashmap.Clauses
 
 #set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
 
-(** [hashmap::hash_key]: forward function
+(** [hashmap::hash_key]:
     Source: 'src/hashmap.rs', lines 27:0-27:32 *)
 let hash_key (k : usize) : result usize =
   Return k
 
-(** [hashmap::{hashmap::HashMap<T>}::allocate_slots]: loop 0: forward function
+(** [hashmap::{hashmap::HashMap<T>}::allocate_slots]: loop 0:
     Source: 'src/hashmap.rs', lines 50:4-56:5 *)
 let rec hashMap_allocate_slots_loop
   (t : Type0) (slots : alloc_vec_Vec (list_t t)) (n : usize) :
@@ -21,12 +21,12 @@ let rec hashMap_allocate_slots_loop
   =
   if n > 0
   then
-    let* slots0 = alloc_vec_Vec_push (list_t t) slots List_Nil in
-    let* n0 = usize_sub n 1 in
-    hashMap_allocate_slots_loop t slots0 n0
+    let* v = alloc_vec_Vec_push (list_t t) slots List_Nil in
+    let* n1 = usize_sub n 1 in
+    hashMap_allocate_slots_loop t v n1
   else Return slots
 
-(** [hashmap::{hashmap::HashMap<T>}::allocate_slots]: forward function
+(** [hashmap::{hashmap::HashMap<T>}::allocate_slots]:
     Source: 'src/hashmap.rs', lines 50:4-50:76 *)
 let hashMap_allocate_slots
   (t : Type0) (slots : alloc_vec_Vec (list_t t)) (n : usize) :
@@ -34,7 +34,7 @@ let hashMap_allocate_slots
   =
   hashMap_allocate_slots_loop t slots n
 
-(** [hashmap::{hashmap::HashMap<T>}::new_with_capacity]: forward function
+(** [hashmap::{hashmap::HashMap<T>}::new_with_capacity]:
     Source: 'src/hashmap.rs', lines 59:4-63:13 *)
 let hashMap_new_with_capacity
   (t : Type0) (capacity : usize) (max_load_dividend : usize)
@@ -44,97 +44,75 @@ let hashMap_new_with_capacity
   let v = alloc_vec_Vec_new (list_t t) in
   let* slots = hashMap_allocate_slots t v capacity in
   let* i = usize_mul capacity max_load_dividend in
-  let* i0 = usize_div i max_load_divisor in
+  let* i1 = usize_div i max_load_divisor in
   Return
     {
       num_entries = 0;
       max_load_factor = (max_load_dividend, max_load_divisor);
-      max_load = i0;
+      max_load = i1;
       slots = slots
     }
 
-(** [hashmap::{hashmap::HashMap<T>}::new]: forward function
+(** [hashmap::{hashmap::HashMap<T>}::new]:
     Source: 'src/hashmap.rs', lines 75:4-75:24 *)
 let hashMap_new (t : Type0) : result (hashMap_t t) =
   hashMap_new_with_capacity t 32 4 5
 
-(** [hashmap::{hashmap::HashMap<T>}::clear]: loop 0: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+(** [hashmap::{hashmap::HashMap<T>}::clear]: loop 0:
     Source: 'src/hashmap.rs', lines 80:4-88:5 *)
 let rec hashMap_clear_loop
   (t : Type0) (slots : alloc_vec_Vec (list_t t)) (i : usize) :
   Tot (result (alloc_vec_Vec (list_t t)))
   (decreases (hashMap_clear_loop_decreases t slots i))
   =
-  let i0 = alloc_vec_Vec_len (list_t t) slots in
-  if i < i0
+  let i1 = alloc_vec_Vec_len (list_t t) slots in
+  if i < i1
   then
-    let* i1 = usize_add i 1 in
-    let* slots0 =
-      alloc_vec_Vec_index_mut_back (list_t t) usize
-        (core_slice_index_SliceIndexUsizeSliceTInst (list_t t)) slots i
-        List_Nil in
-    hashMap_clear_loop t slots0 i1
+    let* (_, index_mut_back) =
+      alloc_vec_Vec_index_mut (list_t t) usize
+        (core_slice_index_SliceIndexUsizeSliceTInst (list_t t)) slots i in
+    let* i2 = usize_add i 1 in
+    let* slots1 = index_mut_back List_Nil in
+    hashMap_clear_loop t slots1 i2
   else Return slots
 
-(** [hashmap::{hashmap::HashMap<T>}::clear]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+(** [hashmap::{hashmap::HashMap<T>}::clear]:
     Source: 'src/hashmap.rs', lines 80:4-80:27 *)
 let hashMap_clear (t : Type0) (self : hashMap_t t) : result (hashMap_t t) =
-  let* v = hashMap_clear_loop t self.slots 0 in
-  Return { self with num_entries = 0; slots = v }
+  let* back = hashMap_clear_loop t self.slots 0 in
+  Return { self with num_entries = 0; slots = back }
 
-(** [hashmap::{hashmap::HashMap<T>}::len]: forward function
+(** [hashmap::{hashmap::HashMap<T>}::len]:
     Source: 'src/hashmap.rs', lines 90:4-90:30 *)
 let hashMap_len (t : Type0) (self : hashMap_t t) : result usize =
   Return self.num_entries
 
-(** [hashmap::{hashmap::HashMap<T>}::insert_in_list]: loop 0: forward function
+(** [hashmap::{hashmap::HashMap<T>}::insert_in_list]: loop 0:
     Source: 'src/hashmap.rs', lines 97:4-114:5 *)
 let rec hashMap_insert_in_list_loop
   (t : Type0) (key : usize) (value : t) (ls : list_t t) :
-  Tot (result bool)
+  Tot (result (bool & (list_t t)))
   (decreases (hashMap_insert_in_list_loop_decreases t key value ls))
   =
   begin match ls with
   | List_Cons ckey cvalue tl ->
     if ckey = key
-    then Return false
-    else hashMap_insert_in_list_loop t key value tl
-  | List_Nil -> Return true
+    then Return (false, List_Cons ckey value tl)
+    else
+      let* (b, back) = hashMap_insert_in_list_loop t key value tl in
+      Return (b, List_Cons ckey cvalue back)
+  | List_Nil -> let l = List_Nil in Return (true, List_Cons key value l)
   end
 
-(** [hashmap::{hashmap::HashMap<T>}::insert_in_list]: forward function
+(** [hashmap::{hashmap::HashMap<T>}::insert_in_list]:
     Source: 'src/hashmap.rs', lines 97:4-97:71 *)
 let hashMap_insert_in_list
-  (t : Type0) (key : usize) (value : t) (ls : list_t t) : result bool =
-  hashMap_insert_in_list_loop t key value ls
-
-(** [hashmap::{hashmap::HashMap<T>}::insert_in_list]: loop 0: backward function 0
-    Source: 'src/hashmap.rs', lines 97:4-114:5 *)
-let rec hashMap_insert_in_list_loop_back
   (t : Type0) (key : usize) (value : t) (ls : list_t t) :
-  Tot (result (list_t t))
-  (decreases (hashMap_insert_in_list_loop_decreases t key value ls))
+  result (bool & (list_t t))
   =
-  begin match ls with
-  | List_Cons ckey cvalue tl ->
-    if ckey = key
-    then Return (List_Cons ckey value tl)
-    else
-      let* tl0 = hashMap_insert_in_list_loop_back t key value tl in
-      Return (List_Cons ckey cvalue tl0)
-  | List_Nil -> let l = List_Nil in Return (List_Cons key value l)
-  end
-
-(** [hashmap::{hashmap::HashMap<T>}::insert_in_list]: backward function 0
-    Source: 'src/hashmap.rs', lines 97:4-97:71 *)
-let hashMap_insert_in_list_back
-  (t : Type0) (key : usize) (value : t) (ls : list_t t) : result (list_t t) =
-  hashMap_insert_in_list_loop_back t key value ls
+  hashMap_insert_in_list_loop t key value ls
 
-(** [hashmap::{hashmap::HashMap<T>}::insert_no_resize]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+(** [hashmap::{hashmap::HashMap<T>}::insert_no_resize]:
     Source: 'src/hashmap.rs', lines 117:4-117:54 *)
 let hashMap_insert_no_resize
   (t : Type0) (self : hashMap_t t) (key : usize) (value : t) :
@@ -143,30 +121,19 @@ let hashMap_insert_no_resize
   let* hash = hash_key key in
   let i = alloc_vec_Vec_len (list_t t) self.slots in
   let* hash_mod = usize_rem hash i in
-  let* l =
+  let* (l, index_mut_back) =
     alloc_vec_Vec_index_mut (list_t t) usize
       (core_slice_index_SliceIndexUsizeSliceTInst (list_t t)) self.slots
       hash_mod in
-  let* inserted = hashMap_insert_in_list t key value l in
+  let* (inserted, l1) = hashMap_insert_in_list t key value l in
   if inserted
   then
-    let* i0 = usize_add self.num_entries 1 in
-    let* l0 = hashMap_insert_in_list_back t key value l in
-    let* v =
-      alloc_vec_Vec_index_mut_back (list_t t) usize
-        (core_slice_index_SliceIndexUsizeSliceTInst (list_t t)) self.slots
-        hash_mod l0 in
-    Return { self with num_entries = i0; slots = v }
-  else
-    let* l0 = hashMap_insert_in_list_back t key value l in
-    let* v =
-      alloc_vec_Vec_index_mut_back (list_t t) usize
-        (core_slice_index_SliceIndexUsizeSliceTInst (list_t t)) self.slots
-        hash_mod l0 in
-    Return { self with slots = v }
-
-(** [hashmap::{hashmap::HashMap<T>}::move_elements_from_list]: loop 0: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+    let* i1 = usize_add self.num_entries 1 in
+    let* v = index_mut_back l1 in
+    Return { self with num_entries = i1; slots = v }
+  else let* v = index_mut_back l1 in Return { self with slots = v }
+
+(** [hashmap::{hashmap::HashMap<T>}::move_elements_from_list]: loop 0:
     Source: 'src/hashmap.rs', lines 183:4-196:5 *)
 let rec hashMap_move_elements_from_list_loop
   (t : Type0) (ntable : hashMap_t t) (ls : list_t t) :
@@ -175,20 +142,18 @@ let rec hashMap_move_elements_from_list_loop
   =
   begin match ls with
   | List_Cons k v tl ->
-    let* ntable0 = hashMap_insert_no_resize t ntable k v in
-    hashMap_move_elements_from_list_loop t ntable0 tl
+    let* hm = hashMap_insert_no_resize t ntable k v in
+    hashMap_move_elements_from_list_loop t hm tl
   | List_Nil -> Return ntable
   end
 
-(** [hashmap::{hashmap::HashMap<T>}::move_elements_from_list]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+(** [hashmap::{hashmap::HashMap<T>}::move_elements_from_list]:
     Source: 'src/hashmap.rs', lines 183:4-183:72 *)
 let hashMap_move_elements_from_list
   (t : Type0) (ntable : hashMap_t t) (ls : list_t t) : result (hashMap_t t) =
   hashMap_move_elements_from_list_loop t ntable ls
 
-(** [hashmap::{hashmap::HashMap<T>}::move_elements]: loop 0: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+(** [hashmap::{hashmap::HashMap<T>}::move_elements]: loop 0:
     Source: 'src/hashmap.rs', lines 171:4-180:5 *)
 let rec hashMap_move_elements_loop
   (t : Type0) (ntable : hashMap_t t) (slots : alloc_vec_Vec (list_t t))
@@ -196,64 +161,63 @@ let rec hashMap_move_elements_loop
   Tot (result ((hashMap_t t) & (alloc_vec_Vec (list_t t))))
   (decreases (hashMap_move_elements_loop_decreases t ntable slots i))
   =
-  let i0 = alloc_vec_Vec_len (list_t t) slots in
-  if i < i0
+  let i1 = alloc_vec_Vec_len (list_t t) slots in
+  if i < i1
   then
-    let* l =
+    let* (l, index_mut_back) =
       alloc_vec_Vec_index_mut (list_t t) usize
         (core_slice_index_SliceIndexUsizeSliceTInst (list_t t)) slots i in
-    let ls = core_mem_replace (list_t t) l List_Nil in
-    let* ntable0 = hashMap_move_elements_from_list t ntable ls in
-    let* i1 = usize_add i 1 in
-    let l0 = core_mem_replace_back (list_t t) l List_Nil in
-    let* slots0 =
-      alloc_vec_Vec_index_mut_back (list_t t) usize
-        (core_slice_index_SliceIndexUsizeSliceTInst (list_t t)) slots i l0 in
-    hashMap_move_elements_loop t ntable0 slots0 i1
+    let (ls, l1) = core_mem_replace (list_t t) l List_Nil in
+    let* hm = hashMap_move_elements_from_list t ntable ls in
+    let* i2 = usize_add i 1 in
+    let* slots1 = index_mut_back l1 in
+    let* back_'a = hashMap_move_elements_loop t hm slots1 i2 in
+    let (hm1, v) = back_'a in
+    Return (hm1, v)
   else Return (ntable, slots)
 
-(** [hashmap::{hashmap::HashMap<T>}::move_elements]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+(** [hashmap::{hashmap::HashMap<T>}::move_elements]:
     Source: 'src/hashmap.rs', lines 171:4-171:95 *)
 let hashMap_move_elements
   (t : Type0) (ntable : hashMap_t t) (slots : alloc_vec_Vec (list_t t))
   (i : usize) :
   result ((hashMap_t t) & (alloc_vec_Vec (list_t t)))
   =
-  hashMap_move_elements_loop t ntable slots i
+  let* back_'a = hashMap_move_elements_loop t ntable slots i in
+  let (hm, v) = back_'a in
+  Return (hm, v)
 
-(** [hashmap::{hashmap::HashMap<T>}::try_resize]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+(** [hashmap::{hashmap::HashMap<T>}::try_resize]:
     Source: 'src/hashmap.rs', lines 140:4-140:28 *)
 let hashMap_try_resize
   (t : Type0) (self : hashMap_t t) : result (hashMap_t t) =
   let* max_usize = scalar_cast U32 Usize core_u32_max in
   let capacity = alloc_vec_Vec_len (list_t t) self.slots in
   let* n1 = usize_div max_usize 2 in
-  let (i, i0) = self.max_load_factor in
-  let* i1 = usize_div n1 i in
-  if capacity <= i1
+  let (i, i1) = self.max_load_factor in
+  let* i2 = usize_div n1 i in
+  if capacity <= i2
   then
-    let* i2 = usize_mul capacity 2 in
-    let* ntable = hashMap_new_with_capacity t i2 i i0 in
-    let* (ntable0, _) = hashMap_move_elements t ntable self.slots 0 in
+    let* i3 = usize_mul capacity 2 in
+    let* ntable = hashMap_new_with_capacity t i3 i i1 in
+    let* p = hashMap_move_elements t ntable self.slots 0 in
+    let (ntable1, _) = p in
     Return
-      { ntable0 with num_entries = self.num_entries; max_load_factor = (i, i0)
+      { ntable1 with num_entries = self.num_entries; max_load_factor = (i, i1)
       }
-  else Return { self with max_load_factor = (i, i0) }
+  else Return { self with max_load_factor = (i, i1) }
 
-(** [hashmap::{hashmap::HashMap<T>}::insert]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+(** [hashmap::{hashmap::HashMap<T>}::insert]:
     Source: 'src/hashmap.rs', lines 129:4-129:48 *)
 let hashMap_insert
   (t : Type0) (self : hashMap_t t) (key : usize) (value : t) :
   result (hashMap_t t)
   =
-  let* self0 = hashMap_insert_no_resize t self key value in
-  let* i = hashMap_len t self0 in
-  if i > self0.max_load then hashMap_try_resize t self0 else Return self0
+  let* hm = hashMap_insert_no_resize t self key value in
+  let* i = hashMap_len t hm in
+  if i > hm.max_load then hashMap_try_resize t hm else Return hm
 
-(** [hashmap::{hashmap::HashMap<T>}::contains_key_in_list]: loop 0: forward function
+(** [hashmap::{hashmap::HashMap<T>}::contains_key_in_list]: loop 0:
     Source: 'src/hashmap.rs', lines 206:4-219:5 *)
 let rec hashMap_contains_key_in_list_loop
   (t : Type0) (key : usize) (ls : list_t t) :
@@ -261,20 +225,20 @@ let rec hashMap_contains_key_in_list_loop
   (decreases (hashMap_contains_key_in_list_loop_decreases t key ls))
   =
   begin match ls with
-  | List_Cons ckey x tl ->
+  | List_Cons ckey _ tl ->
     if ckey = key
     then Return true
     else hashMap_contains_key_in_list_loop t key tl
   | List_Nil -> Return false
   end
 
-(** [hashmap::{hashmap::HashMap<T>}::contains_key_in_list]: forward function
+(** [hashmap::{hashmap::HashMap<T>}::contains_key_in_list]:
     Source: 'src/hashmap.rs', lines 206:4-206:68 *)
 let hashMap_contains_key_in_list
   (t : Type0) (key : usize) (ls : list_t t) : result bool =
   hashMap_contains_key_in_list_loop t key ls
 
-(** [hashmap::{hashmap::HashMap<T>}::contains_key]: forward function
+(** [hashmap::{hashmap::HashMap<T>}::contains_key]:
     Source: 'src/hashmap.rs', lines 199:4-199:49 *)
 let hashMap_contains_key
   (t : Type0) (self : hashMap_t t) (key : usize) : result bool =
@@ -287,7 +251,7 @@ let hashMap_contains_key
       hash_mod in
   hashMap_contains_key_in_list t key l
 
-(** [hashmap::{hashmap::HashMap<T>}::get_in_list]: loop 0: forward function
+(** [hashmap::{hashmap::HashMap<T>}::get_in_list]: loop 0:
     Source: 'src/hashmap.rs', lines 224:4-237:5 *)
 let rec hashMap_get_in_list_loop
   (t : Type0) (key : usize) (ls : list_t t) :
@@ -299,12 +263,12 @@ let rec hashMap_get_in_list_loop
   | List_Nil -> Fail Failure
   end
 
-(** [hashmap::{hashmap::HashMap<T>}::get_in_list]: forward function
+(** [hashmap::{hashmap::HashMap<T>}::get_in_list]:
     Source: 'src/hashmap.rs', lines 224:4-224:70 *)
 let hashMap_get_in_list (t : Type0) (key : usize) (ls : list_t t) : result t =
   hashMap_get_in_list_loop t key ls
 
-(** [hashmap::{hashmap::HashMap<T>}::get]: forward function
+(** [hashmap::{hashmap::HashMap<T>}::get]:
     Source: 'src/hashmap.rs', lines 239:4-239:55 *)
 let hashMap_get (t : Type0) (self : hashMap_t t) (key : usize) : result t =
   let* hash = hash_key key in
@@ -316,214 +280,147 @@ let hashMap_get (t : Type0) (self : hashMap_t t) (key : usize) : result t =
       hash_mod in
   hashMap_get_in_list t key l
 
-(** [hashmap::{hashmap::HashMap<T>}::get_mut_in_list]: loop 0: forward function
+(** [hashmap::{hashmap::HashMap<T>}::get_mut_in_list]: loop 0:
     Source: 'src/hashmap.rs', lines 245:4-254:5 *)
 let rec hashMap_get_mut_in_list_loop
   (t : Type0) (ls : list_t t) (key : usize) :
-  Tot (result t) (decreases (hashMap_get_mut_in_list_loop_decreases t ls key))
-  =
-  begin match ls with
-  | List_Cons ckey cvalue tl ->
-    if ckey = key then Return cvalue else hashMap_get_mut_in_list_loop t tl key
-  | List_Nil -> Fail Failure
-  end
-
-(** [hashmap::{hashmap::HashMap<T>}::get_mut_in_list]: forward function
-    Source: 'src/hashmap.rs', lines 245:4-245:86 *)
-let hashMap_get_mut_in_list
-  (t : Type0) (ls : list_t t) (key : usize) : result t =
-  hashMap_get_mut_in_list_loop t ls key
-
-(** [hashmap::{hashmap::HashMap<T>}::get_mut_in_list]: loop 0: backward function 0
-    Source: 'src/hashmap.rs', lines 245:4-254:5 *)
-let rec hashMap_get_mut_in_list_loop_back
-  (t : Type0) (ls : list_t t) (key : usize) (ret : t) :
-  Tot (result (list_t t))
+  Tot (result (t & (t -> result (list_t t))))
   (decreases (hashMap_get_mut_in_list_loop_decreases t ls key))
   =
   begin match ls with
   | List_Cons ckey cvalue tl ->
     if ckey = key
-    then Return (List_Cons ckey ret tl)
+    then
+      let back_'a = fun ret -> Return (List_Cons ckey ret tl) in
+      Return (cvalue, back_'a)
     else
-      let* tl0 = hashMap_get_mut_in_list_loop_back t tl key ret in
-      Return (List_Cons ckey cvalue tl0)
+      let* (x, back_'a) = hashMap_get_mut_in_list_loop t tl key in
+      let back_'a1 =
+        fun ret -> let* tl1 = back_'a ret in Return (List_Cons ckey cvalue tl1)
+        in
+      Return (x, back_'a1)
   | List_Nil -> Fail Failure
   end
 
-(** [hashmap::{hashmap::HashMap<T>}::get_mut_in_list]: backward function 0
+(** [hashmap::{hashmap::HashMap<T>}::get_mut_in_list]:
     Source: 'src/hashmap.rs', lines 245:4-245:86 *)
-let hashMap_get_mut_in_list_back
-  (t : Type0) (ls : list_t t) (key : usize) (ret : t) : result (list_t t) =
-  hashMap_get_mut_in_list_loop_back t ls key ret
-
-(** [hashmap::{hashmap::HashMap<T>}::get_mut]: forward function
-    Source: 'src/hashmap.rs', lines 257:4-257:67 *)
-let hashMap_get_mut (t : Type0) (self : hashMap_t t) (key : usize) : result t =
-  let* hash = hash_key key in
-  let i = alloc_vec_Vec_len (list_t t) self.slots in
-  let* hash_mod = usize_rem hash i in
-  let* l =
-    alloc_vec_Vec_index_mut (list_t t) usize
-      (core_slice_index_SliceIndexUsizeSliceTInst (list_t t)) self.slots
-      hash_mod in
-  hashMap_get_mut_in_list t l key
+let hashMap_get_mut_in_list
+  (t : Type0) (ls : list_t t) (key : usize) :
+  result (t & (t -> result (list_t t)))
+  =
+  let* (x, back_'a) = hashMap_get_mut_in_list_loop t ls key in
+  let back_'a1 = fun ret -> back_'a ret in
+  Return (x, back_'a1)
 
-(** [hashmap::{hashmap::HashMap<T>}::get_mut]: backward function 0
+(** [hashmap::{hashmap::HashMap<T>}::get_mut]:
     Source: 'src/hashmap.rs', lines 257:4-257:67 *)
-let hashMap_get_mut_back
-  (t : Type0) (self : hashMap_t t) (key : usize) (ret : t) :
-  result (hashMap_t t)
+let hashMap_get_mut
+  (t : Type0) (self : hashMap_t t) (key : usize) :
+  result (t & (t -> result (hashMap_t t)))
   =
   let* hash = hash_key key in
   let i = alloc_vec_Vec_len (list_t t) self.slots in
   let* hash_mod = usize_rem hash i in
-  let* l =
+  let* (l, index_mut_back) =
     alloc_vec_Vec_index_mut (list_t t) usize
       (core_slice_index_SliceIndexUsizeSliceTInst (list_t t)) self.slots
       hash_mod in
-  let* l0 = hashMap_get_mut_in_list_back t l key ret in
-  let* v =
-    alloc_vec_Vec_index_mut_back (list_t t) usize
-      (core_slice_index_SliceIndexUsizeSliceTInst (list_t t)) self.slots
-      hash_mod l0 in
-  Return { self with slots = v }
-
-(** [hashmap::{hashmap::HashMap<T>}::remove_from_list]: loop 0: forward function
+  let* (x, get_mut_in_list_back) = hashMap_get_mut_in_list t l key in
+  let back_'a =
+    fun ret ->
+      let* l1 = get_mut_in_list_back ret in
+      let* v = index_mut_back l1 in
+      Return { self with slots = v } in
+  Return (x, back_'a)
+
+(** [hashmap::{hashmap::HashMap<T>}::remove_from_list]: loop 0:
     Source: 'src/hashmap.rs', lines 265:4-291:5 *)
 let rec hashMap_remove_from_list_loop
   (t : Type0) (key : usize) (ls : list_t t) :
-  Tot (result (option t))
+  Tot (result ((option t) & (list_t t)))
   (decreases (hashMap_remove_from_list_loop_decreases t key ls))
   =
   begin match ls with
   | List_Cons ckey x tl ->
     if ckey = key
     then
-      let mv_ls = core_mem_replace (list_t t) (List_Cons ckey x tl) List_Nil in
+      let (mv_ls, _) =
+        core_mem_replace (list_t t) (List_Cons ckey x tl) List_Nil in
       begin match mv_ls with
-      | List_Cons i cvalue tl0 -> Return (Some cvalue)
+      | List_Cons _ cvalue tl1 -> Return (Some cvalue, tl1)
       | List_Nil -> Fail Failure
       end
-    else hashMap_remove_from_list_loop t key tl
-  | List_Nil -> Return None
+    else
+      let* (o, back) = hashMap_remove_from_list_loop t key tl in
+      Return (o, List_Cons ckey x back)
+  | List_Nil -> Return (None, List_Nil)
   end
 
-(** [hashmap::{hashmap::HashMap<T>}::remove_from_list]: forward function
+(** [hashmap::{hashmap::HashMap<T>}::remove_from_list]:
     Source: 'src/hashmap.rs', lines 265:4-265:69 *)
 let hashMap_remove_from_list
-  (t : Type0) (key : usize) (ls : list_t t) : result (option t) =
-  hashMap_remove_from_list_loop t key ls
-
-(** [hashmap::{hashmap::HashMap<T>}::remove_from_list]: loop 0: backward function 1
-    Source: 'src/hashmap.rs', lines 265:4-291:5 *)
-let rec hashMap_remove_from_list_loop_back
   (t : Type0) (key : usize) (ls : list_t t) :
-  Tot (result (list_t t))
-  (decreases (hashMap_remove_from_list_loop_decreases t key ls))
+  result ((option t) & (list_t t))
   =
-  begin match ls with
-  | List_Cons ckey x tl ->
-    if ckey = key
-    then
-      let mv_ls = core_mem_replace (list_t t) (List_Cons ckey x tl) List_Nil in
-      begin match mv_ls with
-      | List_Cons i cvalue tl0 -> Return tl0
-      | List_Nil -> Fail Failure
-      end
-    else
-      let* tl0 = hashMap_remove_from_list_loop_back t key tl in
-      Return (List_Cons ckey x tl0)
-  | List_Nil -> Return List_Nil
-  end
-
-(** [hashmap::{hashmap::HashMap<T>}::remove_from_list]: backward function 1
-    Source: 'src/hashmap.rs', lines 265:4-265:69 *)
-let hashMap_remove_from_list_back
-  (t : Type0) (key : usize) (ls : list_t t) : result (list_t t) =
-  hashMap_remove_from_list_loop_back t key ls
+  hashMap_remove_from_list_loop t key ls
 
-(** [hashmap::{hashmap::HashMap<T>}::remove]: forward function
+(** [hashmap::{hashmap::HashMap<T>}::remove]:
     Source: 'src/hashmap.rs', lines 294:4-294:52 *)
 let hashMap_remove
-  (t : Type0) (self : hashMap_t t) (key : usize) : result (option t) =
-  let* hash = hash_key key in
-  let i = alloc_vec_Vec_len (list_t t) self.slots in
-  let* hash_mod = usize_rem hash i in
-  let* l =
-    alloc_vec_Vec_index_mut (list_t t) usize
-      (core_slice_index_SliceIndexUsizeSliceTInst (list_t t)) self.slots
-      hash_mod in
-  let* x = hashMap_remove_from_list t key l in
-  begin match x with
-  | None -> Return None
-  | Some x0 -> let* _ = usize_sub self.num_entries 1 in Return (Some x0)
-  end
-
-(** [hashmap::{hashmap::HashMap<T>}::remove]: backward function 0
-    Source: 'src/hashmap.rs', lines 294:4-294:52 *)
-let hashMap_remove_back
-  (t : Type0) (self : hashMap_t t) (key : usize) : result (hashMap_t t) =
+  (t : Type0) (self : hashMap_t t) (key : usize) :
+  result ((option t) & (hashMap_t t))
+  =
   let* hash = hash_key key in
   let i = alloc_vec_Vec_len (list_t t) self.slots in
   let* hash_mod = usize_rem hash i in
-  let* l =
+  let* (l, index_mut_back) =
     alloc_vec_Vec_index_mut (list_t t) usize
       (core_slice_index_SliceIndexUsizeSliceTInst (list_t t)) self.slots
       hash_mod in
-  let* x = hashMap_remove_from_list t key l in
+  let* (x, l1) = hashMap_remove_from_list t key l in
   begin match x with
   | None ->
-    let* l0 = hashMap_remove_from_list_back t key l in
-    let* v =
-      alloc_vec_Vec_index_mut_back (list_t t) usize
-        (core_slice_index_SliceIndexUsizeSliceTInst (list_t t)) self.slots
-        hash_mod l0 in
-    Return { self with slots = v }
-  | Some x0 ->
-    let* i0 = usize_sub self.num_entries 1 in
-    let* l0 = hashMap_remove_from_list_back t key l in
-    let* v =
-      alloc_vec_Vec_index_mut_back (list_t t) usize
-        (core_slice_index_SliceIndexUsizeSliceTInst (list_t t)) self.slots
-        hash_mod l0 in
-    Return { self with num_entries = i0; slots = v }
+    let* v = index_mut_back l1 in Return (None, { self with slots = v })
+  | Some x1 ->
+    let* i1 = usize_sub self.num_entries 1 in
+    let* v = index_mut_back l1 in
+    Return (Some x1, { self with num_entries = i1; slots = v })
   end
 
-(** [hashmap::test1]: forward function
+(** [hashmap::test1]:
     Source: 'src/hashmap.rs', lines 315:0-315:10 *)
 let test1 : result unit =
   let* hm = hashMap_new u64 in
-  let* hm0 = hashMap_insert u64 hm 0 42 in
-  let* hm1 = hashMap_insert u64 hm0 128 18 in
-  let* hm2 = hashMap_insert u64 hm1 1024 138 in
-  let* hm3 = hashMap_insert u64 hm2 1056 256 in
-  let* i = hashMap_get u64 hm3 128 in
+  let* hm1 = hashMap_insert u64 hm 0 42 in
+  let* hm2 = hashMap_insert u64 hm1 128 18 in
+  let* hm3 = hashMap_insert u64 hm2 1024 138 in
+  let* hm4 = hashMap_insert u64 hm3 1056 256 in
+  let* i = hashMap_get u64 hm4 128 in
   if not (i = 18)
   then Fail Failure
   else
-    let* hm4 = hashMap_get_mut_back u64 hm3 1024 56 in
-    let* i0 = hashMap_get u64 hm4 1024 in
-    if not (i0 = 56)
+    let* (_, get_mut_back) = hashMap_get_mut u64 hm4 1024 in
+    let* hm5 = get_mut_back 56 in
+    let* i1 = hashMap_get u64 hm5 1024 in
+    if not (i1 = 56)
     then Fail Failure
     else
-      let* x = hashMap_remove u64 hm4 1024 in
+      let* (x, hm6) = hashMap_remove u64 hm5 1024 in
       begin match x with
       | None -> Fail Failure
-      | Some x0 ->
-        if not (x0 = 56)
+      | Some x1 ->
+        if not (x1 = 56)
         then Fail Failure
         else
-          let* hm5 = hashMap_remove_back u64 hm4 1024 in
-          let* i1 = hashMap_get u64 hm5 0 in
-          if not (i1 = 42)
+          let* i2 = hashMap_get u64 hm6 0 in
+          if not (i2 = 42)
           then Fail Failure
           else
-            let* i2 = hashMap_get u64 hm5 128 in
-            if not (i2 = 18)
+            let* i3 = hashMap_get u64 hm6 128 in
+            if not (i3 = 18)
             then Fail Failure
             else
-              let* i3 = hashMap_get u64 hm5 1056 in
-              if not (i3 = 256) then Fail Failure else Return ()
+              let* i4 = hashMap_get u64 hm6 1056 in
+              if not (i4 = 256) then Fail Failure else Return ()
       end
 
diff --git a/tests/fstar/hashmap/Hashmap.Properties.fst b/tests/fstar/hashmap/Hashmap.Properties.fst
deleted file mode 100644
index def520f0..00000000
--- a/tests/fstar/hashmap/Hashmap.Properties.fst
+++ /dev/null
@@ -1,3186 +0,0 @@
-(** Properties about the hashmap *)
-module Hashmap.Properties
-open Primitives
-open FStar.List.Tot
-open FStar.Mul
-open Hashmap.Types
-open Hashmap.Clauses
-open Hashmap.Funs
-
-#set-options "--z3rlimit 50 --fuel 0 --ifuel 1"
-
-let _align_fsti = ()
-
-/// The proofs:
-/// ===========
-/// 
-/// The proof strategy is to do exactly as with Low* proofs (we initially tried to
-/// prove more properties in one go, but it was a mistake):
-/// - prove that, under some preconditions, the low-level functions translated
-///   from Rust refine some higher-level functions
-/// - do functional proofs about those high-level functions to prove interesting
-///   properties about the hash map operations, and invariant preservation
-/// - combine everything
-///
-/// The fact that we work in a pure setting allows us to be more modular than when
-/// working with effects. For instance we can do a case disjunction (see the proofs
-/// for insert, which study the cases where the key is already/not in the hash map
-/// in separate proofs - we had initially tried to do them in one step: it is doable
-/// but requires some work, and the F* response time quickly becomes annoying while
-/// making progress, so we split them). We can also easily prove a refinement lemma,
-/// study the model, *then* combine those to also prove that the low-level function
-/// preserves the invariants, rather than do everything at once as is usually the
-/// case when doing intrinsic proofs with effects (I remember that having to prove
-/// invariants in one go *and* a refinement step, even small, can be extremely
-/// difficult in Low*).
-
-
-(*** Utilities *)
-
-/// We need many small helpers and lemmas, mostly about lists (and the ones we list
-/// here are not in the standard F* library).
-
-val index_append_lem (#a : Type0) (ls0 ls1 : list a) (i : nat{i < length ls0 + length ls1}) :
-  Lemma (
-    (i < length ls0 ==> index (ls0 @ ls1) i == index ls0 i) /\
-    (i >= length ls0 ==> index (ls0 @ ls1) i == index ls1 (i - length ls0)))
-  [SMTPat (index (ls0 @ ls1) i)]
-
-#push-options "--fuel 1"
-let rec index_append_lem #a ls0 ls1 i =
-  match ls0 with
-  | [] -> ()
-  | x :: ls0' ->
-    if i = 0 then ()
-    else index_append_lem ls0' ls1 (i-1)
-#pop-options
-
-val index_map_lem (#a #b: Type0) (f : a -> Tot b) (ls : list a)
-  (i : nat{i < length ls}) :
-  Lemma (
-    index (map f ls) i == f (index ls i))
-  [SMTPat (index (map f ls) i)]
-
-#push-options "--fuel 1"
-let rec index_map_lem #a #b f ls i =
-  match ls with
-  | [] -> ()
-  | x :: ls' ->
-    if i = 0 then ()
-    else index_map_lem f ls' (i-1)
-#pop-options
-
-val for_all_append (#a : Type0) (f : a -> Tot bool) (ls0 ls1 : list a) :
-  Lemma (for_all f (ls0 @ ls1) = (for_all f ls0 && for_all f ls1))
-
-#push-options "--fuel 1"
-let rec for_all_append #a f ls0 ls1 =
-  match ls0 with
-  | [] -> ()
-  | x :: ls0' ->
-    for_all_append f ls0' ls1
-#pop-options
-
-/// Filter a list, stopping after we removed one element
-val filter_one (#a : Type) (f : a -> bool) (ls : list a) : list a
-
-let rec filter_one #a f ls =
-  match ls with
-  | [] -> []
-  | x :: ls' -> if f x then x :: filter_one f ls' else ls'
-
-val find_append (#a : Type) (f : a -> bool) (ls0 ls1 : list a) :
-  Lemma (
-    find f (ls0 @ ls1) ==
-    begin match find f ls0 with
-    | Some x -> Some x
-    | None -> find f ls1
-    end)
-
-#push-options "--fuel 1"
-let rec find_append #a f ls0 ls1 =
-  match ls0 with
-  | [] -> ()
-  | x :: ls0' ->
-    if f x then
-    begin
-      assert(ls0 @ ls1 == x :: (ls0' @ ls1));
-      assert(find f (ls0 @ ls1) == find f (x :: (ls0' @ ls1)));
-      // Why do I have to do this?! Is it because of subtyping??
-      assert(
-        match find f (ls0 @ ls1) with
-        | Some x' -> x' == x
-        | None -> False)
-    end
-    else find_append f ls0' ls1
-#pop-options
-
-val length_flatten_update :
-     #a:Type
-  -> ls:list (list a)
-  -> i:nat{i < length ls}
-  -> x:list a ->
-  Lemma (
-    // We want this property:
-    // ```
-    // length (flatten (list_update ls i x)) =
-    //   length (flatten ls) - length (index ls i) + length x
-    // ```
-    length (flatten (list_update ls i x)) + length (index ls i) =
-    length (flatten ls) + length x)
-
-#push-options "--fuel 1"
-let rec length_flatten_update #a ls i x =
-  match ls with
-  | x' :: ls' ->
-    assert(flatten ls == x' @ flatten ls'); // Triggers patterns
-    assert(length (flatten ls) == length x' + length (flatten ls'));
-    if i = 0 then
-      begin
-      let ls1 = x :: ls' in
-      assert(list_update ls i x == ls1);
-      assert(flatten ls1 == x @ flatten ls'); // Triggers patterns
-      assert(length (flatten ls1) == length x + length (flatten ls'));
-      ()
-      end
-    else
-      begin
-      length_flatten_update ls' (i-1) x;
-      let ls1 = x' :: list_update ls' (i-1) x in
-      assert(flatten ls1 == x' @ flatten (list_update ls' (i-1) x)) // Triggers patterns
-      end
-#pop-options
-
-val length_flatten_index :
-     #a:Type
-  -> ls:list (list a)
-  -> i:nat{i < length ls} ->
-  Lemma (
-    length (flatten ls) >= length (index ls i))
-
-#push-options "--fuel 1"
-let rec length_flatten_index #a ls i =
-  match ls with
-  | x' :: ls' ->
-    assert(flatten ls == x' @ flatten ls'); // Triggers patterns
-    assert(length (flatten ls) == length x' + length (flatten ls'));
-    if i = 0 then ()
-    else length_flatten_index ls' (i-1)
-#pop-options
-
-val forall_index_equiv_list_for_all
-  (#a : Type) (pred : a -> Tot bool) (ls : list a) :
-  Lemma ((forall (i:nat{i < length ls}). pred (index ls i)) <==> for_all pred ls)
-
-#push-options "--fuel 1"
-let rec forall_index_equiv_list_for_all pred ls =
-  match ls with
-  | [] -> ()
-  | x :: ls' ->
-    assert(forall (i:nat{i < length ls'}). index ls' i == index ls (i+1));
-    assert(forall (i:nat{0 < i /\ i < length ls}). index ls i == index ls' (i-1));
-    assert(index ls 0 == x);
-    forall_index_equiv_list_for_all pred ls'
-#pop-options
-
-val find_update:
-     #a:Type
-  -> f:(a -> Tot bool)
-  -> ls:list a
-  -> x:a
-  -> ls':list a{length ls' == length ls}
-#push-options "--fuel 1"
-let rec find_update #a f ls x =
-  match ls with
-  | [] -> []
-  | hd::tl ->
-    if f hd then x :: tl else hd :: find_update f tl x
-#pop-options
-
-val pairwise_distinct : #a:eqtype -> ls:list a -> Tot bool
-let rec pairwise_distinct (#a : eqtype) (ls : list a) : Tot bool =
-  match ls with
-  | [] -> true
-  | x :: ls' -> List.Tot.for_all (fun y -> x <> y) ls' && pairwise_distinct ls'
-
-val pairwise_rel : #a:Type -> pred:(a -> a -> Tot bool) -> ls:list a -> Tot bool
-let rec pairwise_rel #a pred ls =
-  match ls with
-  | [] -> true
-  | x :: ls' ->
-    for_all (pred x) ls' && pairwise_rel pred ls' 
-
-#push-options "--fuel 1"
-let rec flatten_append (#a : Type) (l1 l2: list (list a)) :
-  Lemma (flatten (l1 @ l2) == flatten l1 @ flatten l2) =
-  match l1 with
-  | [] -> ()
-  | x :: l1' ->
-    flatten_append l1' l2;
-    append_assoc x (flatten l1') (flatten l2)
-#pop-options
-
-/// We don't use anonymous functions as parameters to other functions, but rather
-/// introduce auxiliary functions instead: otherwise we can't reason (because
-/// F*'s encoding to the SMT is imprecise for functions)
-let fst_is_disctinct (#a : eqtype) (#b : Type0) (p0 : a & b) (p1 : a & b) : Type0 =
-  fst p0 <> fst p1
-
-(*** Lemmas about Primitives *)
-/// TODO: move those lemmas
-
-// TODO: rename to 'insert'?
-val list_update_index_dif_lem
-  (#a : Type0) (ls : list a) (i : nat{i < length ls}) (x : a)
-  (j : nat{j < length ls}) :
-  Lemma (requires (j <> i))
-  (ensures (index (list_update ls i x) j == index ls j))
-  [SMTPat (index (list_update ls i x) j)]
-
-#push-options "--fuel 1"
-let rec list_update_index_dif_lem #a ls i x j =
-  match ls with
-  | x' :: ls ->
-    if i = 0 then ()
-    else if j = 0 then ()
-    else
-     list_update_index_dif_lem ls (i-1) x (j-1)
-#pop-options
-
-val map_list_update_lem
-  (#a #b: Type0) (f : a -> Tot b)
-  (ls : list a) (i : nat{i < length ls}) (x : a) :
-  Lemma (list_update (map f ls) i (f x) == map f (list_update ls i x))
-  [SMTPat (list_update (map f ls) i (f x))]
-
-#push-options "--fuel 1"
-let rec map_list_update_lem #a #b f ls i x =
-  match ls with
-  | x' :: ls' ->
-    if i = 0 then ()
-    else map_list_update_lem f ls' (i-1) x
-#pop-options
-
-(*** Invariants, models *)
-
-(**** Internals *)
-/// The following invariants, models, representation functions... are mostly
-/// for the purpose of the proofs.
-
-let is_pos_usize (n : nat) : Type0 = 0 < n /\ n <= usize_max
-type pos_usize = x:usize{x > 0}
-
-type binding (t : Type0) = key & t
-
-type slots_t (t : Type0) = alloc_vec_Vec (list_t t)
-
-/// We represent hash maps as associative lists
-type assoc_list (t : Type0) = list (binding t)
-
-/// Representation function for [list_t]
-let rec list_t_v (#t : Type0) (ls : list_t t) : assoc_list t =
-  match ls with
-  | List_Nil -> []
-  | List_Cons k v tl -> (k,v) :: list_t_v tl
-
-let list_t_len (#t : Type0) (ls : list_t t) : nat = length (list_t_v ls)
-let list_t_index (#t : Type0) (ls : list_t t) (i : nat{i < list_t_len ls}) : binding t =
-  index (list_t_v ls) i
-
-type slot_s (t : Type0) = list (binding t)
-type slots_s (t : Type0) = list (slot_s t)
-
-type slot_t (t : Type0) = list_t t
-let slot_t_v #t = list_t_v #t
-
-/// Representation function for the slots.
-let slots_t_v (#t : Type0) (slots : slots_t t) : slots_s t =
-  map slot_t_v slots
-
-/// Representation function for the slots, seen as an associative list.
-let slots_t_al_v (#t : Type0) (slots : slots_t t) : assoc_list t =
-  flatten (map list_t_v slots)
-
-/// High-level type for the hash-map, seen as a list of associative lists (one
-/// list per slot). This is the representation we use most, internally. Note that
-/// we later introduce a [map_s] representation, which is the one used in the
-/// lemmas shown to the user.
-type hashMap_s t = list (slot_s t)
-
-// TODO: why not always have the condition on the length?
-// 'nes': "non-empty slots"
-type hashMap_s_nes (t : Type0) : Type0 =
-  hm:hashMap_s t{is_pos_usize (length hm)}
-
-/// Representation function for [hashMap_t] as a list of slots
-let hashMap_t_v (#t : Type0) (hm : hashMap_t t) : hashMap_s t =
-  map list_t_v hm.slots
-
-/// Representation function for [hashMap_t] as an associative list
-let hashMap_t_al_v (#t : Type0) (hm : hashMap_t t) : assoc_list t =
-  flatten (hashMap_t_v hm)
-
-// 'nes': "non-empty slots"
-type hashMap_t_nes (t : Type0) : Type0 =
-  hm:hashMap_t t{is_pos_usize (length hm.slots)}
-
-let hash_key_s (k : key) : hash =
-  Return?.v (hash_key k)
-
-let hash_mod_key (k : key) (len : usize{len > 0}) : hash =
-  (hash_key_s k) % len
-
-let not_same_key (#t : Type0) (k : key) (b : binding t) : bool = fst b <> k
-let same_key (#t : Type0) (k : key) (b : binding t) : bool = fst b = k
-
-// We take a [nat] instead of a [hash] on purpose
-let same_hash_mod_key (#t : Type0) (len : usize{len > 0}) (h : nat) (b : binding t) : bool =
-  hash_mod_key (fst b) len = h
-
-let binding_neq (#t : Type0) (b0 b1 : binding t) : bool = fst b0 <> fst b1
-
-let hashMap_t_len_s (#t : Type0) (hm : hashMap_t t) : nat =
-  hm.num_entries
-
-let assoc_list_find (#t : Type0) (k : key) (slot : assoc_list t) : option t =
-  match find (same_key k) slot with
-  | None -> None
-  | Some (_, v) -> Some v
-
-let slot_s_find (#t : Type0) (k : key) (slot : list (binding t)) : option t =
-  assoc_list_find k slot
-
-let slot_t_find_s (#t : Type0) (k : key) (slot : list_t t) : option t =
-  slot_s_find k (slot_t_v slot)
-
-// This is a simpler version of the "find" function, which captures the essence
-// of what happens and operates on [hashMap_s].
-let hashMap_s_find
-  (#t : Type0) (hm : hashMap_s_nes t)
-  (k : key) : option t =
-  let i = hash_mod_key k (length hm) in
-  let slot = index hm i in
-  slot_s_find k slot
-
-let hashMap_s_len
-  (#t : Type0) (hm : hashMap_s t) :
-  nat =
-  length (flatten hm)
-
-// Same as above, but operates on [hashMap_t]
-// Note that we don't reuse the above function on purpose: converting to a
-// [hashMap_s] then looking up an element is not the same as what we
-// wrote below.
-let hashMap_t_find_s
-  (#t : Type0) (hm : hashMap_t t{length hm.slots > 0}) (k : key) : option t =
-  let slots = hm.slots in
-  let i = hash_mod_key k (length slots) in
-  let slot = index slots i in
-  slot_t_find_s k slot
-
-/// Invariants for the slots
-
-let slot_s_inv
-  (#t : Type0) (len : usize{len > 0}) (i : usize) (slot : list (binding t)) : bool =
-  // All the bindings are in the proper slot
-  for_all (same_hash_mod_key len i) slot &&
-  // All the keys are pairwise distinct
-  pairwise_rel binding_neq slot
-
-let slot_t_inv (#t : Type0) (len : usize{len > 0}) (i : usize) (slot : list_t t) : bool =
-  slot_s_inv len i (slot_t_v slot)
-
-let slots_s_inv (#t : Type0) (slots : slots_s t{length slots <= usize_max}) : Type0 =
-  forall(i:nat{i < length slots}).
-  {:pattern index slots i}
-  slot_s_inv (length slots) i (index slots i)
-
-// At some point we tried to rewrite this in terms of [slots_s_inv]. However it
-// made a lot of proofs fail because those proofs relied on the [index_map_lem]
-// pattern. We tried writing others lemmas with patterns (like [slots_s_inv]
-// implies [slots_t_inv]) but it didn't succeed, so we keep things as they are.
-let slots_t_inv (#t : Type0) (slots : slots_t t{length slots <= usize_max}) : Type0 =
-  forall(i:nat{i < length slots}).
-  {:pattern index slots i}
-  slot_t_inv (length slots) i (index slots i)
-
-let hashMap_s_inv (#t : Type0) (hm : hashMap_s t) : Type0 =
-  length hm <= usize_max /\
-  length hm > 0 /\
-  slots_s_inv hm
-
-/// Base invariant for the hashmap (the complete invariant can be temporarily
-/// broken between the moment we inserted an element and the moment we resize)
-let hashMap_t_base_inv (#t : Type0) (hm : hashMap_t t) : Type0 =
-  let al = hashMap_t_al_v hm in
-  // [num_entries] correctly tracks the number of entries in the table
-  // Note that it gives us that the length of the slots array is <= usize_max:
-  // [> length <= usize_max
-  // (because hashMap_num_entries has type `usize`)
-  hm.num_entries = length al /\
-  // Slots invariant
-  slots_t_inv hm.slots /\
-  // The capacity must be > 0 (otherwise we can't resize, because we
-  // multiply the capacity by two!)
-  length hm.slots > 0 /\
-  // Load computation
-  begin
-  let capacity = length hm.slots in
-  let (dividend, divisor) = hm.max_load_factor in
-  0 < dividend /\ dividend < divisor /\
-  capacity * dividend >= divisor /\
-  hm.max_load = (capacity * dividend) / divisor
-  end
-
-/// We often need to frame some values
-let hashMap_t_same_params (#t : Type0) (hm0 hm1 : hashMap_t t) : Type0 =
-  length hm0.slots = length hm1.slots /\
-  hm0.max_load = hm1.max_load /\
-  hm0.max_load_factor = hm1.max_load_factor
-
-/// The following invariants, etc. are meant to be revealed to the user through
-/// the .fsti.
-
-/// Invariant for the hashmap
-let hashMap_t_inv (#t : Type0) (hm : hashMap_t t) : Type0 =
-  // Base invariant
-  hashMap_t_base_inv hm /\
-  // The hash map is either: not overloaded, or we can't resize it
-  begin
-  let (dividend, divisor) = hm.max_load_factor in
-  hm.num_entries <= hm.max_load
-  || length hm.slots * 2 * dividend > usize_max
-  end
-
-(*** .fsti *)
-/// We reveal slightly different version of the above functions to the user
-
-let len_s (#t : Type0) (hm : hashMap_t t) : nat = hashMap_t_len_s hm
-
-/// This version doesn't take any precondition (contrary to [hashMap_t_find_s])
-let find_s (#t : Type0) (hm : hashMap_t t) (k : key) : option t =
-  if length hm.slots = 0 then None
-  else hashMap_t_find_s hm k
-
-(*** Overloading *)
-
-let hashMap_not_overloaded_lem #t hm = ()
-
-(*** allocate_slots *)
-
-/// Auxiliary lemma
-val slots_t_all_nil_inv_lem
-  (#t : Type0) (slots : alloc_vec_Vec (list_t t){length slots <= usize_max}) :
-  Lemma (requires (forall (i:nat{i < length slots}). index slots i == List_Nil))
-  (ensures (slots_t_inv slots))
-
-#push-options "--fuel 1"
-let slots_t_all_nil_inv_lem #t slots = ()
-#pop-options
-
-val slots_t_al_v_all_nil_is_empty_lem
-  (#t : Type0) (slots : alloc_vec_Vec (list_t t)) :
-  Lemma (requires (forall (i:nat{i < length slots}). index slots i == List_Nil))
-  (ensures (slots_t_al_v slots == []))
-
-#push-options "--fuel 1"
-let rec slots_t_al_v_all_nil_is_empty_lem #t slots =
- match slots with
- | [] -> ()
- | s :: slots' ->
-   assert(forall (i:nat{i < length slots'}). index slots' i == index slots (i+1));
-   slots_t_al_v_all_nil_is_empty_lem #t slots';
-   assert(slots_t_al_v slots == list_t_v s @ slots_t_al_v slots');
-   assert(slots_t_al_v slots == list_t_v s);
-   assert(index slots 0 == List_Nil)
-#pop-options
-
-/// [allocate_slots]
-val hashMap_allocate_slots_lem
-  (t : Type0) (slots : alloc_vec_Vec (list_t t)) (n : usize) :
-  Lemma
-  (requires (length slots + n <= usize_max))
-  (ensures (
-   match hashMap_allocate_slots t slots n with
-   | Fail _ -> False
-   | Return slots' ->
-     length slots' = length slots + n /\
-     // We leave the already allocated slots unchanged
-     (forall (i:nat{i < length slots}). index slots' i == index slots i) /\
-     // We allocate n additional empty slots
-     (forall (i:nat{length slots <= i /\ i < length slots'}). index slots' i == List_Nil)))
-  (decreases (hashMap_allocate_slots_loop_decreases t slots n))
-
-#push-options "--fuel 1"
-let rec hashMap_allocate_slots_lem t slots n =
-  begin match n with
-  | 0 -> ()
-  | _ ->
-    begin match alloc_vec_Vec_push (list_t t) slots List_Nil with
-    | Fail _ -> ()
-    | Return slots1 ->
-      begin match usize_sub n 1 with
-      | Fail _ -> ()
-      | Return i ->
-        hashMap_allocate_slots_lem t slots1 i;
-        begin match hashMap_allocate_slots t slots1 i with
-        | Fail _ -> ()
-        | Return slots2 ->
-          assert(length slots1 = length slots + 1);
-          assert(slots1 == slots @ [List_Nil]); // Triggers patterns
-          assert(index slots1 (length slots) == index [List_Nil] 0); // Triggers patterns
-          assert(index slots1 (length slots) == List_Nil)
-        end
-      end
-    end
-  end
-#pop-options
-
-(*** new_with_capacity *)
-/// Under proper conditions, [new_with_capacity] doesn't fail and returns an empty hash map.
-val hashMap_new_with_capacity_lem
-  (t : Type0) (capacity : usize)
-  (max_load_dividend : usize) (max_load_divisor : usize) :
-  Lemma
-  (requires (
-    0 < max_load_dividend /\
-    max_load_dividend < max_load_divisor /\
-    0 < capacity /\
-    capacity * max_load_dividend >= max_load_divisor /\
-    capacity * max_load_dividend <= usize_max))
-  (ensures (
-    match hashMap_new_with_capacity t capacity max_load_dividend max_load_divisor with
-    | Fail _ -> False
-    | Return hm ->
-      // The hash map invariant is satisfied
-      hashMap_t_inv hm /\
-      // The parameters are correct
-      hm.max_load_factor = (max_load_dividend, max_load_divisor) /\
-      hm.max_load = (capacity * max_load_dividend) / max_load_divisor /\
-      // The hash map has the specified capacity - we need to reveal this
-      // otherwise the pre of [hashMap_t_find_s] is not satisfied.
-      length hm.slots = capacity /\
-      // The hash map has 0 values
-      hashMap_t_len_s hm = 0 /\
-      // It contains no bindings
-      (forall k. hashMap_t_find_s hm k == None) /\
-      // We need this low-level property for the invariant
-      (forall(i:nat{i < length hm.slots}). index hm.slots i == List_Nil)))
-
-#push-options "--z3rlimit 50 --fuel 1"
-let hashMap_new_with_capacity_lem (t : Type0) (capacity : usize)
-  (max_load_dividend : usize) (max_load_divisor : usize) =
-  let v = alloc_vec_Vec_new (list_t t) in
-  assert(length v = 0);
-  hashMap_allocate_slots_lem t v capacity;
-  begin match hashMap_allocate_slots t v capacity with
-  | Fail _ -> assert(False)
-  | Return v0 ->
-    begin match usize_mul capacity max_load_dividend with
-    | Fail _ -> assert(False)
-    | Return i ->
-      begin match usize_div i max_load_divisor with
-      | Fail _ -> assert(False)
-      | Return i0 ->
-          let hm = MkhashMap_t 0 (max_load_dividend, max_load_divisor) i0 v0 in
-          slots_t_all_nil_inv_lem v0;
-          slots_t_al_v_all_nil_is_empty_lem hm.slots
-      end
-    end
-  end
-#pop-options
-
-(*** new *)
-
-/// [new] doesn't fail and returns an empty hash map
-val hashMap_new_lem_aux (t : Type0) :
-  Lemma
-  (ensures (
-    match hashMap_new t with
-    | Fail _ -> False
-    | Return hm ->
-      // The hash map invariant is satisfied
-      hashMap_t_inv hm /\
-      // The hash map has 0 values
-      hashMap_t_len_s hm = 0 /\
-      // It contains no bindings
-      (forall k. hashMap_t_find_s hm k == None)))
-
-#push-options "--fuel 1"
-let hashMap_new_lem_aux t =
-  hashMap_new_with_capacity_lem t 32 4 5;
-  match hashMap_new_with_capacity t 32 4 5 with
-  | Fail _ -> ()
-  | Return hm -> ()
-#pop-options
-
-/// The lemma we reveal in the .fsti
-let hashMap_new_lem t = hashMap_new_lem_aux t
-
-(*** clear *)
-/// [clear]: the loop doesn't fail and simply clears the slots starting at index i
-#push-options "--fuel 1"
-let rec hashMap_clear_loop_lem
-  (t : Type0) (slots : alloc_vec_Vec (list_t t)) (i : usize) :
-  Lemma
-  (ensures (
-    match hashMap_clear_loop t slots i with
-    | Fail _ -> False
-    | Return slots' ->
-      // The length is preserved
-      length slots' == length slots /\
-      // The slots before i are left unchanged
-      (forall (j:nat{j < i /\ j < length slots}). index slots' j == index slots j) /\
-      // The slots after i are set to List_Nil
-      (forall (j:nat{i <= j /\ j < length slots}). index slots' j == List_Nil)))
-  (decreases (hashMap_clear_loop_decreases t slots i))
-  =
-  let i0 = alloc_vec_Vec_len (list_t t) slots in
-  let b = i < i0 in
-  if b
-  then
-    begin match alloc_vec_Vec_update_usize slots i List_Nil with
-    | Fail _ -> ()
-    | Return v ->
-      begin match usize_add i 1 with
-      | Fail _ -> ()
-      | Return i1 ->
-        hashMap_clear_loop_lem t v i1;
-        begin match hashMap_clear_loop t v i1 with
-        | Fail _ -> ()
-        | Return slots1 ->
-          assert(length slots1 == length slots);
-          assert(forall (j:nat{i+1 <= j /\ j < length slots}). index slots1 j == List_Nil);
-          assert(index slots1 i == List_Nil)
-        end
-      end
-    end
-  else ()
-#pop-options
-
-/// [clear] doesn't fail and turns the hash map into an empty map
-val hashMap_clear_lem_aux
-  (#t : Type0) (self : hashMap_t t) :
-  Lemma
-  (requires (hashMap_t_base_inv self))
-  (ensures (
-    match hashMap_clear t self with
-    | Fail _ -> False
-    | Return hm ->
-      // The hash map invariant is satisfied
-      hashMap_t_base_inv hm /\
-      // We preserved the parameters
-      hashMap_t_same_params hm self /\
-      // The hash map has 0 values
-      hashMap_t_len_s hm = 0 /\
-      // It contains no bindings
-      (forall k. hashMap_t_find_s hm k == None)))
-
-// Being lazy: fuel 1 helps a lot...
-#push-options "--fuel 1"
-let hashMap_clear_lem_aux #t self =
-  let p = self.max_load_factor in
-  let i = self.max_load in
-  let v = self.slots in
-  hashMap_clear_loop_lem t v 0;
-  begin match hashMap_clear_loop t v 0 with
-  | Fail _ -> ()
-  | Return slots1 ->
-    slots_t_al_v_all_nil_is_empty_lem slots1;
-    let hm1 = MkhashMap_t 0 p i slots1 in
-    assert(hashMap_t_base_inv hm1);
-    assert(hashMap_t_inv hm1)
-  end
-#pop-options
-
-let hashMap_clear_lem #t self = hashMap_clear_lem_aux #t self
-
-(*** len *)
-
-/// [len]: we link it to a non-failing function.
-/// Rk.: we might want to make an analysis to not use an error monad to translate
-/// functions which statically can't fail.
-let hashMap_len_lem #t self = ()
-
-
-(*** insert_in_list *)
-
-(**** insert_in_list'fwd *)
-
-/// [insert_in_list]: returns true iff the key is not in the list (functional version)
-val hashMap_insert_in_list_lem
-  (t : Type0) (key : usize) (value : t) (ls : list_t t) :
-  Lemma
-  (ensures (
-    match hashMap_insert_in_list t key value ls with
-    | Fail _ -> False
-    | Return b ->
-      b <==> (slot_t_find_s key ls == None)))
-  (decreases (hashMap_insert_in_list_loop_decreases t key value ls))
-
-#push-options "--fuel 1"
-let rec hashMap_insert_in_list_lem t key value ls =
-  begin match ls with
-  | List_Cons ckey cvalue ls0 ->
-    let b = ckey = key in
-    if b
-    then ()
-    else
-      begin
-      hashMap_insert_in_list_lem t key value ls0;
-      match hashMap_insert_in_list t key value ls0 with
-      | Fail _ -> ()
-      | Return b0 -> ()
-      end
-  | List_Nil ->
-    assert(list_t_v ls == []);
-    assert_norm(find (same_key #t key) [] == None)
-  end
-#pop-options
-
-(**** insert_in_list'back *)
-
-/// The proofs about [insert_in_list] backward are easier to do in several steps:
-/// extrinsic proofs to the rescue!
-/// We first prove that [insert_in_list] refines the function we wrote above, then
-/// use this function to prove the invariants, etc.
-
-/// We write a helper which "captures" what [insert_in_list] does.
-/// We then reason about this helper to prove the high-level properties we want
-/// (functional properties, preservation of invariants, etc.).
-let hashMap_insert_in_list_s
-  (#t : Type0) (key : usize) (value : t) (ls : list (binding t)) :
-  list (binding t) =
-  // Check if there is already a binding for the key
-  match find (same_key key) ls with
-  | None ->
-    // No binding: append the binding to the end
-    ls @ [(key,value)]
-  | Some _ ->
-    // There is already a binding: update it
-    find_update (same_key key) ls (key,value)
-
-/// [insert_in_list]: if the key is not in the map, appends a new bindings (functional version)
-val hashMap_insert_in_list_back_lem_append_s
-  (t : Type0) (key : usize) (value : t) (ls : list_t t) :
-  Lemma
-  (requires (
-    slot_t_find_s key ls == None))
-  (ensures (
-    match hashMap_insert_in_list_back t key value ls with
-    | Fail _ -> False
-    | Return ls' ->
-      list_t_v ls' == list_t_v ls @ [(key,value)]))
-  (decreases (hashMap_insert_in_list_loop_decreases t key value ls))
-
-#push-options "--fuel 1"
-let rec hashMap_insert_in_list_back_lem_append_s t key value ls =
-  begin match ls with
-  | List_Cons ckey cvalue ls0 ->
-    let b = ckey = key in
-    if b
-    then ()
-    else
-      begin
-      hashMap_insert_in_list_back_lem_append_s t key value ls0;
-      match hashMap_insert_in_list_back t key value ls0 with
-      | Fail _ -> ()
-      | Return l -> ()
-      end
-  | List_Nil -> ()
-  end
-#pop-options
-
-/// [insert_in_list]: if the key is in the map, we update the binding (functional version)
-val hashMap_insert_in_list_back_lem_update_s
-  (t : Type0) (key : usize) (value : t) (ls : list_t t) :
-  Lemma
-  (requires (
-    Some? (find (same_key key) (list_t_v ls))))
-  (ensures (
-    match hashMap_insert_in_list_back t key value ls with
-    | Fail _ -> False
-    | Return ls' ->
-      list_t_v ls' == find_update (same_key key) (list_t_v ls) (key,value)))
-  (decreases (hashMap_insert_in_list_loop_decreases t key value ls))
-
-#push-options "--fuel 1"
-let rec hashMap_insert_in_list_back_lem_update_s t key value ls =
-  begin match ls with
-  | List_Cons ckey cvalue ls0 ->
-    let b = ckey = key in
-    if b
-    then ()
-    else
-      begin
-      hashMap_insert_in_list_back_lem_update_s t key value ls0;
-      match hashMap_insert_in_list_back t key value ls0 with
-      | Fail _ -> ()
-      | Return l -> ()
-      end
-  | List_Nil -> ()
-  end
-#pop-options
-
-/// Put everything together
-val hashMap_insert_in_list_back_lem_s
-  (t : Type0) (key : usize) (value : t) (ls : list_t t) :
-  Lemma
-  (ensures (
-    match hashMap_insert_in_list_back t key value ls with
-    | Fail _ -> False
-    | Return ls' ->
-      list_t_v ls' == hashMap_insert_in_list_s key value (list_t_v ls)))
-
-let hashMap_insert_in_list_back_lem_s t key value ls =
-  match find (same_key key) (list_t_v ls) with
-  | None -> hashMap_insert_in_list_back_lem_append_s t key value ls
-  | Some _ -> hashMap_insert_in_list_back_lem_update_s t key value ls
-
-(**** Invariants of insert_in_list_s *)
-
-/// Auxiliary lemmas
-/// We work on [hashMap_insert_in_list_s], the "high-level" version of [insert_in_list'back].
-///
-/// Note that in F* we can't have recursive proofs inside of other proofs, contrary
-/// to Coq, which makes it a bit cumbersome to prove auxiliary results like the
-/// following ones...
-
-(** Auxiliary lemmas: append case *)
-
-val slot_t_v_for_all_binding_neq_append_lem
-  (t : Type0) (key : usize) (value : t) (ls : list (binding t)) (b : binding t) :
-  Lemma
-  (requires (
-    fst b <> key /\
-    for_all (binding_neq b) ls /\
-    slot_s_find key ls == None))
-  (ensures (
-    for_all (binding_neq b) (ls @ [(key,value)])))
-
-#push-options "--fuel 1"
-let rec slot_t_v_for_all_binding_neq_append_lem t key value ls b =
-  match ls with
-  | [] -> ()
-  | (ck, cv) :: cls ->
-    slot_t_v_for_all_binding_neq_append_lem t key value cls b
-#pop-options
-
-val slot_s_inv_not_find_append_end_inv_lem
-  (t : Type0) (len : usize{len > 0}) (key : usize) (value : t) (ls : list (binding t)) :
-  Lemma
-  (requires (
-    slot_s_inv len (hash_mod_key key len) ls /\
-    slot_s_find key ls == None))
-  (ensures (
-    let ls' = ls @ [(key,value)] in
-    slot_s_inv len (hash_mod_key key len) ls' /\
-    (slot_s_find key ls' == Some value) /\
-    (forall k'. k' <> key ==> slot_s_find k' ls' == slot_s_find k' ls)))
-
-#push-options "--fuel 1"
-let rec slot_s_inv_not_find_append_end_inv_lem t len key value ls =
-  match ls with
-  | [] -> ()
-  | (ck, cv) :: cls ->
-    slot_s_inv_not_find_append_end_inv_lem t len key value cls;
-    let h = hash_mod_key key len in
-    let ls' = ls @ [(key,value)] in
-    assert(for_all (same_hash_mod_key len h) ls');
-    slot_t_v_for_all_binding_neq_append_lem t key value cls (ck, cv);
-    assert(pairwise_rel binding_neq ls');
-    assert(slot_s_inv len h ls')
-#pop-options
-
-/// [insert_in_list]: if the key is not in the map, appends a new bindings
-val hashMap_insert_in_list_s_lem_append
-  (t : Type0) (len : usize{len > 0}) (key : usize) (value : t) (ls : list (binding t)) :
-  Lemma
-  (requires (
-    slot_s_inv len (hash_mod_key key len) ls /\
-    slot_s_find key ls == None))
-  (ensures (
-    let ls' = hashMap_insert_in_list_s key value ls in
-    ls' == ls @ [(key,value)] /\
-    // The invariant is preserved
-    slot_s_inv len (hash_mod_key key len) ls' /\
-    // [key] maps to [value]
-    slot_s_find key ls' == Some value /\
-    // The other bindings are preserved
-    (forall k'. k' <> key ==> slot_s_find k' ls' == slot_s_find k' ls)))
-
-let hashMap_insert_in_list_s_lem_append t len key value ls =
-  slot_s_inv_not_find_append_end_inv_lem t len key value ls
-
-/// [insert_in_list]: if the key is not in the map, appends a new bindings (quantifiers)
-/// Rk.: we don't use this lemma.
-/// TODO: remove?
-val hashMap_insert_in_list_back_lem_append
-  (t : Type0) (len : usize{len > 0}) (key : usize) (value : t) (ls : list_t t) :
-  Lemma
-  (requires (
-    slot_t_inv len (hash_mod_key key len) ls /\
-    slot_t_find_s key ls == None))
-  (ensures (
-    match hashMap_insert_in_list_back t key value ls with
-    | Fail _ -> False
-    | Return ls' ->
-      list_t_v ls' == list_t_v ls @ [(key,value)] /\
-      // The invariant is preserved
-      slot_t_inv len (hash_mod_key key len) ls' /\
-      // [key] maps to [value]
-      slot_t_find_s key ls' == Some value /\
-      // The other bindings are preserved
-      (forall k'. k' <> key ==> slot_t_find_s k' ls' == slot_t_find_s k' ls)))
-
-let hashMap_insert_in_list_back_lem_append t len key value ls =
-  hashMap_insert_in_list_back_lem_s t key value ls;
-  hashMap_insert_in_list_s_lem_append t len key value (list_t_v ls)
-
-(** Auxiliary lemmas: update case *)
-
-val slot_s_find_update_for_all_binding_neq_append_lem
-  (t : Type0) (key : usize) (value : t) (ls : list (binding t)) (b : binding t) :
-  Lemma
-  (requires (
-    fst b <> key /\
-    for_all (binding_neq b) ls))
-  (ensures (
-    let ls' = find_update (same_key key) ls (key, value) in
-    for_all (binding_neq b) ls'))
-
-#push-options "--fuel 1"
-let rec slot_s_find_update_for_all_binding_neq_append_lem t key value ls b =
-  match ls with
-  | [] -> ()
-  | (ck, cv) :: cls ->
-    slot_s_find_update_for_all_binding_neq_append_lem t key value cls b
-#pop-options
-
-/// Annoying auxiliary lemma we have to prove because there is no way to reason
-/// properly about closures.
-/// I'm really enjoying my time.
-val for_all_binding_neq_value_indep
-  (#t : Type0) (key : key) (v0 v1 : t) (ls : list (binding t)) :
-  Lemma (for_all (binding_neq (key,v0)) ls = for_all (binding_neq (key,v1)) ls)
-
-#push-options "--fuel 1"
-let rec for_all_binding_neq_value_indep #t key v0 v1 ls =
-  match ls with
-  | [] -> ()
-  | _ :: ls' -> for_all_binding_neq_value_indep #t key v0 v1 ls'
-#pop-options
-
-val slot_s_inv_find_append_end_inv_lem
-  (t : Type0) (len : usize{len > 0}) (key : usize) (value : t) (ls : list (binding t)) :
-  Lemma
-  (requires (
-    slot_s_inv len (hash_mod_key key len) ls /\
-    Some? (slot_s_find key ls)))
-  (ensures (
-    let ls' = find_update (same_key key) ls (key, value) in
-    slot_s_inv len (hash_mod_key key len) ls' /\
-    (slot_s_find key ls' == Some value) /\
-    (forall k'. k' <> key ==> slot_s_find k' ls' == slot_s_find k' ls)))
-
-#push-options "--z3rlimit 50 --fuel 1"
-let rec slot_s_inv_find_append_end_inv_lem t len key value ls =
-  match ls with
-  | [] -> ()
-  | (ck, cv) :: cls ->
-    let h = hash_mod_key key len in
-    let ls' = find_update (same_key key) ls (key, value) in
-    if ck = key then
-      begin
-      assert(ls' == (ck,value) :: cls);
-      assert(for_all (same_hash_mod_key len h) ls');
-      // For pairwise_rel: binding_neq (ck, value) is actually independent
-      // of `value`. Slightly annoying to prove in F*...
-      assert(for_all (binding_neq (ck,cv)) cls);
-      for_all_binding_neq_value_indep key cv value cls;
-      assert(for_all (binding_neq (ck,value)) cls);
-      assert(pairwise_rel binding_neq ls');
-      assert(slot_s_inv len (hash_mod_key key len) ls')
-      end
-    else
-      begin
-      slot_s_inv_find_append_end_inv_lem t len key value cls;
-      assert(for_all (same_hash_mod_key len h) ls');
-      slot_s_find_update_for_all_binding_neq_append_lem t key value cls (ck, cv);
-      assert(pairwise_rel binding_neq ls');
-      assert(slot_s_inv len h ls')
-      end
-#pop-options
-
-/// [insert_in_list]: if the key is in the map, update the bindings
-val hashMap_insert_in_list_s_lem_update
-  (t : Type0) (len : usize{len > 0}) (key : usize) (value : t) (ls : list (binding t)) :
-  Lemma
-  (requires (
-    slot_s_inv len (hash_mod_key key len) ls /\
-    Some? (slot_s_find key ls)))
-  (ensures (
-    let ls' = hashMap_insert_in_list_s key value ls in
-    ls' == find_update (same_key key) ls (key,value) /\
-    // The invariant is preserved
-    slot_s_inv len (hash_mod_key key len) ls' /\
-    // [key] maps to [value]
-    slot_s_find key ls' == Some value /\
-    // The other bindings are preserved
-    (forall k'. k' <> key ==> slot_s_find k' ls' == slot_s_find k' ls)))
-
-let hashMap_insert_in_list_s_lem_update t len key value ls =
-  slot_s_inv_find_append_end_inv_lem t len key value ls
-
-
-/// [insert_in_list]: if the key is in the map, update the bindings
-/// TODO: not used: remove?
-val hashMap_insert_in_list_back_lem_update
-  (t : Type0) (len : usize{len > 0}) (key : usize) (value : t) (ls : list_t t) :
-  Lemma
-  (requires (
-    slot_t_inv len (hash_mod_key key len) ls /\
-    Some? (slot_t_find_s key ls)))
-  (ensures (
-    match hashMap_insert_in_list_back t key value ls with
-    | Fail _ -> False
-    | Return ls' ->
-      let als = list_t_v ls in
-      list_t_v ls' == find_update (same_key key) als (key,value) /\
-      // The invariant is preserved
-      slot_t_inv len (hash_mod_key key len) ls' /\
-      // [key] maps to [value]
-      slot_t_find_s key ls' == Some value /\
-      // The other bindings are preserved
-      (forall k'. k' <> key ==> slot_t_find_s k' ls' == slot_t_find_s k' ls)))
-
-let hashMap_insert_in_list_back_lem_update t len key value ls =
-  hashMap_insert_in_list_back_lem_s t key value ls;
-  hashMap_insert_in_list_s_lem_update t len key value (list_t_v ls)
-
-(** Final lemmas about [insert_in_list] *)
-
-/// High-level version
-val hashMap_insert_in_list_s_lem
-  (t : Type0) (len : usize{len > 0}) (key : usize) (value : t) (ls : list (binding t)) :
-  Lemma
-  (requires (
-    slot_s_inv len (hash_mod_key key len) ls))
-  (ensures (
-    let ls' = hashMap_insert_in_list_s key value ls in
-    // The invariant is preserved
-    slot_s_inv len (hash_mod_key key len) ls' /\
-    // [key] maps to [value]
-    slot_s_find key ls' == Some value /\
-    // The other bindings are preserved
-    (forall k'. k' <> key ==> slot_s_find k' ls' == slot_s_find k' ls) /\
-    // The length is incremented, iff we inserted a new key
-    (match slot_s_find key ls with
-     | None -> length ls' = length ls + 1
-     | Some _ -> length ls' = length ls)))
-
-let hashMap_insert_in_list_s_lem t len key value ls =
-  match slot_s_find key ls with
-  | None ->
-    assert_norm(length [(key,value)] = 1);
-    hashMap_insert_in_list_s_lem_append t len key value ls
-  | Some _ ->
-    hashMap_insert_in_list_s_lem_update t len key value ls
-
-/// [insert_in_list]
-/// TODO: not used: remove?
-val hashMap_insert_in_list_back_lem
-  (t : Type0) (len : usize{len > 0}) (key : usize) (value : t) (ls : list_t t) :
-  Lemma
-  (requires (slot_t_inv len (hash_mod_key key len) ls))
-  (ensures (
-    match hashMap_insert_in_list_back t key value ls with
-    | Fail _ -> False
-    | Return ls' ->
-      // The invariant is preserved
-      slot_t_inv len (hash_mod_key key len) ls' /\
-      // [key] maps to [value]
-      slot_t_find_s key ls' == Some value /\
-      // The other bindings are preserved
-      (forall k'. k' <> key ==> slot_t_find_s k' ls' == slot_t_find_s k' ls) /\
-      // The length is incremented, iff we inserted a new key
-      (match slot_t_find_s key ls with
-       | None ->
-         list_t_v ls' == list_t_v ls @ [(key,value)] /\
-         list_t_len ls' = list_t_len ls + 1
-       | Some _ ->
-         list_t_v ls' == find_update (same_key key) (list_t_v ls) (key,value) /\
-         list_t_len ls' = list_t_len ls)))
-  (decreases (hashMap_insert_in_list_loop_decreases t key value ls))
-
-let hashMap_insert_in_list_back_lem t len key value ls =
-  hashMap_insert_in_list_back_lem_s t key value ls;
-  hashMap_insert_in_list_s_lem t len key value (list_t_v ls)
-
-(*** insert_no_resize *)
-
-(**** Refinement proof *)
-/// Same strategy as for [insert_in_list]: we introduce a high-level version of
-/// the function, and reason about it.
-/// We work on [hashMap_s] (we use a higher-level view of the hash-map, but
-/// not too high).
-
-/// A high-level version of insert, which doesn't check if the table is saturated
-let hashMap_insert_no_fail_s
-  (#t : Type0) (hm : hashMap_s_nes t)
-  (key : usize) (value : t) :
-  hashMap_s t =
-  let len = length hm in
-  let i = hash_mod_key key len in
-  let slot = index hm i in
-  let slot' = hashMap_insert_in_list_s key value slot in
-  let hm' = list_update hm i slot' in
-  hm'
-
-// TODO: at some point I used hashMap_s_nes and it broke proofs...x
-let hashMap_insert_no_resize_s
-  (#t : Type0) (hm : hashMap_s_nes t)
-  (key : usize) (value : t) :
-  result (hashMap_s t) =
-  // Check if the table is saturated (too many entries, and we need to insert one)
-  let num_entries = length (flatten hm) in
-  if None? (hashMap_s_find hm key) && num_entries = usize_max then Fail Failure
-  else Return (hashMap_insert_no_fail_s hm key value)
-
-/// Prove that [hashMap_insert_no_resize_s] is refined by
-/// [hashMap_insert_no_resize'fwd_back]
-val hashMap_insert_no_resize_lem_s
-  (t : Type0) (self : hashMap_t t) (key : usize) (value : t) :
-  Lemma
-  (requires (
-    hashMap_t_base_inv self /\
-    hashMap_s_len (hashMap_t_v self) = hashMap_t_len_s self))
-  (ensures (
-    begin
-    match hashMap_insert_no_resize t self key value,
-          hashMap_insert_no_resize_s (hashMap_t_v self) key value
-    with
-    | Fail _, Fail _ -> True
-    | Return hm, Return hm_v ->
-      hashMap_t_base_inv hm /\
-      hashMap_t_same_params hm self /\
-      hashMap_t_v hm == hm_v /\
-      hashMap_s_len hm_v == hashMap_t_len_s hm
-    | _ -> False
-    end))
-
-let hashMap_insert_no_resize_lem_s t self key value =
-  begin match hash_key key with
-  | Fail _ -> ()
-  | Return i ->
-    let i0 = self.num_entries in
-    let p = self.max_load_factor in
-    let i1 = self.max_load in
-    let v = self.slots in
-    let i2 = alloc_vec_Vec_len (list_t t) v in
-    let len = length v in
-    begin match usize_rem i i2 with
-    | Fail _ -> ()
-    | Return hash_mod ->
-      begin match alloc_vec_Vec_index_usize v hash_mod with
-      | Fail _ -> ()
-      | Return l ->
-        begin
-        // Checking that: list_t_v (index ...) == index (hashMap_t_v ...) ...
-        assert(list_t_v l == index (hashMap_t_v self) hash_mod);
-        hashMap_insert_in_list_lem t key value l;
-        match hashMap_insert_in_list t key value l with
-        | Fail _ -> ()
-        | Return b ->
-          assert(b = None? (slot_s_find key (list_t_v l)));
-          hashMap_insert_in_list_back_lem t len key value l;
-          if b
-          then
-            begin match usize_add i0 1 with
-            | Fail _ -> ()
-            | Return i3 ->
-              begin
-              match hashMap_insert_in_list_back t key value l with
-              | Fail _ -> ()
-              | Return l0 ->
-                begin match alloc_vec_Vec_update_usize v hash_mod l0 with
-                | Fail _ -> ()
-                | Return v0 ->
-                  let self_v = hashMap_t_v self in
-                  let hm = MkhashMap_t i3 p i1 v0 in
-                  let hm_v = hashMap_t_v hm in
-                  assert(hm_v == list_update self_v hash_mod (list_t_v l0));
-                  assert_norm(length [(key,value)] = 1);
-                  assert(length (list_t_v l0) = length (list_t_v l) + 1);
-                  length_flatten_update self_v hash_mod (list_t_v l0);
-                  assert(hashMap_s_len hm_v = hashMap_t_len_s hm)
-                end
-              end
-            end
-          else
-            begin
-            match hashMap_insert_in_list_back t key value l with
-            | Fail _ -> ()
-            | Return l0 ->
-              begin match alloc_vec_Vec_update_usize v hash_mod l0 with
-              | Fail _ -> ()
-              | Return v0 ->
-                let self_v = hashMap_t_v self in
-                let hm = MkhashMap_t i0 p i1 v0 in
-                let hm_v = hashMap_t_v hm in
-                assert(hm_v == list_update self_v hash_mod (list_t_v l0));
-                assert(length (list_t_v l0) = length (list_t_v l));
-                length_flatten_update self_v hash_mod (list_t_v l0);
-                assert(hashMap_s_len hm_v = hashMap_t_len_s hm)
-              end
-            end
-        end
-      end
-    end
-  end
-
-(**** insert_{no_fail,no_resize}: invariants *)
-
-let hashMap_s_updated_binding
-  (#t : Type0) (hm : hashMap_s_nes t)
-  (key : usize) (opt_value : option t) (hm' : hashMap_s_nes t) : Type0 =
-  // [key] maps to [value]
-  hashMap_s_find hm' key == opt_value /\
-  // The other bindings are preserved
-  (forall k'. k' <> key ==> hashMap_s_find hm' k' == hashMap_s_find hm k')
-
-let insert_post (#t : Type0) (hm : hashMap_s_nes t)
-  (key : usize) (value : t) (hm' : hashMap_s_nes t) : Type0 =
-  // The invariant is preserved
-  hashMap_s_inv hm' /\
-  // [key] maps to [value] and the other bindings are preserved
-  hashMap_s_updated_binding hm key (Some value) hm' /\
-  // The length is incremented, iff we inserted a new key
-  (match hashMap_s_find hm key with
-   | None -> hashMap_s_len hm' = hashMap_s_len hm + 1
-   | Some _ -> hashMap_s_len hm' = hashMap_s_len hm)
-
-val hashMap_insert_no_fail_s_lem
-  (#t : Type0) (hm : hashMap_s_nes t)
-  (key : usize) (value : t) :
-  Lemma
-  (requires (hashMap_s_inv hm))
-  (ensures (
-    let hm' = hashMap_insert_no_fail_s hm key value in
-    insert_post hm key value hm'))
-
-let hashMap_insert_no_fail_s_lem #t hm key value =
-  let len = length hm in
-  let i = hash_mod_key key len in
-  let slot = index hm i in
-  hashMap_insert_in_list_s_lem t len key value slot;
-  let slot' = hashMap_insert_in_list_s key value slot in
-  length_flatten_update hm i slot'
-
-val hashMap_insert_no_resize_s_lem
-  (#t : Type0) (hm : hashMap_s_nes t)
-  (key : usize) (value : t) :
-  Lemma
-  (requires (hashMap_s_inv hm))
-  (ensures (
-    match hashMap_insert_no_resize_s hm key value with
-    | Fail _ ->
-      // Can fail only if we need to create a new binding in
-      // an already saturated map
-      hashMap_s_len hm = usize_max /\
-      None? (hashMap_s_find hm key)
-    | Return hm' ->
-      insert_post hm key value hm'))
-
-let hashMap_insert_no_resize_s_lem #t hm key value =
-  let num_entries = length (flatten hm) in
-  if None? (hashMap_s_find hm key) && num_entries = usize_max then ()
-  else hashMap_insert_no_fail_s_lem hm key value
-
-
-(**** find after insert *)
-/// Lemmas about what happens if we call [find] after an insertion
-
-val hashMap_insert_no_resize_s_get_same_lem
-  (#t : Type0) (hm : hashMap_s t)
-  (key : usize) (value : t) :
-  Lemma (requires (hashMap_s_inv hm))
-  (ensures (
-    match hashMap_insert_no_resize_s hm key value with
-    | Fail _ -> True
-    | Return hm' ->
-      hashMap_s_find hm' key == Some value))
-
-let hashMap_insert_no_resize_s_get_same_lem #t hm key value =
-  let num_entries = length (flatten hm) in
-  if None? (hashMap_s_find hm key) && num_entries = usize_max then ()
-  else
-    begin
-    let hm' = Return?.v (hashMap_insert_no_resize_s hm key value) in
-    let len = length hm in
-    let i = hash_mod_key key len in
-    let slot = index hm i in
-    hashMap_insert_in_list_s_lem t len key value slot
-   end
-
-val hashMap_insert_no_resize_s_get_diff_lem
-  (#t : Type0) (hm : hashMap_s t)
-  (key : usize) (value : t) (key' : usize{key' <> key}) :
-  Lemma (requires (hashMap_s_inv hm))
-  (ensures (
-    match hashMap_insert_no_resize_s hm key value with
-    | Fail _ -> True
-    | Return hm' ->
-      hashMap_s_find hm' key' == hashMap_s_find hm key'))
-
-let hashMap_insert_no_resize_s_get_diff_lem #t hm key value key' =
-  let num_entries = length (flatten hm) in
-  if None? (hashMap_s_find hm key) && num_entries = usize_max then ()
-  else
-    begin
-    let hm' = Return?.v (hashMap_insert_no_resize_s hm key value) in
-    let len = length hm in
-    let i = hash_mod_key key len in
-    let slot = index hm i in
-    hashMap_insert_in_list_s_lem t len key value slot;
-    let i' = hash_mod_key key' len in
-    if i <> i' then ()
-    else
-      begin
-      ()
-      end
-   end
-
-
-(*** move_elements_from_list *)
-
-/// Having a great time here: if we use `result (hashMap_s_res t)` as the
-/// return type for [hashMap_move_elements_from_list_s] instead of having this
-/// awkward match, the proof of [hashMap_move_elements_lem_refin] fails.
-/// I guess it comes from F*'s poor subtyping.
-/// Followingly, I'm not taking any chance and using [result_hashMap_s]
-/// everywhere.
-type result_hashMap_s_nes (t : Type0) : Type0 =
-  res:result (hashMap_s t) {
-    match res with
-    | Fail _ -> True
-    | Return hm -> is_pos_usize (length hm)
-  }
-
-let rec hashMap_move_elements_from_list_s
-  (#t : Type0) (hm : hashMap_s_nes t)
-  (ls : slot_s t) :
-  // Do *NOT* use `result (hashMap_s t)`
-  Tot (result_hashMap_s_nes t)
-  (decreases ls) =
-  match ls with
-  | [] -> Return hm
-  | (key, value) :: ls' ->
-    match hashMap_insert_no_resize_s hm key value with
-    | Fail e -> Fail e
-    | Return hm' ->
-      hashMap_move_elements_from_list_s hm' ls'
-
-/// Refinement lemma
-val hashMap_move_elements_from_list_lem
-  (t : Type0) (ntable : hashMap_t_nes t) (ls : list_t t) :
-  Lemma (requires (hashMap_t_base_inv ntable))
-  (ensures (
-    match hashMap_move_elements_from_list t ntable ls,
-          hashMap_move_elements_from_list_s (hashMap_t_v ntable) (slot_t_v ls)
-    with
-    | Fail _, Fail _ -> True
-    | Return hm', Return hm_v ->
-      hashMap_t_base_inv hm' /\
-      hashMap_t_v hm' == hm_v /\
-      hashMap_t_same_params hm' ntable
-    | _ -> False))
-  (decreases (hashMap_move_elements_from_list_loop_decreases t ntable ls))
-
-#push-options "--fuel 1"
-let rec hashMap_move_elements_from_list_lem t ntable ls =
-  begin match ls with
-  | List_Cons k v tl ->
-    assert(list_t_v ls == (k, v) :: list_t_v tl);
-    let ls_v = list_t_v ls in
-    let (_,_) :: tl_v = ls_v in
-    hashMap_insert_no_resize_lem_s t ntable k v;
-    begin match hashMap_insert_no_resize t ntable k v with
-    | Fail _ -> ()
-    | Return h ->
-      let h_v = Return?.v (hashMap_insert_no_resize_s (hashMap_t_v ntable) k v) in
-      assert(hashMap_t_v h == h_v);
-      hashMap_move_elements_from_list_lem t h tl;
-      begin match hashMap_move_elements_from_list t h tl with
-      | Fail _ -> ()
-      | Return h0 -> ()
-      end
-    end
-  | List_Nil -> ()
-  end
-#pop-options
-
-(*** move_elements *)
-
-(**** move_elements: refinement 0 *)
-/// The proof for [hashMap_move_elements_lem_refin] broke so many times
-/// (while it is supposed to be super simple!) that we decided to add one refinement
-/// level, to really do things step by step...
-/// Doing this refinement layer made me notice that maybe the problem came from
-/// the fact that at some point we have to prove `list_t_v List_Nil == []`: I
-/// added the corresponding assert to help Z3 and everything became stable.
-/// I finally didn't use this "simple" refinement lemma, but I still keep it here
-/// because it allows for easy comparisons with [hashMap_move_elements_s].
-
-/// [hashMap_move_elements] refines this function, which is actually almost
-/// the same (just a little bit shorter and cleaner, and has a pre).
-///
-/// The way I wrote the high-level model is the following:
-/// - I copy-pasted the definition of [hashMap_move_elements], wrote the
-///   signature which links this new definition to [hashMap_move_elements] and
-///   checked that the proof passed
-/// - I gradually simplified it, while making sure the proof still passes
-#push-options "--fuel 1"
-let rec hashMap_move_elements_s_simpl
-  (t : Type0) (ntable : hashMap_t t)
-  (slots : alloc_vec_Vec (list_t t))
-  (i : usize{i <= length slots /\ length slots <= usize_max}) :
-  Pure (result ((hashMap_t t) & (alloc_vec_Vec (list_t t))))
-  (requires (True))
-  (ensures (fun res ->
-    match res, hashMap_move_elements t ntable slots i with
-    | Fail _, Fail _ -> True
-    | Return (ntable1, slots1), Return (ntable2, slots2) ->
-      ntable1 == ntable2 /\
-      slots1 == slots2
-    | _ -> False))
-  (decreases (hashMap_move_elements_loop_decreases t ntable slots i))
-  =
-  if i < length slots
-  then
-    let slot = index slots i in
-    begin match hashMap_move_elements_from_list t ntable slot with
-    | Fail e -> Fail e
-    | Return hm' ->
-      let slots' = list_update slots i List_Nil in
-      hashMap_move_elements_s_simpl t hm' slots' (i+1)
-    end
-  else Return (ntable, slots)
-#pop-options
-
-(**** move_elements: refinement 1 *)
-/// We prove a second refinement lemma: calling [move_elements] refines a function
-/// which, for every slot, moves the element out of the slot. This first model is
-/// almost exactly the translated function, it just uses `list` instead of `list_t`.
-
-// Note that we ignore the returned slots (we thus don't return a pair:
-// only the new hash map in which we moved the elements from the slots):
-// this returned value is not used.
-let rec hashMap_move_elements_s
-  (#t : Type0) (hm : hashMap_s_nes t)
-  (slots : slots_s t) (i : usize{i <= length slots /\ length slots <= usize_max}) :
-  Tot (result_hashMap_s_nes t)
-  (decreases (length slots - i)) =
-  let len = length slots in
-  if i < len then
-    begin
-    let slot = index slots i in
-    match hashMap_move_elements_from_list_s hm slot with
-    | Fail e -> Fail e
-    | Return hm' ->
-      let slots' = list_update slots i [] in
-      hashMap_move_elements_s hm' slots' (i+1)
-    end
-  else Return hm
-
-val hashMap_move_elements_lem_refin
-  (t : Type0) (ntable : hashMap_t t)
-  (slots : alloc_vec_Vec (list_t t)) (i : usize{i <= length slots}) :
-  Lemma
-  (requires (
-    hashMap_t_base_inv ntable))
-  (ensures (
-    match hashMap_move_elements t ntable slots i,
-          hashMap_move_elements_s (hashMap_t_v ntable) (slots_t_v slots) i
-    with
-    | Fail _, Fail _ -> True // We will prove later that this is not possible
-    | Return (ntable', _), Return ntable'_v ->
-      hashMap_t_base_inv ntable' /\
-      hashMap_t_v ntable' == ntable'_v /\
-      hashMap_t_same_params ntable' ntable
-    | _ -> False))
- (decreases (length slots - i))
-
-#restart-solver
-#push-options "--fuel 1"
-let rec hashMap_move_elements_lem_refin t ntable slots i =
-  assert(hashMap_t_base_inv ntable);
-  let i0 = alloc_vec_Vec_len (list_t t) slots in
-  let b = i < i0 in
-  if b
-  then
-    begin match alloc_vec_Vec_index_usize slots i with
-    | Fail _ -> ()
-    | Return l ->
-      let l0 = core_mem_replace (list_t t) l List_Nil in
-      assert(l0 == l);
-      hashMap_move_elements_from_list_lem t ntable l0;
-      begin match hashMap_move_elements_from_list t ntable l0 with
-      | Fail _ -> ()
-      | Return h ->
-        let l1 = core_mem_replace_back (list_t t) l List_Nil in
-        assert(l1 == List_Nil);
-        assert(slot_t_v #t List_Nil == []); // THIS IS IMPORTANT
-        begin match alloc_vec_Vec_update_usize slots i l1 with
-        | Fail _ -> ()
-        | Return v ->
-          begin match usize_add i 1 with
-          | Fail _ -> ()
-          | Return i1 ->
-            hashMap_move_elements_lem_refin t h v i1;
-            begin match hashMap_move_elements t h v i1 with
-            | Fail _ ->
-              assert(Fail? (hashMap_move_elements t ntable slots i));
-              ()
-            | Return (ntable', v0) -> ()
-            end
-          end
-        end
-      end
-    end
-  else ()
-#pop-options
-
-
-(**** move_elements: refinement 2 *)
-/// We prove a second refinement lemma: calling [move_elements] refines a function
-/// which moves every binding of the hash map seen as *one* associative list
-/// (and not a list of lists).
-
-/// [ntable] is the hash map to which we move the elements
-/// [slots] is the current hash map, from which we remove the elements, and seen
-///         as a "flat" associative list (and not a list of lists)
-/// This is actually exactly [hashMap_move_elements_from_list_s]...
-let rec hashMap_move_elements_s_flat
-  (#t : Type0) (ntable : hashMap_s_nes t)
-  (slots : assoc_list t) :
-  Tot (result_hashMap_s_nes t)
-  (decreases slots) =
-  match slots with
-  | [] -> Return ntable
-  | (k,v) :: slots' ->
-    match hashMap_insert_no_resize_s ntable k v with
-    | Fail e -> Fail e
-    | Return ntable' ->
-      hashMap_move_elements_s_flat ntable' slots'
-
-/// The refinment lemmas
-/// First, auxiliary helpers.
-
-/// Flatten a list of lists, starting at index i
-val flatten_i :
-     #a:Type
-  -> l:list (list a)
-  -> i:nat{i <= length l}
-  -> Tot (list a) (decreases (length l - i))
-
-let rec flatten_i l i =
-  if i < length l then
-    index l i @ flatten_i l (i+1)
-  else []
-
-let _ = assert(let l = [1;2] in l == hd l :: tl l)
-
-val flatten_i_incr :
-     #a:Type
-  -> l:list (list a)
-  -> i:nat{Cons? l /\ i+1 <= length l} ->
-  Lemma
-  (ensures (
-    (**) assert_norm(length (hd l :: tl l) == 1 + length (tl l));
-    flatten_i l (i+1) == flatten_i (tl l) i))
-  (decreases (length l - (i+1)))
-
-#push-options "--fuel 1"
-let rec flatten_i_incr l i =
-  let x :: tl = l in
-  if i + 1 < length l then
-    begin
-    assert(flatten_i l (i+1) == index l (i+1) @ flatten_i l (i+2));
-    flatten_i_incr l (i+1);
-    assert(flatten_i l (i+2) == flatten_i tl (i+1));
-    assert(index l (i+1) == index tl i)
-    end
-  else ()
-#pop-options
-
-val flatten_0_is_flatten :
-     #a:Type
-  -> l:list (list a) ->
-  Lemma
-  (ensures (flatten_i l 0 == flatten l))
-
-#push-options "--fuel 1"
-let rec flatten_0_is_flatten #a l =
-  match l with
-  | [] -> ()
-  | x :: l' ->
-    flatten_i_incr l 0;
-    flatten_0_is_flatten l'
-#pop-options
-
-/// Auxiliary lemma
-val flatten_nil_prefix_as_flatten_i :
-     #a:Type
-  -> l:list (list a)
-  -> i:nat{i <= length l} ->
-  Lemma (requires (forall (j:nat{j < i}). index l j == []))
-  (ensures (flatten l == flatten_i l i))
-
-#push-options "--fuel 1"
-let rec flatten_nil_prefix_as_flatten_i #a l i =
-  if i = 0 then flatten_0_is_flatten l
-  else
-    begin
-    let x :: l' = l in
-    assert(index l 0 == []);
-    assert(x == []);
-    assert(flatten l == flatten l');
-    flatten_i_incr l (i-1);
-    assert(flatten_i l i == flatten_i l' (i-1));
-    assert(forall (j:nat{j < length l'}). index l' j == index l (j+1));
-    flatten_nil_prefix_as_flatten_i l' (i-1);
-    assert(flatten l' == flatten_i l' (i-1))
-    end
-#pop-options
-
-/// The proof is trivial, the functions are the same.
-/// Just keeping two definitions to allow changes...
-val hashMap_move_elements_from_list_s_as_flat_lem
-  (#t : Type0) (hm : hashMap_s_nes t)
-  (ls : slot_s t) :
-  Lemma
-  (ensures (
-    hashMap_move_elements_from_list_s hm ls ==
-    hashMap_move_elements_s_flat hm ls))
-  (decreases ls)
-
-#push-options "--fuel 1"
-let rec hashMap_move_elements_from_list_s_as_flat_lem #t hm ls =
-  match ls with
-  | [] -> ()
-  | (key, value) :: ls' ->
-    match hashMap_insert_no_resize_s hm key value with
-    | Fail _ -> ()
-    | Return hm' ->
-      hashMap_move_elements_from_list_s_as_flat_lem hm' ls'
-#pop-options
-
-/// Composition of two calls to [hashMap_move_elements_s_flat]
-let hashMap_move_elements_s_flat_comp
-  (#t : Type0) (hm : hashMap_s_nes t) (slot0 slot1 : slot_s t) :
-  Tot (result_hashMap_s_nes t) =
-  match hashMap_move_elements_s_flat hm slot0 with
-  | Fail e -> Fail e
-  | Return hm1 -> hashMap_move_elements_s_flat hm1 slot1
-
-/// High-level desc:
-/// move_elements (move_elements hm slot0) slo1 == move_elements hm (slot0 @ slot1)
-val hashMap_move_elements_s_flat_append_lem
-  (#t : Type0) (hm : hashMap_s_nes t) (slot0 slot1 : slot_s t) :
-  Lemma
-  (ensures (
-    match hashMap_move_elements_s_flat_comp hm slot0 slot1,
-          hashMap_move_elements_s_flat hm (slot0 @ slot1)
-    with
-    | Fail _, Fail _ -> True
-    | Return hm1, Return hm2 -> hm1 == hm2
-    | _ -> False))
-  (decreases (slot0))
-
-#push-options "--fuel 1"
-let rec hashMap_move_elements_s_flat_append_lem #t hm slot0 slot1 =
-  match slot0 with
-  | [] -> ()
-  | (k,v) :: slot0' ->
-    match hashMap_insert_no_resize_s hm k v with
-    | Fail _ -> ()
-    | Return hm' ->
-      hashMap_move_elements_s_flat_append_lem hm' slot0' slot1
-#pop-options
-
-val flatten_i_same_suffix (#a : Type) (l0 l1 : list (list a)) (i : nat) :
-  Lemma
-  (requires (
-    i <= length l0 /\
-    length l0 = length l1 /\
-    (forall (j:nat{i <= j /\ j < length l0}). index l0 j == index l1 j)))
-  (ensures (flatten_i l0 i == flatten_i l1 i))
-  (decreases (length l0 - i))
-
-#push-options "--fuel 1"
-let rec flatten_i_same_suffix #a l0 l1 i =
-  if i < length l0 then
-    flatten_i_same_suffix l0 l1 (i+1)
-  else ()
-#pop-options
-
-/// Refinement lemma:
-/// [hashMap_move_elements_s] refines [hashMap_move_elements_s_flat]
-/// (actually the functions are equal on all inputs).
-val hashMap_move_elements_s_lem_refin_flat
-  (#t : Type0) (hm : hashMap_s_nes t)
-  (slots : slots_s t)
-  (i : nat{i <= length slots /\ length slots <= usize_max}) :
-  Lemma
-  (ensures (
-    match hashMap_move_elements_s hm slots i,
-          hashMap_move_elements_s_flat hm (flatten_i slots i)
-    with
-    | Fail _, Fail _ -> True
-    | Return hm, Return hm' -> hm == hm'
-    | _ -> False))
-  (decreases (length slots - i))
-
-#push-options "--fuel 1"
-let rec hashMap_move_elements_s_lem_refin_flat #t hm slots i =
-  let len = length slots in
-  if i < len then
-    begin
-    let slot = index slots i in
-    hashMap_move_elements_from_list_s_as_flat_lem hm slot;
-    match hashMap_move_elements_from_list_s hm slot with
-    | Fail _ ->
-      assert(flatten_i slots i == slot @ flatten_i slots (i+1));
-      hashMap_move_elements_s_flat_append_lem hm slot (flatten_i slots (i+1));
-      assert(Fail? (hashMap_move_elements_s_flat hm (flatten_i slots i)))
-    | Return hm' ->
-      let slots' = list_update slots i [] in
-      flatten_i_same_suffix slots slots' (i+1);
-      hashMap_move_elements_s_lem_refin_flat hm' slots' (i+1);
-      hashMap_move_elements_s_flat_append_lem hm slot (flatten_i slots' (i+1));
-      ()
-    end
-  else ()
-#pop-options
-
-let assoc_list_inv (#t : Type0) (al : assoc_list t) : Type0 =
-  // All the keys are pairwise distinct
-  pairwise_rel binding_neq al
-
-let disjoint_hm_al_on_key
-  (#t : Type0) (hm : hashMap_s_nes t) (al : assoc_list t) (k : key) : Type0 =
-  match hashMap_s_find hm k, assoc_list_find k al with
-  | Some _, None
-  | None, Some _
-  | None, None -> True
-  | Some _, Some _ -> False
-
-/// Playing a dangerous game here: using forall quantifiers
-let disjoint_hm_al (#t : Type0) (hm : hashMap_s_nes t) (al : assoc_list t) : Type0 =
-  forall (k:key). disjoint_hm_al_on_key hm al k
-
-let find_in_union_hm_al
-  (#t : Type0) (hm : hashMap_s_nes t) (al : assoc_list t) (k : key) :
-  option t =
-  match hashMap_s_find hm k with
-  | Some b -> Some b
-  | None -> assoc_list_find k al
-
-/// Auxiliary lemma
-val for_all_binding_neq_find_lem (#t : Type0) (k : key) (v : t) (al : assoc_list t) :
-  Lemma (requires (for_all (binding_neq (k,v)) al))
-  (ensures (assoc_list_find k al == None))
-
-#push-options "--fuel 1"
-let rec for_all_binding_neq_find_lem #t k v al =
-  match al with
-  | [] -> ()
-  | b :: al' -> for_all_binding_neq_find_lem k v al'
-#pop-options
-
-val hashMap_move_elements_s_flat_lem
-  (#t : Type0) (hm : hashMap_s_nes t) (al : assoc_list t) :
-  Lemma
-  (requires (
-    // Invariants
-    hashMap_s_inv hm /\
-    assoc_list_inv al /\
-    // The two are disjoint
-    disjoint_hm_al hm al /\
-    // We can add all the elements to the hashmap
-    hashMap_s_len hm + length al <= usize_max))
-  (ensures (
-    match hashMap_move_elements_s_flat hm al with
-    | Fail _ -> False // We can't fail
-    | Return hm' ->
-      // The invariant is preserved
-      hashMap_s_inv hm' /\
-      // The new hash map is the union of the two maps
-      (forall (k:key). hashMap_s_find hm' k == find_in_union_hm_al hm al k) /\
-      hashMap_s_len hm' = hashMap_s_len hm + length al))
-  (decreases al)
-
-#restart-solver
-#push-options "--z3rlimit 200 --fuel 1"
-let rec hashMap_move_elements_s_flat_lem #t hm al =
-  match al with
-  | [] -> ()
-  | (k,v) :: al' ->
-    hashMap_insert_no_resize_s_lem hm k v;
-    match hashMap_insert_no_resize_s hm k v with
-    | Fail _ -> ()
-    | Return hm' ->
-      assert(hashMap_s_inv hm');
-      assert(assoc_list_inv al');
-      let disjoint_lem (k' : key) :
-        Lemma (disjoint_hm_al_on_key hm' al' k')
-        [SMTPat (disjoint_hm_al_on_key hm' al' k')] =
-        if k' = k then
-          begin
-          assert(hashMap_s_find hm' k' == Some v);
-          for_all_binding_neq_find_lem k v al';
-          assert(assoc_list_find k' al' == None)
-          end
-        else
-          begin
-          assert(hashMap_s_find hm' k' == hashMap_s_find hm k');
-          assert(assoc_list_find k' al' == assoc_list_find k' al)
-          end
-      in
-      assert(disjoint_hm_al hm' al');
-      assert(hashMap_s_len hm' + length al' <= usize_max);
-      hashMap_move_elements_s_flat_lem hm' al'
-#pop-options
-
-/// We need to prove that the invariants on the "low-level" representations of
-/// the hash map imply the invariants on the "high-level" representations.
-
-val slots_t_inv_implies_slots_s_inv
-  (#t : Type0) (slots : slots_t t{length slots <= usize_max}) :
-  Lemma (requires (slots_t_inv slots))
-  (ensures (slots_s_inv (slots_t_v slots)))
-
-let slots_t_inv_implies_slots_s_inv #t slots =
-  // Ok, works fine: this lemma was useless.
-  // Problem is: I can never really predict for sure with F*...
-  ()
-
-val hashMap_t_base_inv_implies_hashMap_s_inv
-  (#t : Type0) (hm : hashMap_t t) :
-  Lemma (requires (hashMap_t_base_inv hm))
-  (ensures (hashMap_s_inv (hashMap_t_v hm)))
-
-let hashMap_t_base_inv_implies_hashMap_s_inv #t hm = () // same as previous
-
-/// Introducing a "partial" version of the hash map invariant, which operates on
-/// a suffix of the hash map.
-let partial_hashMap_s_inv
-  (#t : Type0) (len : usize{len > 0}) (offset : usize)
-  (hm : hashMap_s t{offset + length hm <= usize_max}) : Type0 =
-  forall(i:nat{i < length hm}). {:pattern index hm i} slot_s_inv len (offset + i) (index hm i)
-
-/// Auxiliary lemma.
-/// If a binding comes from a slot i, then its key is different from the keys
-/// of the bindings in the other slots (because the hashes of the keys are distinct).
-val binding_in_previous_slot_implies_neq
-  (#t : Type0) (len : usize{len > 0})
-  (i : usize) (b : binding t)
-  (offset : usize{i < offset})
-  (slots : hashMap_s t{offset + length slots <= usize_max}) :
-  Lemma
-  (requires (
-    // The binding comes from a slot not in [slots]
-    hash_mod_key (fst b) len = i /\
-    // The slots are the well-formed suffix of a hash map
-    partial_hashMap_s_inv len offset slots))
-  (ensures (
-    for_all (binding_neq b) (flatten slots)))
-  (decreases slots)
-
-#push-options "--z3rlimit 100 --fuel 1"
-let rec binding_in_previous_slot_implies_neq #t len i b offset slots =
-  match slots with
-  | [] -> ()
-  | s :: slots' ->
-    assert(slot_s_inv len offset (index slots 0)); // Triggers patterns
-    assert(slot_s_inv len offset s);
-    // Proving TARGET. We use quantifiers.
-    assert(for_all (same_hash_mod_key len offset) s);
-    forall_index_equiv_list_for_all (same_hash_mod_key len offset) s;
-    assert(forall (i:nat{i < length s}). same_hash_mod_key len offset (index s i));
-    let aux (i:nat{i < length s}) :
-      Lemma
-      (requires (same_hash_mod_key len offset (index s i)))
-      (ensures (binding_neq b (index s i)))
-      [SMTPat (index s i)] = ()
-    in
-    assert(forall (i:nat{i < length s}). binding_neq b (index s i));
-    forall_index_equiv_list_for_all (binding_neq b) s;
-    assert(for_all (binding_neq b) s); // TARGET
-    //
-    assert(forall (i:nat{i < length slots'}). index slots' i == index slots (i+1)); // Triggers instantiations
-    binding_in_previous_slot_implies_neq len i b (offset+1) slots';
-    for_all_append (binding_neq b) s (flatten slots')    
-#pop-options
-
-val partial_hashMap_s_inv_implies_assoc_list_lem
-  (#t : Type0) (len : usize{len > 0}) (offset : usize)
-  (hm : hashMap_s t{offset + length hm <= usize_max}) :
-  Lemma
-  (requires (
-    partial_hashMap_s_inv len offset hm))
-  (ensures (assoc_list_inv (flatten hm)))
-  (decreases (length hm + length (flatten hm)))
-
-#push-options "--fuel 1"
-let rec partial_hashMap_s_inv_implies_assoc_list_lem #t len offset hm =
-  match hm with
-  | [] -> ()
-  | slot :: hm' ->
-    assert(flatten hm == slot @ flatten hm');
-    assert(forall (i:nat{i < length hm'}). index hm' i == index hm (i+1)); // Triggers instantiations
-    match slot with
-    | [] ->
-      assert(flatten hm == flatten hm');
-      assert(partial_hashMap_s_inv len (offset+1) hm'); // Triggers instantiations
-      partial_hashMap_s_inv_implies_assoc_list_lem len (offset+1) hm'
-    | x :: slot' ->
-      assert(flatten (slot' :: hm') == slot' @ flatten hm');
-      let hm'' = slot' :: hm' in
-      assert(forall (i:nat{0 < i /\ i < length hm''}). index hm'' i == index hm i); // Triggers instantiations
-      assert(forall (i:nat{0 < i /\ i < length hm''}). slot_s_inv len (offset + i) (index hm'' i));
-      assert(index hm 0 == slot); // Triggers instantiations
-      assert(slot_s_inv len offset slot);
-      assert(slot_s_inv len offset slot');
-      assert(partial_hashMap_s_inv len offset hm'');
-      partial_hashMap_s_inv_implies_assoc_list_lem len offset (slot' :: hm');
-      // Proving that the key in `x` is different from all the other keys in
-      // the flattened map
-      assert(for_all (binding_neq x) slot');
-      for_all_append (binding_neq x) slot' (flatten hm');
-      assert(partial_hashMap_s_inv len (offset+1) hm');
-      binding_in_previous_slot_implies_neq #t len offset x (offset+1) hm';
-      assert(for_all (binding_neq x) (flatten hm'));
-      assert(for_all (binding_neq x) (flatten (slot' :: hm')))
-#pop-options
-
-val hashMap_s_inv_implies_assoc_list_lem
-  (#t : Type0) (hm : hashMap_s t) :
-  Lemma (requires (hashMap_s_inv hm))
-  (ensures (assoc_list_inv (flatten hm)))
-
-let hashMap_s_inv_implies_assoc_list_lem #t hm =
-  partial_hashMap_s_inv_implies_assoc_list_lem (length hm) 0 hm
-
-val hashMap_t_base_inv_implies_assoc_list_lem
-  (#t : Type0) (hm : hashMap_t t):
-  Lemma (requires (hashMap_t_base_inv hm))
-  (ensures (assoc_list_inv (hashMap_t_al_v hm)))
-
-let hashMap_t_base_inv_implies_assoc_list_lem #t hm =
-  hashMap_s_inv_implies_assoc_list_lem (hashMap_t_v hm)
-
-/// For some reason, we can't write the below [forall] directly in the [ensures]
-/// clause of the next lemma: it makes Z3 fails even with a huge rlimit.
-/// I have no idea what's going on.
-let hashMap_is_assoc_list
-  (#t : Type0) (ntable : hashMap_t t{length ntable.slots > 0})
-  (al : assoc_list t) : Type0 =
-  (forall (k:key). hashMap_t_find_s ntable k == assoc_list_find k al)
-
-let partial_hashMap_s_find
-  (#t : Type0) (len : usize{len > 0}) (offset : usize)
-  (hm : hashMap_s_nes t{offset + length hm = len})
-  (k : key{hash_mod_key k len >= offset}) : option t =
-  let i = hash_mod_key k len in
-  let slot = index hm (i - offset) in
-  slot_s_find k slot
-
-val not_same_hash_key_not_found_in_slot
-  (#t : Type0) (len : usize{len > 0})
-  (k : key)
-  (i : usize)
-  (slot : slot_s t) :
-  Lemma
-  (requires (
-    hash_mod_key k len <> i /\
-    slot_s_inv len i slot))
-  (ensures (slot_s_find k slot == None))
-
-#push-options "--fuel 1"
-let rec not_same_hash_key_not_found_in_slot #t len k i slot =
-  match slot with
-  | [] -> ()
-  | (k',v) :: slot' -> not_same_hash_key_not_found_in_slot len k i slot'
-#pop-options
-
-/// Small variation of [binding_in_previous_slot_implies_neq]: if the hash of
-/// a key links it to a previous slot, it can't be found in the slots after.
-val key_in_previous_slot_implies_not_found
-  (#t : Type0) (len : usize{len > 0})
-  (k : key)
-  (offset : usize)
-  (slots : hashMap_s t{offset + length slots = len}) :
-  Lemma
-  (requires (
-    // The binding comes from a slot not in [slots]
-    hash_mod_key k len < offset /\
-    // The slots are the well-formed suffix of a hash map
-    partial_hashMap_s_inv len offset slots))
-  (ensures (
-    assoc_list_find k (flatten slots) == None))
-  (decreases slots)
-
-#push-options "--fuel 1"
-let rec key_in_previous_slot_implies_not_found #t len k offset slots =
-  match slots with
-  | [] -> ()
-  | slot :: slots' ->
-    find_append (same_key k) slot (flatten slots');
-    assert(index slots 0 == slot); // Triggers instantiations
-    not_same_hash_key_not_found_in_slot #t len k offset slot;
-    assert(assoc_list_find k slot == None);
-    assert(forall (i:nat{i < length slots'}). index slots' i == index slots (i+1)); // Triggers instantiations
-    key_in_previous_slot_implies_not_found len k (offset+1) slots'
-#pop-options  
-
-val partial_hashMap_s_is_assoc_list_lem
-  (#t : Type0) (len : usize{len > 0}) (offset : usize)
-  (hm : hashMap_s_nes t{offset + length hm = len})
-  (k : key{hash_mod_key k len >= offset}) :
-  Lemma
-  (requires (
-    partial_hashMap_s_inv len offset hm))
-  (ensures (
-    partial_hashMap_s_find len offset hm k == assoc_list_find k (flatten hm)))
-  (decreases hm)
-
-#push-options "--fuel 1"
-let rec partial_hashMap_s_is_assoc_list_lem #t len offset hm k =
-  match hm with
-  | [] -> ()
-  | slot :: hm' ->
-    let h = hash_mod_key k len in
-    let i = h - offset in
-    if i = 0 then
-      begin
-      // We must look in the current slot
-      assert(partial_hashMap_s_find len offset hm k == slot_s_find k slot);
-      find_append (same_key k) slot (flatten hm');
-      assert(forall (i:nat{i < length hm'}). index hm' i == index hm (i+1)); // Triggers instantiations
-      key_in_previous_slot_implies_not_found #t len k (offset+1) hm';
-      assert( // Of course, writing `== None` doesn't work...
-        match find (same_key k) (flatten hm') with
-        | None -> True
-        | Some _ -> False);
-      assert(
-        find (same_key k) (flatten hm) ==
-        begin match find (same_key k) slot with
-        | Some x -> Some x
-        | None -> find (same_key k) (flatten hm')
-        end);
-      ()
-      end
-    else
-      begin
-      // We must ignore the current slot
-      assert(partial_hashMap_s_find len offset hm k ==
-             partial_hashMap_s_find len (offset+1) hm' k);
-      find_append (same_key k) slot (flatten hm');
-      assert(index hm 0 == slot); // Triggers instantiations
-      not_same_hash_key_not_found_in_slot #t len k offset slot;
-      assert(forall (i:nat{i < length hm'}). index hm' i == index hm (i+1)); // Triggers instantiations
-      partial_hashMap_s_is_assoc_list_lem #t len (offset+1) hm' k
-      end
-#pop-options
-
-val hashMap_is_assoc_list_lem (#t : Type0) (hm : hashMap_t t) :
-  Lemma (requires (hashMap_t_base_inv hm))
-  (ensures (hashMap_is_assoc_list hm (hashMap_t_al_v hm)))
-
-let hashMap_is_assoc_list_lem #t hm =
-  let aux (k:key) :
-    Lemma (hashMap_t_find_s hm k == assoc_list_find k (hashMap_t_al_v hm))
-    [SMTPat (hashMap_t_find_s hm k)] =
-    let hm_v = hashMap_t_v hm in
-    let len = length hm_v in
-    partial_hashMap_s_is_assoc_list_lem #t len 0 hm_v k
-  in
-  ()
-
-/// The final lemma about [move_elements]: calling it on an empty hash table moves
-/// all the elements to this empty table.
-val hashMap_move_elements_lem
-  (t : Type0) (ntable : hashMap_t t) (slots : alloc_vec_Vec (list_t t)) :
-  Lemma
-  (requires (
-    let al = flatten (slots_t_v slots) in
-    hashMap_t_base_inv ntable /\
-    length al <= usize_max /\
-    assoc_list_inv al /\
-    // The table is empty
-    hashMap_t_len_s ntable = 0 /\
-    (forall (k:key). hashMap_t_find_s ntable k  == None)))
-  (ensures (
-    let al = flatten (slots_t_v slots) in
-    match hashMap_move_elements t ntable slots 0,
-          hashMap_move_elements_s_flat (hashMap_t_v ntable) al
-    with
-    | Return (ntable', _), Return ntable'_v ->
-      // The invariant is preserved
-      hashMap_t_base_inv ntable' /\
-      // We preserved the parameters
-      hashMap_t_same_params ntable' ntable /\
-      // The table has the same number of slots
-      length ntable'.slots = length ntable.slots /\
-      // The count is good
-      hashMap_t_len_s ntable' = length al /\
-      // The table can be linked to its model (we need this only to reveal
-      // "pretty" functional lemmas to the user in the fsti - so that we
-      // can write lemmas with SMT patterns - this is very F* specific)
-      hashMap_t_v ntable' == ntable'_v /\
-      // The new table contains exactly all the bindings from the slots
-      // Rk.: see the comment for [hashMap_is_assoc_list]
-      hashMap_is_assoc_list ntable' al
-    | _ -> False // We can only succeed
-    ))
-
-// Weird, dirty things happen below.
-// Manually unfolding some postconditions allowed to make the proof pass,
-// and also revealed the reason why some proofs failed with "Unknown assertion
-// failed" (resulting in the call to [flatten_0_is_flatten] for instance).
-// I think manually unfolding the postconditions allowed to account for the
-// lack of ifuel (this kind of proofs is annoying, really).
-#restart-solver
-#push-options "--z3rlimit 100"
-let hashMap_move_elements_lem t ntable slots =
-  let ntable_v = hashMap_t_v ntable in
-  let slots_v = slots_t_v slots in
-  let al = flatten slots_v in
-  hashMap_move_elements_lem_refin t ntable slots 0;
-  begin
-  match hashMap_move_elements t ntable slots 0,
-        hashMap_move_elements_s ntable_v slots_v 0
-  with
-  | Fail _, Fail _ -> ()
-  | Return (ntable', _), Return ntable'_v ->
-    assert(hashMap_t_base_inv ntable');
-    assert(hashMap_t_v ntable' == ntable'_v)
-  | _ -> assert(False)
-  end;
-  hashMap_move_elements_s_lem_refin_flat ntable_v slots_v 0;
-  begin
-  match hashMap_move_elements_s ntable_v slots_v 0,
-        hashMap_move_elements_s_flat ntable_v (flatten_i slots_v 0)
-  with
-  | Fail _, Fail _ -> ()
-  | Return hm, Return hm' -> assert(hm == hm')
-  | _ -> assert(False)
-  end;
-  flatten_0_is_flatten slots_v; // flatten_i slots_v 0 == flatten slots_v
-  hashMap_move_elements_s_flat_lem ntable_v al;
-  match hashMap_move_elements t ntable slots 0,
-        hashMap_move_elements_s_flat ntable_v al
-  with
-  | Return (ntable', _), Return ntable'_v ->
-    assert(hashMap_t_base_inv ntable');
-    assert(length ntable'.slots = length ntable.slots);
-    assert(hashMap_t_len_s ntable' = length al);
-    assert(hashMap_t_v ntable' == ntable'_v);
-    assert(hashMap_is_assoc_list ntable' al)
-  | _ -> assert(False)
-#pop-options
-
-(*** try_resize *)
-
-/// High-level model 1.
-/// This is one is slightly "crude": we just simplify a bit the function.
-
-let hashMap_try_resize_s_simpl
-  (#t : Type0)
-  (hm : hashMap_t t) :
-  Pure  (result (hashMap_t t))
-  (requires (
-    let (divid, divis) = hm.max_load_factor in
-    divid > 0 /\ divis > 0))
-  (ensures (fun _ -> True)) =
-  let capacity = length hm.slots in
-  let (divid, divis) = hm.max_load_factor in
-  if capacity <= (usize_max / 2) / divid then
-    let ncapacity : usize = capacity * 2 in
-    begin match hashMap_new_with_capacity t ncapacity divid divis with
-    | Fail e -> Fail e
-    | Return ntable ->
-      match hashMap_move_elements t ntable hm.slots 0 with
-      | Fail e -> Fail e
-      | Return (ntable', _) ->
-        let hm =
-          { hm with slots = ntable'.slots;
-                    max_load = ntable'.max_load }
-        in
-        Return hm
-    end
-  else Return hm
-
-val hashMap_try_resize_lem_refin
-  (t : Type0) (self : hashMap_t t) :
-  Lemma
-  (requires (
-    let (divid, divis) = self.max_load_factor in
-    divid > 0 /\ divis > 0))
-  (ensures (
-    match hashMap_try_resize t self,
-          hashMap_try_resize_s_simpl self
-    with
-    | Fail _, Fail _ -> True
-    | Return hm1, Return hm2 -> hm1 == hm2
-    | _ -> False))
-
-let hashMap_try_resize_lem_refin t self = ()
-
-/// Isolating arithmetic proofs
-
-let gt_lem0 (n m q : nat) :
-  Lemma (requires (m > 0 /\ n > q))
-  (ensures (n * m > q * m)) = ()
-
-let ge_lem0 (n m q : nat) :
-  Lemma (requires (m > 0 /\ n >= q))
-  (ensures (n * m >= q * m)) = ()
-
-let gt_ge_trans (n m p : nat) :
-  Lemma (requires (n > m /\ m >= p)) (ensures (n > p)) = ()
-
-let ge_trans (n m p : nat) :
-  Lemma (requires (n >= m /\ m >= p)) (ensures (n >= p)) = ()
-
-#push-options "--z3rlimit 200"
-let gt_lem1 (n m q : nat) :
-  Lemma (requires (m > 0 /\ n > q / m)) (ensures (n * m > q)) =
-  assert(n >= q / m + 1);
-  ge_lem0 n m (q / m + 1);
-  assert(n * m >= (q / m) * m + m)
-#pop-options
-
-let gt_lem2 (n m p q : nat) :
-  Lemma (requires (m > 0 /\ p > 0 /\ n > (q / m) / p)) (ensures (n * m * p > q)) =
-  gt_lem1 n p (q / m);
-  assert(n * p > q / m);
-  gt_lem1 (n * p) m q
-
-let ge_lem1 (n m q : nat) :
-  Lemma (requires (n >= m /\ q > 0))
-  (ensures (n / q >= m / q)) =
-  FStar.Math.Lemmas.lemma_div_le m n q
-
-#restart-solver
-#push-options "--z3rlimit 200"
-let times_divid_lem (n m p : pos) : Lemma ((n * m) / p >= n * (m / p))
-  =
-  FStar.Math.Lemmas.multiply_fractions m p;
-  assert(m >= (m / p) * p);
-  assert(n * m >= n * (m / p) * p); //
-  ge_lem1 (n * m) (n * (m / p) * p) p;
-  assert((n * m) / p >= (n * (m / p) * p) / p);
-  assert(n * (m / p) * p = (n * (m / p)) * p);
-  FStar.Math.Lemmas.cancel_mul_div (n * (m / p)) p;
-  assert(((n * (m / p)) * p) / p = n * (m / p))
-#pop-options
-
-/// The good old arithmetic proofs and their unstability...
-/// At some point I thought it was stable because it worked with `--quake 100`.
-/// Of course, it broke the next time I checked the file...
-/// It seems things are ok when we check this proof on its own, but not when
-/// it is sent at the same time as the one above (though we put #restart-solver!).
-/// I also tried `--quake 1/100` to no avail: it seems that when Z3 decides to
-/// fail the first one, it fails them all. I inserted #restart-solver before
-/// the previous lemma to see if it had an effect (of course not).
-val new_max_load_lem
-  (len : usize) (capacity : usize{capacity > 0})
-  (divid : usize{divid > 0}) (divis : usize{divis > 0}) :
-  Lemma
-  (requires (
-    let max_load = (capacity * divid) / divis in
-    let ncapacity = 2 * capacity in
-    let nmax_load = (ncapacity * divid) / divis in
-    capacity > 0 /\ 0 < divid /\ divid < divis /\
-    capacity * divid >= divis /\
-    len = max_load + 1))
-  (ensures (
-    let max_load = (capacity * divid) / divis in
-    let ncapacity = 2 * capacity in
-    let nmax_load = (ncapacity * divid) / divis in
-    len <= nmax_load))
-
-let mul_assoc (a b c : nat) : Lemma (a * b * c == a * (b * c)) = ()
-
-let ge_lem2 (a b c d : nat) : Lemma (requires (a >= b + c /\ c >= d)) (ensures (a >= b + d)) = ()
-let ge_div_lem1 (a b : nat) : Lemma (requires (a >= b /\ b > 0)) (ensures (a / b >= 1)) = ()
-
-#restart-solver
-#push-options "--z3rlimit 100 --z3cliopt smt.arith.nl=false"
-let new_max_load_lem len capacity divid divis =
-  FStar.Math.Lemmas.paren_mul_left 2 capacity divid;
-  mul_assoc 2 capacity divid;
-  // The following assertion often breaks though it is given by the above
-  // lemma. I really don't know what to do (I deactivated non-linear
-  // arithmetic and added the previous lemma call, moved the assertion up,
-  // boosted the rlimit...).
-  assert(2 * capacity * divid == 2 * (capacity * divid));
-  let max_load = (capacity * divid) / divis in
-  let ncapacity = 2 * capacity in
-  let nmax_load = (ncapacity * divid) / divis in
-  assert(nmax_load = (2 * capacity * divid) / divis);
-  times_divid_lem 2 (capacity * divid) divis;
-  assert((2 * (capacity * divid)) / divis >= 2 * ((capacity * divid) / divis));
-  assert(nmax_load >= 2 * ((capacity * divid) / divis));
-  assert(nmax_load >= 2 * max_load);
-  assert(nmax_load >= max_load + max_load);
-  ge_div_lem1 (capacity * divid) divis;
-  ge_lem2 nmax_load max_load max_load 1;
-  assert(nmax_load >= max_load + 1)
-#pop-options
-
-val hashMap_try_resize_s_simpl_lem (#t : Type0) (hm : hashMap_t t) :
-  Lemma
-  (requires (
-    // The base invariant is satisfied
-    hashMap_t_base_inv hm /\
-    // However, the "full" invariant is broken, as we call [try_resize]
-    // only if the current number of entries is > the max load.
-    // 
-    // There are two situations:
-    // - either we just reached the max load
-    // - or we were already saturated and can't resize
-    (let (dividend, divisor) = hm.max_load_factor in
-     hm.num_entries == hm.max_load + 1 \/
-     length hm.slots * 2 * dividend > usize_max)
-  ))
-  (ensures (
-    match hashMap_try_resize_s_simpl hm with
-    | Fail _ -> False
-    | Return hm' ->
-      // The full invariant is now satisfied (the full invariant is "base
-      // invariant" + the map is not overloaded (or can't be resized because
-      // already too big)
-      hashMap_t_inv hm' /\
-      // It contains the same bindings as the initial map
-      (forall (k:key). hashMap_t_find_s hm' k == hashMap_t_find_s hm k)))
-
-#restart-solver
-#push-options "--z3rlimit 400"
-let hashMap_try_resize_s_simpl_lem #t hm =
-  let capacity = length hm.slots in
-  let (divid, divis) = hm.max_load_factor in
-  if capacity <= (usize_max / 2) / divid then
-    begin
-    let ncapacity : usize = capacity * 2 in
-    assert(ncapacity * divid <= usize_max);
-    assert(hashMap_t_len_s hm = hm.max_load + 1);
-    new_max_load_lem (hashMap_t_len_s hm) capacity divid divis;
-    hashMap_new_with_capacity_lem t ncapacity divid divis;
-    match hashMap_new_with_capacity t ncapacity divid divis with
-    | Fail _ -> ()
-    | Return ntable ->
-      let slots = hm.slots in
-      let al = flatten (slots_t_v slots) in
-      // Proving that: length al = hm.num_entries
-      assert(al == flatten (map slot_t_v slots));
-      assert(al == flatten (map list_t_v slots));
-      assert(hashMap_t_al_v hm == flatten (hashMap_t_v hm));
-      assert(hashMap_t_al_v hm == flatten (map list_t_v hm.slots));
-      assert(al == hashMap_t_al_v hm);
-      assert(hashMap_t_base_inv ntable);
-      assert(length al = hm.num_entries);
-      assert(length al <= usize_max);
-      hashMap_t_base_inv_implies_assoc_list_lem hm;
-      assert(assoc_list_inv al);
-      assert(hashMap_t_len_s ntable = 0);
-      assert(forall (k:key). hashMap_t_find_s ntable k  == None);
-      hashMap_move_elements_lem t ntable hm.slots;
-      match hashMap_move_elements t ntable hm.slots 0 with
-      | Fail _ -> ()
-      | Return (ntable', _) ->
-        hashMap_is_assoc_list_lem hm;
-        assert(hashMap_is_assoc_list hm (hashMap_t_al_v hm));
-        let hm' =
-          { hm with slots = ntable'.slots;
-                    max_load = ntable'.max_load }
-        in
-        assert(hashMap_t_base_inv ntable');
-        assert(hashMap_t_base_inv hm');
-        assert(hashMap_t_len_s hm' = hashMap_t_len_s hm);
-        new_max_load_lem (hashMap_t_len_s hm') capacity divid divis;
-        assert(hashMap_t_len_s hm' <= hm'.max_load); // Requires a lemma
-        assert(hashMap_t_inv hm')
-    end
-  else
-    begin
-    gt_lem2 capacity 2 divid usize_max;
-    assert(capacity * 2 * divid > usize_max)
-    end
-#pop-options
-
-let hashMap_t_same_bindings  (#t : Type0) (hm hm' : hashMap_t_nes t) : Type0 =
-  forall (k:key). hashMap_t_find_s hm k == hashMap_t_find_s hm' k
-
-/// The final lemma about [try_resize]
-val hashMap_try_resize_lem (#t : Type0) (hm : hashMap_t t) :
-  Lemma
-  (requires (
-    hashMap_t_base_inv hm /\
-    // However, the "full" invariant is broken, as we call [try_resize]
-    // only if the current number of entries is > the max load.
-    // 
-    // There are two situations:
-    // - either we just reached the max load
-    // - or we were already saturated and can't resize
-    (let (dividend, divisor) = hm.max_load_factor in
-     hm.num_entries == hm.max_load + 1 \/
-     length hm.slots * 2 * dividend > usize_max)))
-  (ensures (
-    match hashMap_try_resize t hm with
-    | Fail _ -> False
-    | Return hm' ->
-      // The full invariant is now satisfied (the full invariant is "base
-      // invariant" + the map is not overloaded (or can't be resized because
-      // already too big)
-      hashMap_t_inv hm' /\
-      // The length is the same
-      hashMap_t_len_s hm' = hashMap_t_len_s hm /\
-      // It contains the same bindings as the initial map
-      hashMap_t_same_bindings hm' hm))
-
-let hashMap_try_resize_lem #t hm =
-  hashMap_try_resize_lem_refin t hm;
-  hashMap_try_resize_s_simpl_lem hm
-
-(*** insert *)
-
-/// The high-level model (very close to the original function: we don't need something
-/// very high level, just to clean it a bit)
-let hashMap_insert_s
-  (#t : Type0) (self : hashMap_t t) (key : usize) (value : t) :
-  result (hashMap_t t) =
-  match hashMap_insert_no_resize t self key value with
-  | Fail e -> Fail e
-  | Return hm' ->
-    if hashMap_t_len_s hm' > hm'.max_load then
-      hashMap_try_resize t hm'
-    else Return hm'
-
-val hashMap_insert_lem_refin
-  (t : Type0) (self : hashMap_t t) (key : usize) (value : t) :
-  Lemma (requires True)
-  (ensures (
-    match hashMap_insert t self key value,
-          hashMap_insert_s self key value
-    with
-    | Fail _, Fail _ -> True
-    | Return hm1, Return hm2 -> hm1 == hm2
-    | _ -> False))
-
-let hashMap_insert_lem_refin t self key value = ()
-
-/// Helper
-let hashMap_insert_bindings_lem
-  (t : Type0) (self : hashMap_t_nes t) (key : usize) (value : t)
-  (hm' hm'' : hashMap_t_nes t) :
-  Lemma
-  (requires (
-     hashMap_s_updated_binding (hashMap_t_v self) key
-                                (Some value) (hashMap_t_v hm') /\
-     hashMap_t_same_bindings hm' hm''))
-  (ensures (
-     hashMap_s_updated_binding (hashMap_t_v self) key
-                                (Some value) (hashMap_t_v hm'')))
-  = ()
-
-val hashMap_insert_lem_aux
-  (#t : Type0) (self : hashMap_t t) (key : usize) (value : t) :
-  Lemma (requires (hashMap_t_inv self))
-  (ensures (
-    match hashMap_insert t self key value with
-    | Fail _ ->
-      // We can fail only if:
-      // - the key is not in the map and we need to add it
-      // - we are already saturated
-      hashMap_t_len_s self = usize_max /\
-      None? (hashMap_t_find_s self key)
-    | Return hm' ->
-      // The invariant is preserved
-      hashMap_t_inv hm' /\
-      // [key] maps to [value] and the other bindings are preserved
-      hashMap_s_updated_binding (hashMap_t_v self) key (Some value) (hashMap_t_v hm') /\
-      // The length is incremented, iff we inserted a new key
-      (match hashMap_t_find_s self key with
-       | None -> hashMap_t_len_s hm' = hashMap_t_len_s self + 1
-       | Some _ -> hashMap_t_len_s hm' = hashMap_t_len_s self)))
-
-#restart-solver
-#push-options "--z3rlimit 200"
-let hashMap_insert_lem_aux #t self key value =
-  hashMap_insert_no_resize_lem_s t self key value;
-  hashMap_insert_no_resize_s_lem (hashMap_t_v self) key value;
-  match hashMap_insert_no_resize t self key value with
-  | Fail _ -> ()
-  | Return hm' ->
-    // Expanding the post of [hashMap_insert_no_resize_lem_s]
-    let self_v = hashMap_t_v self in
-    let hm'_v = Return?.v (hashMap_insert_no_resize_s self_v key value) in
-    assert(hashMap_t_base_inv hm');
-    assert(hashMap_t_same_params hm' self);
-    assert(hashMap_t_v hm' == hm'_v);
-    assert(hashMap_s_len hm'_v == hashMap_t_len_s hm');
-    // Expanding the post of [hashMap_insert_no_resize_s_lem]
-    assert(insert_post self_v key value hm'_v);
-    // Expanding [insert_post]
-    assert(hashMap_s_inv hm'_v);
-    assert(
-      match hashMap_s_find self_v key with
-      | None -> hashMap_s_len hm'_v = hashMap_s_len self_v + 1
-      | Some _ -> hashMap_s_len hm'_v = hashMap_s_len self_v);
-    if hashMap_t_len_s hm' > hm'.max_load then
-      begin
-      hashMap_try_resize_lem hm';
-      // Expanding the post of [hashMap_try_resize_lem]
-      let hm'' = Return?.v (hashMap_try_resize t hm') in
-      assert(hashMap_t_inv hm'');
-      let hm''_v = hashMap_t_v hm'' in
-      assert(forall k. hashMap_t_find_s hm'' k == hashMap_t_find_s hm' k);
-      assert(hashMap_t_len_s hm'' = hashMap_t_len_s hm'); // TODO
-      // Proving the post
-      assert(hashMap_t_inv hm'');
-      hashMap_insert_bindings_lem t self key value hm' hm'';
-      assert(
-        match hashMap_t_find_s self key with
-         | None -> hashMap_t_len_s hm'' = hashMap_t_len_s self + 1
-         | Some _ -> hashMap_t_len_s hm'' = hashMap_t_len_s self)
-      end
-    else ()
-#pop-options
-
-let hashMap_insert_lem #t self key value =
-  hashMap_insert_lem_aux #t self key value
-
-(*** contains_key *)
-
-(**** contains_key_in_list *)
-
-val hashMap_contains_key_in_list_lem
-  (#t : Type0) (key : usize) (ls : list_t t) :
-  Lemma
-  (ensures (
-    match hashMap_contains_key_in_list t key ls with
-    | Fail _ -> False
-    | Return b ->
-      b = Some? (slot_t_find_s key ls)))
-
-
-#push-options "--fuel 1"
-let rec hashMap_contains_key_in_list_lem #t key ls =
-  match ls with
-  | List_Cons ckey x ls0 ->
-    let b = ckey = key in
-    if b
-    then ()
-    else
-      begin
-      hashMap_contains_key_in_list_lem key ls0;
-      match hashMap_contains_key_in_list t key ls0 with
-      | Fail _ -> ()
-      | Return b0 -> ()
-      end
-  | List_Nil -> ()
-#pop-options
-
-(**** contains_key *)
-
-val hashMap_contains_key_lem_aux
-  (#t : Type0) (self : hashMap_t_nes t) (key : usize) :
-  Lemma
-  (ensures (
-    match hashMap_contains_key t self key with
-    | Fail _ -> False
-    | Return b -> b = Some? (hashMap_t_find_s self key)))
-
-let hashMap_contains_key_lem_aux #t self key =
-  begin match hash_key key with
-  | Fail _ -> ()
-  | Return i ->
-    let v = self.slots in
-    let i0 = alloc_vec_Vec_len (list_t t) v in
-    begin match usize_rem i i0 with
-    | Fail _ -> ()
-    | Return hash_mod ->
-      begin match alloc_vec_Vec_index_usize v hash_mod with
-      | Fail _ -> ()
-      | Return l ->
-        hashMap_contains_key_in_list_lem key l;
-        begin match hashMap_contains_key_in_list t key l with
-        | Fail _ -> ()
-        | Return b -> ()
-        end
-      end
-    end
-  end
-
-/// The lemma in the .fsti
-let hashMap_contains_key_lem #t self key =
-  hashMap_contains_key_lem_aux #t self key
-
-(*** get *)
-
-(**** get_in_list *)
-
-val hashMap_get_in_list_lem
-  (#t : Type0) (key : usize) (ls : list_t t) :
-  Lemma
-  (ensures (
-    match hashMap_get_in_list t key ls, slot_t_find_s key ls with
-    | Fail _, None -> True
-    | Return x, Some x' -> x == x'
-    | _ -> False))
-
-#push-options "--fuel 1"
-let rec hashMap_get_in_list_lem #t key ls =
-  begin match ls with
-  | List_Cons ckey cvalue ls0 ->
-    let b = ckey = key in
-    if b
-    then ()
-    else
-      begin
-      hashMap_get_in_list_lem key ls0;
-      match hashMap_get_in_list t key ls0 with
-      | Fail _ -> ()
-      | Return x -> ()
-      end
-  | List_Nil -> ()
-  end
-#pop-options
-
-(**** get *)
-
-val hashMap_get_lem_aux
-  (#t : Type0) (self : hashMap_t_nes t) (key : usize) :
-  Lemma
-  (ensures (
-    match hashMap_get t self key, hashMap_t_find_s self key with
-    | Fail _, None -> True
-    | Return x, Some x' -> x == x'
-    | _ -> False))
-
-let hashMap_get_lem_aux #t self key =
-  begin match hash_key key with
-  | Fail _ -> ()
-  | Return i ->
-    let v = self.slots in
-    let i0 = alloc_vec_Vec_len (list_t t) v in
-    begin match usize_rem i i0 with
-    | Fail _ -> ()
-    | Return hash_mod ->
-      begin match alloc_vec_Vec_index_usize v hash_mod with
-      | Fail _ -> ()
-      | Return l ->
-        begin
-        hashMap_get_in_list_lem key l;
-        match hashMap_get_in_list t key l with
-        | Fail _ -> ()
-        | Return x -> ()
-        end
-      end
-    end
-  end
-
-/// .fsti
-let hashMap_get_lem #t self key = hashMap_get_lem_aux #t self key
-
-(*** get_mut'fwd *)
-
-
-(**** get_mut_in_list'fwd *)
-
-val hashMap_get_mut_in_list_loop_lem
-  (#t : Type0) (ls : list_t t) (key : usize) :
-  Lemma
-  (ensures (
-    match hashMap_get_mut_in_list_loop t ls key, slot_t_find_s key ls with
-    | Fail _, None -> True
-    | Return x, Some x' -> x == x'
-    | _ -> False))
-
-#push-options "--fuel 1"
-let rec hashMap_get_mut_in_list_loop_lem #t ls key =
-  begin match ls with
-  | List_Cons ckey cvalue ls0 ->
-    let b = ckey = key in
-    if b
-    then ()
-    else
-      begin
-      hashMap_get_mut_in_list_loop_lem ls0 key;
-      match hashMap_get_mut_in_list_loop t ls0 key with
-      | Fail _ -> ()
-      | Return x -> ()
-      end
-  | List_Nil -> ()
-  end
-#pop-options
-
-(**** get_mut'fwd *)
-
-val hashMap_get_mut_lem_aux
-  (#t : Type0) (self : hashMap_t_nes t) (key : usize) :
-  Lemma
-  (ensures (
-    match hashMap_get_mut t self key, hashMap_t_find_s self key with
-    | Fail _, None -> True
-    | Return x, Some x' -> x == x'
-    | _ -> False))
-
-let hashMap_get_mut_lem_aux #t self key =
-  begin match hash_key key with
-  | Fail _ -> ()
-  | Return i ->
-    let v = self.slots in
-    let i0 = alloc_vec_Vec_len (list_t t) v in
-    begin match usize_rem i i0 with
-    | Fail _ -> ()
-    | Return hash_mod ->
-      begin match alloc_vec_Vec_index_usize v hash_mod with
-      | Fail _ -> ()
-      | Return l ->
-        begin
-        hashMap_get_mut_in_list_loop_lem l key;
-        match hashMap_get_mut_in_list_loop t l key with
-        | Fail _ -> ()
-        | Return x -> ()
-        end
-      end
-    end
-  end
-
-let hashMap_get_mut_lem #t self key =
-  hashMap_get_mut_lem_aux #t self key
-
-(*** get_mut'back *)
-
-(**** get_mut_in_list'back *)
-
-val hashMap_get_mut_in_list_loop_back_lem
-  (#t : Type0) (ls : list_t t) (key : usize) (ret : t) :
-  Lemma
-  (requires (Some? (slot_t_find_s key ls)))
-  (ensures (
-    match hashMap_get_mut_in_list_loop_back t ls key ret with
-    | Fail _ -> False
-    | Return ls' -> list_t_v ls' == find_update (same_key key) (list_t_v ls) (key,ret)
-    | _ -> False))
-
-#push-options "--fuel 1"
-let rec hashMap_get_mut_in_list_loop_back_lem #t ls key ret =
-  begin match ls with
-  | List_Cons ckey cvalue ls0 ->
-    let b = ckey = key in
-    if b
-    then let ls1 = List_Cons ckey ret ls0 in ()
-    else
-      begin
-      hashMap_get_mut_in_list_loop_back_lem ls0 key ret;
-      match hashMap_get_mut_in_list_loop_back t ls0 key ret with
-      | Fail _ -> ()
-      | Return l -> let ls1 = List_Cons ckey cvalue l in ()
-      end
-  | List_Nil -> ()
-  end
-#pop-options
-
-(**** get_mut'back *)
-
-/// Refinement lemma
-val hashMap_get_mut_back_lem_refin
-  (#t : Type0) (self : hashMap_t t{length self.slots > 0})
-  (key : usize) (ret : t) :
-  Lemma
-  (requires (Some? (hashMap_t_find_s self key)))
-  (ensures (
-    match hashMap_get_mut_back t self key ret with
-    | Fail _ -> False
-    | Return hm' ->
-      hashMap_t_v hm' == hashMap_insert_no_fail_s (hashMap_t_v self) key ret))
-
-let hashMap_get_mut_back_lem_refin #t self key ret =
-  begin match hash_key key with
-  | Fail _ -> ()
-  | Return i ->
-    let i0 = self.num_entries in
-    let p = self.max_load_factor in
-    let i1 = self.max_load in
-    let v = self.slots in
-    let i2 = alloc_vec_Vec_len (list_t t) v in
-    begin match usize_rem i i2 with
-    | Fail _ -> ()
-    | Return hash_mod ->
-      begin match alloc_vec_Vec_index_usize v hash_mod with
-      | Fail _ -> ()
-      | Return l ->
-        begin
-        hashMap_get_mut_in_list_loop_back_lem l key ret;
-        match hashMap_get_mut_in_list_loop_back t l key ret with
-        | Fail _ -> ()
-        | Return l0 ->
-          begin match alloc_vec_Vec_update_usize v hash_mod l0 with
-          | Fail _ -> ()
-          | Return v0 -> let self0 = MkhashMap_t i0 p i1 v0 in ()
-          end
-        end
-      end
-    end
-  end
-
-/// Final lemma
-val hashMap_get_mut_back_lem_aux
-  (#t : Type0) (hm : hashMap_t t)
-  (key : usize) (ret : t) :
-  Lemma
-  (requires (
-    hashMap_t_inv hm /\
-    Some? (hashMap_t_find_s hm key)))
-  (ensures (
-    match hashMap_get_mut_back t hm key ret with
-    | Fail _ -> False
-    | Return hm' ->
-      // Functional spec
-      hashMap_t_v hm' == hashMap_insert_no_fail_s (hashMap_t_v hm) key ret /\
-     // The invariant is preserved
-     hashMap_t_inv hm' /\
-     // The length is preserved
-     hashMap_t_len_s hm' = hashMap_t_len_s hm /\
-     // [key] maps to [value]
-     hashMap_t_find_s hm' key == Some ret /\
-     // The other bindings are preserved
-     (forall k'. k' <> key ==> hashMap_t_find_s hm' k' == hashMap_t_find_s hm k')))
-
-let hashMap_get_mut_back_lem_aux #t hm key ret =
-  let hm_v = hashMap_t_v hm in
-  hashMap_get_mut_back_lem_refin hm key ret;
-  match hashMap_get_mut_back t hm key ret with
-  | Fail _ -> assert(False)
-  | Return hm' ->
-    hashMap_insert_no_fail_s_lem hm_v key ret
-
-/// .fsti
-let hashMap_get_mut_back_lem #t hm key ret = hashMap_get_mut_back_lem_aux hm key ret
-
-(*** remove'fwd *)
-
-val hashMap_remove_from_list_lem
-  (#t : Type0) (key : usize) (ls : list_t t) :
-  Lemma
-  (ensures (
-    match hashMap_remove_from_list t key ls with
-    | Fail _ -> False
-    | Return opt_x ->
-      opt_x == slot_t_find_s key ls /\
-      (Some? opt_x ==> length (slot_t_v ls) > 0)))
-
-#push-options "--fuel 1"
-let rec hashMap_remove_from_list_lem #t key ls =
-  begin match ls with
-  | List_Cons ckey x tl ->
-    let b = ckey = key in
-    if b
-    then
-      let mv_ls = core_mem_replace (list_t t) (List_Cons ckey x tl) List_Nil in
-      begin match mv_ls with
-      | List_Cons i cvalue tl0 -> ()
-      | List_Nil -> ()
-      end
-    else
-      begin
-      hashMap_remove_from_list_lem key tl;
-      match hashMap_remove_from_list t key tl with
-      | Fail _ -> ()
-      | Return opt -> ()
-      end
-  | List_Nil -> ()
-  end
-#pop-options
-
-val hashMap_remove_lem_aux
-  (#t : Type0) (self : hashMap_t t) (key : usize) :
-  Lemma
-  (requires (
-    // We need the invariant to prove that upon decrementing the entries counter,
-    // the counter doesn't become negative
-    hashMap_t_inv self))
-  (ensures (
-    match hashMap_remove t self key with
-    | Fail _ -> False
-    | Return opt_x -> opt_x == hashMap_t_find_s self key))
-
-let hashMap_remove_lem_aux #t self key =
-  begin match hash_key key with
-  | Fail _ -> ()
-  | Return i ->
-    let i0 = self.num_entries in
-    let v = self.slots in
-    let i1 = alloc_vec_Vec_len (list_t t) v in
-    begin match usize_rem i i1 with
-    | Fail _ -> ()
-    | Return hash_mod ->
-      begin match alloc_vec_Vec_index_usize v hash_mod with
-      | Fail _ -> ()
-      | Return l ->
-        begin
-        hashMap_remove_from_list_lem key l;
-        match hashMap_remove_from_list t key l with
-        | Fail _ -> ()
-        | Return x ->
-          begin match x with
-          | None -> ()
-          | Some x0 ->
-            begin
-            assert(l == index v hash_mod);
-            assert(length (list_t_v #t l) > 0);
-            length_flatten_index (hashMap_t_v self) hash_mod;
-            match usize_sub i0 1 with
-            | Fail _ -> ()
-            | Return _ -> ()
-            end
-          end
-        end
-      end
-    end
-  end
-
-/// .fsti
-let hashMap_remove_lem #t self key = hashMap_remove_lem_aux #t self key
-
-(*** remove'back *)
-
-(**** Refinement proofs *)
-
-/// High-level model for [remove_from_list'back]
-let hashMap_remove_from_list_s
-  (#t : Type0) (key : usize) (ls : slot_s t) :
-  slot_s t =
-  filter_one (not_same_key key) ls
-
-/// Refinement lemma
-val hashMap_remove_from_list_back_lem_refin
-  (#t : Type0) (key : usize) (ls : list_t t) :
-  Lemma
-  (ensures (
-    match hashMap_remove_from_list_back t key ls with
-    | Fail _ -> False
-    | Return ls' ->
-      list_t_v ls' == hashMap_remove_from_list_s key (list_t_v ls) /\
-      // The length is decremented, iff the key was in the slot
-      (let len = length (list_t_v ls) in
-       let len' = length (list_t_v ls') in
-       match slot_s_find key (list_t_v ls) with
-       | None -> len = len'
-       | Some _ -> len = len' + 1)))
-
-#push-options "--fuel 1"
-let rec hashMap_remove_from_list_back_lem_refin #t key ls =
-  begin match ls with
-  | List_Cons ckey x tl ->
-    let b = ckey = key in
-    if b
-    then
-      let mv_ls = core_mem_replace (list_t t) (List_Cons ckey x tl) List_Nil in
-      begin match mv_ls with
-      | List_Cons i cvalue tl0 -> ()
-      | List_Nil -> ()
-      end
-    else
-      begin
-      hashMap_remove_from_list_back_lem_refin key tl;
-      match hashMap_remove_from_list_back t key tl with
-      | Fail _ -> ()
-      | Return l -> let ls0 = List_Cons ckey x l in ()
-      end
-  | List_Nil -> ()
-  end
-#pop-options
-
-/// High-level model for [remove_from_list'back]
-let hashMap_remove_s
-  (#t : Type0) (self : hashMap_s_nes t) (key : usize) :
-  hashMap_s t =
-  let len = length self in
-  let hash = hash_mod_key key len in
-  let slot = index self hash in
-  let slot' = hashMap_remove_from_list_s key slot in
-  list_update self hash slot'
-
-/// Refinement lemma
-val hashMap_remove_back_lem_refin
-  (#t : Type0) (self : hashMap_t_nes t) (key : usize) :
-  Lemma
-  (requires (
-    // We need the invariant to prove that upon decrementing the entries counter,
-    // the counter doesn't become negative
-    hashMap_t_inv self))
-  (ensures (
-    match hashMap_remove_back t self key with
-    | Fail _ -> False
-    | Return hm' ->
-      hashMap_t_same_params hm' self /\
-      hashMap_t_v hm' == hashMap_remove_s (hashMap_t_v self) key /\
-      // The length is decremented iff the key was in the map
-      (let len = hashMap_t_len_s self in
-       let len' = hashMap_t_len_s hm' in
-       match hashMap_t_find_s self key with
-       | None -> len = len'
-       | Some _ -> len = len' + 1)))
-
-let hashMap_remove_back_lem_refin #t self key =
-  begin match hash_key key with
-  | Fail _ -> ()
-  | Return i ->
-    let i0 = self.num_entries in
-    let p = self.max_load_factor in
-    let i1 = self.max_load in
-    let v = self.slots in
-    let i2 = alloc_vec_Vec_len (list_t t) v in
-    begin match usize_rem i i2 with
-    | Fail _ -> ()
-    | Return hash_mod ->
-      begin match alloc_vec_Vec_index_usize v hash_mod with
-      | Fail _ -> ()
-      | Return l ->
-        begin
-        hashMap_remove_from_list_lem key l;
-        match hashMap_remove_from_list t key l with
-        | Fail _ -> ()
-        | Return x ->
-          begin match x with
-          | None ->
-            begin
-            hashMap_remove_from_list_back_lem_refin key l;
-            match hashMap_remove_from_list_back t key l with
-            | Fail _ -> ()
-            | Return l0 ->
-              begin
-              length_flatten_update (slots_t_v v) hash_mod (list_t_v l0);
-              match alloc_vec_Vec_update_usize v hash_mod l0 with
-              | Fail _ -> ()
-              | Return v0 -> ()
-              end
-            end
-          | Some x0 ->
-            begin
-            assert(l == index v hash_mod);
-            assert(length (list_t_v #t l) > 0);
-            length_flatten_index (hashMap_t_v self) hash_mod;
-            match usize_sub i0 1 with
-            | Fail _ -> ()
-            | Return i3 ->
-              begin
-              hashMap_remove_from_list_back_lem_refin key l;
-              match hashMap_remove_from_list_back t key l with
-              | Fail _ -> ()
-              | Return l0 ->
-                begin
-                length_flatten_update (slots_t_v v) hash_mod (list_t_v l0);
-                match alloc_vec_Vec_update_usize v hash_mod l0 with
-                | Fail _ -> ()
-                | Return v0 -> ()
-                end
-              end
-            end
-          end
-        end
-      end
-    end
-  end
-
-(**** Invariants, high-level properties *)
-
-val hashMap_remove_from_list_s_lem
-  (#t : Type0) (k : usize) (slot : slot_s t) (len : usize{len > 0}) (i : usize) :
-  Lemma
-  (requires (slot_s_inv len i slot))
-  (ensures (
-    let slot' = hashMap_remove_from_list_s k slot in
-    slot_s_inv len i slot' /\
-    slot_s_find k slot' == None /\
-    (forall (k':key{k' <> k}). slot_s_find k' slot' == slot_s_find k' slot) /\
-    // This postcondition is necessary to prove that the invariant is preserved
-    // in the recursive calls. This allows us to do the proof in one go.
-    (forall (b:binding t). for_all (binding_neq b) slot ==> for_all (binding_neq b) slot')
-  ))
-
-#push-options "--fuel 1"
-let rec hashMap_remove_from_list_s_lem #t key slot len i =
-  match slot with
-  | [] -> ()
-  | (k',v) :: slot' ->
-    if k' <> key then
-      begin
-      hashMap_remove_from_list_s_lem key slot' len i;
-      let slot'' = hashMap_remove_from_list_s key slot' in
-      assert(for_all (same_hash_mod_key len i) ((k',v)::slot''));
-      assert(for_all (binding_neq (k',v)) slot'); // Triggers instanciation
-      assert(for_all (binding_neq (k',v)) slot'')
-      end
-    else
-      begin
-      assert(for_all (binding_neq (k',v)) slot');
-      for_all_binding_neq_find_lem key v slot'
-      end
-#pop-options
-
-val hashMap_remove_s_lem
-  (#t : Type0) (self : hashMap_s_nes t) (key : usize) :
-  Lemma
-  (requires (hashMap_s_inv self))
-  (ensures (
-    let hm' = hashMap_remove_s self key in
-    // The invariant is preserved
-    hashMap_s_inv hm' /\
-    // We updated the binding
-    hashMap_s_updated_binding self key None hm'))
-
-let hashMap_remove_s_lem #t self key =
-  let len = length self in
-  let hash = hash_mod_key key len in
-  let slot = index self hash in
-  hashMap_remove_from_list_s_lem key slot len hash;
-  let slot' = hashMap_remove_from_list_s key slot in
-  let hm' = list_update self hash slot' in
-  assert(hashMap_s_inv self)
-
-/// Final lemma about [remove'back]
-val hashMap_remove_back_lem_aux
-  (#t : Type0) (self : hashMap_t t) (key : usize) :
-  Lemma
-  (requires (hashMap_t_inv self))
-  (ensures (
-    match hashMap_remove_back t self key with
-    | Fail _ -> False
-    | Return hm' ->
-      hashMap_t_inv self /\
-      hashMap_t_same_params hm' self /\
-      // We updated the binding
-      hashMap_s_updated_binding (hashMap_t_v self) key None (hashMap_t_v hm') /\
-      hashMap_t_v hm' == hashMap_remove_s (hashMap_t_v self) key /\
-      // The length is decremented iff the key was in the map
-      (let len = hashMap_t_len_s self in
-       let len' = hashMap_t_len_s hm' in
-       match hashMap_t_find_s self key with
-       | None -> len = len'
-       | Some _ -> len = len' + 1)))
-
-let hashMap_remove_back_lem_aux #t self key =
-  hashMap_remove_back_lem_refin self key;
-  hashMap_remove_s_lem (hashMap_t_v self) key
-
-/// .fsti
-let hashMap_remove_back_lem #t self key =
-  hashMap_remove_back_lem_aux #t self key
diff --git a/tests/fstar/hashmap/Hashmap.Properties.fsti b/tests/fstar/hashmap/Hashmap.Properties.fsti
deleted file mode 100644
index 26c0ec06..00000000
--- a/tests/fstar/hashmap/Hashmap.Properties.fsti
+++ /dev/null
@@ -1,267 +0,0 @@
-(** Properties about the hashmap *)
-module Hashmap.Properties
-open Primitives
-open FStar.List.Tot
-open FStar.Mul
-open Hashmap.Types
-open Hashmap.Clauses
-open Hashmap.Funs
-
-#set-options "--z3rlimit 50 --fuel 0 --ifuel 1"
-
-// Small trick to align the .fst and the .fsti
-val _align_fsti : unit
-
-(*** Utilities *)
-
-type key : eqtype = usize
-
-type hash : eqtype = usize
-
-val hashMap_t_inv (#t : Type0) (hm : hashMap_t t) : Type0
-
-val len_s (#t : Type0) (hm : hashMap_t t) : nat
-
-val find_s (#t : Type0) (hm : hashMap_t t) (k : key) : option t
-
-(*** Overloading *)
-
-/// Upon inserting *new* entries in the hash map, the slots vector is resized
-/// whenever we reach the max load, unless we can't resize anymore because
-/// there are already too many entries. This way, we maintain performance by
-/// limiting the hash collisions.
-/// This is expressed by the following property, which is maintained in the hash
-/// map invariant.
-val hashMap_not_overloaded_lem (#t : Type0) (hm : hashMap_t t) :
-  Lemma
-  (requires (hashMap_t_inv hm))
-  (ensures (
-    // The capacity is the number of slots
-    let capacity = length hm.slots in
-    // The max load factor defines a threshold on the number of entries:
-    // if there are more entries than a given fraction of the number of slots,
-    // we resize the slots vector to limit the hash collisions
-    let (dividend, divisor) = hm.max_load_factor in
-    // technicality: this postcondition won't typecheck if we don't reveal
-    // that divisor > 0 (because of the division)
-    divisor > 0 /\
-    begin
-    // The max load, computed as a fraction of the capacity
-    let max_load = (capacity * dividend) / divisor in
-    // The number of entries inserted in the map is given by [len_s] (see
-    // the functional correctness lemmas, which state how this number evolves):
-    let len = len_s hm in
-    // We prove that:
-    // - either the number of entries is <= than the max load threshold
-    len <= max_load
-    // - or we couldn't resize the map, because then the arithmetic computations
-    //   would overflow (note that we always multiply the number of slots by 2)
-    || 2* capacity * dividend > usize_max
-    end))
-
-(*** Functional correctness *)
-(**** [new'fwd] *)
-
-/// [new] doesn't fail and returns an empty hash map
-val hashMap_new_lem (t : Type0) :
-  Lemma
-  (ensures (
-    match hashMap_new t with
-    | Fail _ -> False
-    | Return hm ->
-      // The hash map invariant is satisfied
-      hashMap_t_inv hm /\
-      // The hash map has a length of 0
-      len_s hm = 0 /\
-      // It contains no bindings
-      (forall k. find_s hm k == None)))
-
-(**** [clear] *)
-
-/// [clear] doesn't fail and turns the hash map into an empty map
-val hashMap_clear_lem
-  (#t : Type0) (self : hashMap_t t) :
-  Lemma
-  (requires (hashMap_t_inv self))
-  (ensures (
-    match hashMap_clear t self with
-    | Fail _ -> False
-    | Return hm ->
-      // The hash map invariant is satisfied
-      hashMap_t_inv hm /\
-      // The hash map has a length of 0
-      len_s hm = 0 /\
-      // It contains no bindings
-      (forall k. find_s hm k == None)))
-
-(**** [len] *)
-
-/// [len] can't fail and returns the length (the number of elements) of the hash map
-val hashMap_len_lem (#t : Type0) (self : hashMap_t t) :
-  Lemma
-  (requires (hashMap_t_inv self))
-  (ensures (
-    match hashMap_len t self with
-    | Fail _ -> False
-    | Return l -> l = len_s self))
-
-
-(**** [insert'fwd_back] *)
-
-/// The backward function for [insert] (note it is named "...insert'fwd_back" because
-/// the forward function doesn't return anything, and was thus filtered - in a
-/// sense the effect of applying the forward function then the backward function is
-/// entirely encompassed by the effect of the backward function alone).
-/// 
-/// [insert'fwd_back] simply inserts a binding.
-val hashMap_insert_lem
-  (#t : Type0) (self : hashMap_t t) (key : usize) (value : t) :
-  Lemma
-  (requires (hashMap_t_inv self))
-  (ensures (
-    match hashMap_insert t self key value with
-    | Fail _ ->
-      // We can fail only if:
-      // - the key is not in the map and we thus need to add it
-      None? (find_s self key) /\
-      // - and we are already saturated (we can't increment the internal counter)
-      len_s self = usize_max
-    | Return hm' ->
-      // The invariant is preserved
-      hashMap_t_inv hm' /\
-      // [key] maps to [value]
-      find_s hm' key == Some value /\
-      // The other bindings are preserved
-      (forall k'. k' <> key ==> find_s hm' k' == find_s self k') /\
-      begin
-      // The length is incremented, iff we inserted a new key
-      match find_s self key with
-      | None -> len_s hm' = len_s self + 1
-      | Some _ -> len_s hm' = len_s self
-      end))
-
-
-(**** [contains_key] *)
-
-/// [contains_key'fwd] can't fail and returns `true` if and only if there is
-/// a binding for key [key]
-val hashMap_contains_key_lem
-  (#t : Type0) (self : hashMap_t t) (key : usize) :
-  Lemma
-  (requires (hashMap_t_inv self))
-  (ensures (
-    match hashMap_contains_key t self key with
-    | Fail _ -> False
-    | Return b -> b = Some? (find_s self key)))
-
-(**** [get'fwd] *)
-
-/// [get] returns (a shared borrow to) the binding for key [key]
-val hashMap_get_lem
-  (#t : Type0) (self : hashMap_t t) (key : usize) :
-  Lemma
-  (requires (hashMap_t_inv self))
-  (ensures (
-    match hashMap_get t self key, find_s self key with
-    | Fail _, None -> True
-    | Return x, Some x' -> x == x'
-    | _ -> False))
-
-(**** [get_mut'fwd] *)
-
-/// [get_mut'fwd] returns (a mutable borrow to) the binding for key [key].
-/// 
-/// The *forward* function models the action of getting a borrow to an element
-/// in Rust, which gives the possibility of modifying this element in place. Then,
-/// upon ending the borrow, the effect of the modification is modelled in the
-/// translation through a call to the backward function.
-val hashMap_get_mut_lem
-  (#t : Type0) (self : hashMap_t t) (key : usize) :
-  Lemma
-  (requires (hashMap_t_inv self))
-  (ensures (
-    match hashMap_get_mut t self key, find_s self key with
-    | Fail _, None -> True
-    | Return x, Some x' -> x == x'
-    | _ -> False))
-
-
-(**** [get_mut'back] *)
-
-/// [get_mut'back] updates the binding for key [key], without failing.
-/// A call to [get_mut'back] must follow a call to [get_mut'fwd], which gives
-/// us that there must be a binding for key [key] in the map (otherwise we
-/// can't prove the absence of failure).
-val hashMap_get_mut_back_lem
-  (#t : Type0) (hm : hashMap_t t) (key : usize) (ret : t) :
-  Lemma
-  (requires (
-    hashMap_t_inv hm /\
-    // A call to the backward function must follow a call to the forward
-    // function, whose success gives us that there is a binding for the key.
-    // In the case of *forward* functions, "success" has to be understood as
-    // the absence of panics. When translating code from Rust to pure lambda
-    // calculus, we have the property that the generated calls to the backward
-    // functions can't fail (because their are preceded by calls to forward
-    // functions, which must then have succeeded before): for a backward function,
-    // "failure" is to be understood as the semantics getting stuck.
-    // This is of course true unless we filtered the call to the forward function
-    // because its effect is encompassed by the backward function, as with
-    // [hashMap_clear]).
-    Some? (find_s hm key)))
-  (ensures (
-    match hashMap_get_mut_back t hm key ret with
-    | Fail _ -> False // Can't fail
-    | Return hm' ->
-     // The invariant is preserved
-     hashMap_t_inv hm' /\
-     // The length is preserved
-     len_s hm' = len_s hm /\
-     // [key] maps to the update value, [ret]
-     find_s hm' key == Some ret /\
-     // The other bindings are preserved
-     (forall k'. k' <> key ==> find_s hm' k' == find_s hm k')))
-
-(**** [remove'fwd] *)
-
-/// [remove'fwd] returns the (optional) element which has been removed from the map
-/// (the rust function *moves* it out of the map). Note that the effect of the update
-/// on the map is modelles through the call to [remove'back] ([remove] takes a
-/// mutable borrow to the hash map as parameter).
-val hashMap_remove_lem
-  (#t : Type0) (self : hashMap_t t) (key : usize) :
-  Lemma
-  (requires (hashMap_t_inv self))
-  (ensures (
-    match hashMap_remove t self key with
-    | Fail _ -> False
-    | Return opt_x -> opt_x == find_s self key))
-
-
-(**** [remove'back] *)
-
-/// The hash map given as parameter to [remove] is given through a mutable borrow:
-/// hence the backward function which gives back the updated map, without the
-/// binding.
-val hashMap_remove_back_lem
-  (#t : Type0) (self : hashMap_t t) (key : usize) :
-  Lemma
-  (requires (hashMap_t_inv self))
-  (ensures (
-    match hashMap_remove_back t self key with
-    | Fail _ -> False
-    | Return hm' ->
-      // The invariant is preserved
-      hashMap_t_inv self /\
-      // The binding for [key] is not there anymore
-      find_s hm' key == None /\
-      // The other bindings are preserved
-      (forall k'. k' <> key ==> find_s hm' k' == find_s self k') /\
-      begin
-      // The length is decremented iff the key was in the map
-      let len = len_s self in
-      let len' = len_s hm' in
-      match find_s self key with
-      | None -> len = len'
-      | Some _ -> len = len' + 1
-      end))
diff --git a/tests/fstar/hashmap/Primitives.fst b/tests/fstar/hashmap/Primitives.fst
index a3ffbde4..fca80829 100644
--- a/tests/fstar/hashmap/Primitives.fst
+++ b/tests/fstar/hashmap/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 = (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 *)
@@ -535,10 +531,18 @@ let array_index_usize (a : Type0) (n : usize) (x : array a n) (i : usize) : resu
   if i < length x then Return (index x i)
   else Fail Failure
 
-let array_update_usize (a : Type0) (n : usize) (x : array a n) (i : usize) (nx : a) : result (array a n) =
+let array_update_usize (a : Type0) (n : usize) (x : array a n) (i : usize) (nx : a) :
+  result (array a n) =
   if i < length x then Return (list_update x i nx)
   else Fail Failure
 
+let array_index_mut_usize (a : Type0) (n : usize) (x : array a n) (i : usize) :
+  result (a & (a -> result (array a n))) =
+  match array_index_usize a n x i with
+  | Fail e -> Fail e
+  | Return v ->
+    Return (v, array_update_usize a n x i)
+
 (*** Slice *)
 type slice (a : Type0) = s:list a{length s <= usize_max}
 
@@ -552,6 +556,13 @@ let slice_update_usize (a : Type0) (x : slice a) (i : usize) (nx : a) : result (
   if i < length x then Return (list_update x i nx)
   else Fail Failure
 
+let slice_index_mut_usize (a : Type0) (s : slice a) (i : usize) :
+  result (a & (a -> result (slice a))) =
+  match slice_index_usize a s i with
+  | Fail e -> Fail e
+  | Return x ->
+    Return (x, slice_update_usize a s i)
+
 (*** Subslices *)
 
 let array_to_slice (a : Type0) (n : usize) (x : array a n) : result (slice a) = Return x
@@ -559,6 +570,10 @@ let array_from_slice (a : Type0) (n : usize) (x : array a n) (s : slice a) : res
   if length s = n then Return s
   else Fail Failure
 
+let array_to_slice_mut (a : Type0) (n : usize) (x : array a n) :
+  result (slice a & (slice a -> result (array a n))) =
+  Return (x, array_from_slice a n x)
+
 // TODO: finish the definitions below (there lacks [List.drop] and [List.take] in the standard library *)
 let array_subslice (a : Type0) (n : usize) (x : array a n) (r : core_ops_range_Range usize) : result (slice a) =
   admit()
@@ -588,8 +603,13 @@ 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 +625,6 @@ 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 +636,11 @@ 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 +658,8 @@ 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 +684,16 @@ 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 +703,8 @@ 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 +718,10 @@ 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 +738,6 @@ 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 +754,6 @@ 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 +762,8 @@ 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 +781,8 @@ 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 +796,10 @@ 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 +809,8 @@ 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 +827,6 @@ 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 +842,7 @@ 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()