Update the failing proofs

12 files changed, 1003 insertions, 1699 deletions

diff --git a/tests/fstar/array/Array.Opaque.fsti b/tests/fstar/array/Array.Opaque.fsti
deleted file mode 100644
index 484cb9ee..00000000
--- a/tests/fstar/array/Array.Opaque.fsti
+++ /dev/null
@@ -1,24 +0,0 @@
-(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
-(** [array]: external function declarations *)
-module Array.Opaque
-open Primitives
-include Array.Types
-
-#set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
-
-(** [core::array::[T; N]::{15}::index]: forward function *)
-val core_array_[T; N]_index_fwd
-  (t i : Type0) (n : usize) (inst : core_ops_index_Index (slice t) i) :
-  array t n -> i -> result inst.core_ops_index_Index_Output
-
-(** [core::array::[T; N]::{16}::index_mut]: forward function *)
-val core_array_[T; N]_index_mut_fwd
-  (t i : Type0) (n : usize) (inst : core_ops_index_IndexMut (slice t) i) :
-  array t n -> i -> result inst.index_inst.core_ops_index_Index_Output
-
-(** [core::array::[T; N]::{16}::index_mut]: backward function 0 *)
-val core_array_[T; N]_index_mut_back
-  (t i : Type0) (n : usize) (inst : core_ops_index_IndexMut (slice t) i) :
-  array t n -> i -> inst.index_inst.core_ops_index_Index_Output -> result
-    (array t n)
-
diff --git a/tests/fstar/array/Primitives.fst b/tests/fstar/array/Primitives.fst
index 71d75c11..3297803c 100644
--- a/tests/fstar/array/Primitives.fst
+++ b/tests/fstar/array/Primitives.fst
@@ -427,7 +427,7 @@ let alloc_vec_Vec_new (a  : Type0) : alloc_vec_Vec a = assert_norm(length #a []
 let alloc_vec_Vec_len (a : Type0) (v : alloc_vec_Vec a) : usize = length v
 
 // Helper
-let alloc_vec_Vec_index_usize (#a : Type0) (v : alloc_vec_Vec a) (i : usize) (x : a) : result a =
+let alloc_vec_Vec_index_usize (#a : Type0) (v : alloc_vec_Vec a) (i : usize) : result a =
   if i < length v then Return (index v i) else Fail Failure
 // Helper
 let alloc_vec_Vec_update_usize (#a : Type0) (v : alloc_vec_Vec a) (i : usize) (x : a) : result (alloc_vec_Vec a) =
@@ -704,6 +704,22 @@ let alloc_vec_Vec_coreopsindexIndexMutInst (t idx : Type0)
 
 (*** Theorems *)
 
+let alloc_vec_Vec_index_eq (#a : Type0) (v : alloc_vec_Vec a) (i : usize) :
+  Lemma (
+    alloc_vec_Vec_index a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i ==
+      alloc_vec_Vec_index_usize v i)
+  [SMTPat (alloc_vec_Vec_index a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i)]
+  =
+  admit()
+
+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_usize_coresliceindexSliceIndexInst a) v i ==
+      alloc_vec_Vec_index_usize v i)
+  [SMTPat (alloc_vec_Vec_index_mut a usize (core_slice_index_usize_coresliceindexSliceIndexInst 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_usize_coresliceindexSliceIndexInst a) v i x ==
diff --git a/tests/fstar/betree/Primitives.fst b/tests/fstar/betree/Primitives.fst
index 71d75c11..3297803c 100644
--- a/tests/fstar/betree/Primitives.fst
+++ b/tests/fstar/betree/Primitives.fst
@@ -427,7 +427,7 @@ let alloc_vec_Vec_new (a  : Type0) : alloc_vec_Vec a = assert_norm(length #a []
 let alloc_vec_Vec_len (a : Type0) (v : alloc_vec_Vec a) : usize = length v
 
 // Helper
-let alloc_vec_Vec_index_usize (#a : Type0) (v : alloc_vec_Vec a) (i : usize) (x : a) : result a =
+let alloc_vec_Vec_index_usize (#a : Type0) (v : alloc_vec_Vec a) (i : usize) : result a =
   if i < length v then Return (index v i) else Fail Failure
 // Helper
 let alloc_vec_Vec_update_usize (#a : Type0) (v : alloc_vec_Vec a) (i : usize) (x : a) : result (alloc_vec_Vec a) =
@@ -704,6 +704,22 @@ let alloc_vec_Vec_coreopsindexIndexMutInst (t idx : Type0)
 
 (*** Theorems *)
 
+let alloc_vec_Vec_index_eq (#a : Type0) (v : alloc_vec_Vec a) (i : usize) :
+  Lemma (
+    alloc_vec_Vec_index a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i ==
+      alloc_vec_Vec_index_usize v i)
+  [SMTPat (alloc_vec_Vec_index a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i)]
+  =
+  admit()
+
+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_usize_coresliceindexSliceIndexInst a) v i ==
+      alloc_vec_Vec_index_usize v i)
+  [SMTPat (alloc_vec_Vec_index_mut a usize (core_slice_index_usize_coresliceindexSliceIndexInst 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_usize_coresliceindexSliceIndexInst a) v i x ==
diff --git a/tests/fstar/betree_back_stateful/Primitives.fst b/tests/fstar/betree_back_stateful/Primitives.fst
index 71d75c11..3297803c 100644
--- a/tests/fstar/betree_back_stateful/Primitives.fst
+++ b/tests/fstar/betree_back_stateful/Primitives.fst
@@ -427,7 +427,7 @@ let alloc_vec_Vec_new (a  : Type0) : alloc_vec_Vec a = assert_norm(length #a []
 let alloc_vec_Vec_len (a : Type0) (v : alloc_vec_Vec a) : usize = length v
 
 // Helper
-let alloc_vec_Vec_index_usize (#a : Type0) (v : alloc_vec_Vec a) (i : usize) (x : a) : result a =
+let alloc_vec_Vec_index_usize (#a : Type0) (v : alloc_vec_Vec a) (i : usize) : result a =
   if i < length v then Return (index v i) else Fail Failure
 // Helper
 let alloc_vec_Vec_update_usize (#a : Type0) (v : alloc_vec_Vec a) (i : usize) (x : a) : result (alloc_vec_Vec a) =
@@ -704,6 +704,22 @@ let alloc_vec_Vec_coreopsindexIndexMutInst (t idx : Type0)
 
 (*** Theorems *)
 
+let alloc_vec_Vec_index_eq (#a : Type0) (v : alloc_vec_Vec a) (i : usize) :
+  Lemma (
+    alloc_vec_Vec_index a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i ==
+      alloc_vec_Vec_index_usize v i)
+  [SMTPat (alloc_vec_Vec_index a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i)]
+  =
+  admit()
+
+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_usize_coresliceindexSliceIndexInst a) v i ==
+      alloc_vec_Vec_index_usize v i)
+  [SMTPat (alloc_vec_Vec_index_mut a usize (core_slice_index_usize_coresliceindexSliceIndexInst 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_usize_coresliceindexSliceIndexInst a) v i x ==
diff --git a/tests/fstar/hashmap/Hashmap.Properties.fst b/tests/fstar/hashmap/Hashmap.Properties.fst
index 49d96cd5..def520f0 100644
--- a/tests/fstar/hashmap/Hashmap.Properties.fst
+++ b/tests/fstar/hashmap/Hashmap.Properties.fst
@@ -272,7 +272,7 @@ type pos_usize = x:usize{x > 0}
 
 type binding (t : Type0) = key & t
 
-type slots_t (t : Type0) = vec (list_t 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)
@@ -280,8 +280,8 @@ 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
-  | ListNil -> []
-  | ListCons k v tl -> (k,v) :: list_t_v tl
+  | 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 =
@@ -305,30 +305,30 @@ let slots_t_al_v (#t : Type0) (slots : slots_t t) : assoc_list t =
 /// 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 hash_map_s t = list (slot_s t)
+type hashMap_s t = list (slot_s t)
 
 // TODO: why not always have the condition on the length?
 // 'nes': "non-empty slots"
-type hash_map_s_nes (t : Type0) : Type0 =
-  hm:hash_map_s t{is_pos_usize (length hm)}
+type hashMap_s_nes (t : Type0) : Type0 =
+  hm:hashMap_s t{is_pos_usize (length hm)}
 
-/// Representation function for [hash_map_t] as a list of slots
-let hash_map_t_v (#t : Type0) (hm : hash_map_t t) : hash_map_s t =
-  map list_t_v hm.hash_map_slots
+/// 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 [hash_map_t] as an associative list
-let hash_map_t_al_v (#t : Type0) (hm : hash_map_t t) : assoc_list t =
-  flatten (hash_map_t_v hm)
+/// 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 hash_map_t_nes (t : Type0) : Type0 =
-  hm:hash_map_t t{is_pos_usize (length hm.hash_map_slots)}
+type hashMap_t_nes (t : Type0) : Type0 =
+  hm:hashMap_t t{is_pos_usize (length hm.slots)}
 
-let hash_key (k : key) : hash =
-  Return?.v (hash_key_fwd k)
+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 k) % len
+  (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
@@ -339,8 +339,8 @@ let same_hash_mod_key (#t : Type0) (len : usize{len > 0}) (h : nat) (b : binding
 
 let binding_neq (#t : Type0) (b0 b1 : binding t) : bool = fst b0 <> fst b1
 
-let hash_map_t_len_s (#t : Type0) (hm : hash_map_t t) : nat =
-  hm.hash_map_num_entries
+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
@@ -354,26 +354,26 @@ 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 [hash_map_s].
-let hash_map_s_find
-  (#t : Type0) (hm : hash_map_s_nes t)
+// 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 hash_map_s_len
-  (#t : Type0) (hm : hash_map_s t) :
+let hashMap_s_len
+  (#t : Type0) (hm : hashMap_s t) :
   nat =
   length (flatten hm)
 
-// Same as above, but operates on [hash_map_t]
+// Same as above, but operates on [hashMap_t]
 // Note that we don't reuse the above function on purpose: converting to a
-// [hash_map_s] then looking up an element is not the same as what we
+// [hashMap_s] then looking up an element is not the same as what we
 // wrote below.
-let hash_map_t_find_s
-  (#t : Type0) (hm : hash_map_t t{length hm.hash_map_slots > 0}) (k : key) : option t =
-  let slots = hm.hash_map_slots in
+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
@@ -404,74 +404,74 @@ let slots_t_inv (#t : Type0) (slots : slots_t t{length slots <= usize_max}) : Ty
   {:pattern index slots i}
   slot_t_inv (length slots) i (index slots i)
 
-let hash_map_s_inv (#t : Type0) (hm : hash_map_s t) : Type0 =
+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 hash_map_t_base_inv (#t : Type0) (hm : hash_map_t t) : Type0 =
-  let al = hash_map_t_al_v hm in
+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 hash_map_num_entries has type `usize`)
-  hm.hash_map_num_entries = length al /\
+  // (because hashMap_num_entries has type `usize`)
+  hm.num_entries = length al /\
   // Slots invariant
-  slots_t_inv hm.hash_map_slots /\
+  slots_t_inv hm.slots /\
   // The capacity must be > 0 (otherwise we can't resize, because we
   // multiply the capacity by two!)
-  length hm.hash_map_slots > 0 /\
+  length hm.slots > 0 /\
   // Load computation
   begin
-  let capacity = length hm.hash_map_slots in
-  let (dividend, divisor) = hm.hash_map_max_load_factor in
+  let capacity = length hm.slots in
+  let (dividend, divisor) = hm.max_load_factor in
   0 < dividend /\ dividend < divisor /\
   capacity * dividend >= divisor /\
-  hm.hash_map_max_load = (capacity * dividend) / divisor
+  hm.max_load = (capacity * dividend) / divisor
   end
 
 /// We often need to frame some values
-let hash_map_t_same_params (#t : Type0) (hm0 hm1 : hash_map_t t) : Type0 =
-  length hm0.hash_map_slots = length hm1.hash_map_slots /\
-  hm0.hash_map_max_load = hm1.hash_map_max_load /\
-  hm0.hash_map_max_load_factor = hm1.hash_map_max_load_factor
+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 hash_map_t_inv (#t : Type0) (hm : hash_map_t t) : Type0 =
+let hashMap_t_inv (#t : Type0) (hm : hashMap_t t) : Type0 =
   // Base invariant
-  hash_map_t_base_inv hm /\
+  hashMap_t_base_inv hm /\
   // The hash map is either: not overloaded, or we can't resize it
   begin
-  let (dividend, divisor) = hm.hash_map_max_load_factor in
-  hm.hash_map_num_entries <= hm.hash_map_max_load
-  || length hm.hash_map_slots * 2 * dividend > usize_max
+  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 : hash_map_t t) : nat = hash_map_t_len_s hm
+let len_s (#t : Type0) (hm : hashMap_t t) : nat = hashMap_t_len_s hm
 
-/// This version doesn't take any precondition (contrary to [hash_map_t_find_s])
-let find_s (#t : Type0) (hm : hash_map_t t) (k : key) : option t =
-  if length hm.hash_map_slots = 0 then None
-  else hash_map_t_find_s hm k
+/// 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 hash_map_not_overloaded_lem #t hm = ()
+let hashMap_not_overloaded_lem #t hm = ()
 
 (*** allocate_slots *)
 
 /// Auxiliary lemma
 val slots_t_all_nil_inv_lem
-  (#t : Type0) (slots : vec (list_t t){length slots <= usize_max}) :
-  Lemma (requires (forall (i:nat{i < length slots}). index slots i == ListNil))
+  (#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"
@@ -479,8 +479,8 @@ let slots_t_all_nil_inv_lem #t slots = ()
 #pop-options
 
 val slots_t_al_v_all_nil_is_empty_lem
-  (#t : Type0) (slots : vec (list_t t)) :
-  Lemma (requires (forall (i:nat{i < length slots}). index slots i == ListNil))
+  (#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"
@@ -492,44 +492,44 @@ let rec slots_t_al_v_all_nil_is_empty_lem #t slots =
    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 == ListNil)
+   assert(index slots 0 == List_Nil)
 #pop-options
 
 /// [allocate_slots]
-val hash_map_allocate_slots_fwd_lem
-  (t : Type0) (slots : vec (list_t t)) (n : usize) :
+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 hash_map_allocate_slots_fwd t slots n with
+   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 == ListNil)))
-  (decreases (hash_map_allocate_slots_loop_decreases t slots n))
+     (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 hash_map_allocate_slots_fwd_lem t slots n =
+let rec hashMap_allocate_slots_lem t slots n =
   begin match n with
   | 0 -> ()
   | _ ->
-    begin match vec_push_back (list_t t) slots ListNil with
+    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 ->
-        hash_map_allocate_slots_fwd_lem t slots1 i;
-        begin match hash_map_allocate_slots_fwd t slots1 i with
+        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 @ [ListNil]); // Triggers patterns
-          assert(index slots1 (length slots) == index [ListNil] 0); // Triggers patterns
-          assert(index slots1 (length slots) == ListNil)
+          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
@@ -538,7 +538,7 @@ let rec hash_map_allocate_slots_fwd_lem t slots n =
 
 (*** new_with_capacity *)
 /// Under proper conditions, [new_with_capacity] doesn't fail and returns an empty hash map.
-val hash_map_new_with_capacity_fwd_lem
+val hashMap_new_with_capacity_lem
   (t : Type0) (capacity : usize)
   (max_load_dividend : usize) (max_load_divisor : usize) :
   Lemma
@@ -549,31 +549,31 @@ val hash_map_new_with_capacity_fwd_lem
     capacity * max_load_dividend >= max_load_divisor /\
     capacity * max_load_dividend <= usize_max))
   (ensures (
-    match hash_map_new_with_capacity_fwd t capacity max_load_dividend max_load_divisor with
+    match hashMap_new_with_capacity t capacity max_load_dividend max_load_divisor with
     | Fail _ -> False
     | Return hm ->
       // The hash map invariant is satisfied
-      hash_map_t_inv hm /\
+      hashMap_t_inv hm /\
       // The parameters are correct
-      hm.hash_map_max_load_factor = (max_load_dividend, max_load_divisor) /\
-      hm.hash_map_max_load = (capacity * max_load_dividend) / max_load_divisor /\
+      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 [hash_map_t_find_s] is not satisfied.
-      length hm.hash_map_slots = capacity /\
+      // otherwise the pre of [hashMap_t_find_s] is not satisfied.
+      length hm.slots = capacity /\
       // The hash map has 0 values
-      hash_map_t_len_s hm = 0 /\
+      hashMap_t_len_s hm = 0 /\
       // It contains no bindings
-      (forall k. hash_map_t_find_s hm k == None) /\
+      (forall k. hashMap_t_find_s hm k == None) /\
       // We need this low-level property for the invariant
-      (forall(i:nat{i < length hm.hash_map_slots}). index hm.hash_map_slots i == ListNil)))
+      (forall(i:nat{i < length hm.slots}). index hm.slots i == List_Nil)))
 
 #push-options "--z3rlimit 50 --fuel 1"
-let hash_map_new_with_capacity_fwd_lem (t : Type0) (capacity : usize)
+let hashMap_new_with_capacity_lem (t : Type0) (capacity : usize)
   (max_load_dividend : usize) (max_load_divisor : usize) =
-  let v = vec_new (list_t t) in
+  let v = alloc_vec_Vec_new (list_t t) in
   assert(length v = 0);
-  hash_map_allocate_slots_fwd_lem t v capacity;
-  begin match hash_map_allocate_slots_fwd t v capacity with
+  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
@@ -582,9 +582,9 @@ let hash_map_new_with_capacity_fwd_lem (t : Type0) (capacity : usize)
       begin match usize_div i max_load_divisor with
       | Fail _ -> assert(False)
       | Return i0 ->
-          let hm = Mkhash_map_t 0 (max_load_dividend, max_load_divisor) i0 v0 in
+          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.hash_map_slots
+          slots_t_al_v_all_nil_is_empty_lem hm.slots
       end
     end
   end
@@ -593,65 +593,65 @@ let hash_map_new_with_capacity_fwd_lem (t : Type0) (capacity : usize)
 (*** new *)
 
 /// [new] doesn't fail and returns an empty hash map
-val hash_map_new_fwd_lem_aux (t : Type0) :
+val hashMap_new_lem_aux (t : Type0) :
   Lemma
   (ensures (
-    match hash_map_new_fwd t with
+    match hashMap_new t with
     | Fail _ -> False
     | Return hm ->
       // The hash map invariant is satisfied
-      hash_map_t_inv hm /\
+      hashMap_t_inv hm /\
       // The hash map has 0 values
-      hash_map_t_len_s hm = 0 /\
+      hashMap_t_len_s hm = 0 /\
       // It contains no bindings
-      (forall k. hash_map_t_find_s hm k == None)))
+      (forall k. hashMap_t_find_s hm k == None)))
 
 #push-options "--fuel 1"
-let hash_map_new_fwd_lem_aux t =
-  hash_map_new_with_capacity_fwd_lem t 32 4 5;
-  match hash_map_new_with_capacity_fwd t 32 4 5 with
+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 hash_map_new_fwd_lem t = hash_map_new_fwd_lem_aux t
+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 hash_map_clear_loop_fwd_back_lem
-  (t : Type0) (slots : vec (list_t t)) (i : usize) :
+let rec hashMap_clear_loop_lem
+  (t : Type0) (slots : alloc_vec_Vec (list_t t)) (i : usize) :
   Lemma
   (ensures (
-    match hash_map_clear_loop_fwd_back t slots i with
+    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 ListNil
-      (forall (j:nat{i <= j /\ j < length slots}). index slots' j == ListNil)))
-  (decreases (hash_map_clear_loop_decreases t slots i))
+      // 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 = vec_len (list_t t) slots in
+  let i0 = alloc_vec_Vec_len (list_t t) slots in
   let b = i < i0 in
   if b
   then
-    begin match vec_index_mut_back (list_t t) slots i ListNil with
+    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 ->
-        hash_map_clear_loop_fwd_back_lem t v i1;
-        begin match hash_map_clear_loop_fwd_back t v i1 with
+        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 == ListNil);
-          assert(index slots1 i == ListNil)
+          assert(forall (j:nat{i+1 <= j /\ j < length slots}). index slots1 j == List_Nil);
+          assert(index slots1 i == List_Nil)
         end
       end
     end
@@ -659,80 +659,80 @@ let rec hash_map_clear_loop_fwd_back_lem
 #pop-options
 
 /// [clear] doesn't fail and turns the hash map into an empty map
-val hash_map_clear_fwd_back_lem_aux
-  (#t : Type0) (self : hash_map_t t) :
+val hashMap_clear_lem_aux
+  (#t : Type0) (self : hashMap_t t) :
   Lemma
-  (requires (hash_map_t_base_inv self))
+  (requires (hashMap_t_base_inv self))
   (ensures (
-    match hash_map_clear_fwd_back t self with
+    match hashMap_clear t self with
     | Fail _ -> False
     | Return hm ->
       // The hash map invariant is satisfied
-      hash_map_t_base_inv hm /\
+      hashMap_t_base_inv hm /\
       // We preserved the parameters
-      hash_map_t_same_params hm self /\
+      hashMap_t_same_params hm self /\
       // The hash map has 0 values
-      hash_map_t_len_s hm = 0 /\
+      hashMap_t_len_s hm = 0 /\
       // It contains no bindings
-      (forall k. hash_map_t_find_s hm k == None)))
+      (forall k. hashMap_t_find_s hm k == None)))
 
 // Being lazy: fuel 1 helps a lot...
 #push-options "--fuel 1"
-let hash_map_clear_fwd_back_lem_aux #t self =
-  let p = self.hash_map_max_load_factor in
-  let i = self.hash_map_max_load in
-  let v = self.hash_map_slots in
-  hash_map_clear_loop_fwd_back_lem t v 0;
-  begin match hash_map_clear_loop_fwd_back t v 0 with
+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 = Mkhash_map_t 0 p i slots1 in
-    assert(hash_map_t_base_inv hm1);
-    assert(hash_map_t_inv hm1)
+    let hm1 = MkhashMap_t 0 p i slots1 in
+    assert(hashMap_t_base_inv hm1);
+    assert(hashMap_t_inv hm1)
   end
 #pop-options
 
-let hash_map_clear_fwd_back_lem #t self = hash_map_clear_fwd_back_lem_aux #t self
+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 hash_map_len_fwd_lem #t self = ()
+let hashMap_len_lem #t self = ()
 
 
 (*** insert_in_list *)
 
 (**** insert_in_list'fwd *)
 
-/// [insert_in_list_fwd]: returns true iff the key is not in the list (functional version)
-val hash_map_insert_in_list_fwd_lem
+/// [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 hash_map_insert_in_list_fwd t key value ls with
+    match hashMap_insert_in_list t key value ls with
     | Fail _ -> False
     | Return b ->
       b <==> (slot_t_find_s key ls == None)))
-  (decreases (hash_map_insert_in_list_loop_decreases t key value ls))
+  (decreases (hashMap_insert_in_list_loop_decreases t key value ls))
 
 #push-options "--fuel 1"
-let rec hash_map_insert_in_list_fwd_lem t key value ls =
+let rec hashMap_insert_in_list_lem t key value ls =
   begin match ls with
-  | ListCons ckey cvalue ls0 ->
+  | List_Cons ckey cvalue ls0 ->
     let b = ckey = key in
     if b
     then ()
     else
       begin
-      hash_map_insert_in_list_fwd_lem t key value ls0;
-      match hash_map_insert_in_list_fwd t key value ls0 with
+      hashMap_insert_in_list_lem t key value ls0;
+      match hashMap_insert_in_list t key value ls0 with
       | Fail _ -> ()
       | Return b0 -> ()
       end
-  | ListNil ->
+  | List_Nil ->
     assert(list_t_v ls == []);
     assert_norm(find (same_key #t key) [] == None)
   end
@@ -748,7 +748,7 @@ let rec hash_map_insert_in_list_fwd_lem t key value ls =
 /// 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 hash_map_insert_in_list_s
+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
@@ -761,86 +761,86 @@ let hash_map_insert_in_list_s
     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 hash_map_insert_in_list_back_lem_append_s
+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 hash_map_insert_in_list_back t key value ls with
+    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 (hash_map_insert_in_list_loop_decreases t key value ls))
+  (decreases (hashMap_insert_in_list_loop_decreases t key value ls))
 
 #push-options "--fuel 1"
-let rec hash_map_insert_in_list_back_lem_append_s t key value ls =
+let rec hashMap_insert_in_list_back_lem_append_s t key value ls =
   begin match ls with
-  | ListCons ckey cvalue ls0 ->
+  | List_Cons ckey cvalue ls0 ->
     let b = ckey = key in
     if b
     then ()
     else
       begin
-      hash_map_insert_in_list_back_lem_append_s t key value ls0;
-      match hash_map_insert_in_list_back t key value ls0 with
+      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
-  | ListNil -> ()
+  | List_Nil -> ()
   end
 #pop-options
 
 /// [insert_in_list]: if the key is in the map, we update the binding (functional version)
-val hash_map_insert_in_list_back_lem_update_s
+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 hash_map_insert_in_list_back t key value ls with
+    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 (hash_map_insert_in_list_loop_decreases t key value ls))
+  (decreases (hashMap_insert_in_list_loop_decreases t key value ls))
 
 #push-options "--fuel 1"
-let rec hash_map_insert_in_list_back_lem_update_s t key value ls =
+let rec hashMap_insert_in_list_back_lem_update_s t key value ls =
   begin match ls with
-  | ListCons ckey cvalue ls0 ->
+  | List_Cons ckey cvalue ls0 ->
     let b = ckey = key in
     if b
     then ()
     else
       begin
-      hash_map_insert_in_list_back_lem_update_s t key value ls0;
-      match hash_map_insert_in_list_back t key value ls0 with
+      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
-  | ListNil -> ()
+  | List_Nil -> ()
   end
 #pop-options
 
 /// Put everything together
-val hash_map_insert_in_list_back_lem_s
+val hashMap_insert_in_list_back_lem_s
   (t : Type0) (key : usize) (value : t) (ls : list_t t) :
   Lemma
   (ensures (
-    match hash_map_insert_in_list_back t key value ls with
+    match hashMap_insert_in_list_back t key value ls with
     | Fail _ -> False
     | Return ls' ->
-      list_t_v ls' == hash_map_insert_in_list_s key value (list_t_v ls)))
+      list_t_v ls' == hashMap_insert_in_list_s key value (list_t_v ls)))
 
-let hash_map_insert_in_list_back_lem_s t key value ls =
+let hashMap_insert_in_list_back_lem_s t key value ls =
   match find (same_key key) (list_t_v ls) with
-  | None -> hash_map_insert_in_list_back_lem_append_s t key value ls
-  | Some _ -> hash_map_insert_in_list_back_lem_update_s t key value ls
+  | 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 [hash_map_insert_in_list_s], the "high-level" version of [insert_in_list'back].
+/// 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
@@ -893,14 +893,14 @@ let rec slot_s_inv_not_find_append_end_inv_lem t len key value ls =
 #pop-options
 
 /// [insert_in_list]: if the key is not in the map, appends a new bindings
-val hash_map_insert_in_list_s_lem_append
+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' = hash_map_insert_in_list_s key value ls in
+    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' /\
@@ -909,20 +909,20 @@ val hash_map_insert_in_list_s_lem_append
     // The other bindings are preserved
     (forall k'. k' <> key ==> slot_s_find k' ls' == slot_s_find k' ls)))
 
-let hash_map_insert_in_list_s_lem_append t len key value 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 hash_map_insert_in_list_back_lem_append
+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 hash_map_insert_in_list_back t key value ls with
+    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)] /\
@@ -933,9 +933,9 @@ val hash_map_insert_in_list_back_lem_append
       // The other bindings are preserved
       (forall k'. k' <> key ==> slot_t_find_s k' ls' == slot_t_find_s k' ls)))
 
-let hash_map_insert_in_list_back_lem_append t len key value ls =
-  hash_map_insert_in_list_back_lem_s t key value ls;
-  hash_map_insert_in_list_s_lem_append t len key value (list_t_v 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 *)
 
@@ -1013,14 +1013,14 @@ let rec slot_s_inv_find_append_end_inv_lem t len key value ls =
 #pop-options
 
 /// [insert_in_list]: if the key is in the map, update the bindings
-val hash_map_insert_in_list_s_lem_update
+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' = hash_map_insert_in_list_s key value ls in
+    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' /\
@@ -1029,20 +1029,20 @@ val hash_map_insert_in_list_s_lem_update
     // The other bindings are preserved
     (forall k'. k' <> key ==> slot_s_find k' ls' == slot_s_find k' ls)))
 
-let hash_map_insert_in_list_s_lem_update t len key value 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 hash_map_insert_in_list_back_lem_update
+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 hash_map_insert_in_list_back t key value ls with
+    match hashMap_insert_in_list_back t key value ls with
     | Fail _ -> False
     | Return ls' ->
       let als = list_t_v ls in
@@ -1054,20 +1054,20 @@ val hash_map_insert_in_list_back_lem_update
       // The other bindings are preserved
       (forall k'. k' <> key ==> slot_t_find_s k' ls' == slot_t_find_s k' ls)))
 
-let hash_map_insert_in_list_back_lem_update t len key value ls =
-  hash_map_insert_in_list_back_lem_s t key value ls;
-  hash_map_insert_in_list_s_lem_update t len key value (list_t_v 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 hash_map_insert_in_list_s_lem
+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' = hash_map_insert_in_list_s key value ls in
+    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]
@@ -1079,22 +1079,22 @@ val hash_map_insert_in_list_s_lem
      | None -> length ls' = length ls + 1
      | Some _ -> length ls' = length ls)))
 
-let hash_map_insert_in_list_s_lem t len key value 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);
-    hash_map_insert_in_list_s_lem_append t len key value ls
+    hashMap_insert_in_list_s_lem_append t len key value ls
   | Some _ ->
-    hash_map_insert_in_list_s_lem_update t len key value ls
+    hashMap_insert_in_list_s_lem_update t len key value ls
 
 /// [insert_in_list]
 /// TODO: not used: remove?
-val hash_map_insert_in_list_back_lem
+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 hash_map_insert_in_list_back t key value ls with
+    match hashMap_insert_in_list_back t key value ls with
     | Fail _ -> False
     | Return ls' ->
       // The invariant is preserved
@@ -1111,127 +1111,127 @@ val hash_map_insert_in_list_back_lem
        | 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 (hash_map_insert_in_list_loop_decreases t key value ls))
+  (decreases (hashMap_insert_in_list_loop_decreases t key value ls))
 
-let hash_map_insert_in_list_back_lem t len key value ls =
-  hash_map_insert_in_list_back_lem_s t key value ls;
-  hash_map_insert_in_list_s_lem t len key value (list_t_v 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 [hash_map_s] (we use a higher-level view of the hash-map, but
+/// 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 hash_map_insert_no_fail_s
-  (#t : Type0) (hm : hash_map_s_nes t)
+let hashMap_insert_no_fail_s
+  (#t : Type0) (hm : hashMap_s_nes t)
   (key : usize) (value : t) :
-  hash_map_s 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' = hash_map_insert_in_list_s key value slot 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 hash_map_s_nes and it broke proofs...x
-let hash_map_insert_no_resize_s
-  (#t : Type0) (hm : hash_map_s_nes t)
+// 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 (hash_map_s 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? (hash_map_s_find hm key) && num_entries = usize_max then Fail Failure
-  else Return (hash_map_insert_no_fail_s hm key value)
+  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 [hash_map_insert_no_resize_s] is refined by
-/// [hash_map_insert_no_resize'fwd_back]
-val hash_map_insert_no_resize_fwd_back_lem_s
-  (t : Type0) (self : hash_map_t t) (key : usize) (value : t) :
+/// 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 (
-    hash_map_t_base_inv self /\
-    hash_map_s_len (hash_map_t_v self) = hash_map_t_len_s self))
+    hashMap_t_base_inv self /\
+    hashMap_s_len (hashMap_t_v self) = hashMap_t_len_s self))
   (ensures (
     begin
-    match hash_map_insert_no_resize_fwd_back t self key value,
-          hash_map_insert_no_resize_s (hash_map_t_v self) key value
+    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 ->
-      hash_map_t_base_inv hm /\
-      hash_map_t_same_params hm self /\
-      hash_map_t_v hm == hm_v /\
-      hash_map_s_len hm_v == hash_map_t_len_s hm
+      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 hash_map_insert_no_resize_fwd_back_lem_s t self key value =
-  begin match hash_key_fwd key with
+let hashMap_insert_no_resize_lem_s t self key value =
+  begin match hash_key key with
   | Fail _ -> ()
   | Return i ->
-    let i0 = self.hash_map_num_entries in
-    let p = self.hash_map_max_load_factor in
-    let i1 = self.hash_map_max_load in
-    let v = self.hash_map_slots in
-    let i2 = vec_len (list_t t) v in
+    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 vec_index_mut_fwd (list_t t) v hash_mod with
+      begin match alloc_vec_Vec_index_usize v hash_mod with
       | Fail _ -> ()
       | Return l ->
         begin
-        // Checking that: list_t_v (index ...) == index (hash_map_t_v ...) ...
-        assert(list_t_v l == index (hash_map_t_v self) hash_mod);
-        hash_map_insert_in_list_fwd_lem t key value l;
-        match hash_map_insert_in_list_fwd t key value l with
+        // 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)));
-          hash_map_insert_in_list_back_lem t len key value 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 hash_map_insert_in_list_back t key value l with
+              match hashMap_insert_in_list_back t key value l with
               | Fail _ -> ()
               | Return l0 ->
-                begin match vec_index_mut_back (list_t t) v hash_mod l0 with
+                begin match alloc_vec_Vec_update_usize v hash_mod l0 with
                 | Fail _ -> ()
                 | Return v0 ->
-                  let self_v = hash_map_t_v self in
-                  let hm = Mkhash_map_t i3 p i1 v0 in
-                  let hm_v = hash_map_t_v hm in
+                  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(hash_map_s_len hm_v = hash_map_t_len_s hm)
+                  assert(hashMap_s_len hm_v = hashMap_t_len_s hm)
                 end
               end
             end
           else
             begin
-            match hash_map_insert_in_list_back t key value l with
+            match hashMap_insert_in_list_back t key value l with
             | Fail _ -> ()
             | Return l0 ->
-              begin match vec_index_mut_back (list_t t) v hash_mod l0 with
+              begin match alloc_vec_Vec_update_usize v hash_mod l0 with
               | Fail _ -> ()
               | Return v0 ->
-                let self_v = hash_map_t_v self in
-                let hm = Mkhash_map_t i0 p i1 v0 in
-                let hm_v = hash_map_t_v hm in
+                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(hash_map_s_len hm_v = hash_map_t_len_s hm)
+                assert(hashMap_s_len hm_v = hashMap_t_len_s hm)
               end
             end
         end
@@ -1241,108 +1241,108 @@ let hash_map_insert_no_resize_fwd_back_lem_s t self key value =
 
 (**** insert_{no_fail,no_resize}: invariants *)
 
-let hash_map_s_updated_binding
-  (#t : Type0) (hm : hash_map_s_nes t)
-  (key : usize) (opt_value : option t) (hm' : hash_map_s_nes t) : Type0 =
+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]
-  hash_map_s_find hm' key == opt_value /\
+  hashMap_s_find hm' key == opt_value /\
   // The other bindings are preserved
-  (forall k'. k' <> key ==> hash_map_s_find hm' k' == hash_map_s_find hm k')
+  (forall k'. k' <> key ==> hashMap_s_find hm' k' == hashMap_s_find hm k')
 
-let insert_post (#t : Type0) (hm : hash_map_s_nes t)
-  (key : usize) (value : t) (hm' : hash_map_s_nes t) : Type0 =
+let insert_post (#t : Type0) (hm : hashMap_s_nes t)
+  (key : usize) (value : t) (hm' : hashMap_s_nes t) : Type0 =
   // The invariant is preserved
-  hash_map_s_inv hm' /\
+  hashMap_s_inv hm' /\
   // [key] maps to [value] and the other bindings are preserved
-  hash_map_s_updated_binding hm key (Some value) hm' /\
+  hashMap_s_updated_binding hm key (Some value) hm' /\
   // The length is incremented, iff we inserted a new key
-  (match hash_map_s_find hm key with
-   | None -> hash_map_s_len hm' = hash_map_s_len hm + 1
-   | Some _ -> hash_map_s_len hm' = hash_map_s_len hm)
+  (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 hash_map_insert_no_fail_s_lem
-  (#t : Type0) (hm : hash_map_s_nes t)
+val hashMap_insert_no_fail_s_lem
+  (#t : Type0) (hm : hashMap_s_nes t)
   (key : usize) (value : t) :
   Lemma
-  (requires (hash_map_s_inv hm))
+  (requires (hashMap_s_inv hm))
   (ensures (
-    let hm' = hash_map_insert_no_fail_s hm key value in
+    let hm' = hashMap_insert_no_fail_s hm key value in
     insert_post hm key value hm'))
 
-let hash_map_insert_no_fail_s_lem #t hm key value =
+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
-  hash_map_insert_in_list_s_lem t len key value slot;
-  let slot' = hash_map_insert_in_list_s key value slot 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 hash_map_insert_no_resize_s_lem
-  (#t : Type0) (hm : hash_map_s_nes t)
+val hashMap_insert_no_resize_s_lem
+  (#t : Type0) (hm : hashMap_s_nes t)
   (key : usize) (value : t) :
   Lemma
-  (requires (hash_map_s_inv hm))
+  (requires (hashMap_s_inv hm))
   (ensures (
-    match hash_map_insert_no_resize_s hm key value with
+    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
-      hash_map_s_len hm = usize_max /\
-      None? (hash_map_s_find hm key)
+      hashMap_s_len hm = usize_max /\
+      None? (hashMap_s_find hm key)
     | Return hm' ->
       insert_post hm key value hm'))
 
-let hash_map_insert_no_resize_s_lem #t hm key value =
+let hashMap_insert_no_resize_s_lem #t hm key value =
   let num_entries = length (flatten hm) in
-  if None? (hash_map_s_find hm key) && num_entries = usize_max then ()
-  else hash_map_insert_no_fail_s_lem hm key value
+  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 hash_map_insert_no_resize_s_get_same_lem
-  (#t : Type0) (hm : hash_map_s t)
+val hashMap_insert_no_resize_s_get_same_lem
+  (#t : Type0) (hm : hashMap_s t)
   (key : usize) (value : t) :
-  Lemma (requires (hash_map_s_inv hm))
+  Lemma (requires (hashMap_s_inv hm))
   (ensures (
-    match hash_map_insert_no_resize_s hm key value with
+    match hashMap_insert_no_resize_s hm key value with
     | Fail _ -> True
     | Return hm' ->
-      hash_map_s_find hm' key == Some value))
+      hashMap_s_find hm' key == Some value))
 
-let hash_map_insert_no_resize_s_get_same_lem #t hm key value =
+let hashMap_insert_no_resize_s_get_same_lem #t hm key value =
   let num_entries = length (flatten hm) in
-  if None? (hash_map_s_find hm key) && num_entries = usize_max then ()
+  if None? (hashMap_s_find hm key) && num_entries = usize_max then ()
   else
     begin
-    let hm' = Return?.v (hash_map_insert_no_resize_s hm key value) in
+    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
-    hash_map_insert_in_list_s_lem t len key value slot
+    hashMap_insert_in_list_s_lem t len key value slot
    end
 
-val hash_map_insert_no_resize_s_get_diff_lem
-  (#t : Type0) (hm : hash_map_s t)
+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 (hash_map_s_inv hm))
+  Lemma (requires (hashMap_s_inv hm))
   (ensures (
-    match hash_map_insert_no_resize_s hm key value with
+    match hashMap_insert_no_resize_s hm key value with
     | Fail _ -> True
     | Return hm' ->
-      hash_map_s_find hm' key' == hash_map_s_find hm key'))
+      hashMap_s_find hm' key' == hashMap_s_find hm key'))
 
-let hash_map_insert_no_resize_s_get_diff_lem #t hm key value key' =
+let hashMap_insert_no_resize_s_get_diff_lem #t hm key value key' =
   let num_entries = length (flatten hm) in
-  if None? (hash_map_s_find hm key) && num_entries = usize_max then ()
+  if None? (hashMap_s_find hm key) && num_entries = usize_max then ()
   else
     begin
-    let hm' = Return?.v (hash_map_insert_no_resize_s hm key value) in
+    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
-    hash_map_insert_in_list_s_lem t len key value slot;
+    hashMap_insert_in_list_s_lem t len key value slot;
     let i' = hash_mod_key key' len in
     if i <> i' then ()
     else
@@ -1354,116 +1354,116 @@ let hash_map_insert_no_resize_s_get_diff_lem #t hm key value key' =
 
 (*** move_elements_from_list *)
 
-/// Having a great time here: if we use `result (hash_map_s_res t)` as the
-/// return type for [hash_map_move_elements_from_list_s] instead of having this
-/// awkward match, the proof of [hash_map_move_elements_fwd_back_lem_refin] fails.
+/// 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_hash_map_s]
+/// Followingly, I'm not taking any chance and using [result_hashMap_s]
 /// everywhere.
-type result_hash_map_s_nes (t : Type0) : Type0 =
-  res:result (hash_map_s t) {
+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 hash_map_move_elements_from_list_s
-  (#t : Type0) (hm : hash_map_s_nes t)
+let rec hashMap_move_elements_from_list_s
+  (#t : Type0) (hm : hashMap_s_nes t)
   (ls : slot_s t) :
-  // Do *NOT* use `result (hash_map_s t)`
-  Tot (result_hash_map_s_nes 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 hash_map_insert_no_resize_s hm key value with
+    match hashMap_insert_no_resize_s hm key value with
     | Fail e -> Fail e
     | Return hm' ->
-      hash_map_move_elements_from_list_s hm' ls'
+      hashMap_move_elements_from_list_s hm' ls'
 
 /// Refinement lemma
-val hash_map_move_elements_from_list_fwd_back_lem
-  (t : Type0) (ntable : hash_map_t_nes t) (ls : list_t t) :
-  Lemma (requires (hash_map_t_base_inv ntable))
+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 hash_map_move_elements_from_list_fwd_back t ntable ls,
-          hash_map_move_elements_from_list_s (hash_map_t_v ntable) (slot_t_v ls)
+    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 ->
-      hash_map_t_base_inv hm' /\
-      hash_map_t_v hm' == hm_v /\
-      hash_map_t_same_params hm' ntable
+      hashMap_t_base_inv hm' /\
+      hashMap_t_v hm' == hm_v /\
+      hashMap_t_same_params hm' ntable
     | _ -> False))
-  (decreases (hash_map_move_elements_from_list_loop_decreases t ntable ls))
+  (decreases (hashMap_move_elements_from_list_loop_decreases t ntable ls))
 
 #push-options "--fuel 1"
-let rec hash_map_move_elements_from_list_fwd_back_lem t ntable ls =
+let rec hashMap_move_elements_from_list_lem t ntable ls =
   begin match ls with
-  | ListCons k v tl ->
+  | 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
-    hash_map_insert_no_resize_fwd_back_lem_s t ntable k v;
-    begin match hash_map_insert_no_resize_fwd_back t ntable k v with
+    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 (hash_map_insert_no_resize_s (hash_map_t_v ntable) k v) in
-      assert(hash_map_t_v h == h_v);
-      hash_map_move_elements_from_list_fwd_back_lem t h tl;
-      begin match hash_map_move_elements_from_list_fwd_back t h tl with
+      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
-  | ListNil -> ()
+  | List_Nil -> ()
   end
 #pop-options
 
 (*** move_elements *)
 
 (**** move_elements: refinement 0 *)
-/// The proof for [hash_map_move_elements_fwd_back_lem_refin] broke so many times
+/// 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 ListNil == []`: I
+/// 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 [hash_map_move_elements_s].
+/// because it allows for easy comparisons with [hashMap_move_elements_s].
 
-/// [hash_map_move_elements_fwd] refines this function, which is actually almost
+/// [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 [hash_map_move_elements_fwd], wrote the
-///   signature which links this new definition to [hash_map_move_elements_fwd] and
+/// - 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 hash_map_move_elements_s_simpl
-  (t : Type0) (ntable : hash_map_t t)
-  (slots : vec (list_t t))
+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 ((hash_map_t t) & (vec (list_t t))))
+  Pure (result ((hashMap_t t) & (alloc_vec_Vec (list_t t))))
   (requires (True))
   (ensures (fun res ->
-    match res, hash_map_move_elements_fwd_back t ntable slots i with
+    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 (hash_map_move_elements_loop_decreases t ntable slots i))
+  (decreases (hashMap_move_elements_loop_decreases t ntable slots i))
   =
   if i < length slots
   then
     let slot = index slots i in
-    begin match hash_map_move_elements_from_list_fwd_back t ntable slot with
+    begin match hashMap_move_elements_from_list t ntable slot with
     | Fail e -> Fail e
     | Return hm' ->
-      let slots' = list_update slots i ListNil in
-      hash_map_move_elements_s_simpl t hm' slots' (i+1)
+      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
@@ -1476,71 +1476,71 @@ let rec hash_map_move_elements_s_simpl
 // 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 hash_map_move_elements_s
-  (#t : Type0) (hm : hash_map_s_nes t)
+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_hash_map_s_nes t)
+  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 hash_map_move_elements_from_list_s hm slot with
+    match hashMap_move_elements_from_list_s hm slot with
     | Fail e -> Fail e
     | Return hm' ->
       let slots' = list_update slots i [] in
-      hash_map_move_elements_s hm' slots' (i+1)
+      hashMap_move_elements_s hm' slots' (i+1)
     end
   else Return hm
 
-val hash_map_move_elements_fwd_back_lem_refin
-  (t : Type0) (ntable : hash_map_t t)
-  (slots : vec (list_t t)) (i : usize{i <= length slots}) :
+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 (
-    hash_map_t_base_inv ntable))
+    hashMap_t_base_inv ntable))
   (ensures (
-    match hash_map_move_elements_fwd_back t ntable slots i,
-          hash_map_move_elements_s (hash_map_t_v ntable) (slots_t_v slots) i
+    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 ->
-      hash_map_t_base_inv ntable' /\
-      hash_map_t_v ntable' == ntable'_v /\
-      hash_map_t_same_params ntable' ntable
+      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 hash_map_move_elements_fwd_back_lem_refin t ntable slots i =
-  assert(hash_map_t_base_inv ntable);
-  let i0 = vec_len (list_t t) slots in
+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 vec_index_mut_fwd (list_t t) slots i with
+    begin match alloc_vec_Vec_index_usize slots i with
     | Fail _ -> ()
     | Return l ->
-      let l0 = mem_replace_fwd (list_t t) l ListNil in
+      let l0 = core_mem_replace (list_t t) l List_Nil in
       assert(l0 == l);
-      hash_map_move_elements_from_list_fwd_back_lem t ntable l0;
-      begin match hash_map_move_elements_from_list_fwd_back t ntable l0 with
+      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 = mem_replace_back (list_t t) l ListNil in
-        assert(l1 == ListNil);
-        assert(slot_t_v #t ListNil == []); // THIS IS IMPORTANT
-        begin match vec_index_mut_back (list_t t) slots i l1 with
+        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 ->
-            hash_map_move_elements_fwd_back_lem_refin t h v i1;
-            begin match hash_map_move_elements_fwd_back t h v i1 with
+            hashMap_move_elements_lem_refin t h v i1;
+            begin match hashMap_move_elements t h v i1 with
             | Fail _ ->
-              assert(Fail? (hash_map_move_elements_fwd_back t ntable slots i));
+              assert(Fail? (hashMap_move_elements t ntable slots i));
               ()
             | Return (ntable', v0) -> ()
             end
@@ -1560,19 +1560,19 @@ let rec hash_map_move_elements_fwd_back_lem_refin t ntable slots i =
 /// [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 [hash_map_move_elements_from_list_s]...
-let rec hash_map_move_elements_s_flat
-  (#t : Type0) (ntable : hash_map_s_nes t)
+/// 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_hash_map_s_nes t)
+  Tot (result_hashMap_s_nes t)
   (decreases slots) =
   match slots with
   | [] -> Return ntable
   | (k,v) :: slots' ->
-    match hash_map_insert_no_resize_s ntable k v with
+    match hashMap_insert_no_resize_s ntable k v with
     | Fail e -> Fail e
     | Return ntable' ->
-      hash_map_move_elements_s_flat ntable' slots'
+      hashMap_move_elements_s_flat ntable' slots'
 
 /// The refinment lemmas
 /// First, auxiliary helpers.
@@ -1656,42 +1656,42 @@ let rec flatten_nil_prefix_as_flatten_i #a l i =
 
 /// The proof is trivial, the functions are the same.
 /// Just keeping two definitions to allow changes...
-val hash_map_move_elements_from_list_s_as_flat_lem
-  (#t : Type0) (hm : hash_map_s_nes t)
+val hashMap_move_elements_from_list_s_as_flat_lem
+  (#t : Type0) (hm : hashMap_s_nes t)
   (ls : slot_s t) :
   Lemma
   (ensures (
-    hash_map_move_elements_from_list_s hm ls ==
-    hash_map_move_elements_s_flat hm ls))
+    hashMap_move_elements_from_list_s hm ls ==
+    hashMap_move_elements_s_flat hm ls))
   (decreases ls)
 
 #push-options "--fuel 1"
-let rec hash_map_move_elements_from_list_s_as_flat_lem #t hm ls =
+let rec hashMap_move_elements_from_list_s_as_flat_lem #t hm ls =
   match ls with
   | [] -> ()
   | (key, value) :: ls' ->
-    match hash_map_insert_no_resize_s hm key value with
+    match hashMap_insert_no_resize_s hm key value with
     | Fail _ -> ()
     | Return hm' ->
-      hash_map_move_elements_from_list_s_as_flat_lem hm' ls'
+      hashMap_move_elements_from_list_s_as_flat_lem hm' ls'
 #pop-options
 
-/// Composition of two calls to [hash_map_move_elements_s_flat]
-let hash_map_move_elements_s_flat_comp
-  (#t : Type0) (hm : hash_map_s_nes t) (slot0 slot1 : slot_s t) :
-  Tot (result_hash_map_s_nes t) =
-  match hash_map_move_elements_s_flat hm slot0 with
+/// 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 -> hash_map_move_elements_s_flat hm1 slot1
+  | 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 hash_map_move_elements_s_flat_append_lem
-  (#t : Type0) (hm : hash_map_s_nes t) (slot0 slot1 : slot_s t) :
+val hashMap_move_elements_s_flat_append_lem
+  (#t : Type0) (hm : hashMap_s_nes t) (slot0 slot1 : slot_s t) :
   Lemma
   (ensures (
-    match hash_map_move_elements_s_flat_comp hm slot0 slot1,
-          hash_map_move_elements_s_flat hm (slot0 @ slot1)
+    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
@@ -1699,14 +1699,14 @@ val hash_map_move_elements_s_flat_append_lem
   (decreases (slot0))
 
 #push-options "--fuel 1"
-let rec hash_map_move_elements_s_flat_append_lem #t hm slot0 slot1 =
+let rec hashMap_move_elements_s_flat_append_lem #t hm slot0 slot1 =
   match slot0 with
   | [] -> ()
   | (k,v) :: slot0' ->
-    match hash_map_insert_no_resize_s hm k v with
+    match hashMap_insert_no_resize_s hm k v with
     | Fail _ -> ()
     | Return hm' ->
-      hash_map_move_elements_s_flat_append_lem hm' slot0' slot1
+      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) :
@@ -1726,16 +1726,16 @@ let rec flatten_i_same_suffix #a l0 l1 i =
 #pop-options
 
 /// Refinement lemma:
-/// [hash_map_move_elements_s] refines [hash_map_move_elements_s_flat]
+/// [hashMap_move_elements_s] refines [hashMap_move_elements_s_flat]
 /// (actually the functions are equal on all inputs).
-val hash_map_move_elements_s_lem_refin_flat
-  (#t : Type0) (hm : hash_map_s_nes t)
+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 hash_map_move_elements_s hm slots i,
-          hash_map_move_elements_s_flat hm (flatten_i slots i)
+    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'
@@ -1743,22 +1743,22 @@ val hash_map_move_elements_s_lem_refin_flat
   (decreases (length slots - i))
 
 #push-options "--fuel 1"
-let rec hash_map_move_elements_s_lem_refin_flat #t hm slots i =
+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
-    hash_map_move_elements_from_list_s_as_flat_lem hm slot;
-    match hash_map_move_elements_from_list_s hm slot with
+    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));
-      hash_map_move_elements_s_flat_append_lem hm slot (flatten_i slots (i+1));
-      assert(Fail? (hash_map_move_elements_s_flat hm (flatten_i slots i)))
+      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);
-      hash_map_move_elements_s_lem_refin_flat hm' slots' (i+1);
-      hash_map_move_elements_s_flat_append_lem hm slot (flatten_i 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 ()
@@ -1769,21 +1769,21 @@ let assoc_list_inv (#t : Type0) (al : assoc_list t) : Type0 =
   pairwise_rel binding_neq al
 
 let disjoint_hm_al_on_key
-  (#t : Type0) (hm : hash_map_s_nes t) (al : assoc_list t) (k : key) : Type0 =
-  match hash_map_s_find hm k, assoc_list_find k al with
+  (#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 : hash_map_s_nes t) (al : assoc_list t) : Type0 =
+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 : hash_map_s_nes t) (al : assoc_list t) (k : key) :
+  (#t : Type0) (hm : hashMap_s_nes t) (al : assoc_list t) (k : key) :
   option t =
-  match hash_map_s_find hm k with
+  match hashMap_s_find hm k with
   | Some b -> Some b
   | None -> assoc_list_find k al
 
@@ -1799,58 +1799,58 @@ let rec for_all_binding_neq_find_lem #t k v al =
   | b :: al' -> for_all_binding_neq_find_lem k v al'
 #pop-options
 
-val hash_map_move_elements_s_flat_lem
-  (#t : Type0) (hm : hash_map_s_nes t) (al : assoc_list t) :
+val hashMap_move_elements_s_flat_lem
+  (#t : Type0) (hm : hashMap_s_nes t) (al : assoc_list t) :
   Lemma
   (requires (
     // Invariants
-    hash_map_s_inv hm /\
+    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
-    hash_map_s_len hm + length al <= usize_max))
+    hashMap_s_len hm + length al <= usize_max))
   (ensures (
-    match hash_map_move_elements_s_flat hm al with
+    match hashMap_move_elements_s_flat hm al with
     | Fail _ -> False // We can't fail
     | Return hm' ->
       // The invariant is preserved
-      hash_map_s_inv hm' /\
+      hashMap_s_inv hm' /\
       // The new hash map is the union of the two maps
-      (forall (k:key). hash_map_s_find hm' k == find_in_union_hm_al hm al k) /\
-      hash_map_s_len hm' = hash_map_s_len hm + length al))
+      (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 hash_map_move_elements_s_flat_lem #t hm al =
+let rec hashMap_move_elements_s_flat_lem #t hm al =
   match al with
   | [] -> ()
   | (k,v) :: al' ->
-    hash_map_insert_no_resize_s_lem hm k v;
-    match hash_map_insert_no_resize_s hm k v with
+    hashMap_insert_no_resize_s_lem hm k v;
+    match hashMap_insert_no_resize_s hm k v with
     | Fail _ -> ()
     | Return hm' ->
-      assert(hash_map_s_inv 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(hash_map_s_find hm' k' == Some v);
+          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(hash_map_s_find hm' k' == hash_map_s_find hm k');
+          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(hash_map_s_len hm' + length al' <= usize_max);
-      hash_map_move_elements_s_flat_lem 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
@@ -1866,18 +1866,18 @@ let slots_t_inv_implies_slots_s_inv #t slots =
   // Problem is: I can never really predict for sure with F*...
   ()
 
-val hash_map_t_base_inv_implies_hash_map_s_inv
-  (#t : Type0) (hm : hash_map_t t) :
-  Lemma (requires (hash_map_t_base_inv hm))
-  (ensures (hash_map_s_inv (hash_map_t_v hm)))
+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 hash_map_t_base_inv_implies_hash_map_s_inv #t hm = () // same as previous
+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_hash_map_s_inv
+let partial_hashMap_s_inv
   (#t : Type0) (len : usize{len > 0}) (offset : usize)
-  (hm : hash_map_s t{offset + length hm <= usize_max}) : Type0 =
+  (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.
@@ -1887,13 +1887,13 @@ val binding_in_previous_slot_implies_neq
   (#t : Type0) (len : usize{len > 0})
   (i : usize) (b : binding t)
   (offset : usize{i < offset})
-  (slots : hash_map_s t{offset + length slots <= usize_max}) :
+  (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_hash_map_s_inv len offset slots))
+    partial_hashMap_s_inv len offset slots))
   (ensures (
     for_all (binding_neq b) (flatten slots)))
   (decreases slots)
@@ -1924,17 +1924,17 @@ let rec binding_in_previous_slot_implies_neq #t len i b offset slots =
     for_all_append (binding_neq b) s (flatten slots')    
 #pop-options
 
-val partial_hash_map_s_inv_implies_assoc_list_lem
+val partial_hashMap_s_inv_implies_assoc_list_lem
   (#t : Type0) (len : usize{len > 0}) (offset : usize)
-  (hm : hash_map_s t{offset + length hm <= usize_max}) :
+  (hm : hashMap_s t{offset + length hm <= usize_max}) :
   Lemma
   (requires (
-    partial_hash_map_s_inv len offset hm))
+    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_hash_map_s_inv_implies_assoc_list_lem #t len offset hm =
+let rec partial_hashMap_s_inv_implies_assoc_list_lem #t len offset hm =
   match hm with
   | [] -> ()
   | slot :: hm' ->
@@ -1943,8 +1943,8 @@ let rec partial_hash_map_s_inv_implies_assoc_list_lem #t len offset hm =
     match slot with
     | [] ->
       assert(flatten hm == flatten hm');
-      assert(partial_hash_map_s_inv len (offset+1) hm'); // Triggers instantiations
-      partial_hash_map_s_inv_implies_assoc_list_lem len (offset+1) 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
@@ -1953,45 +1953,45 @@ let rec partial_hash_map_s_inv_implies_assoc_list_lem #t len offset hm =
       assert(index hm 0 == slot); // Triggers instantiations
       assert(slot_s_inv len offset slot);
       assert(slot_s_inv len offset slot');
-      assert(partial_hash_map_s_inv len offset hm'');
-      partial_hash_map_s_inv_implies_assoc_list_lem len offset (slot' :: hm');
+      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_hash_map_s_inv len (offset+1) 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 hash_map_s_inv_implies_assoc_list_lem
-  (#t : Type0) (hm : hash_map_s t) :
-  Lemma (requires (hash_map_s_inv hm))
+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 hash_map_s_inv_implies_assoc_list_lem #t hm =
-  partial_hash_map_s_inv_implies_assoc_list_lem (length hm) 0 hm
+let hashMap_s_inv_implies_assoc_list_lem #t hm =
+  partial_hashMap_s_inv_implies_assoc_list_lem (length hm) 0 hm
 
-val hash_map_t_base_inv_implies_assoc_list_lem
-  (#t : Type0) (hm : hash_map_t t):
-  Lemma (requires (hash_map_t_base_inv hm))
-  (ensures (assoc_list_inv (hash_map_t_al_v 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 hash_map_t_base_inv_implies_assoc_list_lem #t hm =
-  hash_map_s_inv_implies_assoc_list_lem (hash_map_t_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 hash_map_is_assoc_list
-  (#t : Type0) (ntable : hash_map_t t{length ntable.hash_map_slots > 0})
+let hashMap_is_assoc_list
+  (#t : Type0) (ntable : hashMap_t t{length ntable.slots > 0})
   (al : assoc_list t) : Type0 =
-  (forall (k:key). hash_map_t_find_s ntable k == assoc_list_find k al)
+  (forall (k:key). hashMap_t_find_s ntable k == assoc_list_find k al)
 
-let partial_hash_map_s_find
+let partial_hashMap_s_find
   (#t : Type0) (len : usize{len > 0}) (offset : usize)
-  (hm : hash_map_s_nes t{offset + length hm = len})
+  (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
@@ -2021,13 +2021,13 @@ val key_in_previous_slot_implies_not_found
   (#t : Type0) (len : usize{len > 0})
   (k : key)
   (offset : usize)
-  (slots : hash_map_s t{offset + length slots = len}) :
+  (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_hash_map_s_inv len offset slots))
+    partial_hashMap_s_inv len offset slots))
   (ensures (
     assoc_list_find k (flatten slots) == None))
   (decreases slots)
@@ -2045,19 +2045,19 @@ let rec key_in_previous_slot_implies_not_found #t len k offset slots =
     key_in_previous_slot_implies_not_found len k (offset+1) slots'
 #pop-options  
 
-val partial_hash_map_s_is_assoc_list_lem
+val partial_hashMap_s_is_assoc_list_lem
   (#t : Type0) (len : usize{len > 0}) (offset : usize)
-  (hm : hash_map_s_nes t{offset + length hm = len})
+  (hm : hashMap_s_nes t{offset + length hm = len})
   (k : key{hash_mod_key k len >= offset}) :
   Lemma
   (requires (
-    partial_hash_map_s_inv len offset hm))
+    partial_hashMap_s_inv len offset hm))
   (ensures (
-    partial_hash_map_s_find len offset hm k == assoc_list_find k (flatten hm)))
+    partial_hashMap_s_find len offset hm k == assoc_list_find k (flatten hm)))
   (decreases hm)
 
 #push-options "--fuel 1"
-let rec partial_hash_map_s_is_assoc_list_lem #t len offset hm k =
+let rec partial_hashMap_s_is_assoc_list_lem #t len offset hm k =
   match hm with
   | [] -> ()
   | slot :: hm' ->
@@ -2066,7 +2066,7 @@ let rec partial_hash_map_s_is_assoc_list_lem #t len offset hm k =
     if i = 0 then
       begin
       // We must look in the current slot
-      assert(partial_hash_map_s_find len offset hm k == slot_s_find k 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';
@@ -2085,64 +2085,64 @@ let rec partial_hash_map_s_is_assoc_list_lem #t len offset hm k =
     else
       begin
       // We must ignore the current slot
-      assert(partial_hash_map_s_find len offset hm k ==
-             partial_hash_map_s_find len (offset+1) hm' k);
+      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_hash_map_s_is_assoc_list_lem #t len (offset+1) hm' k
+      partial_hashMap_s_is_assoc_list_lem #t len (offset+1) hm' k
       end
 #pop-options
 
-val hash_map_is_assoc_list_lem (#t : Type0) (hm : hash_map_t t) :
-  Lemma (requires (hash_map_t_base_inv hm))
-  (ensures (hash_map_is_assoc_list hm (hash_map_t_al_v hm)))
+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 hash_map_is_assoc_list_lem #t hm =
+let hashMap_is_assoc_list_lem #t hm =
   let aux (k:key) :
-    Lemma (hash_map_t_find_s hm k == assoc_list_find k (hash_map_t_al_v hm))
-    [SMTPat (hash_map_t_find_s hm k)] =
-    let hm_v = hash_map_t_v hm in
+    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_hash_map_s_is_assoc_list_lem #t len 0 hm_v k
+    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 hash_map_move_elements_fwd_back_lem
-  (t : Type0) (ntable : hash_map_t t) (slots : vec (list_t t)) :
+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
-    hash_map_t_base_inv ntable /\
+    hashMap_t_base_inv ntable /\
     length al <= usize_max /\
     assoc_list_inv al /\
     // The table is empty
-    hash_map_t_len_s ntable = 0 /\
-    (forall (k:key). hash_map_t_find_s ntable k  == None)))
+    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 hash_map_move_elements_fwd_back t ntable slots 0,
-          hash_map_move_elements_s_flat (hash_map_t_v ntable) al
+    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
-      hash_map_t_base_inv ntable' /\
+      hashMap_t_base_inv ntable' /\
       // We preserved the parameters
-      hash_map_t_same_params ntable' ntable /\
+      hashMap_t_same_params ntable' ntable /\
       // The table has the same number of slots
-      length ntable'.hash_map_slots = length ntable.hash_map_slots /\
+      length ntable'.slots = length ntable.slots /\
       // The count is good
-      hash_map_t_len_s ntable' = length al /\
+      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)
-      hash_map_t_v ntable' == ntable'_v /\
+      hashMap_t_v ntable' == ntable'_v /\
       // The new table contains exactly all the bindings from the slots
-      // Rk.: see the comment for [hash_map_is_assoc_list]
-      hash_map_is_assoc_list ntable' al
+      // Rk.: see the comment for [hashMap_is_assoc_list]
+      hashMap_is_assoc_list ntable' al
     | _ -> False // We can only succeed
     ))
 
@@ -2154,41 +2154,41 @@ val hash_map_move_elements_fwd_back_lem
 // lack of ifuel (this kind of proofs is annoying, really).
 #restart-solver
 #push-options "--z3rlimit 100"
-let hash_map_move_elements_fwd_back_lem t ntable slots =
-  let ntable_v = hash_map_t_v ntable in
+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
-  hash_map_move_elements_fwd_back_lem_refin t ntable slots 0;
+  hashMap_move_elements_lem_refin t ntable slots 0;
   begin
-  match hash_map_move_elements_fwd_back t ntable slots 0,
-        hash_map_move_elements_s ntable_v slots_v 0
+  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(hash_map_t_base_inv ntable');
-    assert(hash_map_t_v ntable' == ntable'_v)
+    assert(hashMap_t_base_inv ntable');
+    assert(hashMap_t_v ntable' == ntable'_v)
   | _ -> assert(False)
   end;
-  hash_map_move_elements_s_lem_refin_flat ntable_v slots_v 0;
+  hashMap_move_elements_s_lem_refin_flat ntable_v slots_v 0;
   begin
-  match hash_map_move_elements_s ntable_v slots_v 0,
-        hash_map_move_elements_s_flat ntable_v (flatten_i slots_v 0)
+  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
-  hash_map_move_elements_s_flat_lem ntable_v al;
-  match hash_map_move_elements_fwd_back t ntable slots 0,
-        hash_map_move_elements_s_flat ntable_v al
+  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(hash_map_t_base_inv ntable');
-    assert(length ntable'.hash_map_slots = length ntable.hash_map_slots);
-    assert(hash_map_t_len_s ntable' = length al);
-    assert(hash_map_t_v ntable' == ntable'_v);
-    assert(hash_map_is_assoc_list ntable' al)
+    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
 
@@ -2197,47 +2197,47 @@ let hash_map_move_elements_fwd_back_lem t ntable slots =
 /// High-level model 1.
 /// This is one is slightly "crude": we just simplify a bit the function.
 
-let hash_map_try_resize_s_simpl
+let hashMap_try_resize_s_simpl
   (#t : Type0)
-  (hm : hash_map_t t) :
-  Pure  (result (hash_map_t t))
+  (hm : hashMap_t t) :
+  Pure  (result (hashMap_t t))
   (requires (
-    let (divid, divis) = hm.hash_map_max_load_factor in
+    let (divid, divis) = hm.max_load_factor in
     divid > 0 /\ divis > 0))
   (ensures (fun _ -> True)) =
-  let capacity = length hm.hash_map_slots in
-  let (divid, divis) = hm.hash_map_max_load_factor in
+  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 hash_map_new_with_capacity_fwd t ncapacity divid divis with
+    begin match hashMap_new_with_capacity t ncapacity divid divis with
     | Fail e -> Fail e
     | Return ntable ->
-      match hash_map_move_elements_fwd_back t ntable hm.hash_map_slots 0 with
+      match hashMap_move_elements t ntable hm.slots 0 with
       | Fail e -> Fail e
       | Return (ntable', _) ->
         let hm =
-          { hm with hash_map_slots = ntable'.hash_map_slots;
-                    hash_map_max_load = ntable'.hash_map_max_load }
+          { hm with slots = ntable'.slots;
+                    max_load = ntable'.max_load }
         in
         Return hm
     end
   else Return hm
 
-val hash_map_try_resize_fwd_back_lem_refin
-  (t : Type0) (self : hash_map_t t) :
+val hashMap_try_resize_lem_refin
+  (t : Type0) (self : hashMap_t t) :
   Lemma
   (requires (
-    let (divid, divis) = self.hash_map_max_load_factor in
+    let (divid, divis) = self.max_load_factor in
     divid > 0 /\ divis > 0))
   (ensures (
-    match hash_map_try_resize_fwd_back t self,
-          hash_map_try_resize_s_simpl self
+    match hashMap_try_resize t self,
+          hashMap_try_resize_s_simpl self
     with
     | Fail _, Fail _ -> True
     | Return hm1, Return hm2 -> hm1 == hm2
     | _ -> False))
 
-let hash_map_try_resize_fwd_back_lem_refin t self = ()
+let hashMap_try_resize_lem_refin t self = ()
 
 /// Isolating arithmetic proofs
 
@@ -2342,78 +2342,78 @@ let new_max_load_lem len capacity divid divis =
   assert(nmax_load >= max_load + 1)
 #pop-options
 
-val hash_map_try_resize_s_simpl_lem (#t : Type0) (hm : hash_map_t t) :
+val hashMap_try_resize_s_simpl_lem (#t : Type0) (hm : hashMap_t t) :
   Lemma
   (requires (
     // The base invariant is satisfied
-    hash_map_t_base_inv hm /\
+    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.hash_map_max_load_factor in
-     hm.hash_map_num_entries == hm.hash_map_max_load + 1 \/
-     length hm.hash_map_slots * 2 * dividend > usize_max)
+    (let (dividend, divisor) = hm.max_load_factor in
+     hm.num_entries == hm.max_load + 1 \/
+     length hm.slots * 2 * dividend > usize_max)
   ))
   (ensures (
-    match hash_map_try_resize_s_simpl hm with
+    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)
-      hash_map_t_inv hm' /\
+      hashMap_t_inv hm' /\
       // It contains the same bindings as the initial map
-      (forall (k:key). hash_map_t_find_s hm' k == hash_map_t_find_s hm k)))
+      (forall (k:key). hashMap_t_find_s hm' k == hashMap_t_find_s hm k)))
 
 #restart-solver
 #push-options "--z3rlimit 400"
-let hash_map_try_resize_s_simpl_lem #t hm =
-  let capacity = length hm.hash_map_slots in
-  let (divid, divis) = hm.hash_map_max_load_factor in
+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(hash_map_t_len_s hm = hm.hash_map_max_load + 1);
-    new_max_load_lem (hash_map_t_len_s hm) capacity divid divis;
-    hash_map_new_with_capacity_fwd_lem t ncapacity divid divis;
-    match hash_map_new_with_capacity_fwd t ncapacity divid divis with
+    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.hash_map_slots in
+      let slots = hm.slots in
       let al = flatten (slots_t_v slots) in
-      // Proving that: length al = hm.hash_map_num_entries
+      // Proving that: length al = hm.num_entries
       assert(al == flatten (map slot_t_v slots));
       assert(al == flatten (map list_t_v slots));
-      assert(hash_map_t_al_v hm == flatten (hash_map_t_v hm));
-      assert(hash_map_t_al_v hm == flatten (map list_t_v hm.hash_map_slots));
-      assert(al == hash_map_t_al_v hm);
-      assert(hash_map_t_base_inv ntable);
-      assert(length al = hm.hash_map_num_entries);
+      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);
-      hash_map_t_base_inv_implies_assoc_list_lem hm;
+      hashMap_t_base_inv_implies_assoc_list_lem hm;
       assert(assoc_list_inv al);
-      assert(hash_map_t_len_s ntable = 0);
-      assert(forall (k:key). hash_map_t_find_s ntable k  == None);
-      hash_map_move_elements_fwd_back_lem t ntable hm.hash_map_slots;
-      match hash_map_move_elements_fwd_back t ntable hm.hash_map_slots 0 with
+      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', _) ->
-        hash_map_is_assoc_list_lem hm;
-        assert(hash_map_is_assoc_list hm (hash_map_t_al_v hm));
+        hashMap_is_assoc_list_lem hm;
+        assert(hashMap_is_assoc_list hm (hashMap_t_al_v hm));
         let hm' =
-          { hm with hash_map_slots = ntable'.hash_map_slots;
-                    hash_map_max_load = ntable'.hash_map_max_load }
+          { hm with slots = ntable'.slots;
+                    max_load = ntable'.max_load }
         in
-        assert(hash_map_t_base_inv ntable');
-        assert(hash_map_t_base_inv hm');
-        assert(hash_map_t_len_s hm' = hash_map_t_len_s hm);
-        new_max_load_lem (hash_map_t_len_s hm') capacity divid divis;
-        assert(hash_map_t_len_s hm' <= hm'.hash_map_max_load); // Requires a lemma
-        assert(hash_map_t_inv hm')
+        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
@@ -2422,203 +2422,203 @@ let hash_map_try_resize_s_simpl_lem #t hm =
     end
 #pop-options
 
-let hash_map_t_same_bindings  (#t : Type0) (hm hm' : hash_map_t_nes t) : Type0 =
-  forall (k:key). hash_map_t_find_s hm k == hash_map_t_find_s hm' k
+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 hash_map_try_resize_fwd_back_lem (#t : Type0) (hm : hash_map_t t) :
+val hashMap_try_resize_lem (#t : Type0) (hm : hashMap_t t) :
   Lemma
   (requires (
-    hash_map_t_base_inv hm /\
+    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.hash_map_max_load_factor in
-     hm.hash_map_num_entries == hm.hash_map_max_load + 1 \/
-     length hm.hash_map_slots * 2 * dividend > usize_max)))
+    (let (dividend, divisor) = hm.max_load_factor in
+     hm.num_entries == hm.max_load + 1 \/
+     length hm.slots * 2 * dividend > usize_max)))
   (ensures (
-    match hash_map_try_resize_fwd_back t hm with
+    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)
-      hash_map_t_inv hm' /\
+      hashMap_t_inv hm' /\
       // The length is the same
-      hash_map_t_len_s hm' = hash_map_t_len_s hm /\
+      hashMap_t_len_s hm' = hashMap_t_len_s hm /\
       // It contains the same bindings as the initial map
-      hash_map_t_same_bindings hm' hm))
+      hashMap_t_same_bindings hm' hm))
 
-let hash_map_try_resize_fwd_back_lem #t hm =
-  hash_map_try_resize_fwd_back_lem_refin t hm;
-  hash_map_try_resize_s_simpl_lem 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 hash_map_insert_s
-  (#t : Type0) (self : hash_map_t t) (key : usize) (value : t) :
-  result (hash_map_t t) =
-  match hash_map_insert_no_resize_fwd_back t self key value with
+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 hash_map_t_len_s hm' > hm'.hash_map_max_load then
-      hash_map_try_resize_fwd_back t hm'
+    if hashMap_t_len_s hm' > hm'.max_load then
+      hashMap_try_resize t hm'
     else Return hm'
 
-val hash_map_insert_fwd_back_lem_refin
-  (t : Type0) (self : hash_map_t t) (key : usize) (value : t) :
+val hashMap_insert_lem_refin
+  (t : Type0) (self : hashMap_t t) (key : usize) (value : t) :
   Lemma (requires True)
   (ensures (
-    match hash_map_insert_fwd_back t self key value,
-          hash_map_insert_s self key value
+    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 hash_map_insert_fwd_back_lem_refin t self key value = ()
+let hashMap_insert_lem_refin t self key value = ()
 
 /// Helper
-let hash_map_insert_fwd_back_bindings_lem
-  (t : Type0) (self : hash_map_t_nes t) (key : usize) (value : t)
-  (hm' hm'' : hash_map_t_nes t) :
+let hashMap_insert_bindings_lem
+  (t : Type0) (self : hashMap_t_nes t) (key : usize) (value : t)
+  (hm' hm'' : hashMap_t_nes t) :
   Lemma
   (requires (
-     hash_map_s_updated_binding (hash_map_t_v self) key
-                                (Some value) (hash_map_t_v hm') /\
-     hash_map_t_same_bindings hm' hm''))
+     hashMap_s_updated_binding (hashMap_t_v self) key
+                                (Some value) (hashMap_t_v hm') /\
+     hashMap_t_same_bindings hm' hm''))
   (ensures (
-     hash_map_s_updated_binding (hash_map_t_v self) key
-                                (Some value) (hash_map_t_v hm'')))
+     hashMap_s_updated_binding (hashMap_t_v self) key
+                                (Some value) (hashMap_t_v hm'')))
   = ()
 
-val hash_map_insert_fwd_back_lem_aux
-  (#t : Type0) (self : hash_map_t t) (key : usize) (value : t) :
-  Lemma (requires (hash_map_t_inv self))
+val hashMap_insert_lem_aux
+  (#t : Type0) (self : hashMap_t t) (key : usize) (value : t) :
+  Lemma (requires (hashMap_t_inv self))
   (ensures (
-    match hash_map_insert_fwd_back t self key value with
+    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
-      hash_map_t_len_s self = usize_max /\
-      None? (hash_map_t_find_s self key)
+      hashMap_t_len_s self = usize_max /\
+      None? (hashMap_t_find_s self key)
     | Return hm' ->
       // The invariant is preserved
-      hash_map_t_inv hm' /\
+      hashMap_t_inv hm' /\
       // [key] maps to [value] and the other bindings are preserved
-      hash_map_s_updated_binding (hash_map_t_v self) key (Some value) (hash_map_t_v hm') /\
+      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 hash_map_t_find_s self key with
-       | None -> hash_map_t_len_s hm' = hash_map_t_len_s self + 1
-       | Some _ -> hash_map_t_len_s hm' = hash_map_t_len_s self)))
+      (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 hash_map_insert_fwd_back_lem_aux #t self key value =
-  hash_map_insert_no_resize_fwd_back_lem_s t self key value;
-  hash_map_insert_no_resize_s_lem (hash_map_t_v self) key value;
-  match hash_map_insert_no_resize_fwd_back t self key value with
+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 [hash_map_insert_no_resize_fwd_back_lem_s]
-    let self_v = hash_map_t_v self in
-    let hm'_v = Return?.v (hash_map_insert_no_resize_s self_v key value) in
-    assert(hash_map_t_base_inv hm');
-    assert(hash_map_t_same_params hm' self);
-    assert(hash_map_t_v hm' == hm'_v);
-    assert(hash_map_s_len hm'_v == hash_map_t_len_s hm');
-    // Expanding the post of [hash_map_insert_no_resize_s_lem]
+    // 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(hash_map_s_inv hm'_v);
+    assert(hashMap_s_inv hm'_v);
     assert(
-      match hash_map_s_find self_v key with
-      | None -> hash_map_s_len hm'_v = hash_map_s_len self_v + 1
-      | Some _ -> hash_map_s_len hm'_v = hash_map_s_len self_v);
-    if hash_map_t_len_s hm' > hm'.hash_map_max_load then
+      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
-      hash_map_try_resize_fwd_back_lem hm';
-      // Expanding the post of [hash_map_try_resize_fwd_back_lem]
-      let hm'' = Return?.v (hash_map_try_resize_fwd_back t hm') in
-      assert(hash_map_t_inv hm'');
-      let hm''_v = hash_map_t_v hm'' in
-      assert(forall k. hash_map_t_find_s hm'' k == hash_map_t_find_s hm' k);
-      assert(hash_map_t_len_s hm'' = hash_map_t_len_s hm'); // TODO
+      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(hash_map_t_inv hm'');
-      hash_map_insert_fwd_back_bindings_lem t self key value hm' hm'';
+      assert(hashMap_t_inv hm'');
+      hashMap_insert_bindings_lem t self key value hm' hm'';
       assert(
-        match hash_map_t_find_s self key with
-         | None -> hash_map_t_len_s hm'' = hash_map_t_len_s self + 1
-         | Some _ -> hash_map_t_len_s hm'' = hash_map_t_len_s self)
+        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 hash_map_insert_fwd_back_lem #t self key value =
-  hash_map_insert_fwd_back_lem_aux #t self key value
+let hashMap_insert_lem #t self key value =
+  hashMap_insert_lem_aux #t self key value
 
 (*** contains_key *)
 
 (**** contains_key_in_list *)
 
-val hash_map_contains_key_in_list_fwd_lem
+val hashMap_contains_key_in_list_lem
   (#t : Type0) (key : usize) (ls : list_t t) :
   Lemma
   (ensures (
-    match hash_map_contains_key_in_list_fwd t key ls with
+    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 hash_map_contains_key_in_list_fwd_lem #t key ls =
+let rec hashMap_contains_key_in_list_lem #t key ls =
   match ls with
-  | ListCons ckey x ls0 ->
+  | List_Cons ckey x ls0 ->
     let b = ckey = key in
     if b
     then ()
     else
       begin
-      hash_map_contains_key_in_list_fwd_lem key ls0;
-      match hash_map_contains_key_in_list_fwd t key ls0 with
+      hashMap_contains_key_in_list_lem key ls0;
+      match hashMap_contains_key_in_list t key ls0 with
       | Fail _ -> ()
       | Return b0 -> ()
       end
-  | ListNil -> ()
+  | List_Nil -> ()
 #pop-options
 
 (**** contains_key *)
 
-val hash_map_contains_key_fwd_lem_aux
-  (#t : Type0) (self : hash_map_t_nes t) (key : usize) :
+val hashMap_contains_key_lem_aux
+  (#t : Type0) (self : hashMap_t_nes t) (key : usize) :
   Lemma
   (ensures (
-    match hash_map_contains_key_fwd t self key with
+    match hashMap_contains_key t self key with
     | Fail _ -> False
-    | Return b -> b = Some? (hash_map_t_find_s self key)))
+    | Return b -> b = Some? (hashMap_t_find_s self key)))
 
-let hash_map_contains_key_fwd_lem_aux #t self key =
-  begin match hash_key_fwd key with
+let hashMap_contains_key_lem_aux #t self key =
+  begin match hash_key key with
   | Fail _ -> ()
   | Return i ->
-    let v = self.hash_map_slots in
-    let i0 = vec_len (list_t t) v in
+    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 vec_index_fwd (list_t t) v hash_mod with
+      begin match alloc_vec_Vec_index_usize v hash_mod with
       | Fail _ -> ()
       | Return l ->
-        hash_map_contains_key_in_list_fwd_lem key l;
-        begin match hash_map_contains_key_in_list_fwd t key l with
+        hashMap_contains_key_in_list_lem key l;
+        begin match hashMap_contains_key_in_list t key l with
         | Fail _ -> ()
         | Return b -> ()
         end
@@ -2627,66 +2627,66 @@ let hash_map_contains_key_fwd_lem_aux #t self key =
   end
 
 /// The lemma in the .fsti
-let hash_map_contains_key_fwd_lem #t self key =
-  hash_map_contains_key_fwd_lem_aux #t self key
+let hashMap_contains_key_lem #t self key =
+  hashMap_contains_key_lem_aux #t self key
 
 (*** get *)
 
 (**** get_in_list *)
 
-val hash_map_get_in_list_fwd_lem
+val hashMap_get_in_list_lem
   (#t : Type0) (key : usize) (ls : list_t t) :
   Lemma
   (ensures (
-    match hash_map_get_in_list_fwd t key ls, slot_t_find_s key ls with
+    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 hash_map_get_in_list_fwd_lem #t key ls =
+let rec hashMap_get_in_list_lem #t key ls =
   begin match ls with
-  | ListCons ckey cvalue ls0 ->
+  | List_Cons ckey cvalue ls0 ->
     let b = ckey = key in
     if b
     then ()
     else
       begin
-      hash_map_get_in_list_fwd_lem key ls0;
-      match hash_map_get_in_list_fwd t key ls0 with
+      hashMap_get_in_list_lem key ls0;
+      match hashMap_get_in_list t key ls0 with
       | Fail _ -> ()
       | Return x -> ()
       end
-  | ListNil -> ()
+  | List_Nil -> ()
   end
 #pop-options
 
 (**** get *)
 
-val hash_map_get_fwd_lem_aux
-  (#t : Type0) (self : hash_map_t_nes t) (key : usize) :
+val hashMap_get_lem_aux
+  (#t : Type0) (self : hashMap_t_nes t) (key : usize) :
   Lemma
   (ensures (
-    match hash_map_get_fwd t self key, hash_map_t_find_s self key with
+    match hashMap_get t self key, hashMap_t_find_s self key with
     | Fail _, None -> True
     | Return x, Some x' -> x == x'
     | _ -> False))
 
-let hash_map_get_fwd_lem_aux #t self key =
-  begin match hash_key_fwd key with
+let hashMap_get_lem_aux #t self key =
+  begin match hash_key key with
   | Fail _ -> ()
   | Return i ->
-    let v = self.hash_map_slots in
-    let i0 = vec_len (list_t t) v in
+    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 vec_index_fwd (list_t t) v hash_mod with
+      begin match alloc_vec_Vec_index_usize v hash_mod with
       | Fail _ -> ()
       | Return l ->
         begin
-        hash_map_get_in_list_fwd_lem key l;
-        match hash_map_get_in_list_fwd t key l with
+        hashMap_get_in_list_lem key l;
+        match hashMap_get_in_list t key l with
         | Fail _ -> ()
         | Return x -> ()
         end
@@ -2695,66 +2695,66 @@ let hash_map_get_fwd_lem_aux #t self key =
   end
 
 /// .fsti
-let hash_map_get_fwd_lem #t self key = hash_map_get_fwd_lem_aux #t self key
+let hashMap_get_lem #t self key = hashMap_get_lem_aux #t self key
 
 (*** get_mut'fwd *)
 
 
 (**** get_mut_in_list'fwd *)
 
-val hash_map_get_mut_in_list_loop_fwd_lem
+val hashMap_get_mut_in_list_loop_lem
   (#t : Type0) (ls : list_t t) (key : usize) :
   Lemma
   (ensures (
-    match hash_map_get_mut_in_list_loop_fwd t ls key, slot_t_find_s key ls with
+    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 hash_map_get_mut_in_list_loop_fwd_lem #t ls key =
+let rec hashMap_get_mut_in_list_loop_lem #t ls key =
   begin match ls with
-  | ListCons ckey cvalue ls0 ->
+  | List_Cons ckey cvalue ls0 ->
     let b = ckey = key in
     if b
     then ()
     else
       begin
-      hash_map_get_mut_in_list_loop_fwd_lem ls0 key;
-      match hash_map_get_mut_in_list_loop_fwd t ls0 key with
+      hashMap_get_mut_in_list_loop_lem ls0 key;
+      match hashMap_get_mut_in_list_loop t ls0 key with
       | Fail _ -> ()
       | Return x -> ()
       end
-  | ListNil -> ()
+  | List_Nil -> ()
   end
 #pop-options
 
 (**** get_mut'fwd *)
 
-val hash_map_get_mut_fwd_lem_aux
-  (#t : Type0) (self : hash_map_t_nes t) (key : usize) :
+val hashMap_get_mut_lem_aux
+  (#t : Type0) (self : hashMap_t_nes t) (key : usize) :
   Lemma
   (ensures (
-    match hash_map_get_mut_fwd t self key, hash_map_t_find_s self key with
+    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 hash_map_get_mut_fwd_lem_aux #t self key =
-  begin match hash_key_fwd key with
+let hashMap_get_mut_lem_aux #t self key =
+  begin match hash_key key with
   | Fail _ -> ()
   | Return i ->
-    let v = self.hash_map_slots in
-    let i0 = vec_len (list_t t) v in
+    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 vec_index_fwd (list_t t) v hash_mod with
+      begin match alloc_vec_Vec_index_usize v hash_mod with
       | Fail _ -> ()
       | Return l ->
         begin
-        hash_map_get_mut_in_list_loop_fwd_lem l key;
-        match hash_map_get_mut_in_list_loop_fwd t l key with
+        hashMap_get_mut_in_list_loop_lem l key;
+        match hashMap_get_mut_in_list_loop t l key with
         | Fail _ -> ()
         | Return x -> ()
         end
@@ -2762,78 +2762,78 @@ let hash_map_get_mut_fwd_lem_aux #t self key =
     end
   end
 
-let hash_map_get_mut_fwd_lem #t self key =
-  hash_map_get_mut_fwd_lem_aux #t self key
+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 hash_map_get_mut_in_list_loop_back_lem
+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 hash_map_get_mut_in_list_loop_back t ls key ret with
+    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 hash_map_get_mut_in_list_loop_back_lem #t ls key ret =
+let rec hashMap_get_mut_in_list_loop_back_lem #t ls key ret =
   begin match ls with
-  | ListCons ckey cvalue ls0 ->
+  | List_Cons ckey cvalue ls0 ->
     let b = ckey = key in
     if b
-    then let ls1 = ListCons ckey ret ls0 in ()
+    then let ls1 = List_Cons ckey ret ls0 in ()
     else
       begin
-      hash_map_get_mut_in_list_loop_back_lem ls0 key ret;
-      match hash_map_get_mut_in_list_loop_back t ls0 key ret with
+      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 = ListCons ckey cvalue l in ()
+      | Return l -> let ls1 = List_Cons ckey cvalue l in ()
       end
-  | ListNil -> ()
+  | List_Nil -> ()
   end
 #pop-options
 
 (**** get_mut'back *)
 
 /// Refinement lemma
-val hash_map_get_mut_back_lem_refin
-  (#t : Type0) (self : hash_map_t t{length self.hash_map_slots > 0})
+val hashMap_get_mut_back_lem_refin
+  (#t : Type0) (self : hashMap_t t{length self.slots > 0})
   (key : usize) (ret : t) :
   Lemma
-  (requires (Some? (hash_map_t_find_s self key)))
+  (requires (Some? (hashMap_t_find_s self key)))
   (ensures (
-    match hash_map_get_mut_back t self key ret with
+    match hashMap_get_mut_back t self key ret with
     | Fail _ -> False
     | Return hm' ->
-      hash_map_t_v hm' == hash_map_insert_no_fail_s (hash_map_t_v self) key ret))
+      hashMap_t_v hm' == hashMap_insert_no_fail_s (hashMap_t_v self) key ret))
 
-let hash_map_get_mut_back_lem_refin #t self key ret =
-  begin match hash_key_fwd key with
+let hashMap_get_mut_back_lem_refin #t self key ret =
+  begin match hash_key key with
   | Fail _ -> ()
   | Return i ->
-    let i0 = self.hash_map_num_entries in
-    let p = self.hash_map_max_load_factor in
-    let i1 = self.hash_map_max_load in
-    let v = self.hash_map_slots in
-    let i2 = vec_len (list_t t) v in
+    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 vec_index_mut_fwd (list_t t) v hash_mod with
+      begin match alloc_vec_Vec_index_usize v hash_mod with
       | Fail _ -> ()
       | Return l ->
         begin
-        hash_map_get_mut_in_list_loop_back_lem l key ret;
-        match hash_map_get_mut_in_list_loop_back t l key ret with
+        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 vec_index_mut_back (list_t t) v hash_mod l0 with
+          begin match alloc_vec_Vec_update_usize v hash_mod l0 with
           | Fail _ -> ()
-          | Return v0 -> let self0 = Mkhash_map_t i0 p i1 v0 in ()
+          | Return v0 -> let self0 = MkhashMap_t i0 p i1 v0 in ()
           end
         end
       end
@@ -2841,102 +2841,102 @@ let hash_map_get_mut_back_lem_refin #t self key ret =
   end
 
 /// Final lemma
-val hash_map_get_mut_back_lem_aux
-  (#t : Type0) (hm : hash_map_t t)
+val hashMap_get_mut_back_lem_aux
+  (#t : Type0) (hm : hashMap_t t)
   (key : usize) (ret : t) :
   Lemma
   (requires (
-    hash_map_t_inv hm /\
-    Some? (hash_map_t_find_s hm key)))
+    hashMap_t_inv hm /\
+    Some? (hashMap_t_find_s hm key)))
   (ensures (
-    match hash_map_get_mut_back t hm key ret with
+    match hashMap_get_mut_back t hm key ret with
     | Fail _ -> False
     | Return hm' ->
       // Functional spec
-      hash_map_t_v hm' == hash_map_insert_no_fail_s (hash_map_t_v hm) key ret /\
+      hashMap_t_v hm' == hashMap_insert_no_fail_s (hashMap_t_v hm) key ret /\
      // The invariant is preserved
-     hash_map_t_inv hm' /\
+     hashMap_t_inv hm' /\
      // The length is preserved
-     hash_map_t_len_s hm' = hash_map_t_len_s hm /\
+     hashMap_t_len_s hm' = hashMap_t_len_s hm /\
      // [key] maps to [value]
-     hash_map_t_find_s hm' key == Some ret /\
+     hashMap_t_find_s hm' key == Some ret /\
      // The other bindings are preserved
-     (forall k'. k' <> key ==> hash_map_t_find_s hm' k' == hash_map_t_find_s hm k')))
+     (forall k'. k' <> key ==> hashMap_t_find_s hm' k' == hashMap_t_find_s hm k')))
 
-let hash_map_get_mut_back_lem_aux #t hm key ret =
-  let hm_v = hash_map_t_v hm in
-  hash_map_get_mut_back_lem_refin hm key ret;
-  match hash_map_get_mut_back t hm key ret with
+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' ->
-    hash_map_insert_no_fail_s_lem hm_v key ret
+    hashMap_insert_no_fail_s_lem hm_v key ret
 
 /// .fsti
-let hash_map_get_mut_back_lem #t hm key ret = hash_map_get_mut_back_lem_aux hm key ret
+let hashMap_get_mut_back_lem #t hm key ret = hashMap_get_mut_back_lem_aux hm key ret
 
 (*** remove'fwd *)
 
-val hash_map_remove_from_list_fwd_lem
+val hashMap_remove_from_list_lem
   (#t : Type0) (key : usize) (ls : list_t t) :
   Lemma
   (ensures (
-    match hash_map_remove_from_list_fwd t key ls with
+    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 hash_map_remove_from_list_fwd_lem #t key ls =
+let rec hashMap_remove_from_list_lem #t key ls =
   begin match ls with
-  | ListCons ckey x tl ->
+  | List_Cons ckey x tl ->
     let b = ckey = key in
     if b
     then
-      let mv_ls = mem_replace_fwd (list_t t) (ListCons ckey x tl) ListNil in
+      let mv_ls = core_mem_replace (list_t t) (List_Cons ckey x tl) List_Nil in
       begin match mv_ls with
-      | ListCons i cvalue tl0 -> ()
-      | ListNil -> ()
+      | List_Cons i cvalue tl0 -> ()
+      | List_Nil -> ()
       end
     else
       begin
-      hash_map_remove_from_list_fwd_lem key tl;
-      match hash_map_remove_from_list_fwd t key tl with
+      hashMap_remove_from_list_lem key tl;
+      match hashMap_remove_from_list t key tl with
       | Fail _ -> ()
       | Return opt -> ()
       end
-  | ListNil -> ()
+  | List_Nil -> ()
   end
 #pop-options
 
-val hash_map_remove_fwd_lem_aux
-  (#t : Type0) (self : hash_map_t t) (key : usize) :
+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
-    hash_map_t_inv self))
+    hashMap_t_inv self))
   (ensures (
-    match hash_map_remove_fwd t self key with
+    match hashMap_remove t self key with
     | Fail _ -> False
-    | Return opt_x -> opt_x == hash_map_t_find_s self key))
+    | Return opt_x -> opt_x == hashMap_t_find_s self key))
 
-let hash_map_remove_fwd_lem_aux #t self key =
-  begin match hash_key_fwd key with
+let hashMap_remove_lem_aux #t self key =
+  begin match hash_key key with
   | Fail _ -> ()
   | Return i ->
-    let i0 = self.hash_map_num_entries in
-    let v = self.hash_map_slots in
-    let i1 = vec_len (list_t t) v in
+    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 vec_index_mut_fwd (list_t t) v hash_mod with
+      begin match alloc_vec_Vec_index_usize v hash_mod with
       | Fail _ -> ()
       | Return l ->
         begin
-        hash_map_remove_from_list_fwd_lem key l;
-        match hash_map_remove_from_list_fwd t key l with
+        hashMap_remove_from_list_lem key l;
+        match hashMap_remove_from_list t key l with
         | Fail _ -> ()
         | Return x ->
           begin match x with
@@ -2945,7 +2945,7 @@ let hash_map_remove_fwd_lem_aux #t self key =
             begin
             assert(l == index v hash_mod);
             assert(length (list_t_v #t l) > 0);
-            length_flatten_index (hash_map_t_v self) hash_mod;
+            length_flatten_index (hashMap_t_v self) hash_mod;
             match usize_sub i0 1 with
             | Fail _ -> ()
             | Return _ -> ()
@@ -2957,27 +2957,27 @@ let hash_map_remove_fwd_lem_aux #t self key =
   end
 
 /// .fsti
-let hash_map_remove_fwd_lem #t self key = hash_map_remove_fwd_lem_aux #t self key
+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 hash_map_remove_from_list_s
+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 hash_map_remove_from_list_back_lem_refin
+val hashMap_remove_from_list_back_lem_refin
   (#t : Type0) (key : usize) (ls : list_t t) :
   Lemma
   (ensures (
-    match hash_map_remove_from_list_back t key ls with
+    match hashMap_remove_from_list_back t key ls with
     | Fail _ -> False
     | Return ls' ->
-      list_t_v ls' == hash_map_remove_from_list_s key (list_t_v 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
@@ -2986,89 +2986,89 @@ val hash_map_remove_from_list_back_lem_refin
        | Some _ -> len = len' + 1)))
 
 #push-options "--fuel 1"
-let rec hash_map_remove_from_list_back_lem_refin #t key ls =
+let rec hashMap_remove_from_list_back_lem_refin #t key ls =
   begin match ls with
-  | ListCons ckey x tl ->
+  | List_Cons ckey x tl ->
     let b = ckey = key in
     if b
     then
-      let mv_ls = mem_replace_fwd (list_t t) (ListCons ckey x tl) ListNil in
+      let mv_ls = core_mem_replace (list_t t) (List_Cons ckey x tl) List_Nil in
       begin match mv_ls with
-      | ListCons i cvalue tl0 -> ()
-      | ListNil -> ()
+      | List_Cons i cvalue tl0 -> ()
+      | List_Nil -> ()
       end
     else
       begin
-      hash_map_remove_from_list_back_lem_refin key tl;
-      match hash_map_remove_from_list_back t key tl with
+      hashMap_remove_from_list_back_lem_refin key tl;
+      match hashMap_remove_from_list_back t key tl with
       | Fail _ -> ()
-      | Return l -> let ls0 = ListCons ckey x l in ()
+      | Return l -> let ls0 = List_Cons ckey x l in ()
       end
-  | ListNil -> ()
+  | List_Nil -> ()
   end
 #pop-options
 
 /// High-level model for [remove_from_list'back]
-let hash_map_remove_s
-  (#t : Type0) (self : hash_map_s_nes t) (key : usize) :
-  hash_map_s t =
+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' = hash_map_remove_from_list_s key slot in
+  let slot' = hashMap_remove_from_list_s key slot in
   list_update self hash slot'
 
 /// Refinement lemma
-val hash_map_remove_back_lem_refin
-  (#t : Type0) (self : hash_map_t_nes t) (key : usize) :
+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
-    hash_map_t_inv self))
+    hashMap_t_inv self))
   (ensures (
-    match hash_map_remove_back t self key with
+    match hashMap_remove_back t self key with
     | Fail _ -> False
     | Return hm' ->
-      hash_map_t_same_params hm' self /\
-      hash_map_t_v hm' == hash_map_remove_s (hash_map_t_v self) key /\
+      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 = hash_map_t_len_s self in
-       let len' = hash_map_t_len_s hm' in
-       match hash_map_t_find_s self key with
+      (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 hash_map_remove_back_lem_refin #t self key =
-  begin match hash_key_fwd key with
+let hashMap_remove_back_lem_refin #t self key =
+  begin match hash_key key with
   | Fail _ -> ()
   | Return i ->
-    let i0 = self.hash_map_num_entries in
-    let p = self.hash_map_max_load_factor in
-    let i1 = self.hash_map_max_load in
-    let v = self.hash_map_slots in
-    let i2 = vec_len (list_t t) v in
+    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 vec_index_mut_fwd (list_t t) v hash_mod with
+      begin match alloc_vec_Vec_index_usize v hash_mod with
       | Fail _ -> ()
       | Return l ->
         begin
-        hash_map_remove_from_list_fwd_lem key l;
-        match hash_map_remove_from_list_fwd t key l with
+        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
-            hash_map_remove_from_list_back_lem_refin key l;
-            match hash_map_remove_from_list_back t key l with
+            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 vec_index_mut_back (list_t t) v hash_mod l0 with
+              match alloc_vec_Vec_update_usize v hash_mod l0 with
               | Fail _ -> ()
               | Return v0 -> ()
               end
@@ -3077,18 +3077,18 @@ let hash_map_remove_back_lem_refin #t self key =
             begin
             assert(l == index v hash_mod);
             assert(length (list_t_v #t l) > 0);
-            length_flatten_index (hash_map_t_v self) hash_mod;
+            length_flatten_index (hashMap_t_v self) hash_mod;
             match usize_sub i0 1 with
             | Fail _ -> ()
             | Return i3 ->
               begin
-              hash_map_remove_from_list_back_lem_refin key l;
-              match hash_map_remove_from_list_back t key l with
+              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 vec_index_mut_back (list_t t) v hash_mod l0 with
+                match alloc_vec_Vec_update_usize v hash_mod l0 with
                 | Fail _ -> ()
                 | Return v0 -> ()
                 end
@@ -3102,12 +3102,12 @@ let hash_map_remove_back_lem_refin #t self key =
 
 (**** Invariants, high-level properties *)
 
-val hash_map_remove_from_list_s_lem
+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' = hash_map_remove_from_list_s k slot in
+    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) /\
@@ -3117,14 +3117,14 @@ val hash_map_remove_from_list_s_lem
   ))
 
 #push-options "--fuel 1"
-let rec hash_map_remove_from_list_s_lem #t key slot len i =
+let rec hashMap_remove_from_list_s_lem #t key slot len i =
   match slot with
   | [] -> ()
   | (k',v) :: slot' ->
     if k' <> key then
       begin
-      hash_map_remove_from_list_s_lem key slot' len i;
-      let slot'' = hash_map_remove_from_list_s key slot' in
+      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'')
@@ -3136,51 +3136,51 @@ let rec hash_map_remove_from_list_s_lem #t key slot len i =
       end
 #pop-options
 
-val hash_map_remove_s_lem
-  (#t : Type0) (self : hash_map_s_nes t) (key : usize) :
+val hashMap_remove_s_lem
+  (#t : Type0) (self : hashMap_s_nes t) (key : usize) :
   Lemma
-  (requires (hash_map_s_inv self))
+  (requires (hashMap_s_inv self))
   (ensures (
-    let hm' = hash_map_remove_s self key in
+    let hm' = hashMap_remove_s self key in
     // The invariant is preserved
-    hash_map_s_inv hm' /\
+    hashMap_s_inv hm' /\
     // We updated the binding
-    hash_map_s_updated_binding self key None hm'))
+    hashMap_s_updated_binding self key None hm'))
 
-let hash_map_remove_s_lem #t self key =
+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
-  hash_map_remove_from_list_s_lem key slot len hash;
-  let slot' = hash_map_remove_from_list_s key slot 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(hash_map_s_inv self)
+  assert(hashMap_s_inv self)
 
 /// Final lemma about [remove'back]
-val hash_map_remove_back_lem_aux
-  (#t : Type0) (self : hash_map_t t) (key : usize) :
+val hashMap_remove_back_lem_aux
+  (#t : Type0) (self : hashMap_t t) (key : usize) :
   Lemma
-  (requires (hash_map_t_inv self))
+  (requires (hashMap_t_inv self))
   (ensures (
-    match hash_map_remove_back t self key with
+    match hashMap_remove_back t self key with
     | Fail _ -> False
     | Return hm' ->
-      hash_map_t_inv self /\
-      hash_map_t_same_params hm' self /\
+      hashMap_t_inv self /\
+      hashMap_t_same_params hm' self /\
       // We updated the binding
-      hash_map_s_updated_binding (hash_map_t_v self) key None (hash_map_t_v hm') /\
-      hash_map_t_v hm' == hash_map_remove_s (hash_map_t_v self) key /\
+      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 = hash_map_t_len_s self in
-       let len' = hash_map_t_len_s hm' in
-       match hash_map_t_find_s self key with
+      (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 hash_map_remove_back_lem_aux #t self key =
-  hash_map_remove_back_lem_refin self key;
-  hash_map_remove_s_lem (hash_map_t_v self) key
+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 hash_map_remove_back_lem #t self key =
-  hash_map_remove_back_lem_aux #t self key
+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
index 0a4f0134..26c0ec06 100644
--- a/tests/fstar/hashmap/Hashmap.Properties.fsti
+++ b/tests/fstar/hashmap/Hashmap.Properties.fsti
@@ -18,11 +18,11 @@ type key : eqtype = usize
 
 type hash : eqtype = usize
 
-val hash_map_t_inv (#t : Type0) (hm : hash_map_t t) : Type0
+val hashMap_t_inv (#t : Type0) (hm : hashMap_t t) : Type0
 
-val len_s (#t : Type0) (hm : hash_map_t t) : nat
+val len_s (#t : Type0) (hm : hashMap_t t) : nat
 
-val find_s (#t : Type0) (hm : hash_map_t t) (k : key) : option t
+val find_s (#t : Type0) (hm : hashMap_t t) (k : key) : option t
 
 (*** Overloading *)
 
@@ -32,16 +32,16 @@ val find_s (#t : Type0) (hm : hash_map_t t) (k : key) : option t
 /// limiting the hash collisions.
 /// This is expressed by the following property, which is maintained in the hash
 /// map invariant.
-val hash_map_not_overloaded_lem (#t : Type0) (hm : hash_map_t t) :
+val hashMap_not_overloaded_lem (#t : Type0) (hm : hashMap_t t) :
   Lemma
-  (requires (hash_map_t_inv hm))
+  (requires (hashMap_t_inv hm))
   (ensures (
     // The capacity is the number of slots
-    let capacity = length hm.hash_map_slots in
+    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.hash_map_max_load_factor in
+    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 /\
@@ -63,14 +63,14 @@ val hash_map_not_overloaded_lem (#t : Type0) (hm : hash_map_t t) :
 (**** [new'fwd] *)
 
 /// [new] doesn't fail and returns an empty hash map
-val hash_map_new_fwd_lem (t : Type0) :
+val hashMap_new_lem (t : Type0) :
   Lemma
   (ensures (
-    match hash_map_new_fwd t with
+    match hashMap_new t with
     | Fail _ -> False
     | Return hm ->
       // The hash map invariant is satisfied
-      hash_map_t_inv hm /\
+      hashMap_t_inv hm /\
       // The hash map has a length of 0
       len_s hm = 0 /\
       // It contains no bindings
@@ -79,16 +79,16 @@ val hash_map_new_fwd_lem (t : Type0) :
 (**** [clear] *)
 
 /// [clear] doesn't fail and turns the hash map into an empty map
-val hash_map_clear_fwd_back_lem
-  (#t : Type0) (self : hash_map_t t) :
+val hashMap_clear_lem
+  (#t : Type0) (self : hashMap_t t) :
   Lemma
-  (requires (hash_map_t_inv self))
+  (requires (hashMap_t_inv self))
   (ensures (
-    match hash_map_clear_fwd_back t self with
+    match hashMap_clear t self with
     | Fail _ -> False
     | Return hm ->
       // The hash map invariant is satisfied
-      hash_map_t_inv hm /\
+      hashMap_t_inv hm /\
       // The hash map has a length of 0
       len_s hm = 0 /\
       // It contains no bindings
@@ -97,11 +97,11 @@ val hash_map_clear_fwd_back_lem
 (**** [len] *)
 
 /// [len] can't fail and returns the length (the number of elements) of the hash map
-val hash_map_len_fwd_lem (#t : Type0) (self : hash_map_t t) :
+val hashMap_len_lem (#t : Type0) (self : hashMap_t t) :
   Lemma
-  (requires (hash_map_t_inv self))
+  (requires (hashMap_t_inv self))
   (ensures (
-    match hash_map_len_fwd t self with
+    match hashMap_len t self with
     | Fail _ -> False
     | Return l -> l = len_s self))
 
@@ -114,12 +114,12 @@ val hash_map_len_fwd_lem (#t : Type0) (self : hash_map_t t) :
 /// entirely encompassed by the effect of the backward function alone).
 /// 
 /// [insert'fwd_back] simply inserts a binding.
-val hash_map_insert_fwd_back_lem
-  (#t : Type0) (self : hash_map_t t) (key : usize) (value : t) :
+val hashMap_insert_lem
+  (#t : Type0) (self : hashMap_t t) (key : usize) (value : t) :
   Lemma
-  (requires (hash_map_t_inv self))
+  (requires (hashMap_t_inv self))
   (ensures (
-    match hash_map_insert_fwd_back t self key value with
+    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
@@ -128,7 +128,7 @@ val hash_map_insert_fwd_back_lem
       len_s self = usize_max
     | Return hm' ->
       // The invariant is preserved
-      hash_map_t_inv hm' /\
+      hashMap_t_inv hm' /\
       // [key] maps to [value]
       find_s hm' key == Some value /\
       // The other bindings are preserved
@@ -145,24 +145,24 @@ val hash_map_insert_fwd_back_lem
 
 /// [contains_key'fwd] can't fail and returns `true` if and only if there is
 /// a binding for key [key]
-val hash_map_contains_key_fwd_lem
-  (#t : Type0) (self : hash_map_t t) (key : usize) :
+val hashMap_contains_key_lem
+  (#t : Type0) (self : hashMap_t t) (key : usize) :
   Lemma
-  (requires (hash_map_t_inv self))
+  (requires (hashMap_t_inv self))
   (ensures (
-    match hash_map_contains_key_fwd t self key with
+    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 hash_map_get_fwd_lem
-  (#t : Type0) (self : hash_map_t t) (key : usize) :
+val hashMap_get_lem
+  (#t : Type0) (self : hashMap_t t) (key : usize) :
   Lemma
-  (requires (hash_map_t_inv self))
+  (requires (hashMap_t_inv self))
   (ensures (
-    match hash_map_get_fwd t self key, find_s self key with
+    match hashMap_get t self key, find_s self key with
     | Fail _, None -> True
     | Return x, Some x' -> x == x'
     | _ -> False))
@@ -175,12 +175,12 @@ val hash_map_get_fwd_lem
 /// 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 hash_map_get_mut_fwd_lem
-  (#t : Type0) (self : hash_map_t t) (key : usize) :
+val hashMap_get_mut_lem
+  (#t : Type0) (self : hashMap_t t) (key : usize) :
   Lemma
-  (requires (hash_map_t_inv self))
+  (requires (hashMap_t_inv self))
   (ensures (
-    match hash_map_get_mut_fwd t self key, find_s self key with
+    match hashMap_get_mut t self key, find_s self key with
     | Fail _, None -> True
     | Return x, Some x' -> x == x'
     | _ -> False))
@@ -192,11 +192,11 @@ val hash_map_get_mut_fwd_lem
 /// 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 hash_map_get_mut_back_lem
-  (#t : Type0) (hm : hash_map_t t) (key : usize) (ret : t) :
+val hashMap_get_mut_back_lem
+  (#t : Type0) (hm : hashMap_t t) (key : usize) (ret : t) :
   Lemma
   (requires (
-    hash_map_t_inv hm /\
+    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
@@ -207,14 +207,14 @@ val hash_map_get_mut_back_lem
     // "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
-    // [hash_map_clear_fwd_back]).
+    // [hashMap_clear]).
     Some? (find_s hm key)))
   (ensures (
-    match hash_map_get_mut_back t hm key ret with
+    match hashMap_get_mut_back t hm key ret with
     | Fail _ -> False // Can't fail
     | Return hm' ->
      // The invariant is preserved
-     hash_map_t_inv hm' /\
+     hashMap_t_inv hm' /\
      // The length is preserved
      len_s hm' = len_s hm /\
      // [key] maps to the update value, [ret]
@@ -228,12 +228,12 @@ val hash_map_get_mut_back_lem
 /// (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 hash_map_remove_fwd_lem
-  (#t : Type0) (self : hash_map_t t) (key : usize) :
+val hashMap_remove_lem
+  (#t : Type0) (self : hashMap_t t) (key : usize) :
   Lemma
-  (requires (hash_map_t_inv self))
+  (requires (hashMap_t_inv self))
   (ensures (
-    match hash_map_remove_fwd t self key with
+    match hashMap_remove t self key with
     | Fail _ -> False
     | Return opt_x -> opt_x == find_s self key))
 
@@ -243,16 +243,16 @@ val hash_map_remove_fwd_lem
 /// 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 hash_map_remove_back_lem
-  (#t : Type0) (self : hash_map_t t) (key : usize) :
+val hashMap_remove_back_lem
+  (#t : Type0) (self : hashMap_t t) (key : usize) :
   Lemma
-  (requires (hash_map_t_inv self))
+  (requires (hashMap_t_inv self))
   (ensures (
-    match hash_map_remove_back t self key with
+    match hashMap_remove_back t self key with
     | Fail _ -> False
     | Return hm' ->
       // The invariant is preserved
-      hash_map_t_inv self /\
+      hashMap_t_inv self /\
       // The binding for [key] is not there anymore
       find_s hm' key == None /\
       // The other bindings are preserved
diff --git a/tests/fstar/hashmap/Primitives.fst b/tests/fstar/hashmap/Primitives.fst
index 71d75c11..3297803c 100644
--- a/tests/fstar/hashmap/Primitives.fst
+++ b/tests/fstar/hashmap/Primitives.fst
@@ -427,7 +427,7 @@ let alloc_vec_Vec_new (a  : Type0) : alloc_vec_Vec a = assert_norm(length #a []
 let alloc_vec_Vec_len (a : Type0) (v : alloc_vec_Vec a) : usize = length v
 
 // Helper
-let alloc_vec_Vec_index_usize (#a : Type0) (v : alloc_vec_Vec a) (i : usize) (x : a) : result a =
+let alloc_vec_Vec_index_usize (#a : Type0) (v : alloc_vec_Vec a) (i : usize) : result a =
   if i < length v then Return (index v i) else Fail Failure
 // Helper
 let alloc_vec_Vec_update_usize (#a : Type0) (v : alloc_vec_Vec a) (i : usize) (x : a) : result (alloc_vec_Vec a) =
@@ -704,6 +704,22 @@ let alloc_vec_Vec_coreopsindexIndexMutInst (t idx : Type0)
 
 (*** Theorems *)
 
+let alloc_vec_Vec_index_eq (#a : Type0) (v : alloc_vec_Vec a) (i : usize) :
+  Lemma (
+    alloc_vec_Vec_index a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i ==
+      alloc_vec_Vec_index_usize v i)
+  [SMTPat (alloc_vec_Vec_index a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i)]
+  =
+  admit()
+
+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_usize_coresliceindexSliceIndexInst a) v i ==
+      alloc_vec_Vec_index_usize v i)
+  [SMTPat (alloc_vec_Vec_index_mut a usize (core_slice_index_usize_coresliceindexSliceIndexInst 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_usize_coresliceindexSliceIndexInst a) v i x ==
diff --git a/tests/fstar/hashmap_on_disk/HashmapMain.Properties.fst b/tests/fstar/hashmap_on_disk/HashmapMain.Properties.fst
index 106fe05a..358df29e 100644
--- a/tests/fstar/hashmap_on_disk/HashmapMain.Properties.fst
+++ b/tests/fstar/hashmap_on_disk/HashmapMain.Properties.fst
@@ -13,36 +13,36 @@ open HashmapMain.Funs
 
 /// [state_v] gives us the hash map currently stored on disk
 assume
-val state_v : state -> hashmap_hash_map_t u64
+val state_v : state -> hashmap_HashMap_t u64
 
 /// [serialize] updates the hash map stored on disk
 assume
-val serialize_lem (hm : hashmap_hash_map_t u64) (st : state) : Lemma (
-  match hashmap_utils_serialize_fwd hm st with
+val serialize_lem (hm : hashmap_HashMap_t u64) (st : state) : Lemma (
+  match hashmap_utils_serialize hm st with
   | Fail _ -> True
   | Return (st', ()) -> state_v st' == hm)
-  [SMTPat (hashmap_utils_serialize_fwd hm st)]
+  [SMTPat (hashmap_utils_serialize hm st)]
 
 /// [deserialize] gives us the hash map stored on disk, without updating it
 assume
 val deserialize_lem (st : state) : Lemma (
-  match hashmap_utils_deserialize_fwd st with
+  match hashmap_utils_deserialize st with
   | Fail _ -> True
   | Return (st', hm) -> hm == state_v st /\ st' == st)
-  [SMTPat (hashmap_utils_deserialize_fwd st)]
+  [SMTPat (hashmap_utils_deserialize st)]
 
 (*** Lemmas *)
 
 /// The obvious lemma about [insert_on_disk]: the updated hash map stored on disk
 /// is exactly the hash map produced from inserting the binding ([key], [value])
 /// in the hash map previously stored on disk.
-val insert_on_disk_fwd_lem (key : usize) (value : u64) (st : state) : Lemma (
-  match insert_on_disk_fwd key value st with
+val insert_on_disk_lem (key : usize) (value : u64) (st : state) : Lemma (
+  match insert_on_disk key value st with
   | Fail _ -> True
   | Return (st', ()) ->
     let hm = state_v st in
-    match hashmap_hash_map_insert_fwd_back u64 hm key value with
+    match hashmap_HashMap_insert u64 hm key value with
     | Fail _ -> False
     | Return hm' -> hm' == state_v st')
 
-let insert_on_disk_fwd_lem key value st = ()
+let insert_on_disk_lem key value st = ()
diff --git a/tests/fstar/hashmap_on_disk/Primitives.fst b/tests/fstar/hashmap_on_disk/Primitives.fst
index 71d75c11..3297803c 100644
--- a/tests/fstar/hashmap_on_disk/Primitives.fst
+++ b/tests/fstar/hashmap_on_disk/Primitives.fst
@@ -427,7 +427,7 @@ let alloc_vec_Vec_new (a  : Type0) : alloc_vec_Vec a = assert_norm(length #a []
 let alloc_vec_Vec_len (a : Type0) (v : alloc_vec_Vec a) : usize = length v
 
 // Helper
-let alloc_vec_Vec_index_usize (#a : Type0) (v : alloc_vec_Vec a) (i : usize) (x : a) : result a =
+let alloc_vec_Vec_index_usize (#a : Type0) (v : alloc_vec_Vec a) (i : usize) : result a =
   if i < length v then Return (index v i) else Fail Failure
 // Helper
 let alloc_vec_Vec_update_usize (#a : Type0) (v : alloc_vec_Vec a) (i : usize) (x : a) : result (alloc_vec_Vec a) =
@@ -704,6 +704,22 @@ let alloc_vec_Vec_coreopsindexIndexMutInst (t idx : Type0)
 
 (*** Theorems *)
 
+let alloc_vec_Vec_index_eq (#a : Type0) (v : alloc_vec_Vec a) (i : usize) :
+  Lemma (
+    alloc_vec_Vec_index a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i ==
+      alloc_vec_Vec_index_usize v i)
+  [SMTPat (alloc_vec_Vec_index a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i)]
+  =
+  admit()
+
+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_usize_coresliceindexSliceIndexInst a) v i ==
+      alloc_vec_Vec_index_usize v i)
+  [SMTPat (alloc_vec_Vec_index_mut a usize (core_slice_index_usize_coresliceindexSliceIndexInst 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_usize_coresliceindexSliceIndexInst a) v i x ==
diff --git a/tests/fstar/misc/Loops.fst b/tests/fstar/misc/Loops.fst
deleted file mode 100644
index 823acdd4..00000000
--- a/tests/fstar/misc/Loops.fst
+++ /dev/null
@@ -1,784 +0,0 @@
-(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
-(** [loops] *)
-module Loops
-open Primitives
-
-#set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
-
-(** [loops::sum]: decreases clause *)
-unfold let sum_loop_decreases (max : u32) (i : u32) (s : u32) : nat = admit ()
-
-(** [loops::sum]: loop 0: forward function *)
-let rec sum_loop
-  (max : u32) (i : u32) (s : u32) :
-  Tot (result u32) (decreases (sum_loop_decreases max i s))
-  =
-  if i < max
-  then let* s0 = u32_add s i in let* i0 = u32_add i 1 in sum_loop max i0 s0
-  else u32_mul s 2
-
-(** [loops::sum]: forward function *)
-let sum (max : u32) : result u32 =
-  sum_loop max 0 0
-
-(** [loops::sum_with_mut_borrows]: decreases clause *)
-unfold
-let sum_with_mut_borrows_loop_decreases (max : u32) (mi : u32) (ms : u32) : nat
-  =
-  admit ()
-
-(** [loops::sum_with_mut_borrows]: loop 0: forward function *)
-let rec sum_with_mut_borrows_loop
-  (max : u32) (mi : u32) (ms : u32) :
-  Tot (result u32) (decreases (sum_with_mut_borrows_loop_decreases max mi ms))
-  =
-  if mi < max
-  then
-    let* ms0 = u32_add ms mi in
-    let* mi0 = u32_add mi 1 in
-    sum_with_mut_borrows_loop max mi0 ms0
-  else u32_mul ms 2
-
-(** [loops::sum_with_mut_borrows]: forward function *)
-let sum_with_mut_borrows (max : u32) : result u32 =
-  sum_with_mut_borrows_loop max 0 0
-
-(** [loops::sum_with_shared_borrows]: decreases clause *)
-unfold
-let sum_with_shared_borrows_loop_decreases (max : u32) (i : u32) (s : u32) :
-  nat =
-  admit ()
-
-(** [loops::sum_with_shared_borrows]: loop 0: forward function *)
-let rec sum_with_shared_borrows_loop
-  (max : u32) (i : u32) (s : u32) :
-  Tot (result u32) (decreases (sum_with_shared_borrows_loop_decreases max i s))
-  =
-  if i < max
-  then
-    let* i0 = u32_add i 1 in
-    let* s0 = u32_add s i0 in
-    sum_with_shared_borrows_loop max i0 s0
-  else u32_mul s 2
-
-(** [loops::sum_with_shared_borrows]: forward function *)
-let sum_with_shared_borrows (max : u32) : result u32 =
-  sum_with_shared_borrows_loop max 0 0
-
-(** [loops::clear]: decreases clause *)
-unfold
-let clear_loop_decreases (v : alloc_vec_Vec u32) (i : usize) : nat = admit ()
-
-(** [loops::clear]: loop 0: merged forward/backward function
-    (there is a single backward function, and the forward function returns ()) *)
-let rec clear_loop
-  (v : alloc_vec_Vec u32) (i : usize) :
-  Tot (result (alloc_vec_Vec u32)) (decreases (clear_loop_decreases v i))
-  =
-  let i0 = alloc_vec_Vec_len u32 v in
-  if i < i0
-  then
-    let* i1 = usize_add i 1 in
-    let* v0 =
-      alloc_vec_Vec_index_mut_back u32 usize
-        (core_slice_index_usize_coresliceindexSliceIndexInst u32) v i 0 in
-    clear_loop v0 i1
-  else Return v
-
-(** [loops::clear]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ()) *)
-let clear (v : alloc_vec_Vec u32) : result (alloc_vec_Vec u32) =
-  clear_loop v 0
-
-(** [loops::List] *)
-type list_t (t : Type0) =
-| List_Cons : t -> list_t t -> list_t t
-| List_Nil : list_t t
-
-(** [loops::list_mem]: decreases clause *)
-unfold let list_mem_loop_decreases (x : u32) (ls : list_t u32) : nat = admit ()
-
-(** [loops::list_mem]: loop 0: forward function *)
-let rec list_mem_loop
-  (x : u32) (ls : list_t u32) :
-  Tot (result bool) (decreases (list_mem_loop_decreases x ls))
-  =
-  begin match ls with
-  | List_Cons y tl -> if y = x then Return true else list_mem_loop x tl
-  | List_Nil -> Return false
-  end
-
-(** [loops::list_mem]: forward function *)
-let list_mem (x : u32) (ls : list_t u32) : result bool =
-  list_mem_loop x ls
-
-(** [loops::list_nth_mut_loop]: decreases clause *)
-unfold
-let list_nth_mut_loop_loop_decreases (t : Type0) (ls : list_t t) (i : u32) :
-  nat =
-  admit ()
-
-(** [loops::list_nth_mut_loop]: loop 0: forward function *)
-let rec list_nth_mut_loop_loop
-  (t : Type0) (ls : list_t t) (i : u32) :
-  Tot (result t) (decreases (list_nth_mut_loop_loop_decreases t ls i))
-  =
-  begin match ls with
-  | List_Cons x tl ->
-    if i = 0
-    then Return x
-    else let* i0 = u32_sub i 1 in list_nth_mut_loop_loop t tl i0
-  | List_Nil -> Fail Failure
-  end
-
-(** [loops::list_nth_mut_loop]: forward function *)
-let list_nth_mut_loop (t : Type0) (ls : list_t t) (i : u32) : result t =
-  list_nth_mut_loop_loop t ls i
-
-(** [loops::list_nth_mut_loop]: loop 0: backward function 0 *)
-let rec list_nth_mut_loop_loop_back
-  (t : Type0) (ls : list_t t) (i : u32) (ret : t) :
-  Tot (result (list_t t)) (decreases (list_nth_mut_loop_loop_decreases t ls i))
-  =
-  begin match ls with
-  | List_Cons x tl ->
-    if i = 0
-    then Return (List_Cons ret tl)
-    else
-      let* i0 = u32_sub i 1 in
-      let* tl0 = list_nth_mut_loop_loop_back t tl i0 ret in
-      Return (List_Cons x tl0)
-  | List_Nil -> Fail Failure
-  end
-
-(** [loops::list_nth_mut_loop]: backward function 0 *)
-let list_nth_mut_loop_back
-  (t : Type0) (ls : list_t t) (i : u32) (ret : t) : result (list_t t) =
-  list_nth_mut_loop_loop_back t ls i ret
-
-(** [loops::list_nth_shared_loop]: decreases clause *)
-unfold
-let list_nth_shared_loop_loop_decreases (t : Type0) (ls : list_t t) (i : u32) :
-  nat =
-  admit ()
-
-(** [loops::list_nth_shared_loop]: loop 0: forward function *)
-let rec list_nth_shared_loop_loop
-  (t : Type0) (ls : list_t t) (i : u32) :
-  Tot (result t) (decreases (list_nth_shared_loop_loop_decreases t ls i))
-  =
-  begin match ls with
-  | List_Cons x tl ->
-    if i = 0
-    then Return x
-    else let* i0 = u32_sub i 1 in list_nth_shared_loop_loop t tl i0
-  | List_Nil -> Fail Failure
-  end
-
-(** [loops::list_nth_shared_loop]: forward function *)
-let list_nth_shared_loop (t : Type0) (ls : list_t t) (i : u32) : result t =
-  list_nth_shared_loop_loop t ls i
-
-(** [loops::get_elem_mut]: decreases clause *)
-unfold
-let get_elem_mut_loop_decreases (x : usize) (ls : list_t usize) : nat =
-  admit ()
-
-(** [loops::get_elem_mut]: loop 0: forward function *)
-let rec get_elem_mut_loop
-  (x : usize) (ls : list_t usize) :
-  Tot (result usize) (decreases (get_elem_mut_loop_decreases x ls))
-  =
-  begin match ls with
-  | List_Cons y tl -> if y = x then Return y else get_elem_mut_loop x tl
-  | List_Nil -> Fail Failure
-  end
-
-(** [loops::get_elem_mut]: forward function *)
-let get_elem_mut
-  (slots : alloc_vec_Vec (list_t usize)) (x : usize) : result usize =
-  let* l =
-    alloc_vec_Vec_index_mut (list_t usize) usize
-      (core_slice_index_usize_coresliceindexSliceIndexInst (list_t usize))
-      slots 0 in
-  get_elem_mut_loop x l
-
-(** [loops::get_elem_mut]: loop 0: backward function 0 *)
-let rec get_elem_mut_loop_back
-  (x : usize) (ls : list_t usize) (ret : usize) :
-  Tot (result (list_t usize)) (decreases (get_elem_mut_loop_decreases x ls))
-  =
-  begin match ls with
-  | List_Cons y tl ->
-    if y = x
-    then Return (List_Cons ret tl)
-    else let* tl0 = get_elem_mut_loop_back x tl ret in Return (List_Cons y tl0)
-  | List_Nil -> Fail Failure
-  end
-
-(** [loops::get_elem_mut]: backward function 0 *)
-let get_elem_mut_back
-  (slots : alloc_vec_Vec (list_t usize)) (x : usize) (ret : usize) :
-  result (alloc_vec_Vec (list_t usize))
-  =
-  let* l =
-    alloc_vec_Vec_index_mut (list_t usize) usize
-      (core_slice_index_usize_coresliceindexSliceIndexInst (list_t usize))
-      slots 0 in
-  let* l0 = get_elem_mut_loop_back x l ret in
-  alloc_vec_Vec_index_mut_back (list_t usize) usize
-    (core_slice_index_usize_coresliceindexSliceIndexInst (list_t usize)) slots
-    0 l0
-
-(** [loops::get_elem_shared]: decreases clause *)
-unfold
-let get_elem_shared_loop_decreases (x : usize) (ls : list_t usize) : nat =
-  admit ()
-
-(** [loops::get_elem_shared]: loop 0: forward function *)
-let rec get_elem_shared_loop
-  (x : usize) (ls : list_t usize) :
-  Tot (result usize) (decreases (get_elem_shared_loop_decreases x ls))
-  =
-  begin match ls with
-  | List_Cons y tl -> if y = x then Return y else get_elem_shared_loop x tl
-  | List_Nil -> Fail Failure
-  end
-
-(** [loops::get_elem_shared]: forward function *)
-let get_elem_shared
-  (slots : alloc_vec_Vec (list_t usize)) (x : usize) : result usize =
-  let* l =
-    alloc_vec_Vec_index (list_t usize) usize
-      (core_slice_index_usize_coresliceindexSliceIndexInst (list_t usize))
-      slots 0 in
-  get_elem_shared_loop x l
-
-(** [loops::id_mut]: forward function *)
-let id_mut (t : Type0) (ls : list_t t) : result (list_t t) =
-  Return ls
-
-(** [loops::id_mut]: backward function 0 *)
-let id_mut_back
-  (t : Type0) (ls : list_t t) (ret : list_t t) : result (list_t t) =
-  Return ret
-
-(** [loops::id_shared]: forward function *)
-let id_shared (t : Type0) (ls : list_t t) : result (list_t t) =
-  Return ls
-
-(** [loops::list_nth_mut_loop_with_id]: decreases clause *)
-unfold
-let list_nth_mut_loop_with_id_loop_decreases (t : Type0) (i : u32)
-  (ls : list_t t) : nat =
-  admit ()
-
-(** [loops::list_nth_mut_loop_with_id]: loop 0: forward function *)
-let rec list_nth_mut_loop_with_id_loop
-  (t : Type0) (i : u32) (ls : list_t t) :
-  Tot (result t) (decreases (list_nth_mut_loop_with_id_loop_decreases t i ls))
-  =
-  begin match ls with
-  | List_Cons x tl ->
-    if i = 0
-    then Return x
-    else let* i0 = u32_sub i 1 in list_nth_mut_loop_with_id_loop t i0 tl
-  | List_Nil -> Fail Failure
-  end
-
-(** [loops::list_nth_mut_loop_with_id]: forward function *)
-let list_nth_mut_loop_with_id
-  (t : Type0) (ls : list_t t) (i : u32) : result t =
-  let* ls0 = id_mut t ls in list_nth_mut_loop_with_id_loop t i ls0
-
-(** [loops::list_nth_mut_loop_with_id]: loop 0: backward function 0 *)
-let rec list_nth_mut_loop_with_id_loop_back
-  (t : Type0) (i : u32) (ls : list_t t) (ret : t) :
-  Tot (result (list_t t))
-  (decreases (list_nth_mut_loop_with_id_loop_decreases t i ls))
-  =
-  begin match ls with
-  | List_Cons x tl ->
-    if i = 0
-    then Return (List_Cons ret tl)
-    else
-      let* i0 = u32_sub i 1 in
-      let* tl0 = list_nth_mut_loop_with_id_loop_back t i0 tl ret in
-      Return (List_Cons x tl0)
-  | List_Nil -> Fail Failure
-  end
-
-(** [loops::list_nth_mut_loop_with_id]: backward function 0 *)
-let list_nth_mut_loop_with_id_back
-  (t : Type0) (ls : list_t t) (i : u32) (ret : t) : result (list_t t) =
-  let* ls0 = id_mut t ls in
-  let* l = list_nth_mut_loop_with_id_loop_back t i ls0 ret in
-  id_mut_back t ls l
-
-(** [loops::list_nth_shared_loop_with_id]: decreases clause *)
-unfold
-let list_nth_shared_loop_with_id_loop_decreases (t : Type0) (i : u32)
-  (ls : list_t t) : nat =
-  admit ()
-
-(** [loops::list_nth_shared_loop_with_id]: loop 0: forward function *)
-let rec list_nth_shared_loop_with_id_loop
-  (t : Type0) (i : u32) (ls : list_t t) :
-  Tot (result t)
-  (decreases (list_nth_shared_loop_with_id_loop_decreases t i ls))
-  =
-  begin match ls with
-  | List_Cons x tl ->
-    if i = 0
-    then Return x
-    else let* i0 = u32_sub i 1 in list_nth_shared_loop_with_id_loop t i0 tl
-  | List_Nil -> Fail Failure
-  end
-
-(** [loops::list_nth_shared_loop_with_id]: forward function *)
-let list_nth_shared_loop_with_id
-  (t : Type0) (ls : list_t t) (i : u32) : result t =
-  let* ls0 = id_shared t ls in list_nth_shared_loop_with_id_loop t i ls0
-
-(** [loops::list_nth_mut_loop_pair]: decreases clause *)
-unfold
-let list_nth_mut_loop_pair_loop_decreases (t : Type0) (ls0 : list_t t)
-  (ls1 : list_t t) (i : u32) : nat =
-  admit ()
-
-(** [loops::list_nth_mut_loop_pair]: loop 0: forward function *)
-let rec list_nth_mut_loop_pair_loop
-  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) :
-  Tot (result (t & t))
-  (decreases (list_nth_mut_loop_pair_loop_decreases t ls0 ls1 i))
-  =
-  begin match ls0 with
-  | List_Cons x0 tl0 ->
-    begin match ls1 with
-    | List_Cons x1 tl1 ->
-      if i = 0
-      then Return (x0, x1)
-      else let* i0 = u32_sub i 1 in list_nth_mut_loop_pair_loop t tl0 tl1 i0
-    | List_Nil -> Fail Failure
-    end
-  | List_Nil -> Fail Failure
-  end
-
-(** [loops::list_nth_mut_loop_pair]: forward function *)
-let list_nth_mut_loop_pair
-  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) : result (t & t) =
-  list_nth_mut_loop_pair_loop t ls0 ls1 i
-
-(** [loops::list_nth_mut_loop_pair]: loop 0: backward function 0 *)
-let rec list_nth_mut_loop_pair_loop_back'a
-  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) :
-  Tot (result (list_t t))
-  (decreases (list_nth_mut_loop_pair_loop_decreases t ls0 ls1 i))
-  =
-  begin match ls0 with
-  | List_Cons x0 tl0 ->
-    begin match ls1 with
-    | List_Cons x1 tl1 ->
-      if i = 0
-      then Return (List_Cons ret tl0)
-      else
-        let* i0 = u32_sub i 1 in
-        let* tl00 = list_nth_mut_loop_pair_loop_back'a t tl0 tl1 i0 ret in
-        Return (List_Cons x0 tl00)
-    | List_Nil -> Fail Failure
-    end
-  | List_Nil -> Fail Failure
-  end
-
-(** [loops::list_nth_mut_loop_pair]: backward function 0 *)
-let list_nth_mut_loop_pair_back'a
-  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) :
-  result (list_t t)
-  =
-  list_nth_mut_loop_pair_loop_back'a t ls0 ls1 i ret
-
-(** [loops::list_nth_mut_loop_pair]: loop 0: backward function 1 *)
-let rec list_nth_mut_loop_pair_loop_back'b
-  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) :
-  Tot (result (list_t t))
-  (decreases (list_nth_mut_loop_pair_loop_decreases t ls0 ls1 i))
-  =
-  begin match ls0 with
-  | List_Cons x0 tl0 ->
-    begin match ls1 with
-    | List_Cons x1 tl1 ->
-      if i = 0
-      then Return (List_Cons ret tl1)
-      else
-        let* i0 = u32_sub i 1 in
-        let* tl10 = list_nth_mut_loop_pair_loop_back'b t tl0 tl1 i0 ret in
-        Return (List_Cons x1 tl10)
-    | List_Nil -> Fail Failure
-    end
-  | List_Nil -> Fail Failure
-  end
-
-(** [loops::list_nth_mut_loop_pair]: backward function 1 *)
-let list_nth_mut_loop_pair_back'b
-  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) :
-  result (list_t t)
-  =
-  list_nth_mut_loop_pair_loop_back'b t ls0 ls1 i ret
-
-(** [loops::list_nth_shared_loop_pair]: decreases clause *)
-unfold
-let list_nth_shared_loop_pair_loop_decreases (t : Type0) (ls0 : list_t t)
-  (ls1 : list_t t) (i : u32) : nat =
-  admit ()
-
-(** [loops::list_nth_shared_loop_pair]: loop 0: forward function *)
-let rec list_nth_shared_loop_pair_loop
-  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) :
-  Tot (result (t & t))
-  (decreases (list_nth_shared_loop_pair_loop_decreases t ls0 ls1 i))
-  =
-  begin match ls0 with
-  | List_Cons x0 tl0 ->
-    begin match ls1 with
-    | List_Cons x1 tl1 ->
-      if i = 0
-      then Return (x0, x1)
-      else let* i0 = u32_sub i 1 in list_nth_shared_loop_pair_loop t tl0 tl1 i0
-    | List_Nil -> Fail Failure
-    end
-  | List_Nil -> Fail Failure
-  end
-
-(** [loops::list_nth_shared_loop_pair]: forward function *)
-let list_nth_shared_loop_pair
-  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) : result (t & t) =
-  list_nth_shared_loop_pair_loop t ls0 ls1 i
-
-(** [loops::list_nth_mut_loop_pair_merge]: decreases clause *)
-unfold
-let list_nth_mut_loop_pair_merge_loop_decreases (t : Type0) (ls0 : list_t t)
-  (ls1 : list_t t) (i : u32) : nat =
-  admit ()
-
-(** [loops::list_nth_mut_loop_pair_merge]: loop 0: forward function *)
-let rec list_nth_mut_loop_pair_merge_loop
-  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) :
-  Tot (result (t & t))
-  (decreases (list_nth_mut_loop_pair_merge_loop_decreases t ls0 ls1 i))
-  =
-  begin match ls0 with
-  | List_Cons x0 tl0 ->
-    begin match ls1 with
-    | List_Cons x1 tl1 ->
-      if i = 0
-      then Return (x0, x1)
-      else
-        let* i0 = u32_sub i 1 in list_nth_mut_loop_pair_merge_loop t tl0 tl1 i0
-    | List_Nil -> Fail Failure
-    end
-  | List_Nil -> Fail Failure
-  end
-
-(** [loops::list_nth_mut_loop_pair_merge]: forward function *)
-let list_nth_mut_loop_pair_merge
-  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) : result (t & t) =
-  list_nth_mut_loop_pair_merge_loop t ls0 ls1 i
-
-(** [loops::list_nth_mut_loop_pair_merge]: loop 0: backward function 0 *)
-let rec list_nth_mut_loop_pair_merge_loop_back
-  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : (t & t)) :
-  Tot (result ((list_t t) & (list_t t)))
-  (decreases (list_nth_mut_loop_pair_merge_loop_decreases t ls0 ls1 i))
-  =
-  begin match ls0 with
-  | List_Cons x0 tl0 ->
-    begin match ls1 with
-    | List_Cons x1 tl1 ->
-      if i = 0
-      then let (x, x2) = ret in Return (List_Cons x tl0, List_Cons x2 tl1)
-      else
-        let* i0 = u32_sub i 1 in
-        let* (tl00, tl10) =
-          list_nth_mut_loop_pair_merge_loop_back t tl0 tl1 i0 ret in
-        Return (List_Cons x0 tl00, List_Cons x1 tl10)
-    | List_Nil -> Fail Failure
-    end
-  | List_Nil -> Fail Failure
-  end
-
-(** [loops::list_nth_mut_loop_pair_merge]: backward function 0 *)
-let list_nth_mut_loop_pair_merge_back
-  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : (t & t)) :
-  result ((list_t t) & (list_t t))
-  =
-  list_nth_mut_loop_pair_merge_loop_back t ls0 ls1 i ret
-
-(** [loops::list_nth_shared_loop_pair_merge]: decreases clause *)
-unfold
-let list_nth_shared_loop_pair_merge_loop_decreases (t : Type0) (ls0 : list_t t)
-  (ls1 : list_t t) (i : u32) : nat =
-  admit ()
-
-(** [loops::list_nth_shared_loop_pair_merge]: loop 0: forward function *)
-let rec list_nth_shared_loop_pair_merge_loop
-  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) :
-  Tot (result (t & t))
-  (decreases (list_nth_shared_loop_pair_merge_loop_decreases t ls0 ls1 i))
-  =
-  begin match ls0 with
-  | List_Cons x0 tl0 ->
-    begin match ls1 with
-    | List_Cons x1 tl1 ->
-      if i = 0
-      then Return (x0, x1)
-      else
-        let* i0 = u32_sub i 1 in
-        list_nth_shared_loop_pair_merge_loop t tl0 tl1 i0
-    | List_Nil -> Fail Failure
-    end
-  | List_Nil -> Fail Failure
-  end
-
-(** [loops::list_nth_shared_loop_pair_merge]: forward function *)
-let list_nth_shared_loop_pair_merge
-  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) : result (t & t) =
-  list_nth_shared_loop_pair_merge_loop t ls0 ls1 i
-
-(** [loops::list_nth_mut_shared_loop_pair]: decreases clause *)
-unfold
-let list_nth_mut_shared_loop_pair_loop_decreases (t : Type0) (ls0 : list_t t)
-  (ls1 : list_t t) (i : u32) : nat =
-  admit ()
-
-(** [loops::list_nth_mut_shared_loop_pair]: loop 0: forward function *)
-let rec list_nth_mut_shared_loop_pair_loop
-  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) :
-  Tot (result (t & t))
-  (decreases (list_nth_mut_shared_loop_pair_loop_decreases t ls0 ls1 i))
-  =
-  begin match ls0 with
-  | List_Cons x0 tl0 ->
-    begin match ls1 with
-    | List_Cons x1 tl1 ->
-      if i = 0
-      then Return (x0, x1)
-      else
-        let* i0 = u32_sub i 1 in
-        list_nth_mut_shared_loop_pair_loop t tl0 tl1 i0
-    | List_Nil -> Fail Failure
-    end
-  | List_Nil -> Fail Failure
-  end
-
-(** [loops::list_nth_mut_shared_loop_pair]: forward function *)
-let list_nth_mut_shared_loop_pair
-  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) : result (t & t) =
-  list_nth_mut_shared_loop_pair_loop t ls0 ls1 i
-
-(** [loops::list_nth_mut_shared_loop_pair]: loop 0: backward function 0 *)
-let rec list_nth_mut_shared_loop_pair_loop_back
-  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) :
-  Tot (result (list_t t))
-  (decreases (list_nth_mut_shared_loop_pair_loop_decreases t ls0 ls1 i))
-  =
-  begin match ls0 with
-  | List_Cons x0 tl0 ->
-    begin match ls1 with
-    | List_Cons x1 tl1 ->
-      if i = 0
-      then Return (List_Cons ret tl0)
-      else
-        let* i0 = u32_sub i 1 in
-        let* tl00 = list_nth_mut_shared_loop_pair_loop_back t tl0 tl1 i0 ret in
-        Return (List_Cons x0 tl00)
-    | List_Nil -> Fail Failure
-    end
-  | List_Nil -> Fail Failure
-  end
-
-(** [loops::list_nth_mut_shared_loop_pair]: backward function 0 *)
-let list_nth_mut_shared_loop_pair_back
-  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) :
-  result (list_t t)
-  =
-  list_nth_mut_shared_loop_pair_loop_back t ls0 ls1 i ret
-
-(** [loops::list_nth_mut_shared_loop_pair_merge]: decreases clause *)
-unfold
-let list_nth_mut_shared_loop_pair_merge_loop_decreases (t : Type0)
-  (ls0 : list_t t) (ls1 : list_t t) (i : u32) : nat =
-  admit ()
-
-(** [loops::list_nth_mut_shared_loop_pair_merge]: loop 0: forward function *)
-let rec list_nth_mut_shared_loop_pair_merge_loop
-  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) :
-  Tot (result (t & t))
-  (decreases (list_nth_mut_shared_loop_pair_merge_loop_decreases t ls0 ls1 i))
-  =
-  begin match ls0 with
-  | List_Cons x0 tl0 ->
-    begin match ls1 with
-    | List_Cons x1 tl1 ->
-      if i = 0
-      then Return (x0, x1)
-      else
-        let* i0 = u32_sub i 1 in
-        list_nth_mut_shared_loop_pair_merge_loop t tl0 tl1 i0
-    | List_Nil -> Fail Failure
-    end
-  | List_Nil -> Fail Failure
-  end
-
-(** [loops::list_nth_mut_shared_loop_pair_merge]: forward function *)
-let list_nth_mut_shared_loop_pair_merge
-  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) : result (t & t) =
-  list_nth_mut_shared_loop_pair_merge_loop t ls0 ls1 i
-
-(** [loops::list_nth_mut_shared_loop_pair_merge]: loop 0: backward function 0 *)
-let rec list_nth_mut_shared_loop_pair_merge_loop_back
-  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) :
-  Tot (result (list_t t))
-  (decreases (list_nth_mut_shared_loop_pair_merge_loop_decreases t ls0 ls1 i))
-  =
-  begin match ls0 with
-  | List_Cons x0 tl0 ->
-    begin match ls1 with
-    | List_Cons x1 tl1 ->
-      if i = 0
-      then Return (List_Cons ret tl0)
-      else
-        let* i0 = u32_sub i 1 in
-        let* tl00 =
-          list_nth_mut_shared_loop_pair_merge_loop_back t tl0 tl1 i0 ret in
-        Return (List_Cons x0 tl00)
-    | List_Nil -> Fail Failure
-    end
-  | List_Nil -> Fail Failure
-  end
-
-(** [loops::list_nth_mut_shared_loop_pair_merge]: backward function 0 *)
-let list_nth_mut_shared_loop_pair_merge_back
-  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) :
-  result (list_t t)
-  =
-  list_nth_mut_shared_loop_pair_merge_loop_back t ls0 ls1 i ret
-
-(** [loops::list_nth_shared_mut_loop_pair]: decreases clause *)
-unfold
-let list_nth_shared_mut_loop_pair_loop_decreases (t : Type0) (ls0 : list_t t)
-  (ls1 : list_t t) (i : u32) : nat =
-  admit ()
-
-(** [loops::list_nth_shared_mut_loop_pair]: loop 0: forward function *)
-let rec list_nth_shared_mut_loop_pair_loop
-  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) :
-  Tot (result (t & t))
-  (decreases (list_nth_shared_mut_loop_pair_loop_decreases t ls0 ls1 i))
-  =
-  begin match ls0 with
-  | List_Cons x0 tl0 ->
-    begin match ls1 with
-    | List_Cons x1 tl1 ->
-      if i = 0
-      then Return (x0, x1)
-      else
-        let* i0 = u32_sub i 1 in
-        list_nth_shared_mut_loop_pair_loop t tl0 tl1 i0
-    | List_Nil -> Fail Failure
-    end
-  | List_Nil -> Fail Failure
-  end
-
-(** [loops::list_nth_shared_mut_loop_pair]: forward function *)
-let list_nth_shared_mut_loop_pair
-  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) : result (t & t) =
-  list_nth_shared_mut_loop_pair_loop t ls0 ls1 i
-
-(** [loops::list_nth_shared_mut_loop_pair]: loop 0: backward function 1 *)
-let rec list_nth_shared_mut_loop_pair_loop_back
-  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) :
-  Tot (result (list_t t))
-  (decreases (list_nth_shared_mut_loop_pair_loop_decreases t ls0 ls1 i))
-  =
-  begin match ls0 with
-  | List_Cons x0 tl0 ->
-    begin match ls1 with
-    | List_Cons x1 tl1 ->
-      if i = 0
-      then Return (List_Cons ret tl1)
-      else
-        let* i0 = u32_sub i 1 in
-        let* tl10 = list_nth_shared_mut_loop_pair_loop_back t tl0 tl1 i0 ret in
-        Return (List_Cons x1 tl10)
-    | List_Nil -> Fail Failure
-    end
-  | List_Nil -> Fail Failure
-  end
-
-(** [loops::list_nth_shared_mut_loop_pair]: backward function 1 *)
-let list_nth_shared_mut_loop_pair_back
-  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) :
-  result (list_t t)
-  =
-  list_nth_shared_mut_loop_pair_loop_back t ls0 ls1 i ret
-
-(** [loops::list_nth_shared_mut_loop_pair_merge]: decreases clause *)
-unfold
-let list_nth_shared_mut_loop_pair_merge_loop_decreases (t : Type0)
-  (ls0 : list_t t) (ls1 : list_t t) (i : u32) : nat =
-  admit ()
-
-(** [loops::list_nth_shared_mut_loop_pair_merge]: loop 0: forward function *)
-let rec list_nth_shared_mut_loop_pair_merge_loop
-  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) :
-  Tot (result (t & t))
-  (decreases (list_nth_shared_mut_loop_pair_merge_loop_decreases t ls0 ls1 i))
-  =
-  begin match ls0 with
-  | List_Cons x0 tl0 ->
-    begin match ls1 with
-    | List_Cons x1 tl1 ->
-      if i = 0
-      then Return (x0, x1)
-      else
-        let* i0 = u32_sub i 1 in
-        list_nth_shared_mut_loop_pair_merge_loop t tl0 tl1 i0
-    | List_Nil -> Fail Failure
-    end
-  | List_Nil -> Fail Failure
-  end
-
-(** [loops::list_nth_shared_mut_loop_pair_merge]: forward function *)
-let list_nth_shared_mut_loop_pair_merge
-  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) : result (t & t) =
-  list_nth_shared_mut_loop_pair_merge_loop t ls0 ls1 i
-
-(** [loops::list_nth_shared_mut_loop_pair_merge]: loop 0: backward function 0 *)
-let rec list_nth_shared_mut_loop_pair_merge_loop_back
-  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) :
-  Tot (result (list_t t))
-  (decreases (list_nth_shared_mut_loop_pair_merge_loop_decreases t ls0 ls1 i))
-  =
-  begin match ls0 with
-  | List_Cons x0 tl0 ->
-    begin match ls1 with
-    | List_Cons x1 tl1 ->
-      if i = 0
-      then Return (List_Cons ret tl1)
-      else
-        let* i0 = u32_sub i 1 in
-        let* tl10 =
-          list_nth_shared_mut_loop_pair_merge_loop_back t tl0 tl1 i0 ret in
-        Return (List_Cons x1 tl10)
-    | List_Nil -> Fail Failure
-    end
-  | List_Nil -> Fail Failure
-  end
-
-(** [loops::list_nth_shared_mut_loop_pair_merge]: backward function 0 *)
-let list_nth_shared_mut_loop_pair_merge_back
-  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) :
-  result (list_t t)
-  =
-  list_nth_shared_mut_loop_pair_merge_loop_back t ls0 ls1 i ret
-
diff --git a/tests/fstar/misc/Primitives.fst b/tests/fstar/misc/Primitives.fst
index 71d75c11..3297803c 100644
--- a/tests/fstar/misc/Primitives.fst
+++ b/tests/fstar/misc/Primitives.fst
@@ -427,7 +427,7 @@ let alloc_vec_Vec_new (a  : Type0) : alloc_vec_Vec a = assert_norm(length #a []
 let alloc_vec_Vec_len (a : Type0) (v : alloc_vec_Vec a) : usize = length v
 
 // Helper
-let alloc_vec_Vec_index_usize (#a : Type0) (v : alloc_vec_Vec a) (i : usize) (x : a) : result a =
+let alloc_vec_Vec_index_usize (#a : Type0) (v : alloc_vec_Vec a) (i : usize) : result a =
   if i < length v then Return (index v i) else Fail Failure
 // Helper
 let alloc_vec_Vec_update_usize (#a : Type0) (v : alloc_vec_Vec a) (i : usize) (x : a) : result (alloc_vec_Vec a) =
@@ -704,6 +704,22 @@ let alloc_vec_Vec_coreopsindexIndexMutInst (t idx : Type0)
 
 (*** Theorems *)
 
+let alloc_vec_Vec_index_eq (#a : Type0) (v : alloc_vec_Vec a) (i : usize) :
+  Lemma (
+    alloc_vec_Vec_index a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i ==
+      alloc_vec_Vec_index_usize v i)
+  [SMTPat (alloc_vec_Vec_index a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i)]
+  =
+  admit()
+
+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_usize_coresliceindexSliceIndexInst a) v i ==
+      alloc_vec_Vec_index_usize v i)
+  [SMTPat (alloc_vec_Vec_index_mut a usize (core_slice_index_usize_coresliceindexSliceIndexInst 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_usize_coresliceindexSliceIndexInst a) v i x ==
diff --git a/tests/fstar/traits/Primitives.fst b/tests/fstar/traits/Primitives.fst
index 71d75c11..3297803c 100644
--- a/tests/fstar/traits/Primitives.fst
+++ b/tests/fstar/traits/Primitives.fst
@@ -427,7 +427,7 @@ let alloc_vec_Vec_new (a  : Type0) : alloc_vec_Vec a = assert_norm(length #a []
 let alloc_vec_Vec_len (a : Type0) (v : alloc_vec_Vec a) : usize = length v
 
 // Helper
-let alloc_vec_Vec_index_usize (#a : Type0) (v : alloc_vec_Vec a) (i : usize) (x : a) : result a =
+let alloc_vec_Vec_index_usize (#a : Type0) (v : alloc_vec_Vec a) (i : usize) : result a =
   if i < length v then Return (index v i) else Fail Failure
 // Helper
 let alloc_vec_Vec_update_usize (#a : Type0) (v : alloc_vec_Vec a) (i : usize) (x : a) : result (alloc_vec_Vec a) =
@@ -704,6 +704,22 @@ let alloc_vec_Vec_coreopsindexIndexMutInst (t idx : Type0)
 
 (*** Theorems *)
 
+let alloc_vec_Vec_index_eq (#a : Type0) (v : alloc_vec_Vec a) (i : usize) :
+  Lemma (
+    alloc_vec_Vec_index a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i ==
+      alloc_vec_Vec_index_usize v i)
+  [SMTPat (alloc_vec_Vec_index a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i)]
+  =
+  admit()
+
+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_usize_coresliceindexSliceIndexInst a) v i ==
+      alloc_vec_Vec_index_usize v i)
+  [SMTPat (alloc_vec_Vec_index_mut a usize (core_slice_index_usize_coresliceindexSliceIndexInst 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_usize_coresliceindexSliceIndexInst a) v i x ==