Regenerate the test files and add the fstar-split tests

8 files changed, 5070 insertions, 0 deletions

diff --git a/tests/fstar-split/hashmap/Hashmap.Clauses.Template.fst b/tests/fstar-split/hashmap/Hashmap.Clauses.Template.fst
new file mode 100644
index 00000000..2733b371
--- /dev/null
+++ b/tests/fstar-split/hashmap/Hashmap.Clauses.Template.fst
@@ -0,0 +1,71 @@
+(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
+(** [hashmap]: templates for the decreases clauses *)
+module Hashmap.Clauses.Template
+open Primitives
+open Hashmap.Types
+
+#set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
+
+(** [hashmap::{hashmap::HashMap<T>}::allocate_slots]: decreases clause
+    Source: 'src/hashmap.rs', lines 50:4-56:5 *)
+unfold
+let hashMap_allocate_slots_loop_decreases (t : Type0)
+  (slots : alloc_vec_Vec (list_t t)) (n : usize) : nat =
+  admit ()
+
+(** [hashmap::{hashmap::HashMap<T>}::clear]: decreases clause
+    Source: 'src/hashmap.rs', lines 80:4-88:5 *)
+unfold
+let hashMap_clear_loop_decreases (t : Type0) (slots : alloc_vec_Vec (list_t t))
+  (i : usize) : nat =
+  admit ()
+
+(** [hashmap::{hashmap::HashMap<T>}::insert_in_list]: decreases clause
+    Source: 'src/hashmap.rs', lines 97:4-114:5 *)
+unfold
+let hashMap_insert_in_list_loop_decreases (t : Type0) (key : usize) (value : t)
+  (ls : list_t t) : nat =
+  admit ()
+
+(** [hashmap::{hashmap::HashMap<T>}::move_elements_from_list]: decreases clause
+    Source: 'src/hashmap.rs', lines 183:4-196:5 *)
+unfold
+let hashMap_move_elements_from_list_loop_decreases (t : Type0)
+  (ntable : hashMap_t t) (ls : list_t t) : nat =
+  admit ()
+
+(** [hashmap::{hashmap::HashMap<T>}::move_elements]: decreases clause
+    Source: 'src/hashmap.rs', lines 171:4-180:5 *)
+unfold
+let hashMap_move_elements_loop_decreases (t : Type0) (ntable : hashMap_t t)
+  (slots : alloc_vec_Vec (list_t t)) (i : usize) : nat =
+  admit ()
+
+(** [hashmap::{hashmap::HashMap<T>}::contains_key_in_list]: decreases clause
+    Source: 'src/hashmap.rs', lines 206:4-219:5 *)
+unfold
+let hashMap_contains_key_in_list_loop_decreases (t : Type0) (key : usize)
+  (ls : list_t t) : nat =
+  admit ()
+
+(** [hashmap::{hashmap::HashMap<T>}::get_in_list]: decreases clause
+    Source: 'src/hashmap.rs', lines 224:4-237:5 *)
+unfold
+let hashMap_get_in_list_loop_decreases (t : Type0) (key : usize)
+  (ls : list_t t) : nat =
+  admit ()
+
+(** [hashmap::{hashmap::HashMap<T>}::get_mut_in_list]: decreases clause
+    Source: 'src/hashmap.rs', lines 245:4-254:5 *)
+unfold
+let hashMap_get_mut_in_list_loop_decreases (t : Type0) (ls : list_t t)
+  (key : usize) : nat =
+  admit ()
+
+(** [hashmap::{hashmap::HashMap<T>}::remove_from_list]: decreases clause
+    Source: 'src/hashmap.rs', lines 265:4-291:5 *)
+unfold
+let hashMap_remove_from_list_loop_decreases (t : Type0) (key : usize)
+  (ls : list_t t) : nat =
+  admit ()
+
diff --git a/tests/fstar-split/hashmap/Hashmap.Clauses.fst b/tests/fstar-split/hashmap/Hashmap.Clauses.fst
new file mode 100644
index 00000000..6c699d05
--- /dev/null
+++ b/tests/fstar-split/hashmap/Hashmap.Clauses.fst
@@ -0,0 +1,61 @@
+(** [hashmap]: the decreases clauses *)
+module Hashmap.Clauses
+open Primitives
+open FStar.List.Tot
+open Hashmap.Types
+
+#set-options "--z3rlimit 50 --fuel 0 --ifuel 1"
+
+(** [hashmap::HashMap::allocate_slots]: decreases clause *)
+unfold
+let hashMap_allocate_slots_loop_decreases (t : Type0)
+  (slots : alloc_vec_Vec (list_t t)) (n : usize) : nat = n
+
+(** [hashmap::HashMap::clear]: decreases clause *)
+unfold
+let hashMap_clear_loop_decreases (t : Type0) (slots : alloc_vec_Vec (list_t t))
+  (i : usize) : nat =
+  if i < length slots then length slots - i else 0
+
+(** [hashmap::HashMap::insert_in_list]: decreases clause *)
+unfold
+let hashMap_insert_in_list_loop_decreases (t : Type0) (key : usize) (value : t)
+  (ls : list_t t) : list_t t =
+  ls
+
+(** [hashmap::HashMap::move_elements_from_list]: decreases clause *)
+unfold
+let hashMap_move_elements_from_list_loop_decreases (t : Type0)
+  (ntable : hashMap_t t) (ls : list_t t) : list_t t =
+  ls
+
+(** [hashmap::HashMap::move_elements]: decreases clause *)
+unfold
+let hashMap_move_elements_loop_decreases (t : Type0) (ntable : hashMap_t t)
+  (slots : alloc_vec_Vec (list_t t)) (i : usize) : nat =
+  if i < length slots then length slots - i else 0
+
+(** [hashmap::HashMap::contains_key_in_list]: decreases clause *)
+unfold
+let hashMap_contains_key_in_list_loop_decreases (t : Type0) (key : usize)
+  (ls : list_t t) : list_t t =
+  ls
+
+(** [hashmap::HashMap::get_in_list]: decreases clause *)
+unfold
+let hashMap_get_in_list_loop_decreases (t : Type0) (key : usize) (ls : list_t t) :
+  list_t t =
+  ls
+
+(** [hashmap::HashMap::get_mut_in_list]: decreases clause *)
+unfold
+let hashMap_get_mut_in_list_loop_decreases (t : Type0) (ls : list_t t)
+  (key : usize) : list_t t =
+  ls
+
+(** [hashmap::HashMap::remove_from_list]: decreases clause *)
+unfold
+let hashMap_remove_from_list_loop_decreases (t : Type0) (key : usize)
+  (ls : list_t t) : list_t t =
+  ls
+
diff --git a/tests/fstar-split/hashmap/Hashmap.Funs.fst b/tests/fstar-split/hashmap/Hashmap.Funs.fst
new file mode 100644
index 00000000..79327183
--- /dev/null
+++ b/tests/fstar-split/hashmap/Hashmap.Funs.fst
@@ -0,0 +1,529 @@
+(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
+(** [hashmap]: function definitions *)
+module Hashmap.Funs
+open Primitives
+include Hashmap.Types
+include Hashmap.Clauses
+
+#set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
+
+(** [hashmap::hash_key]: forward function
+    Source: 'src/hashmap.rs', lines 27:0-27:32 *)
+let hash_key (k : usize) : result usize =
+  Return k
+
+(** [hashmap::{hashmap::HashMap<T>}::allocate_slots]: loop 0: forward function
+    Source: 'src/hashmap.rs', lines 50:4-56:5 *)
+let rec hashMap_allocate_slots_loop
+  (t : Type0) (slots : alloc_vec_Vec (list_t t)) (n : usize) :
+  Tot (result (alloc_vec_Vec (list_t t)))
+  (decreases (hashMap_allocate_slots_loop_decreases t slots n))
+  =
+  if n > 0
+  then
+    let* slots1 = alloc_vec_Vec_push (list_t t) slots List_Nil in
+    let* n1 = usize_sub n 1 in
+    hashMap_allocate_slots_loop t slots1 n1
+  else Return slots
+
+(** [hashmap::{hashmap::HashMap<T>}::allocate_slots]: forward function
+    Source: 'src/hashmap.rs', lines 50:4-50:76 *)
+let hashMap_allocate_slots
+  (t : Type0) (slots : alloc_vec_Vec (list_t t)) (n : usize) :
+  result (alloc_vec_Vec (list_t t))
+  =
+  hashMap_allocate_slots_loop t slots n
+
+(** [hashmap::{hashmap::HashMap<T>}::new_with_capacity]: forward function
+    Source: 'src/hashmap.rs', lines 59:4-63:13 *)
+let hashMap_new_with_capacity
+  (t : Type0) (capacity : usize) (max_load_dividend : usize)
+  (max_load_divisor : usize) :
+  result (hashMap_t t)
+  =
+  let v = alloc_vec_Vec_new (list_t t) in
+  let* slots = hashMap_allocate_slots t v capacity in
+  let* i = usize_mul capacity max_load_dividend in
+  let* i1 = usize_div i max_load_divisor in
+  Return
+    {
+      num_entries = 0;
+      max_load_factor = (max_load_dividend, max_load_divisor);
+      max_load = i1;
+      slots = slots
+    }
+
+(** [hashmap::{hashmap::HashMap<T>}::new]: forward function
+    Source: 'src/hashmap.rs', lines 75:4-75:24 *)
+let hashMap_new (t : Type0) : result (hashMap_t t) =
+  hashMap_new_with_capacity t 32 4 5
+
+(** [hashmap::{hashmap::HashMap<T>}::clear]: loop 0: merged forward/backward function
+    (there is a single backward function, and the forward function returns ())
+    Source: 'src/hashmap.rs', lines 80:4-88:5 *)
+let rec hashMap_clear_loop
+  (t : Type0) (slots : alloc_vec_Vec (list_t t)) (i : usize) :
+  Tot (result (alloc_vec_Vec (list_t t)))
+  (decreases (hashMap_clear_loop_decreases t slots i))
+  =
+  let i1 = alloc_vec_Vec_len (list_t t) slots in
+  if i < i1
+  then
+    let* i2 = usize_add i 1 in
+    let* slots1 =
+      alloc_vec_Vec_index_mut_back (list_t t) usize
+        (core_slice_index_SliceIndexUsizeSliceTInst (list_t t)) slots i
+        List_Nil in
+    hashMap_clear_loop t slots1 i2
+  else Return slots
+
+(** [hashmap::{hashmap::HashMap<T>}::clear]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ())
+    Source: 'src/hashmap.rs', lines 80:4-80:27 *)
+let hashMap_clear (t : Type0) (self : hashMap_t t) : result (hashMap_t t) =
+  let* v = hashMap_clear_loop t self.slots 0 in
+  Return { self with num_entries = 0; slots = v }
+
+(** [hashmap::{hashmap::HashMap<T>}::len]: forward function
+    Source: 'src/hashmap.rs', lines 90:4-90:30 *)
+let hashMap_len (t : Type0) (self : hashMap_t t) : result usize =
+  Return self.num_entries
+
+(** [hashmap::{hashmap::HashMap<T>}::insert_in_list]: loop 0: forward function
+    Source: 'src/hashmap.rs', lines 97:4-114:5 *)
+let rec hashMap_insert_in_list_loop
+  (t : Type0) (key : usize) (value : t) (ls : list_t t) :
+  Tot (result bool)
+  (decreases (hashMap_insert_in_list_loop_decreases t key value ls))
+  =
+  begin match ls with
+  | List_Cons ckey _ tl ->
+    if ckey = key
+    then Return false
+    else hashMap_insert_in_list_loop t key value tl
+  | List_Nil -> Return true
+  end
+
+(** [hashmap::{hashmap::HashMap<T>}::insert_in_list]: forward function
+    Source: 'src/hashmap.rs', lines 97:4-97:71 *)
+let hashMap_insert_in_list
+  (t : Type0) (key : usize) (value : t) (ls : list_t t) : result bool =
+  hashMap_insert_in_list_loop t key value ls
+
+(** [hashmap::{hashmap::HashMap<T>}::insert_in_list]: loop 0: backward function 0
+    Source: 'src/hashmap.rs', lines 97:4-114:5 *)
+let rec hashMap_insert_in_list_loop_back
+  (t : Type0) (key : usize) (value : t) (ls : list_t t) :
+  Tot (result (list_t t))
+  (decreases (hashMap_insert_in_list_loop_decreases t key value ls))
+  =
+  begin match ls with
+  | List_Cons ckey cvalue tl ->
+    if ckey = key
+    then Return (List_Cons ckey value tl)
+    else
+      let* tl1 = hashMap_insert_in_list_loop_back t key value tl in
+      Return (List_Cons ckey cvalue tl1)
+  | List_Nil -> let l = List_Nil in Return (List_Cons key value l)
+  end
+
+(** [hashmap::{hashmap::HashMap<T>}::insert_in_list]: backward function 0
+    Source: 'src/hashmap.rs', lines 97:4-97:71 *)
+let hashMap_insert_in_list_back
+  (t : Type0) (key : usize) (value : t) (ls : list_t t) : result (list_t t) =
+  hashMap_insert_in_list_loop_back t key value ls
+
+(** [hashmap::{hashmap::HashMap<T>}::insert_no_resize]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ())
+    Source: 'src/hashmap.rs', lines 117:4-117:54 *)
+let hashMap_insert_no_resize
+  (t : Type0) (self : hashMap_t t) (key : usize) (value : t) :
+  result (hashMap_t t)
+  =
+  let* hash = hash_key key in
+  let i = alloc_vec_Vec_len (list_t t) self.slots in
+  let* hash_mod = usize_rem hash i in
+  let* l =
+    alloc_vec_Vec_index_mut (list_t t) usize
+      (core_slice_index_SliceIndexUsizeSliceTInst (list_t t)) self.slots
+      hash_mod in
+  let* inserted = hashMap_insert_in_list t key value l in
+  if inserted
+  then
+    let* i1 = usize_add self.num_entries 1 in
+    let* l1 = hashMap_insert_in_list_back t key value l in
+    let* v =
+      alloc_vec_Vec_index_mut_back (list_t t) usize
+        (core_slice_index_SliceIndexUsizeSliceTInst (list_t t)) self.slots
+        hash_mod l1 in
+    Return { self with num_entries = i1; slots = v }
+  else
+    let* l1 = hashMap_insert_in_list_back t key value l in
+    let* v =
+      alloc_vec_Vec_index_mut_back (list_t t) usize
+        (core_slice_index_SliceIndexUsizeSliceTInst (list_t t)) self.slots
+        hash_mod l1 in
+    Return { self with slots = v }
+
+(** [hashmap::{hashmap::HashMap<T>}::move_elements_from_list]: loop 0: merged forward/backward function
+    (there is a single backward function, and the forward function returns ())
+    Source: 'src/hashmap.rs', lines 183:4-196:5 *)
+let rec hashMap_move_elements_from_list_loop
+  (t : Type0) (ntable : hashMap_t t) (ls : list_t t) :
+  Tot (result (hashMap_t t))
+  (decreases (hashMap_move_elements_from_list_loop_decreases t ntable ls))
+  =
+  begin match ls with
+  | List_Cons k v tl ->
+    let* ntable1 = hashMap_insert_no_resize t ntable k v in
+    hashMap_move_elements_from_list_loop t ntable1 tl
+  | List_Nil -> Return ntable
+  end
+
+(** [hashmap::{hashmap::HashMap<T>}::move_elements_from_list]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ())
+    Source: 'src/hashmap.rs', lines 183:4-183:72 *)
+let hashMap_move_elements_from_list
+  (t : Type0) (ntable : hashMap_t t) (ls : list_t t) : result (hashMap_t t) =
+  hashMap_move_elements_from_list_loop t ntable ls
+
+(** [hashmap::{hashmap::HashMap<T>}::move_elements]: loop 0: merged forward/backward function
+    (there is a single backward function, and the forward function returns ())
+    Source: 'src/hashmap.rs', lines 171:4-180:5 *)
+let rec hashMap_move_elements_loop
+  (t : Type0) (ntable : hashMap_t t) (slots : alloc_vec_Vec (list_t t))
+  (i : usize) :
+  Tot (result ((hashMap_t t) & (alloc_vec_Vec (list_t t))))
+  (decreases (hashMap_move_elements_loop_decreases t ntable slots i))
+  =
+  let i1 = alloc_vec_Vec_len (list_t t) slots in
+  if i < i1
+  then
+    let* l =
+      alloc_vec_Vec_index_mut (list_t t) usize
+        (core_slice_index_SliceIndexUsizeSliceTInst (list_t t)) slots i in
+    let ls = core_mem_replace (list_t t) l List_Nil in
+    let* ntable1 = hashMap_move_elements_from_list t ntable ls in
+    let* i2 = usize_add i 1 in
+    let l1 = core_mem_replace_back (list_t t) l List_Nil in
+    let* slots1 =
+      alloc_vec_Vec_index_mut_back (list_t t) usize
+        (core_slice_index_SliceIndexUsizeSliceTInst (list_t t)) slots i l1 in
+    hashMap_move_elements_loop t ntable1 slots1 i2
+  else Return (ntable, slots)
+
+(** [hashmap::{hashmap::HashMap<T>}::move_elements]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ())
+    Source: 'src/hashmap.rs', lines 171:4-171:95 *)
+let hashMap_move_elements
+  (t : Type0) (ntable : hashMap_t t) (slots : alloc_vec_Vec (list_t t))
+  (i : usize) :
+  result ((hashMap_t t) & (alloc_vec_Vec (list_t t)))
+  =
+  hashMap_move_elements_loop t ntable slots i
+
+(** [hashmap::{hashmap::HashMap<T>}::try_resize]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ())
+    Source: 'src/hashmap.rs', lines 140:4-140:28 *)
+let hashMap_try_resize
+  (t : Type0) (self : hashMap_t t) : result (hashMap_t t) =
+  let* max_usize = scalar_cast U32 Usize core_u32_max in
+  let capacity = alloc_vec_Vec_len (list_t t) self.slots in
+  let* n1 = usize_div max_usize 2 in
+  let (i, i1) = self.max_load_factor in
+  let* i2 = usize_div n1 i in
+  if capacity <= i2
+  then
+    let* i3 = usize_mul capacity 2 in
+    let* ntable = hashMap_new_with_capacity t i3 i i1 in
+    let* (ntable1, _) = hashMap_move_elements t ntable self.slots 0 in
+    Return
+      { ntable1 with num_entries = self.num_entries; max_load_factor = (i, i1)
+      }
+  else Return { self with max_load_factor = (i, i1) }
+
+(** [hashmap::{hashmap::HashMap<T>}::insert]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ())
+    Source: 'src/hashmap.rs', lines 129:4-129:48 *)
+let hashMap_insert
+  (t : Type0) (self : hashMap_t t) (key : usize) (value : t) :
+  result (hashMap_t t)
+  =
+  let* self1 = hashMap_insert_no_resize t self key value in
+  let* i = hashMap_len t self1 in
+  if i > self1.max_load then hashMap_try_resize t self1 else Return self1
+
+(** [hashmap::{hashmap::HashMap<T>}::contains_key_in_list]: loop 0: forward function
+    Source: 'src/hashmap.rs', lines 206:4-219:5 *)
+let rec hashMap_contains_key_in_list_loop
+  (t : Type0) (key : usize) (ls : list_t t) :
+  Tot (result bool)
+  (decreases (hashMap_contains_key_in_list_loop_decreases t key ls))
+  =
+  begin match ls with
+  | List_Cons ckey _ tl ->
+    if ckey = key
+    then Return true
+    else hashMap_contains_key_in_list_loop t key tl
+  | List_Nil -> Return false
+  end
+
+(** [hashmap::{hashmap::HashMap<T>}::contains_key_in_list]: forward function
+    Source: 'src/hashmap.rs', lines 206:4-206:68 *)
+let hashMap_contains_key_in_list
+  (t : Type0) (key : usize) (ls : list_t t) : result bool =
+  hashMap_contains_key_in_list_loop t key ls
+
+(** [hashmap::{hashmap::HashMap<T>}::contains_key]: forward function
+    Source: 'src/hashmap.rs', lines 199:4-199:49 *)
+let hashMap_contains_key
+  (t : Type0) (self : hashMap_t t) (key : usize) : result bool =
+  let* hash = hash_key key in
+  let i = alloc_vec_Vec_len (list_t t) self.slots in
+  let* hash_mod = usize_rem hash i in
+  let* l =
+    alloc_vec_Vec_index (list_t t) usize
+      (core_slice_index_SliceIndexUsizeSliceTInst (list_t t)) self.slots
+      hash_mod in
+  hashMap_contains_key_in_list t key l
+
+(** [hashmap::{hashmap::HashMap<T>}::get_in_list]: loop 0: forward function
+    Source: 'src/hashmap.rs', lines 224:4-237:5 *)
+let rec hashMap_get_in_list_loop
+  (t : Type0) (key : usize) (ls : list_t t) :
+  Tot (result t) (decreases (hashMap_get_in_list_loop_decreases t key ls))
+  =
+  begin match ls with
+  | List_Cons ckey cvalue tl ->
+    if ckey = key then Return cvalue else hashMap_get_in_list_loop t key tl
+  | List_Nil -> Fail Failure
+  end
+
+(** [hashmap::{hashmap::HashMap<T>}::get_in_list]: forward function
+    Source: 'src/hashmap.rs', lines 224:4-224:70 *)
+let hashMap_get_in_list (t : Type0) (key : usize) (ls : list_t t) : result t =
+  hashMap_get_in_list_loop t key ls
+
+(** [hashmap::{hashmap::HashMap<T>}::get]: forward function
+    Source: 'src/hashmap.rs', lines 239:4-239:55 *)
+let hashMap_get (t : Type0) (self : hashMap_t t) (key : usize) : result t =
+  let* hash = hash_key key in
+  let i = alloc_vec_Vec_len (list_t t) self.slots in
+  let* hash_mod = usize_rem hash i in
+  let* l =
+    alloc_vec_Vec_index (list_t t) usize
+      (core_slice_index_SliceIndexUsizeSliceTInst (list_t t)) self.slots
+      hash_mod in
+  hashMap_get_in_list t key l
+
+(** [hashmap::{hashmap::HashMap<T>}::get_mut_in_list]: loop 0: forward function
+    Source: 'src/hashmap.rs', lines 245:4-254:5 *)
+let rec hashMap_get_mut_in_list_loop
+  (t : Type0) (ls : list_t t) (key : usize) :
+  Tot (result t) (decreases (hashMap_get_mut_in_list_loop_decreases t ls key))
+  =
+  begin match ls with
+  | List_Cons ckey cvalue tl ->
+    if ckey = key then Return cvalue else hashMap_get_mut_in_list_loop t tl key
+  | List_Nil -> Fail Failure
+  end
+
+(** [hashmap::{hashmap::HashMap<T>}::get_mut_in_list]: forward function
+    Source: 'src/hashmap.rs', lines 245:4-245:86 *)
+let hashMap_get_mut_in_list
+  (t : Type0) (ls : list_t t) (key : usize) : result t =
+  hashMap_get_mut_in_list_loop t ls key
+
+(** [hashmap::{hashmap::HashMap<T>}::get_mut_in_list]: loop 0: backward function 0
+    Source: 'src/hashmap.rs', lines 245:4-254:5 *)
+let rec hashMap_get_mut_in_list_loop_back
+  (t : Type0) (ls : list_t t) (key : usize) (ret : t) :
+  Tot (result (list_t t))
+  (decreases (hashMap_get_mut_in_list_loop_decreases t ls key))
+  =
+  begin match ls with
+  | List_Cons ckey cvalue tl ->
+    if ckey = key
+    then Return (List_Cons ckey ret tl)
+    else
+      let* tl1 = hashMap_get_mut_in_list_loop_back t tl key ret in
+      Return (List_Cons ckey cvalue tl1)
+  | List_Nil -> Fail Failure
+  end
+
+(** [hashmap::{hashmap::HashMap<T>}::get_mut_in_list]: backward function 0
+    Source: 'src/hashmap.rs', lines 245:4-245:86 *)
+let hashMap_get_mut_in_list_back
+  (t : Type0) (ls : list_t t) (key : usize) (ret : t) : result (list_t t) =
+  hashMap_get_mut_in_list_loop_back t ls key ret
+
+(** [hashmap::{hashmap::HashMap<T>}::get_mut]: forward function
+    Source: 'src/hashmap.rs', lines 257:4-257:67 *)
+let hashMap_get_mut (t : Type0) (self : hashMap_t t) (key : usize) : result t =
+  let* hash = hash_key key in
+  let i = alloc_vec_Vec_len (list_t t) self.slots in
+  let* hash_mod = usize_rem hash i in
+  let* l =
+    alloc_vec_Vec_index_mut (list_t t) usize
+      (core_slice_index_SliceIndexUsizeSliceTInst (list_t t)) self.slots
+      hash_mod in
+  hashMap_get_mut_in_list t l key
+
+(** [hashmap::{hashmap::HashMap<T>}::get_mut]: backward function 0
+    Source: 'src/hashmap.rs', lines 257:4-257:67 *)
+let hashMap_get_mut_back
+  (t : Type0) (self : hashMap_t t) (key : usize) (ret : t) :
+  result (hashMap_t t)
+  =
+  let* hash = hash_key key in
+  let i = alloc_vec_Vec_len (list_t t) self.slots in
+  let* hash_mod = usize_rem hash i in
+  let* l =
+    alloc_vec_Vec_index_mut (list_t t) usize
+      (core_slice_index_SliceIndexUsizeSliceTInst (list_t t)) self.slots
+      hash_mod in
+  let* l1 = hashMap_get_mut_in_list_back t l key ret in
+  let* v =
+    alloc_vec_Vec_index_mut_back (list_t t) usize
+      (core_slice_index_SliceIndexUsizeSliceTInst (list_t t)) self.slots
+      hash_mod l1 in
+  Return { self with slots = v }
+
+(** [hashmap::{hashmap::HashMap<T>}::remove_from_list]: loop 0: forward function
+    Source: 'src/hashmap.rs', lines 265:4-291:5 *)
+let rec hashMap_remove_from_list_loop
+  (t : Type0) (key : usize) (ls : list_t t) :
+  Tot (result (option t))
+  (decreases (hashMap_remove_from_list_loop_decreases t key ls))
+  =
+  begin match ls with
+  | List_Cons ckey x tl ->
+    if ckey = key
+    then
+      let mv_ls = core_mem_replace (list_t t) (List_Cons ckey x tl) List_Nil in
+      begin match mv_ls with
+      | List_Cons _ cvalue _ -> Return (Some cvalue)
+      | List_Nil -> Fail Failure
+      end
+    else hashMap_remove_from_list_loop t key tl
+  | List_Nil -> Return None
+  end
+
+(** [hashmap::{hashmap::HashMap<T>}::remove_from_list]: forward function
+    Source: 'src/hashmap.rs', lines 265:4-265:69 *)
+let hashMap_remove_from_list
+  (t : Type0) (key : usize) (ls : list_t t) : result (option t) =
+  hashMap_remove_from_list_loop t key ls
+
+(** [hashmap::{hashmap::HashMap<T>}::remove_from_list]: loop 0: backward function 1
+    Source: 'src/hashmap.rs', lines 265:4-291:5 *)
+let rec hashMap_remove_from_list_loop_back
+  (t : Type0) (key : usize) (ls : list_t t) :
+  Tot (result (list_t t))
+  (decreases (hashMap_remove_from_list_loop_decreases t key ls))
+  =
+  begin match ls with
+  | List_Cons ckey x tl ->
+    if ckey = key
+    then
+      let mv_ls = core_mem_replace (list_t t) (List_Cons ckey x tl) List_Nil in
+      begin match mv_ls with
+      | List_Cons _ _ tl1 -> Return tl1
+      | List_Nil -> Fail Failure
+      end
+    else
+      let* tl1 = hashMap_remove_from_list_loop_back t key tl in
+      Return (List_Cons ckey x tl1)
+  | List_Nil -> Return List_Nil
+  end
+
+(** [hashmap::{hashmap::HashMap<T>}::remove_from_list]: backward function 1
+    Source: 'src/hashmap.rs', lines 265:4-265:69 *)
+let hashMap_remove_from_list_back
+  (t : Type0) (key : usize) (ls : list_t t) : result (list_t t) =
+  hashMap_remove_from_list_loop_back t key ls
+
+(** [hashmap::{hashmap::HashMap<T>}::remove]: forward function
+    Source: 'src/hashmap.rs', lines 294:4-294:52 *)
+let hashMap_remove
+  (t : Type0) (self : hashMap_t t) (key : usize) : result (option t) =
+  let* hash = hash_key key in
+  let i = alloc_vec_Vec_len (list_t t) self.slots in
+  let* hash_mod = usize_rem hash i in
+  let* l =
+    alloc_vec_Vec_index_mut (list_t t) usize
+      (core_slice_index_SliceIndexUsizeSliceTInst (list_t t)) self.slots
+      hash_mod in
+  let* x = hashMap_remove_from_list t key l in
+  begin match x with
+  | None -> Return None
+  | Some x1 -> let* _ = usize_sub self.num_entries 1 in Return (Some x1)
+  end
+
+(** [hashmap::{hashmap::HashMap<T>}::remove]: backward function 0
+    Source: 'src/hashmap.rs', lines 294:4-294:52 *)
+let hashMap_remove_back
+  (t : Type0) (self : hashMap_t t) (key : usize) : result (hashMap_t t) =
+  let* hash = hash_key key in
+  let i = alloc_vec_Vec_len (list_t t) self.slots in
+  let* hash_mod = usize_rem hash i in
+  let* l =
+    alloc_vec_Vec_index_mut (list_t t) usize
+      (core_slice_index_SliceIndexUsizeSliceTInst (list_t t)) self.slots
+      hash_mod in
+  let* x = hashMap_remove_from_list t key l in
+  begin match x with
+  | None ->
+    let* l1 = hashMap_remove_from_list_back t key l in
+    let* v =
+      alloc_vec_Vec_index_mut_back (list_t t) usize
+        (core_slice_index_SliceIndexUsizeSliceTInst (list_t t)) self.slots
+        hash_mod l1 in
+    Return { self with slots = v }
+  | Some _ ->
+    let* i1 = usize_sub self.num_entries 1 in
+    let* l1 = hashMap_remove_from_list_back t key l in
+    let* v =
+      alloc_vec_Vec_index_mut_back (list_t t) usize
+        (core_slice_index_SliceIndexUsizeSliceTInst (list_t t)) self.slots
+        hash_mod l1 in
+    Return { self with num_entries = i1; slots = v }
+  end
+
+(** [hashmap::test1]: forward function
+    Source: 'src/hashmap.rs', lines 315:0-315:10 *)
+let test1 : result unit =
+  let* hm = hashMap_new u64 in
+  let* hm1 = hashMap_insert u64 hm 0 42 in
+  let* hm2 = hashMap_insert u64 hm1 128 18 in
+  let* hm3 = hashMap_insert u64 hm2 1024 138 in
+  let* hm4 = hashMap_insert u64 hm3 1056 256 in
+  let* i = hashMap_get u64 hm4 128 in
+  if not (i = 18)
+  then Fail Failure
+  else
+    let* hm5 = hashMap_get_mut_back u64 hm4 1024 56 in
+    let* i1 = hashMap_get u64 hm5 1024 in
+    if not (i1 = 56)
+    then Fail Failure
+    else
+      let* x = hashMap_remove u64 hm5 1024 in
+      begin match x with
+      | None -> Fail Failure
+      | Some x1 ->
+        if not (x1 = 56)
+        then Fail Failure
+        else
+          let* hm6 = hashMap_remove_back u64 hm5 1024 in
+          let* i2 = hashMap_get u64 hm6 0 in
+          if not (i2 = 42)
+          then Fail Failure
+          else
+            let* i3 = hashMap_get u64 hm6 128 in
+            if not (i3 = 18)
+            then Fail Failure
+            else
+              let* i4 = hashMap_get u64 hm6 1056 in
+              if not (i4 = 256) then Fail Failure else Return ()
+      end
+
diff --git a/tests/fstar-split/hashmap/Hashmap.Properties.fst b/tests/fstar-split/hashmap/Hashmap.Properties.fst
new file mode 100644
index 00000000..def520f0
--- /dev/null
+++ b/tests/fstar-split/hashmap/Hashmap.Properties.fst
@@ -0,0 +1,3186 @@
+(** Properties about the hashmap *)
+module Hashmap.Properties
+open Primitives
+open FStar.List.Tot
+open FStar.Mul
+open Hashmap.Types
+open Hashmap.Clauses
+open Hashmap.Funs
+
+#set-options "--z3rlimit 50 --fuel 0 --ifuel 1"
+
+let _align_fsti = ()
+
+/// The proofs:
+/// ===========
+/// 
+/// The proof strategy is to do exactly as with Low* proofs (we initially tried to
+/// prove more properties in one go, but it was a mistake):
+/// - prove that, under some preconditions, the low-level functions translated
+///   from Rust refine some higher-level functions
+/// - do functional proofs about those high-level functions to prove interesting
+///   properties about the hash map operations, and invariant preservation
+/// - combine everything
+///
+/// The fact that we work in a pure setting allows us to be more modular than when
+/// working with effects. For instance we can do a case disjunction (see the proofs
+/// for insert, which study the cases where the key is already/not in the hash map
+/// in separate proofs - we had initially tried to do them in one step: it is doable
+/// but requires some work, and the F* response time quickly becomes annoying while
+/// making progress, so we split them). We can also easily prove a refinement lemma,
+/// study the model, *then* combine those to also prove that the low-level function
+/// preserves the invariants, rather than do everything at once as is usually the
+/// case when doing intrinsic proofs with effects (I remember that having to prove
+/// invariants in one go *and* a refinement step, even small, can be extremely
+/// difficult in Low*).
+
+
+(*** Utilities *)
+
+/// We need many small helpers and lemmas, mostly about lists (and the ones we list
+/// here are not in the standard F* library).
+
+val index_append_lem (#a : Type0) (ls0 ls1 : list a) (i : nat{i < length ls0 + length ls1}) :
+  Lemma (
+    (i < length ls0 ==> index (ls0 @ ls1) i == index ls0 i) /\
+    (i >= length ls0 ==> index (ls0 @ ls1) i == index ls1 (i - length ls0)))
+  [SMTPat (index (ls0 @ ls1) i)]
+
+#push-options "--fuel 1"
+let rec index_append_lem #a ls0 ls1 i =
+  match ls0 with
+  | [] -> ()
+  | x :: ls0' ->
+    if i = 0 then ()
+    else index_append_lem ls0' ls1 (i-1)
+#pop-options
+
+val index_map_lem (#a #b: Type0) (f : a -> Tot b) (ls : list a)
+  (i : nat{i < length ls}) :
+  Lemma (
+    index (map f ls) i == f (index ls i))
+  [SMTPat (index (map f ls) i)]
+
+#push-options "--fuel 1"
+let rec index_map_lem #a #b f ls i =
+  match ls with
+  | [] -> ()
+  | x :: ls' ->
+    if i = 0 then ()
+    else index_map_lem f ls' (i-1)
+#pop-options
+
+val for_all_append (#a : Type0) (f : a -> Tot bool) (ls0 ls1 : list a) :
+  Lemma (for_all f (ls0 @ ls1) = (for_all f ls0 && for_all f ls1))
+
+#push-options "--fuel 1"
+let rec for_all_append #a f ls0 ls1 =
+  match ls0 with
+  | [] -> ()
+  | x :: ls0' ->
+    for_all_append f ls0' ls1
+#pop-options
+
+/// Filter a list, stopping after we removed one element
+val filter_one (#a : Type) (f : a -> bool) (ls : list a) : list a
+
+let rec filter_one #a f ls =
+  match ls with
+  | [] -> []
+  | x :: ls' -> if f x then x :: filter_one f ls' else ls'
+
+val find_append (#a : Type) (f : a -> bool) (ls0 ls1 : list a) :
+  Lemma (
+    find f (ls0 @ ls1) ==
+    begin match find f ls0 with
+    | Some x -> Some x
+    | None -> find f ls1
+    end)
+
+#push-options "--fuel 1"
+let rec find_append #a f ls0 ls1 =
+  match ls0 with
+  | [] -> ()
+  | x :: ls0' ->
+    if f x then
+    begin
+      assert(ls0 @ ls1 == x :: (ls0' @ ls1));
+      assert(find f (ls0 @ ls1) == find f (x :: (ls0' @ ls1)));
+      // Why do I have to do this?! Is it because of subtyping??
+      assert(
+        match find f (ls0 @ ls1) with
+        | Some x' -> x' == x
+        | None -> False)
+    end
+    else find_append f ls0' ls1
+#pop-options
+
+val length_flatten_update :
+     #a:Type
+  -> ls:list (list a)
+  -> i:nat{i < length ls}
+  -> x:list a ->
+  Lemma (
+    // We want this property:
+    // ```
+    // length (flatten (list_update ls i x)) =
+    //   length (flatten ls) - length (index ls i) + length x
+    // ```
+    length (flatten (list_update ls i x)) + length (index ls i) =
+    length (flatten ls) + length x)
+
+#push-options "--fuel 1"
+let rec length_flatten_update #a ls i x =
+  match ls with
+  | x' :: ls' ->
+    assert(flatten ls == x' @ flatten ls'); // Triggers patterns
+    assert(length (flatten ls) == length x' + length (flatten ls'));
+    if i = 0 then
+      begin
+      let ls1 = x :: ls' in
+      assert(list_update ls i x == ls1);
+      assert(flatten ls1 == x @ flatten ls'); // Triggers patterns
+      assert(length (flatten ls1) == length x + length (flatten ls'));
+      ()
+      end
+    else
+      begin
+      length_flatten_update ls' (i-1) x;
+      let ls1 = x' :: list_update ls' (i-1) x in
+      assert(flatten ls1 == x' @ flatten (list_update ls' (i-1) x)) // Triggers patterns
+      end
+#pop-options
+
+val length_flatten_index :
+     #a:Type
+  -> ls:list (list a)
+  -> i:nat{i < length ls} ->
+  Lemma (
+    length (flatten ls) >= length (index ls i))
+
+#push-options "--fuel 1"
+let rec length_flatten_index #a ls i =
+  match ls with
+  | x' :: ls' ->
+    assert(flatten ls == x' @ flatten ls'); // Triggers patterns
+    assert(length (flatten ls) == length x' + length (flatten ls'));
+    if i = 0 then ()
+    else length_flatten_index ls' (i-1)
+#pop-options
+
+val forall_index_equiv_list_for_all
+  (#a : Type) (pred : a -> Tot bool) (ls : list a) :
+  Lemma ((forall (i:nat{i < length ls}). pred (index ls i)) <==> for_all pred ls)
+
+#push-options "--fuel 1"
+let rec forall_index_equiv_list_for_all pred ls =
+  match ls with
+  | [] -> ()
+  | x :: ls' ->
+    assert(forall (i:nat{i < length ls'}). index ls' i == index ls (i+1));
+    assert(forall (i:nat{0 < i /\ i < length ls}). index ls i == index ls' (i-1));
+    assert(index ls 0 == x);
+    forall_index_equiv_list_for_all pred ls'
+#pop-options
+
+val find_update:
+     #a:Type
+  -> f:(a -> Tot bool)
+  -> ls:list a
+  -> x:a
+  -> ls':list a{length ls' == length ls}
+#push-options "--fuel 1"
+let rec find_update #a f ls x =
+  match ls with
+  | [] -> []
+  | hd::tl ->
+    if f hd then x :: tl else hd :: find_update f tl x
+#pop-options
+
+val pairwise_distinct : #a:eqtype -> ls:list a -> Tot bool
+let rec pairwise_distinct (#a : eqtype) (ls : list a) : Tot bool =
+  match ls with
+  | [] -> true
+  | x :: ls' -> List.Tot.for_all (fun y -> x <> y) ls' && pairwise_distinct ls'
+
+val pairwise_rel : #a:Type -> pred:(a -> a -> Tot bool) -> ls:list a -> Tot bool
+let rec pairwise_rel #a pred ls =
+  match ls with
+  | [] -> true
+  | x :: ls' ->
+    for_all (pred x) ls' && pairwise_rel pred ls' 
+
+#push-options "--fuel 1"
+let rec flatten_append (#a : Type) (l1 l2: list (list a)) :
+  Lemma (flatten (l1 @ l2) == flatten l1 @ flatten l2) =
+  match l1 with
+  | [] -> ()
+  | x :: l1' ->
+    flatten_append l1' l2;
+    append_assoc x (flatten l1') (flatten l2)
+#pop-options
+
+/// We don't use anonymous functions as parameters to other functions, but rather
+/// introduce auxiliary functions instead: otherwise we can't reason (because
+/// F*'s encoding to the SMT is imprecise for functions)
+let fst_is_disctinct (#a : eqtype) (#b : Type0) (p0 : a & b) (p1 : a & b) : Type0 =
+  fst p0 <> fst p1
+
+(*** Lemmas about Primitives *)
+/// TODO: move those lemmas
+
+// TODO: rename to 'insert'?
+val list_update_index_dif_lem
+  (#a : Type0) (ls : list a) (i : nat{i < length ls}) (x : a)
+  (j : nat{j < length ls}) :
+  Lemma (requires (j <> i))
+  (ensures (index (list_update ls i x) j == index ls j))
+  [SMTPat (index (list_update ls i x) j)]
+
+#push-options "--fuel 1"
+let rec list_update_index_dif_lem #a ls i x j =
+  match ls with
+  | x' :: ls ->
+    if i = 0 then ()
+    else if j = 0 then ()
+    else
+     list_update_index_dif_lem ls (i-1) x (j-1)
+#pop-options
+
+val map_list_update_lem
+  (#a #b: Type0) (f : a -> Tot b)
+  (ls : list a) (i : nat{i < length ls}) (x : a) :
+  Lemma (list_update (map f ls) i (f x) == map f (list_update ls i x))
+  [SMTPat (list_update (map f ls) i (f x))]
+
+#push-options "--fuel 1"
+let rec map_list_update_lem #a #b f ls i x =
+  match ls with
+  | x' :: ls' ->
+    if i = 0 then ()
+    else map_list_update_lem f ls' (i-1) x
+#pop-options
+
+(*** Invariants, models *)
+
+(**** Internals *)
+/// The following invariants, models, representation functions... are mostly
+/// for the purpose of the proofs.
+
+let is_pos_usize (n : nat) : Type0 = 0 < n /\ n <= usize_max
+type pos_usize = x:usize{x > 0}
+
+type binding (t : Type0) = key & t
+
+type slots_t (t : Type0) = alloc_vec_Vec (list_t t)
+
+/// We represent hash maps as associative lists
+type assoc_list (t : Type0) = list (binding t)
+
+/// Representation function for [list_t]
+let rec list_t_v (#t : Type0) (ls : list_t t) : assoc_list t =
+  match ls with
+  | List_Nil -> []
+  | List_Cons k v tl -> (k,v) :: list_t_v tl
+
+let list_t_len (#t : Type0) (ls : list_t t) : nat = length (list_t_v ls)
+let list_t_index (#t : Type0) (ls : list_t t) (i : nat{i < list_t_len ls}) : binding t =
+  index (list_t_v ls) i
+
+type slot_s (t : Type0) = list (binding t)
+type slots_s (t : Type0) = list (slot_s t)
+
+type slot_t (t : Type0) = list_t t
+let slot_t_v #t = list_t_v #t
+
+/// Representation function for the slots.
+let slots_t_v (#t : Type0) (slots : slots_t t) : slots_s t =
+  map slot_t_v slots
+
+/// Representation function for the slots, seen as an associative list.
+let slots_t_al_v (#t : Type0) (slots : slots_t t) : assoc_list t =
+  flatten (map list_t_v slots)
+
+/// High-level type for the hash-map, seen as a list of associative lists (one
+/// list per slot). This is the representation we use most, internally. Note that
+/// we later introduce a [map_s] representation, which is the one used in the
+/// lemmas shown to the user.
+type hashMap_s t = list (slot_s t)
+
+// TODO: why not always have the condition on the length?
+// 'nes': "non-empty slots"
+type hashMap_s_nes (t : Type0) : Type0 =
+  hm:hashMap_s t{is_pos_usize (length hm)}
+
+/// Representation function for [hashMap_t] as a list of slots
+let hashMap_t_v (#t : Type0) (hm : hashMap_t t) : hashMap_s t =
+  map list_t_v hm.slots
+
+/// Representation function for [hashMap_t] as an associative list
+let hashMap_t_al_v (#t : Type0) (hm : hashMap_t t) : assoc_list t =
+  flatten (hashMap_t_v hm)
+
+// 'nes': "non-empty slots"
+type hashMap_t_nes (t : Type0) : Type0 =
+  hm:hashMap_t t{is_pos_usize (length hm.slots)}
+
+let hash_key_s (k : key) : hash =
+  Return?.v (hash_key k)
+
+let hash_mod_key (k : key) (len : usize{len > 0}) : hash =
+  (hash_key_s k) % len
+
+let not_same_key (#t : Type0) (k : key) (b : binding t) : bool = fst b <> k
+let same_key (#t : Type0) (k : key) (b : binding t) : bool = fst b = k
+
+// We take a [nat] instead of a [hash] on purpose
+let same_hash_mod_key (#t : Type0) (len : usize{len > 0}) (h : nat) (b : binding t) : bool =
+  hash_mod_key (fst b) len = h
+
+let binding_neq (#t : Type0) (b0 b1 : binding t) : bool = fst b0 <> fst b1
+
+let hashMap_t_len_s (#t : Type0) (hm : hashMap_t t) : nat =
+  hm.num_entries
+
+let assoc_list_find (#t : Type0) (k : key) (slot : assoc_list t) : option t =
+  match find (same_key k) slot with
+  | None -> None
+  | Some (_, v) -> Some v
+
+let slot_s_find (#t : Type0) (k : key) (slot : list (binding t)) : option t =
+  assoc_list_find k slot
+
+let slot_t_find_s (#t : Type0) (k : key) (slot : list_t t) : option t =
+  slot_s_find k (slot_t_v slot)
+
+// This is a simpler version of the "find" function, which captures the essence
+// of what happens and operates on [hashMap_s].
+let hashMap_s_find
+  (#t : Type0) (hm : hashMap_s_nes t)
+  (k : key) : option t =
+  let i = hash_mod_key k (length hm) in
+  let slot = index hm i in
+  slot_s_find k slot
+
+let hashMap_s_len
+  (#t : Type0) (hm : hashMap_s t) :
+  nat =
+  length (flatten hm)
+
+// Same as above, but operates on [hashMap_t]
+// Note that we don't reuse the above function on purpose: converting to a
+// [hashMap_s] then looking up an element is not the same as what we
+// wrote below.
+let hashMap_t_find_s
+  (#t : Type0) (hm : hashMap_t t{length hm.slots > 0}) (k : key) : option t =
+  let slots = hm.slots in
+  let i = hash_mod_key k (length slots) in
+  let slot = index slots i in
+  slot_t_find_s k slot
+
+/// Invariants for the slots
+
+let slot_s_inv
+  (#t : Type0) (len : usize{len > 0}) (i : usize) (slot : list (binding t)) : bool =
+  // All the bindings are in the proper slot
+  for_all (same_hash_mod_key len i) slot &&
+  // All the keys are pairwise distinct
+  pairwise_rel binding_neq slot
+
+let slot_t_inv (#t : Type0) (len : usize{len > 0}) (i : usize) (slot : list_t t) : bool =
+  slot_s_inv len i (slot_t_v slot)
+
+let slots_s_inv (#t : Type0) (slots : slots_s t{length slots <= usize_max}) : Type0 =
+  forall(i:nat{i < length slots}).
+  {:pattern index slots i}
+  slot_s_inv (length slots) i (index slots i)
+
+// At some point we tried to rewrite this in terms of [slots_s_inv]. However it
+// made a lot of proofs fail because those proofs relied on the [index_map_lem]
+// pattern. We tried writing others lemmas with patterns (like [slots_s_inv]
+// implies [slots_t_inv]) but it didn't succeed, so we keep things as they are.
+let slots_t_inv (#t : Type0) (slots : slots_t t{length slots <= usize_max}) : Type0 =
+  forall(i:nat{i < length slots}).
+  {:pattern index slots i}
+  slot_t_inv (length slots) i (index slots i)
+
+let hashMap_s_inv (#t : Type0) (hm : hashMap_s t) : Type0 =
+  length hm <= usize_max /\
+  length hm > 0 /\
+  slots_s_inv hm
+
+/// Base invariant for the hashmap (the complete invariant can be temporarily
+/// broken between the moment we inserted an element and the moment we resize)
+let hashMap_t_base_inv (#t : Type0) (hm : hashMap_t t) : Type0 =
+  let al = hashMap_t_al_v hm in
+  // [num_entries] correctly tracks the number of entries in the table
+  // Note that it gives us that the length of the slots array is <= usize_max:
+  // [> length <= usize_max
+  // (because hashMap_num_entries has type `usize`)
+  hm.num_entries = length al /\
+  // Slots invariant
+  slots_t_inv hm.slots /\
+  // The capacity must be > 0 (otherwise we can't resize, because we
+  // multiply the capacity by two!)
+  length hm.slots > 0 /\
+  // Load computation
+  begin
+  let capacity = length hm.slots in
+  let (dividend, divisor) = hm.max_load_factor in
+  0 < dividend /\ dividend < divisor /\
+  capacity * dividend >= divisor /\
+  hm.max_load = (capacity * dividend) / divisor
+  end
+
+/// We often need to frame some values
+let hashMap_t_same_params (#t : Type0) (hm0 hm1 : hashMap_t t) : Type0 =
+  length hm0.slots = length hm1.slots /\
+  hm0.max_load = hm1.max_load /\
+  hm0.max_load_factor = hm1.max_load_factor
+
+/// The following invariants, etc. are meant to be revealed to the user through
+/// the .fsti.
+
+/// Invariant for the hashmap
+let hashMap_t_inv (#t : Type0) (hm : hashMap_t t) : Type0 =
+  // Base invariant
+  hashMap_t_base_inv hm /\
+  // The hash map is either: not overloaded, or we can't resize it
+  begin
+  let (dividend, divisor) = hm.max_load_factor in
+  hm.num_entries <= hm.max_load
+  || length hm.slots * 2 * dividend > usize_max
+  end
+
+(*** .fsti *)
+/// We reveal slightly different version of the above functions to the user
+
+let len_s (#t : Type0) (hm : hashMap_t t) : nat = hashMap_t_len_s hm
+
+/// This version doesn't take any precondition (contrary to [hashMap_t_find_s])
+let find_s (#t : Type0) (hm : hashMap_t t) (k : key) : option t =
+  if length hm.slots = 0 then None
+  else hashMap_t_find_s hm k
+
+(*** Overloading *)
+
+let hashMap_not_overloaded_lem #t hm = ()
+
+(*** allocate_slots *)
+
+/// Auxiliary lemma
+val slots_t_all_nil_inv_lem
+  (#t : Type0) (slots : alloc_vec_Vec (list_t t){length slots <= usize_max}) :
+  Lemma (requires (forall (i:nat{i < length slots}). index slots i == List_Nil))
+  (ensures (slots_t_inv slots))
+
+#push-options "--fuel 1"
+let slots_t_all_nil_inv_lem #t slots = ()
+#pop-options
+
+val slots_t_al_v_all_nil_is_empty_lem
+  (#t : Type0) (slots : alloc_vec_Vec (list_t t)) :
+  Lemma (requires (forall (i:nat{i < length slots}). index slots i == List_Nil))
+  (ensures (slots_t_al_v slots == []))
+
+#push-options "--fuel 1"
+let rec slots_t_al_v_all_nil_is_empty_lem #t slots =
+ match slots with
+ | [] -> ()
+ | s :: slots' ->
+   assert(forall (i:nat{i < length slots'}). index slots' i == index slots (i+1));
+   slots_t_al_v_all_nil_is_empty_lem #t slots';
+   assert(slots_t_al_v slots == list_t_v s @ slots_t_al_v slots');
+   assert(slots_t_al_v slots == list_t_v s);
+   assert(index slots 0 == List_Nil)
+#pop-options
+
+/// [allocate_slots]
+val hashMap_allocate_slots_lem
+  (t : Type0) (slots : alloc_vec_Vec (list_t t)) (n : usize) :
+  Lemma
+  (requires (length slots + n <= usize_max))
+  (ensures (
+   match hashMap_allocate_slots t slots n with
+   | Fail _ -> False
+   | Return slots' ->
+     length slots' = length slots + n /\
+     // We leave the already allocated slots unchanged
+     (forall (i:nat{i < length slots}). index slots' i == index slots i) /\
+     // We allocate n additional empty slots
+     (forall (i:nat{length slots <= i /\ i < length slots'}). index slots' i == List_Nil)))
+  (decreases (hashMap_allocate_slots_loop_decreases t slots n))
+
+#push-options "--fuel 1"
+let rec hashMap_allocate_slots_lem t slots n =
+  begin match n with
+  | 0 -> ()
+  | _ ->
+    begin match alloc_vec_Vec_push (list_t t) slots List_Nil with
+    | Fail _ -> ()
+    | Return slots1 ->
+      begin match usize_sub n 1 with
+      | Fail _ -> ()
+      | Return i ->
+        hashMap_allocate_slots_lem t slots1 i;
+        begin match hashMap_allocate_slots t slots1 i with
+        | Fail _ -> ()
+        | Return slots2 ->
+          assert(length slots1 = length slots + 1);
+          assert(slots1 == slots @ [List_Nil]); // Triggers patterns
+          assert(index slots1 (length slots) == index [List_Nil] 0); // Triggers patterns
+          assert(index slots1 (length slots) == List_Nil)
+        end
+      end
+    end
+  end
+#pop-options
+
+(*** new_with_capacity *)
+/// Under proper conditions, [new_with_capacity] doesn't fail and returns an empty hash map.
+val hashMap_new_with_capacity_lem
+  (t : Type0) (capacity : usize)
+  (max_load_dividend : usize) (max_load_divisor : usize) :
+  Lemma
+  (requires (
+    0 < max_load_dividend /\
+    max_load_dividend < max_load_divisor /\
+    0 < capacity /\
+    capacity * max_load_dividend >= max_load_divisor /\
+    capacity * max_load_dividend <= usize_max))
+  (ensures (
+    match hashMap_new_with_capacity t capacity max_load_dividend max_load_divisor with
+    | Fail _ -> False
+    | Return hm ->
+      // The hash map invariant is satisfied
+      hashMap_t_inv hm /\
+      // The parameters are correct
+      hm.max_load_factor = (max_load_dividend, max_load_divisor) /\
+      hm.max_load = (capacity * max_load_dividend) / max_load_divisor /\
+      // The hash map has the specified capacity - we need to reveal this
+      // otherwise the pre of [hashMap_t_find_s] is not satisfied.
+      length hm.slots = capacity /\
+      // The hash map has 0 values
+      hashMap_t_len_s hm = 0 /\
+      // It contains no bindings
+      (forall k. hashMap_t_find_s hm k == None) /\
+      // We need this low-level property for the invariant
+      (forall(i:nat{i < length hm.slots}). index hm.slots i == List_Nil)))
+
+#push-options "--z3rlimit 50 --fuel 1"
+let hashMap_new_with_capacity_lem (t : Type0) (capacity : usize)
+  (max_load_dividend : usize) (max_load_divisor : usize) =
+  let v = alloc_vec_Vec_new (list_t t) in
+  assert(length v = 0);
+  hashMap_allocate_slots_lem t v capacity;
+  begin match hashMap_allocate_slots t v capacity with
+  | Fail _ -> assert(False)
+  | Return v0 ->
+    begin match usize_mul capacity max_load_dividend with
+    | Fail _ -> assert(False)
+    | Return i ->
+      begin match usize_div i max_load_divisor with
+      | Fail _ -> assert(False)
+      | Return i0 ->
+          let hm = MkhashMap_t 0 (max_load_dividend, max_load_divisor) i0 v0 in
+          slots_t_all_nil_inv_lem v0;
+          slots_t_al_v_all_nil_is_empty_lem hm.slots
+      end
+    end
+  end
+#pop-options
+
+(*** new *)
+
+/// [new] doesn't fail and returns an empty hash map
+val hashMap_new_lem_aux (t : Type0) :
+  Lemma
+  (ensures (
+    match hashMap_new t with
+    | Fail _ -> False
+    | Return hm ->
+      // The hash map invariant is satisfied
+      hashMap_t_inv hm /\
+      // The hash map has 0 values
+      hashMap_t_len_s hm = 0 /\
+      // It contains no bindings
+      (forall k. hashMap_t_find_s hm k == None)))
+
+#push-options "--fuel 1"
+let hashMap_new_lem_aux t =
+  hashMap_new_with_capacity_lem t 32 4 5;
+  match hashMap_new_with_capacity t 32 4 5 with
+  | Fail _ -> ()
+  | Return hm -> ()
+#pop-options
+
+/// The lemma we reveal in the .fsti
+let hashMap_new_lem t = hashMap_new_lem_aux t
+
+(*** clear *)
+/// [clear]: the loop doesn't fail and simply clears the slots starting at index i
+#push-options "--fuel 1"
+let rec hashMap_clear_loop_lem
+  (t : Type0) (slots : alloc_vec_Vec (list_t t)) (i : usize) :
+  Lemma
+  (ensures (
+    match hashMap_clear_loop t slots i with
+    | Fail _ -> False
+    | Return slots' ->
+      // The length is preserved
+      length slots' == length slots /\
+      // The slots before i are left unchanged
+      (forall (j:nat{j < i /\ j < length slots}). index slots' j == index slots j) /\
+      // The slots after i are set to List_Nil
+      (forall (j:nat{i <= j /\ j < length slots}). index slots' j == List_Nil)))
+  (decreases (hashMap_clear_loop_decreases t slots i))
+  =
+  let i0 = alloc_vec_Vec_len (list_t t) slots in
+  let b = i < i0 in
+  if b
+  then
+    begin match alloc_vec_Vec_update_usize slots i List_Nil with
+    | Fail _ -> ()
+    | Return v ->
+      begin match usize_add i 1 with
+      | Fail _ -> ()
+      | Return i1 ->
+        hashMap_clear_loop_lem t v i1;
+        begin match hashMap_clear_loop t v i1 with
+        | Fail _ -> ()
+        | Return slots1 ->
+          assert(length slots1 == length slots);
+          assert(forall (j:nat{i+1 <= j /\ j < length slots}). index slots1 j == List_Nil);
+          assert(index slots1 i == List_Nil)
+        end
+      end
+    end
+  else ()
+#pop-options
+
+/// [clear] doesn't fail and turns the hash map into an empty map
+val hashMap_clear_lem_aux
+  (#t : Type0) (self : hashMap_t t) :
+  Lemma
+  (requires (hashMap_t_base_inv self))
+  (ensures (
+    match hashMap_clear t self with
+    | Fail _ -> False
+    | Return hm ->
+      // The hash map invariant is satisfied
+      hashMap_t_base_inv hm /\
+      // We preserved the parameters
+      hashMap_t_same_params hm self /\
+      // The hash map has 0 values
+      hashMap_t_len_s hm = 0 /\
+      // It contains no bindings
+      (forall k. hashMap_t_find_s hm k == None)))
+
+// Being lazy: fuel 1 helps a lot...
+#push-options "--fuel 1"
+let hashMap_clear_lem_aux #t self =
+  let p = self.max_load_factor in
+  let i = self.max_load in
+  let v = self.slots in
+  hashMap_clear_loop_lem t v 0;
+  begin match hashMap_clear_loop t v 0 with
+  | Fail _ -> ()
+  | Return slots1 ->
+    slots_t_al_v_all_nil_is_empty_lem slots1;
+    let hm1 = MkhashMap_t 0 p i slots1 in
+    assert(hashMap_t_base_inv hm1);
+    assert(hashMap_t_inv hm1)
+  end
+#pop-options
+
+let hashMap_clear_lem #t self = hashMap_clear_lem_aux #t self
+
+(*** len *)
+
+/// [len]: we link it to a non-failing function.
+/// Rk.: we might want to make an analysis to not use an error monad to translate
+/// functions which statically can't fail.
+let hashMap_len_lem #t self = ()
+
+
+(*** insert_in_list *)
+
+(**** insert_in_list'fwd *)
+
+/// [insert_in_list]: returns true iff the key is not in the list (functional version)
+val hashMap_insert_in_list_lem
+  (t : Type0) (key : usize) (value : t) (ls : list_t t) :
+  Lemma
+  (ensures (
+    match hashMap_insert_in_list t key value ls with
+    | Fail _ -> False
+    | Return b ->
+      b <==> (slot_t_find_s key ls == None)))
+  (decreases (hashMap_insert_in_list_loop_decreases t key value ls))
+
+#push-options "--fuel 1"
+let rec hashMap_insert_in_list_lem t key value ls =
+  begin match ls with
+  | List_Cons ckey cvalue ls0 ->
+    let b = ckey = key in
+    if b
+    then ()
+    else
+      begin
+      hashMap_insert_in_list_lem t key value ls0;
+      match hashMap_insert_in_list t key value ls0 with
+      | Fail _ -> ()
+      | Return b0 -> ()
+      end
+  | List_Nil ->
+    assert(list_t_v ls == []);
+    assert_norm(find (same_key #t key) [] == None)
+  end
+#pop-options
+
+(**** insert_in_list'back *)
+
+/// The proofs about [insert_in_list] backward are easier to do in several steps:
+/// extrinsic proofs to the rescue!
+/// We first prove that [insert_in_list] refines the function we wrote above, then
+/// use this function to prove the invariants, etc.
+
+/// We write a helper which "captures" what [insert_in_list] does.
+/// We then reason about this helper to prove the high-level properties we want
+/// (functional properties, preservation of invariants, etc.).
+let hashMap_insert_in_list_s
+  (#t : Type0) (key : usize) (value : t) (ls : list (binding t)) :
+  list (binding t) =
+  // Check if there is already a binding for the key
+  match find (same_key key) ls with
+  | None ->
+    // No binding: append the binding to the end
+    ls @ [(key,value)]
+  | Some _ ->
+    // There is already a binding: update it
+    find_update (same_key key) ls (key,value)
+
+/// [insert_in_list]: if the key is not in the map, appends a new bindings (functional version)
+val hashMap_insert_in_list_back_lem_append_s
+  (t : Type0) (key : usize) (value : t) (ls : list_t t) :
+  Lemma
+  (requires (
+    slot_t_find_s key ls == None))
+  (ensures (
+    match hashMap_insert_in_list_back t key value ls with
+    | Fail _ -> False
+    | Return ls' ->
+      list_t_v ls' == list_t_v ls @ [(key,value)]))
+  (decreases (hashMap_insert_in_list_loop_decreases t key value ls))
+
+#push-options "--fuel 1"
+let rec hashMap_insert_in_list_back_lem_append_s t key value ls =
+  begin match ls with
+  | List_Cons ckey cvalue ls0 ->
+    let b = ckey = key in
+    if b
+    then ()
+    else
+      begin
+      hashMap_insert_in_list_back_lem_append_s t key value ls0;
+      match hashMap_insert_in_list_back t key value ls0 with
+      | Fail _ -> ()
+      | Return l -> ()
+      end
+  | List_Nil -> ()
+  end
+#pop-options
+
+/// [insert_in_list]: if the key is in the map, we update the binding (functional version)
+val hashMap_insert_in_list_back_lem_update_s
+  (t : Type0) (key : usize) (value : t) (ls : list_t t) :
+  Lemma
+  (requires (
+    Some? (find (same_key key) (list_t_v ls))))
+  (ensures (
+    match hashMap_insert_in_list_back t key value ls with
+    | Fail _ -> False
+    | Return ls' ->
+      list_t_v ls' == find_update (same_key key) (list_t_v ls) (key,value)))
+  (decreases (hashMap_insert_in_list_loop_decreases t key value ls))
+
+#push-options "--fuel 1"
+let rec hashMap_insert_in_list_back_lem_update_s t key value ls =
+  begin match ls with
+  | List_Cons ckey cvalue ls0 ->
+    let b = ckey = key in
+    if b
+    then ()
+    else
+      begin
+      hashMap_insert_in_list_back_lem_update_s t key value ls0;
+      match hashMap_insert_in_list_back t key value ls0 with
+      | Fail _ -> ()
+      | Return l -> ()
+      end
+  | List_Nil -> ()
+  end
+#pop-options
+
+/// Put everything together
+val hashMap_insert_in_list_back_lem_s
+  (t : Type0) (key : usize) (value : t) (ls : list_t t) :
+  Lemma
+  (ensures (
+    match hashMap_insert_in_list_back t key value ls with
+    | Fail _ -> False
+    | Return ls' ->
+      list_t_v ls' == hashMap_insert_in_list_s key value (list_t_v ls)))
+
+let hashMap_insert_in_list_back_lem_s t key value ls =
+  match find (same_key key) (list_t_v ls) with
+  | None -> hashMap_insert_in_list_back_lem_append_s t key value ls
+  | Some _ -> hashMap_insert_in_list_back_lem_update_s t key value ls
+
+(**** Invariants of insert_in_list_s *)
+
+/// Auxiliary lemmas
+/// We work on [hashMap_insert_in_list_s], the "high-level" version of [insert_in_list'back].
+///
+/// Note that in F* we can't have recursive proofs inside of other proofs, contrary
+/// to Coq, which makes it a bit cumbersome to prove auxiliary results like the
+/// following ones...
+
+(** Auxiliary lemmas: append case *)
+
+val slot_t_v_for_all_binding_neq_append_lem
+  (t : Type0) (key : usize) (value : t) (ls : list (binding t)) (b : binding t) :
+  Lemma
+  (requires (
+    fst b <> key /\
+    for_all (binding_neq b) ls /\
+    slot_s_find key ls == None))
+  (ensures (
+    for_all (binding_neq b) (ls @ [(key,value)])))
+
+#push-options "--fuel 1"
+let rec slot_t_v_for_all_binding_neq_append_lem t key value ls b =
+  match ls with
+  | [] -> ()
+  | (ck, cv) :: cls ->
+    slot_t_v_for_all_binding_neq_append_lem t key value cls b
+#pop-options
+
+val slot_s_inv_not_find_append_end_inv_lem
+  (t : Type0) (len : usize{len > 0}) (key : usize) (value : t) (ls : list (binding t)) :
+  Lemma
+  (requires (
+    slot_s_inv len (hash_mod_key key len) ls /\
+    slot_s_find key ls == None))
+  (ensures (
+    let ls' = ls @ [(key,value)] in
+    slot_s_inv len (hash_mod_key key len) ls' /\
+    (slot_s_find key ls' == Some value) /\
+    (forall k'. k' <> key ==> slot_s_find k' ls' == slot_s_find k' ls)))
+
+#push-options "--fuel 1"
+let rec slot_s_inv_not_find_append_end_inv_lem t len key value ls =
+  match ls with
+  | [] -> ()
+  | (ck, cv) :: cls ->
+    slot_s_inv_not_find_append_end_inv_lem t len key value cls;
+    let h = hash_mod_key key len in
+    let ls' = ls @ [(key,value)] in
+    assert(for_all (same_hash_mod_key len h) ls');
+    slot_t_v_for_all_binding_neq_append_lem t key value cls (ck, cv);
+    assert(pairwise_rel binding_neq ls');
+    assert(slot_s_inv len h ls')
+#pop-options
+
+/// [insert_in_list]: if the key is not in the map, appends a new bindings
+val hashMap_insert_in_list_s_lem_append
+  (t : Type0) (len : usize{len > 0}) (key : usize) (value : t) (ls : list (binding t)) :
+  Lemma
+  (requires (
+    slot_s_inv len (hash_mod_key key len) ls /\
+    slot_s_find key ls == None))
+  (ensures (
+    let ls' = hashMap_insert_in_list_s key value ls in
+    ls' == ls @ [(key,value)] /\
+    // The invariant is preserved
+    slot_s_inv len (hash_mod_key key len) ls' /\
+    // [key] maps to [value]
+    slot_s_find key ls' == Some value /\
+    // The other bindings are preserved
+    (forall k'. k' <> key ==> slot_s_find k' ls' == slot_s_find k' ls)))
+
+let hashMap_insert_in_list_s_lem_append t len key value ls =
+  slot_s_inv_not_find_append_end_inv_lem t len key value ls
+
+/// [insert_in_list]: if the key is not in the map, appends a new bindings (quantifiers)
+/// Rk.: we don't use this lemma.
+/// TODO: remove?
+val hashMap_insert_in_list_back_lem_append
+  (t : Type0) (len : usize{len > 0}) (key : usize) (value : t) (ls : list_t t) :
+  Lemma
+  (requires (
+    slot_t_inv len (hash_mod_key key len) ls /\
+    slot_t_find_s key ls == None))
+  (ensures (
+    match hashMap_insert_in_list_back t key value ls with
+    | Fail _ -> False
+    | Return ls' ->
+      list_t_v ls' == list_t_v ls @ [(key,value)] /\
+      // The invariant is preserved
+      slot_t_inv len (hash_mod_key key len) ls' /\
+      // [key] maps to [value]
+      slot_t_find_s key ls' == Some value /\
+      // The other bindings are preserved
+      (forall k'. k' <> key ==> slot_t_find_s k' ls' == slot_t_find_s k' ls)))
+
+let hashMap_insert_in_list_back_lem_append t len key value ls =
+  hashMap_insert_in_list_back_lem_s t key value ls;
+  hashMap_insert_in_list_s_lem_append t len key value (list_t_v ls)
+
+(** Auxiliary lemmas: update case *)
+
+val slot_s_find_update_for_all_binding_neq_append_lem
+  (t : Type0) (key : usize) (value : t) (ls : list (binding t)) (b : binding t) :
+  Lemma
+  (requires (
+    fst b <> key /\
+    for_all (binding_neq b) ls))
+  (ensures (
+    let ls' = find_update (same_key key) ls (key, value) in
+    for_all (binding_neq b) ls'))
+
+#push-options "--fuel 1"
+let rec slot_s_find_update_for_all_binding_neq_append_lem t key value ls b =
+  match ls with
+  | [] -> ()
+  | (ck, cv) :: cls ->
+    slot_s_find_update_for_all_binding_neq_append_lem t key value cls b
+#pop-options
+
+/// Annoying auxiliary lemma we have to prove because there is no way to reason
+/// properly about closures.
+/// I'm really enjoying my time.
+val for_all_binding_neq_value_indep
+  (#t : Type0) (key : key) (v0 v1 : t) (ls : list (binding t)) :
+  Lemma (for_all (binding_neq (key,v0)) ls = for_all (binding_neq (key,v1)) ls)
+
+#push-options "--fuel 1"
+let rec for_all_binding_neq_value_indep #t key v0 v1 ls =
+  match ls with
+  | [] -> ()
+  | _ :: ls' -> for_all_binding_neq_value_indep #t key v0 v1 ls'
+#pop-options
+
+val slot_s_inv_find_append_end_inv_lem
+  (t : Type0) (len : usize{len > 0}) (key : usize) (value : t) (ls : list (binding t)) :
+  Lemma
+  (requires (
+    slot_s_inv len (hash_mod_key key len) ls /\
+    Some? (slot_s_find key ls)))
+  (ensures (
+    let ls' = find_update (same_key key) ls (key, value) in
+    slot_s_inv len (hash_mod_key key len) ls' /\
+    (slot_s_find key ls' == Some value) /\
+    (forall k'. k' <> key ==> slot_s_find k' ls' == slot_s_find k' ls)))
+
+#push-options "--z3rlimit 50 --fuel 1"
+let rec slot_s_inv_find_append_end_inv_lem t len key value ls =
+  match ls with
+  | [] -> ()
+  | (ck, cv) :: cls ->
+    let h = hash_mod_key key len in
+    let ls' = find_update (same_key key) ls (key, value) in
+    if ck = key then
+      begin
+      assert(ls' == (ck,value) :: cls);
+      assert(for_all (same_hash_mod_key len h) ls');
+      // For pairwise_rel: binding_neq (ck, value) is actually independent
+      // of `value`. Slightly annoying to prove in F*...
+      assert(for_all (binding_neq (ck,cv)) cls);
+      for_all_binding_neq_value_indep key cv value cls;
+      assert(for_all (binding_neq (ck,value)) cls);
+      assert(pairwise_rel binding_neq ls');
+      assert(slot_s_inv len (hash_mod_key key len) ls')
+      end
+    else
+      begin
+      slot_s_inv_find_append_end_inv_lem t len key value cls;
+      assert(for_all (same_hash_mod_key len h) ls');
+      slot_s_find_update_for_all_binding_neq_append_lem t key value cls (ck, cv);
+      assert(pairwise_rel binding_neq ls');
+      assert(slot_s_inv len h ls')
+      end
+#pop-options
+
+/// [insert_in_list]: if the key is in the map, update the bindings
+val hashMap_insert_in_list_s_lem_update
+  (t : Type0) (len : usize{len > 0}) (key : usize) (value : t) (ls : list (binding t)) :
+  Lemma
+  (requires (
+    slot_s_inv len (hash_mod_key key len) ls /\
+    Some? (slot_s_find key ls)))
+  (ensures (
+    let ls' = hashMap_insert_in_list_s key value ls in
+    ls' == find_update (same_key key) ls (key,value) /\
+    // The invariant is preserved
+    slot_s_inv len (hash_mod_key key len) ls' /\
+    // [key] maps to [value]
+    slot_s_find key ls' == Some value /\
+    // The other bindings are preserved
+    (forall k'. k' <> key ==> slot_s_find k' ls' == slot_s_find k' ls)))
+
+let hashMap_insert_in_list_s_lem_update t len key value ls =
+  slot_s_inv_find_append_end_inv_lem t len key value ls
+
+
+/// [insert_in_list]: if the key is in the map, update the bindings
+/// TODO: not used: remove?
+val hashMap_insert_in_list_back_lem_update
+  (t : Type0) (len : usize{len > 0}) (key : usize) (value : t) (ls : list_t t) :
+  Lemma
+  (requires (
+    slot_t_inv len (hash_mod_key key len) ls /\
+    Some? (slot_t_find_s key ls)))
+  (ensures (
+    match hashMap_insert_in_list_back t key value ls with
+    | Fail _ -> False
+    | Return ls' ->
+      let als = list_t_v ls in
+      list_t_v ls' == find_update (same_key key) als (key,value) /\
+      // The invariant is preserved
+      slot_t_inv len (hash_mod_key key len) ls' /\
+      // [key] maps to [value]
+      slot_t_find_s key ls' == Some value /\
+      // The other bindings are preserved
+      (forall k'. k' <> key ==> slot_t_find_s k' ls' == slot_t_find_s k' ls)))
+
+let hashMap_insert_in_list_back_lem_update t len key value ls =
+  hashMap_insert_in_list_back_lem_s t key value ls;
+  hashMap_insert_in_list_s_lem_update t len key value (list_t_v ls)
+
+(** Final lemmas about [insert_in_list] *)
+
+/// High-level version
+val hashMap_insert_in_list_s_lem
+  (t : Type0) (len : usize{len > 0}) (key : usize) (value : t) (ls : list (binding t)) :
+  Lemma
+  (requires (
+    slot_s_inv len (hash_mod_key key len) ls))
+  (ensures (
+    let ls' = hashMap_insert_in_list_s key value ls in
+    // The invariant is preserved
+    slot_s_inv len (hash_mod_key key len) ls' /\
+    // [key] maps to [value]
+    slot_s_find key ls' == Some value /\
+    // The other bindings are preserved
+    (forall k'. k' <> key ==> slot_s_find k' ls' == slot_s_find k' ls) /\
+    // The length is incremented, iff we inserted a new key
+    (match slot_s_find key ls with
+     | None -> length ls' = length ls + 1
+     | Some _ -> length ls' = length ls)))
+
+let hashMap_insert_in_list_s_lem t len key value ls =
+  match slot_s_find key ls with
+  | None ->
+    assert_norm(length [(key,value)] = 1);
+    hashMap_insert_in_list_s_lem_append t len key value ls
+  | Some _ ->
+    hashMap_insert_in_list_s_lem_update t len key value ls
+
+/// [insert_in_list]
+/// TODO: not used: remove?
+val hashMap_insert_in_list_back_lem
+  (t : Type0) (len : usize{len > 0}) (key : usize) (value : t) (ls : list_t t) :
+  Lemma
+  (requires (slot_t_inv len (hash_mod_key key len) ls))
+  (ensures (
+    match hashMap_insert_in_list_back t key value ls with
+    | Fail _ -> False
+    | Return ls' ->
+      // The invariant is preserved
+      slot_t_inv len (hash_mod_key key len) ls' /\
+      // [key] maps to [value]
+      slot_t_find_s key ls' == Some value /\
+      // The other bindings are preserved
+      (forall k'. k' <> key ==> slot_t_find_s k' ls' == slot_t_find_s k' ls) /\
+      // The length is incremented, iff we inserted a new key
+      (match slot_t_find_s key ls with
+       | None ->
+         list_t_v ls' == list_t_v ls @ [(key,value)] /\
+         list_t_len ls' = list_t_len ls + 1
+       | Some _ ->
+         list_t_v ls' == find_update (same_key key) (list_t_v ls) (key,value) /\
+         list_t_len ls' = list_t_len ls)))
+  (decreases (hashMap_insert_in_list_loop_decreases t key value ls))
+
+let hashMap_insert_in_list_back_lem t len key value ls =
+  hashMap_insert_in_list_back_lem_s t key value ls;
+  hashMap_insert_in_list_s_lem t len key value (list_t_v ls)
+
+(*** insert_no_resize *)
+
+(**** Refinement proof *)
+/// Same strategy as for [insert_in_list]: we introduce a high-level version of
+/// the function, and reason about it.
+/// We work on [hashMap_s] (we use a higher-level view of the hash-map, but
+/// not too high).
+
+/// A high-level version of insert, which doesn't check if the table is saturated
+let hashMap_insert_no_fail_s
+  (#t : Type0) (hm : hashMap_s_nes t)
+  (key : usize) (value : t) :
+  hashMap_s t =
+  let len = length hm in
+  let i = hash_mod_key key len in
+  let slot = index hm i in
+  let slot' = hashMap_insert_in_list_s key value slot in
+  let hm' = list_update hm i slot' in
+  hm'
+
+// TODO: at some point I used hashMap_s_nes and it broke proofs...x
+let hashMap_insert_no_resize_s
+  (#t : Type0) (hm : hashMap_s_nes t)
+  (key : usize) (value : t) :
+  result (hashMap_s t) =
+  // Check if the table is saturated (too many entries, and we need to insert one)
+  let num_entries = length (flatten hm) in
+  if None? (hashMap_s_find hm key) && num_entries = usize_max then Fail Failure
+  else Return (hashMap_insert_no_fail_s hm key value)
+
+/// Prove that [hashMap_insert_no_resize_s] is refined by
+/// [hashMap_insert_no_resize'fwd_back]
+val hashMap_insert_no_resize_lem_s
+  (t : Type0) (self : hashMap_t t) (key : usize) (value : t) :
+  Lemma
+  (requires (
+    hashMap_t_base_inv self /\
+    hashMap_s_len (hashMap_t_v self) = hashMap_t_len_s self))
+  (ensures (
+    begin
+    match hashMap_insert_no_resize t self key value,
+          hashMap_insert_no_resize_s (hashMap_t_v self) key value
+    with
+    | Fail _, Fail _ -> True
+    | Return hm, Return hm_v ->
+      hashMap_t_base_inv hm /\
+      hashMap_t_same_params hm self /\
+      hashMap_t_v hm == hm_v /\
+      hashMap_s_len hm_v == hashMap_t_len_s hm
+    | _ -> False
+    end))
+
+let hashMap_insert_no_resize_lem_s t self key value =
+  begin match hash_key key with
+  | Fail _ -> ()
+  | Return i ->
+    let i0 = self.num_entries in
+    let p = self.max_load_factor in
+    let i1 = self.max_load in
+    let v = self.slots in
+    let i2 = alloc_vec_Vec_len (list_t t) v in
+    let len = length v in
+    begin match usize_rem i i2 with
+    | Fail _ -> ()
+    | Return hash_mod ->
+      begin match alloc_vec_Vec_index_usize v hash_mod with
+      | Fail _ -> ()
+      | Return l ->
+        begin
+        // Checking that: list_t_v (index ...) == index (hashMap_t_v ...) ...
+        assert(list_t_v l == index (hashMap_t_v self) hash_mod);
+        hashMap_insert_in_list_lem t key value l;
+        match hashMap_insert_in_list t key value l with
+        | Fail _ -> ()
+        | Return b ->
+          assert(b = None? (slot_s_find key (list_t_v l)));
+          hashMap_insert_in_list_back_lem t len key value l;
+          if b
+          then
+            begin match usize_add i0 1 with
+            | Fail _ -> ()
+            | Return i3 ->
+              begin
+              match hashMap_insert_in_list_back t key value l with
+              | Fail _ -> ()
+              | Return l0 ->
+                begin match alloc_vec_Vec_update_usize v hash_mod l0 with
+                | Fail _ -> ()
+                | Return v0 ->
+                  let self_v = hashMap_t_v self in
+                  let hm = MkhashMap_t i3 p i1 v0 in
+                  let hm_v = hashMap_t_v hm in
+                  assert(hm_v == list_update self_v hash_mod (list_t_v l0));
+                  assert_norm(length [(key,value)] = 1);
+                  assert(length (list_t_v l0) = length (list_t_v l) + 1);
+                  length_flatten_update self_v hash_mod (list_t_v l0);
+                  assert(hashMap_s_len hm_v = hashMap_t_len_s hm)
+                end
+              end
+            end
+          else
+            begin
+            match hashMap_insert_in_list_back t key value l with
+            | Fail _ -> ()
+            | Return l0 ->
+              begin match alloc_vec_Vec_update_usize v hash_mod l0 with
+              | Fail _ -> ()
+              | Return v0 ->
+                let self_v = hashMap_t_v self in
+                let hm = MkhashMap_t i0 p i1 v0 in
+                let hm_v = hashMap_t_v hm in
+                assert(hm_v == list_update self_v hash_mod (list_t_v l0));
+                assert(length (list_t_v l0) = length (list_t_v l));
+                length_flatten_update self_v hash_mod (list_t_v l0);
+                assert(hashMap_s_len hm_v = hashMap_t_len_s hm)
+              end
+            end
+        end
+      end
+    end
+  end
+
+(**** insert_{no_fail,no_resize}: invariants *)
+
+let hashMap_s_updated_binding
+  (#t : Type0) (hm : hashMap_s_nes t)
+  (key : usize) (opt_value : option t) (hm' : hashMap_s_nes t) : Type0 =
+  // [key] maps to [value]
+  hashMap_s_find hm' key == opt_value /\
+  // The other bindings are preserved
+  (forall k'. k' <> key ==> hashMap_s_find hm' k' == hashMap_s_find hm k')
+
+let insert_post (#t : Type0) (hm : hashMap_s_nes t)
+  (key : usize) (value : t) (hm' : hashMap_s_nes t) : Type0 =
+  // The invariant is preserved
+  hashMap_s_inv hm' /\
+  // [key] maps to [value] and the other bindings are preserved
+  hashMap_s_updated_binding hm key (Some value) hm' /\
+  // The length is incremented, iff we inserted a new key
+  (match hashMap_s_find hm key with
+   | None -> hashMap_s_len hm' = hashMap_s_len hm + 1
+   | Some _ -> hashMap_s_len hm' = hashMap_s_len hm)
+
+val hashMap_insert_no_fail_s_lem
+  (#t : Type0) (hm : hashMap_s_nes t)
+  (key : usize) (value : t) :
+  Lemma
+  (requires (hashMap_s_inv hm))
+  (ensures (
+    let hm' = hashMap_insert_no_fail_s hm key value in
+    insert_post hm key value hm'))
+
+let hashMap_insert_no_fail_s_lem #t hm key value =
+  let len = length hm in
+  let i = hash_mod_key key len in
+  let slot = index hm i in
+  hashMap_insert_in_list_s_lem t len key value slot;
+  let slot' = hashMap_insert_in_list_s key value slot in
+  length_flatten_update hm i slot'
+
+val hashMap_insert_no_resize_s_lem
+  (#t : Type0) (hm : hashMap_s_nes t)
+  (key : usize) (value : t) :
+  Lemma
+  (requires (hashMap_s_inv hm))
+  (ensures (
+    match hashMap_insert_no_resize_s hm key value with
+    | Fail _ ->
+      // Can fail only if we need to create a new binding in
+      // an already saturated map
+      hashMap_s_len hm = usize_max /\
+      None? (hashMap_s_find hm key)
+    | Return hm' ->
+      insert_post hm key value hm'))
+
+let hashMap_insert_no_resize_s_lem #t hm key value =
+  let num_entries = length (flatten hm) in
+  if None? (hashMap_s_find hm key) && num_entries = usize_max then ()
+  else hashMap_insert_no_fail_s_lem hm key value
+
+
+(**** find after insert *)
+/// Lemmas about what happens if we call [find] after an insertion
+
+val hashMap_insert_no_resize_s_get_same_lem
+  (#t : Type0) (hm : hashMap_s t)
+  (key : usize) (value : t) :
+  Lemma (requires (hashMap_s_inv hm))
+  (ensures (
+    match hashMap_insert_no_resize_s hm key value with
+    | Fail _ -> True
+    | Return hm' ->
+      hashMap_s_find hm' key == Some value))
+
+let hashMap_insert_no_resize_s_get_same_lem #t hm key value =
+  let num_entries = length (flatten hm) in
+  if None? (hashMap_s_find hm key) && num_entries = usize_max then ()
+  else
+    begin
+    let hm' = Return?.v (hashMap_insert_no_resize_s hm key value) in
+    let len = length hm in
+    let i = hash_mod_key key len in
+    let slot = index hm i in
+    hashMap_insert_in_list_s_lem t len key value slot
+   end
+
+val hashMap_insert_no_resize_s_get_diff_lem
+  (#t : Type0) (hm : hashMap_s t)
+  (key : usize) (value : t) (key' : usize{key' <> key}) :
+  Lemma (requires (hashMap_s_inv hm))
+  (ensures (
+    match hashMap_insert_no_resize_s hm key value with
+    | Fail _ -> True
+    | Return hm' ->
+      hashMap_s_find hm' key' == hashMap_s_find hm key'))
+
+let hashMap_insert_no_resize_s_get_diff_lem #t hm key value key' =
+  let num_entries = length (flatten hm) in
+  if None? (hashMap_s_find hm key) && num_entries = usize_max then ()
+  else
+    begin
+    let hm' = Return?.v (hashMap_insert_no_resize_s hm key value) in
+    let len = length hm in
+    let i = hash_mod_key key len in
+    let slot = index hm i in
+    hashMap_insert_in_list_s_lem t len key value slot;
+    let i' = hash_mod_key key' len in
+    if i <> i' then ()
+    else
+      begin
+      ()
+      end
+   end
+
+
+(*** move_elements_from_list *)
+
+/// Having a great time here: if we use `result (hashMap_s_res t)` as the
+/// return type for [hashMap_move_elements_from_list_s] instead of having this
+/// awkward match, the proof of [hashMap_move_elements_lem_refin] fails.
+/// I guess it comes from F*'s poor subtyping.
+/// Followingly, I'm not taking any chance and using [result_hashMap_s]
+/// everywhere.
+type result_hashMap_s_nes (t : Type0) : Type0 =
+  res:result (hashMap_s t) {
+    match res with
+    | Fail _ -> True
+    | Return hm -> is_pos_usize (length hm)
+  }
+
+let rec hashMap_move_elements_from_list_s
+  (#t : Type0) (hm : hashMap_s_nes t)
+  (ls : slot_s t) :
+  // Do *NOT* use `result (hashMap_s t)`
+  Tot (result_hashMap_s_nes t)
+  (decreases ls) =
+  match ls with
+  | [] -> Return hm
+  | (key, value) :: ls' ->
+    match hashMap_insert_no_resize_s hm key value with
+    | Fail e -> Fail e
+    | Return hm' ->
+      hashMap_move_elements_from_list_s hm' ls'
+
+/// Refinement lemma
+val hashMap_move_elements_from_list_lem
+  (t : Type0) (ntable : hashMap_t_nes t) (ls : list_t t) :
+  Lemma (requires (hashMap_t_base_inv ntable))
+  (ensures (
+    match hashMap_move_elements_from_list t ntable ls,
+          hashMap_move_elements_from_list_s (hashMap_t_v ntable) (slot_t_v ls)
+    with
+    | Fail _, Fail _ -> True
+    | Return hm', Return hm_v ->
+      hashMap_t_base_inv hm' /\
+      hashMap_t_v hm' == hm_v /\
+      hashMap_t_same_params hm' ntable
+    | _ -> False))
+  (decreases (hashMap_move_elements_from_list_loop_decreases t ntable ls))
+
+#push-options "--fuel 1"
+let rec hashMap_move_elements_from_list_lem t ntable ls =
+  begin match ls with
+  | List_Cons k v tl ->
+    assert(list_t_v ls == (k, v) :: list_t_v tl);
+    let ls_v = list_t_v ls in
+    let (_,_) :: tl_v = ls_v in
+    hashMap_insert_no_resize_lem_s t ntable k v;
+    begin match hashMap_insert_no_resize t ntable k v with
+    | Fail _ -> ()
+    | Return h ->
+      let h_v = Return?.v (hashMap_insert_no_resize_s (hashMap_t_v ntable) k v) in
+      assert(hashMap_t_v h == h_v);
+      hashMap_move_elements_from_list_lem t h tl;
+      begin match hashMap_move_elements_from_list t h tl with
+      | Fail _ -> ()
+      | Return h0 -> ()
+      end
+    end
+  | List_Nil -> ()
+  end
+#pop-options
+
+(*** move_elements *)
+
+(**** move_elements: refinement 0 *)
+/// The proof for [hashMap_move_elements_lem_refin] broke so many times
+/// (while it is supposed to be super simple!) that we decided to add one refinement
+/// level, to really do things step by step...
+/// Doing this refinement layer made me notice that maybe the problem came from
+/// the fact that at some point we have to prove `list_t_v List_Nil == []`: I
+/// added the corresponding assert to help Z3 and everything became stable.
+/// I finally didn't use this "simple" refinement lemma, but I still keep it here
+/// because it allows for easy comparisons with [hashMap_move_elements_s].
+
+/// [hashMap_move_elements] refines this function, which is actually almost
+/// the same (just a little bit shorter and cleaner, and has a pre).
+///
+/// The way I wrote the high-level model is the following:
+/// - I copy-pasted the definition of [hashMap_move_elements], wrote the
+///   signature which links this new definition to [hashMap_move_elements] and
+///   checked that the proof passed
+/// - I gradually simplified it, while making sure the proof still passes
+#push-options "--fuel 1"
+let rec hashMap_move_elements_s_simpl
+  (t : Type0) (ntable : hashMap_t t)
+  (slots : alloc_vec_Vec (list_t t))
+  (i : usize{i <= length slots /\ length slots <= usize_max}) :
+  Pure (result ((hashMap_t t) & (alloc_vec_Vec (list_t t))))
+  (requires (True))
+  (ensures (fun res ->
+    match res, hashMap_move_elements t ntable slots i with
+    | Fail _, Fail _ -> True
+    | Return (ntable1, slots1), Return (ntable2, slots2) ->
+      ntable1 == ntable2 /\
+      slots1 == slots2
+    | _ -> False))
+  (decreases (hashMap_move_elements_loop_decreases t ntable slots i))
+  =
+  if i < length slots
+  then
+    let slot = index slots i in
+    begin match hashMap_move_elements_from_list t ntable slot with
+    | Fail e -> Fail e
+    | Return hm' ->
+      let slots' = list_update slots i List_Nil in
+      hashMap_move_elements_s_simpl t hm' slots' (i+1)
+    end
+  else Return (ntable, slots)
+#pop-options
+
+(**** move_elements: refinement 1 *)
+/// We prove a second refinement lemma: calling [move_elements] refines a function
+/// which, for every slot, moves the element out of the slot. This first model is
+/// almost exactly the translated function, it just uses `list` instead of `list_t`.
+
+// Note that we ignore the returned slots (we thus don't return a pair:
+// only the new hash map in which we moved the elements from the slots):
+// this returned value is not used.
+let rec hashMap_move_elements_s
+  (#t : Type0) (hm : hashMap_s_nes t)
+  (slots : slots_s t) (i : usize{i <= length slots /\ length slots <= usize_max}) :
+  Tot (result_hashMap_s_nes t)
+  (decreases (length slots - i)) =
+  let len = length slots in
+  if i < len then
+    begin
+    let slot = index slots i in
+    match hashMap_move_elements_from_list_s hm slot with
+    | Fail e -> Fail e
+    | Return hm' ->
+      let slots' = list_update slots i [] in
+      hashMap_move_elements_s hm' slots' (i+1)
+    end
+  else Return hm
+
+val hashMap_move_elements_lem_refin
+  (t : Type0) (ntable : hashMap_t t)
+  (slots : alloc_vec_Vec (list_t t)) (i : usize{i <= length slots}) :
+  Lemma
+  (requires (
+    hashMap_t_base_inv ntable))
+  (ensures (
+    match hashMap_move_elements t ntable slots i,
+          hashMap_move_elements_s (hashMap_t_v ntable) (slots_t_v slots) i
+    with
+    | Fail _, Fail _ -> True // We will prove later that this is not possible
+    | Return (ntable', _), Return ntable'_v ->
+      hashMap_t_base_inv ntable' /\
+      hashMap_t_v ntable' == ntable'_v /\
+      hashMap_t_same_params ntable' ntable
+    | _ -> False))
+ (decreases (length slots - i))
+
+#restart-solver
+#push-options "--fuel 1"
+let rec hashMap_move_elements_lem_refin t ntable slots i =
+  assert(hashMap_t_base_inv ntable);
+  let i0 = alloc_vec_Vec_len (list_t t) slots in
+  let b = i < i0 in
+  if b
+  then
+    begin match alloc_vec_Vec_index_usize slots i with
+    | Fail _ -> ()
+    | Return l ->
+      let l0 = core_mem_replace (list_t t) l List_Nil in
+      assert(l0 == l);
+      hashMap_move_elements_from_list_lem t ntable l0;
+      begin match hashMap_move_elements_from_list t ntable l0 with
+      | Fail _ -> ()
+      | Return h ->
+        let l1 = core_mem_replace_back (list_t t) l List_Nil in
+        assert(l1 == List_Nil);
+        assert(slot_t_v #t List_Nil == []); // THIS IS IMPORTANT
+        begin match alloc_vec_Vec_update_usize slots i l1 with
+        | Fail _ -> ()
+        | Return v ->
+          begin match usize_add i 1 with
+          | Fail _ -> ()
+          | Return i1 ->
+            hashMap_move_elements_lem_refin t h v i1;
+            begin match hashMap_move_elements t h v i1 with
+            | Fail _ ->
+              assert(Fail? (hashMap_move_elements t ntable slots i));
+              ()
+            | Return (ntable', v0) -> ()
+            end
+          end
+        end
+      end
+    end
+  else ()
+#pop-options
+
+
+(**** move_elements: refinement 2 *)
+/// We prove a second refinement lemma: calling [move_elements] refines a function
+/// which moves every binding of the hash map seen as *one* associative list
+/// (and not a list of lists).
+
+/// [ntable] is the hash map to which we move the elements
+/// [slots] is the current hash map, from which we remove the elements, and seen
+///         as a "flat" associative list (and not a list of lists)
+/// This is actually exactly [hashMap_move_elements_from_list_s]...
+let rec hashMap_move_elements_s_flat
+  (#t : Type0) (ntable : hashMap_s_nes t)
+  (slots : assoc_list t) :
+  Tot (result_hashMap_s_nes t)
+  (decreases slots) =
+  match slots with
+  | [] -> Return ntable
+  | (k,v) :: slots' ->
+    match hashMap_insert_no_resize_s ntable k v with
+    | Fail e -> Fail e
+    | Return ntable' ->
+      hashMap_move_elements_s_flat ntable' slots'
+
+/// The refinment lemmas
+/// First, auxiliary helpers.
+
+/// Flatten a list of lists, starting at index i
+val flatten_i :
+     #a:Type
+  -> l:list (list a)
+  -> i:nat{i <= length l}
+  -> Tot (list a) (decreases (length l - i))
+
+let rec flatten_i l i =
+  if i < length l then
+    index l i @ flatten_i l (i+1)
+  else []
+
+let _ = assert(let l = [1;2] in l == hd l :: tl l)
+
+val flatten_i_incr :
+     #a:Type
+  -> l:list (list a)
+  -> i:nat{Cons? l /\ i+1 <= length l} ->
+  Lemma
+  (ensures (
+    (**) assert_norm(length (hd l :: tl l) == 1 + length (tl l));
+    flatten_i l (i+1) == flatten_i (tl l) i))
+  (decreases (length l - (i+1)))
+
+#push-options "--fuel 1"
+let rec flatten_i_incr l i =
+  let x :: tl = l in
+  if i + 1 < length l then
+    begin
+    assert(flatten_i l (i+1) == index l (i+1) @ flatten_i l (i+2));
+    flatten_i_incr l (i+1);
+    assert(flatten_i l (i+2) == flatten_i tl (i+1));
+    assert(index l (i+1) == index tl i)
+    end
+  else ()
+#pop-options
+
+val flatten_0_is_flatten :
+     #a:Type
+  -> l:list (list a) ->
+  Lemma
+  (ensures (flatten_i l 0 == flatten l))
+
+#push-options "--fuel 1"
+let rec flatten_0_is_flatten #a l =
+  match l with
+  | [] -> ()
+  | x :: l' ->
+    flatten_i_incr l 0;
+    flatten_0_is_flatten l'
+#pop-options
+
+/// Auxiliary lemma
+val flatten_nil_prefix_as_flatten_i :
+     #a:Type
+  -> l:list (list a)
+  -> i:nat{i <= length l} ->
+  Lemma (requires (forall (j:nat{j < i}). index l j == []))
+  (ensures (flatten l == flatten_i l i))
+
+#push-options "--fuel 1"
+let rec flatten_nil_prefix_as_flatten_i #a l i =
+  if i = 0 then flatten_0_is_flatten l
+  else
+    begin
+    let x :: l' = l in
+    assert(index l 0 == []);
+    assert(x == []);
+    assert(flatten l == flatten l');
+    flatten_i_incr l (i-1);
+    assert(flatten_i l i == flatten_i l' (i-1));
+    assert(forall (j:nat{j < length l'}). index l' j == index l (j+1));
+    flatten_nil_prefix_as_flatten_i l' (i-1);
+    assert(flatten l' == flatten_i l' (i-1))
+    end
+#pop-options
+
+/// The proof is trivial, the functions are the same.
+/// Just keeping two definitions to allow changes...
+val hashMap_move_elements_from_list_s_as_flat_lem
+  (#t : Type0) (hm : hashMap_s_nes t)
+  (ls : slot_s t) :
+  Lemma
+  (ensures (
+    hashMap_move_elements_from_list_s hm ls ==
+    hashMap_move_elements_s_flat hm ls))
+  (decreases ls)
+
+#push-options "--fuel 1"
+let rec hashMap_move_elements_from_list_s_as_flat_lem #t hm ls =
+  match ls with
+  | [] -> ()
+  | (key, value) :: ls' ->
+    match hashMap_insert_no_resize_s hm key value with
+    | Fail _ -> ()
+    | Return hm' ->
+      hashMap_move_elements_from_list_s_as_flat_lem hm' ls'
+#pop-options
+
+/// Composition of two calls to [hashMap_move_elements_s_flat]
+let hashMap_move_elements_s_flat_comp
+  (#t : Type0) (hm : hashMap_s_nes t) (slot0 slot1 : slot_s t) :
+  Tot (result_hashMap_s_nes t) =
+  match hashMap_move_elements_s_flat hm slot0 with
+  | Fail e -> Fail e
+  | Return hm1 -> hashMap_move_elements_s_flat hm1 slot1
+
+/// High-level desc:
+/// move_elements (move_elements hm slot0) slo1 == move_elements hm (slot0 @ slot1)
+val hashMap_move_elements_s_flat_append_lem
+  (#t : Type0) (hm : hashMap_s_nes t) (slot0 slot1 : slot_s t) :
+  Lemma
+  (ensures (
+    match hashMap_move_elements_s_flat_comp hm slot0 slot1,
+          hashMap_move_elements_s_flat hm (slot0 @ slot1)
+    with
+    | Fail _, Fail _ -> True
+    | Return hm1, Return hm2 -> hm1 == hm2
+    | _ -> False))
+  (decreases (slot0))
+
+#push-options "--fuel 1"
+let rec hashMap_move_elements_s_flat_append_lem #t hm slot0 slot1 =
+  match slot0 with
+  | [] -> ()
+  | (k,v) :: slot0' ->
+    match hashMap_insert_no_resize_s hm k v with
+    | Fail _ -> ()
+    | Return hm' ->
+      hashMap_move_elements_s_flat_append_lem hm' slot0' slot1
+#pop-options
+
+val flatten_i_same_suffix (#a : Type) (l0 l1 : list (list a)) (i : nat) :
+  Lemma
+  (requires (
+    i <= length l0 /\
+    length l0 = length l1 /\
+    (forall (j:nat{i <= j /\ j < length l0}). index l0 j == index l1 j)))
+  (ensures (flatten_i l0 i == flatten_i l1 i))
+  (decreases (length l0 - i))
+
+#push-options "--fuel 1"
+let rec flatten_i_same_suffix #a l0 l1 i =
+  if i < length l0 then
+    flatten_i_same_suffix l0 l1 (i+1)
+  else ()
+#pop-options
+
+/// Refinement lemma:
+/// [hashMap_move_elements_s] refines [hashMap_move_elements_s_flat]
+/// (actually the functions are equal on all inputs).
+val hashMap_move_elements_s_lem_refin_flat
+  (#t : Type0) (hm : hashMap_s_nes t)
+  (slots : slots_s t)
+  (i : nat{i <= length slots /\ length slots <= usize_max}) :
+  Lemma
+  (ensures (
+    match hashMap_move_elements_s hm slots i,
+          hashMap_move_elements_s_flat hm (flatten_i slots i)
+    with
+    | Fail _, Fail _ -> True
+    | Return hm, Return hm' -> hm == hm'
+    | _ -> False))
+  (decreases (length slots - i))
+
+#push-options "--fuel 1"
+let rec hashMap_move_elements_s_lem_refin_flat #t hm slots i =
+  let len = length slots in
+  if i < len then
+    begin
+    let slot = index slots i in
+    hashMap_move_elements_from_list_s_as_flat_lem hm slot;
+    match hashMap_move_elements_from_list_s hm slot with
+    | Fail _ ->
+      assert(flatten_i slots i == slot @ flatten_i slots (i+1));
+      hashMap_move_elements_s_flat_append_lem hm slot (flatten_i slots (i+1));
+      assert(Fail? (hashMap_move_elements_s_flat hm (flatten_i slots i)))
+    | Return hm' ->
+      let slots' = list_update slots i [] in
+      flatten_i_same_suffix slots slots' (i+1);
+      hashMap_move_elements_s_lem_refin_flat hm' slots' (i+1);
+      hashMap_move_elements_s_flat_append_lem hm slot (flatten_i slots' (i+1));
+      ()
+    end
+  else ()
+#pop-options
+
+let assoc_list_inv (#t : Type0) (al : assoc_list t) : Type0 =
+  // All the keys are pairwise distinct
+  pairwise_rel binding_neq al
+
+let disjoint_hm_al_on_key
+  (#t : Type0) (hm : hashMap_s_nes t) (al : assoc_list t) (k : key) : Type0 =
+  match hashMap_s_find hm k, assoc_list_find k al with
+  | Some _, None
+  | None, Some _
+  | None, None -> True
+  | Some _, Some _ -> False
+
+/// Playing a dangerous game here: using forall quantifiers
+let disjoint_hm_al (#t : Type0) (hm : hashMap_s_nes t) (al : assoc_list t) : Type0 =
+  forall (k:key). disjoint_hm_al_on_key hm al k
+
+let find_in_union_hm_al
+  (#t : Type0) (hm : hashMap_s_nes t) (al : assoc_list t) (k : key) :
+  option t =
+  match hashMap_s_find hm k with
+  | Some b -> Some b
+  | None -> assoc_list_find k al
+
+/// Auxiliary lemma
+val for_all_binding_neq_find_lem (#t : Type0) (k : key) (v : t) (al : assoc_list t) :
+  Lemma (requires (for_all (binding_neq (k,v)) al))
+  (ensures (assoc_list_find k al == None))
+
+#push-options "--fuel 1"
+let rec for_all_binding_neq_find_lem #t k v al =
+  match al with
+  | [] -> ()
+  | b :: al' -> for_all_binding_neq_find_lem k v al'
+#pop-options
+
+val hashMap_move_elements_s_flat_lem
+  (#t : Type0) (hm : hashMap_s_nes t) (al : assoc_list t) :
+  Lemma
+  (requires (
+    // Invariants
+    hashMap_s_inv hm /\
+    assoc_list_inv al /\
+    // The two are disjoint
+    disjoint_hm_al hm al /\
+    // We can add all the elements to the hashmap
+    hashMap_s_len hm + length al <= usize_max))
+  (ensures (
+    match hashMap_move_elements_s_flat hm al with
+    | Fail _ -> False // We can't fail
+    | Return hm' ->
+      // The invariant is preserved
+      hashMap_s_inv hm' /\
+      // The new hash map is the union of the two maps
+      (forall (k:key). hashMap_s_find hm' k == find_in_union_hm_al hm al k) /\
+      hashMap_s_len hm' = hashMap_s_len hm + length al))
+  (decreases al)
+
+#restart-solver
+#push-options "--z3rlimit 200 --fuel 1"
+let rec hashMap_move_elements_s_flat_lem #t hm al =
+  match al with
+  | [] -> ()
+  | (k,v) :: al' ->
+    hashMap_insert_no_resize_s_lem hm k v;
+    match hashMap_insert_no_resize_s hm k v with
+    | Fail _ -> ()
+    | Return hm' ->
+      assert(hashMap_s_inv hm');
+      assert(assoc_list_inv al');
+      let disjoint_lem (k' : key) :
+        Lemma (disjoint_hm_al_on_key hm' al' k')
+        [SMTPat (disjoint_hm_al_on_key hm' al' k')] =
+        if k' = k then
+          begin
+          assert(hashMap_s_find hm' k' == Some v);
+          for_all_binding_neq_find_lem k v al';
+          assert(assoc_list_find k' al' == None)
+          end
+        else
+          begin
+          assert(hashMap_s_find hm' k' == hashMap_s_find hm k');
+          assert(assoc_list_find k' al' == assoc_list_find k' al)
+          end
+      in
+      assert(disjoint_hm_al hm' al');
+      assert(hashMap_s_len hm' + length al' <= usize_max);
+      hashMap_move_elements_s_flat_lem hm' al'
+#pop-options
+
+/// We need to prove that the invariants on the "low-level" representations of
+/// the hash map imply the invariants on the "high-level" representations.
+
+val slots_t_inv_implies_slots_s_inv
+  (#t : Type0) (slots : slots_t t{length slots <= usize_max}) :
+  Lemma (requires (slots_t_inv slots))
+  (ensures (slots_s_inv (slots_t_v slots)))
+
+let slots_t_inv_implies_slots_s_inv #t slots =
+  // Ok, works fine: this lemma was useless.
+  // Problem is: I can never really predict for sure with F*...
+  ()
+
+val hashMap_t_base_inv_implies_hashMap_s_inv
+  (#t : Type0) (hm : hashMap_t t) :
+  Lemma (requires (hashMap_t_base_inv hm))
+  (ensures (hashMap_s_inv (hashMap_t_v hm)))
+
+let hashMap_t_base_inv_implies_hashMap_s_inv #t hm = () // same as previous
+
+/// Introducing a "partial" version of the hash map invariant, which operates on
+/// a suffix of the hash map.
+let partial_hashMap_s_inv
+  (#t : Type0) (len : usize{len > 0}) (offset : usize)
+  (hm : hashMap_s t{offset + length hm <= usize_max}) : Type0 =
+  forall(i:nat{i < length hm}). {:pattern index hm i} slot_s_inv len (offset + i) (index hm i)
+
+/// Auxiliary lemma.
+/// If a binding comes from a slot i, then its key is different from the keys
+/// of the bindings in the other slots (because the hashes of the keys are distinct).
+val binding_in_previous_slot_implies_neq
+  (#t : Type0) (len : usize{len > 0})
+  (i : usize) (b : binding t)
+  (offset : usize{i < offset})
+  (slots : hashMap_s t{offset + length slots <= usize_max}) :
+  Lemma
+  (requires (
+    // The binding comes from a slot not in [slots]
+    hash_mod_key (fst b) len = i /\
+    // The slots are the well-formed suffix of a hash map
+    partial_hashMap_s_inv len offset slots))
+  (ensures (
+    for_all (binding_neq b) (flatten slots)))
+  (decreases slots)
+
+#push-options "--z3rlimit 100 --fuel 1"
+let rec binding_in_previous_slot_implies_neq #t len i b offset slots =
+  match slots with
+  | [] -> ()
+  | s :: slots' ->
+    assert(slot_s_inv len offset (index slots 0)); // Triggers patterns
+    assert(slot_s_inv len offset s);
+    // Proving TARGET. We use quantifiers.
+    assert(for_all (same_hash_mod_key len offset) s);
+    forall_index_equiv_list_for_all (same_hash_mod_key len offset) s;
+    assert(forall (i:nat{i < length s}). same_hash_mod_key len offset (index s i));
+    let aux (i:nat{i < length s}) :
+      Lemma
+      (requires (same_hash_mod_key len offset (index s i)))
+      (ensures (binding_neq b (index s i)))
+      [SMTPat (index s i)] = ()
+    in
+    assert(forall (i:nat{i < length s}). binding_neq b (index s i));
+    forall_index_equiv_list_for_all (binding_neq b) s;
+    assert(for_all (binding_neq b) s); // TARGET
+    //
+    assert(forall (i:nat{i < length slots'}). index slots' i == index slots (i+1)); // Triggers instantiations
+    binding_in_previous_slot_implies_neq len i b (offset+1) slots';
+    for_all_append (binding_neq b) s (flatten slots')    
+#pop-options
+
+val partial_hashMap_s_inv_implies_assoc_list_lem
+  (#t : Type0) (len : usize{len > 0}) (offset : usize)
+  (hm : hashMap_s t{offset + length hm <= usize_max}) :
+  Lemma
+  (requires (
+    partial_hashMap_s_inv len offset hm))
+  (ensures (assoc_list_inv (flatten hm)))
+  (decreases (length hm + length (flatten hm)))
+
+#push-options "--fuel 1"
+let rec partial_hashMap_s_inv_implies_assoc_list_lem #t len offset hm =
+  match hm with
+  | [] -> ()
+  | slot :: hm' ->
+    assert(flatten hm == slot @ flatten hm');
+    assert(forall (i:nat{i < length hm'}). index hm' i == index hm (i+1)); // Triggers instantiations
+    match slot with
+    | [] ->
+      assert(flatten hm == flatten hm');
+      assert(partial_hashMap_s_inv len (offset+1) hm'); // Triggers instantiations
+      partial_hashMap_s_inv_implies_assoc_list_lem len (offset+1) hm'
+    | x :: slot' ->
+      assert(flatten (slot' :: hm') == slot' @ flatten hm');
+      let hm'' = slot' :: hm' in
+      assert(forall (i:nat{0 < i /\ i < length hm''}). index hm'' i == index hm i); // Triggers instantiations
+      assert(forall (i:nat{0 < i /\ i < length hm''}). slot_s_inv len (offset + i) (index hm'' i));
+      assert(index hm 0 == slot); // Triggers instantiations
+      assert(slot_s_inv len offset slot);
+      assert(slot_s_inv len offset slot');
+      assert(partial_hashMap_s_inv len offset hm'');
+      partial_hashMap_s_inv_implies_assoc_list_lem len offset (slot' :: hm');
+      // Proving that the key in `x` is different from all the other keys in
+      // the flattened map
+      assert(for_all (binding_neq x) slot');
+      for_all_append (binding_neq x) slot' (flatten hm');
+      assert(partial_hashMap_s_inv len (offset+1) hm');
+      binding_in_previous_slot_implies_neq #t len offset x (offset+1) hm';
+      assert(for_all (binding_neq x) (flatten hm'));
+      assert(for_all (binding_neq x) (flatten (slot' :: hm')))
+#pop-options
+
+val hashMap_s_inv_implies_assoc_list_lem
+  (#t : Type0) (hm : hashMap_s t) :
+  Lemma (requires (hashMap_s_inv hm))
+  (ensures (assoc_list_inv (flatten hm)))
+
+let hashMap_s_inv_implies_assoc_list_lem #t hm =
+  partial_hashMap_s_inv_implies_assoc_list_lem (length hm) 0 hm
+
+val hashMap_t_base_inv_implies_assoc_list_lem
+  (#t : Type0) (hm : hashMap_t t):
+  Lemma (requires (hashMap_t_base_inv hm))
+  (ensures (assoc_list_inv (hashMap_t_al_v hm)))
+
+let hashMap_t_base_inv_implies_assoc_list_lem #t hm =
+  hashMap_s_inv_implies_assoc_list_lem (hashMap_t_v hm)
+
+/// For some reason, we can't write the below [forall] directly in the [ensures]
+/// clause of the next lemma: it makes Z3 fails even with a huge rlimit.
+/// I have no idea what's going on.
+let hashMap_is_assoc_list
+  (#t : Type0) (ntable : hashMap_t t{length ntable.slots > 0})
+  (al : assoc_list t) : Type0 =
+  (forall (k:key). hashMap_t_find_s ntable k == assoc_list_find k al)
+
+let partial_hashMap_s_find
+  (#t : Type0) (len : usize{len > 0}) (offset : usize)
+  (hm : hashMap_s_nes t{offset + length hm = len})
+  (k : key{hash_mod_key k len >= offset}) : option t =
+  let i = hash_mod_key k len in
+  let slot = index hm (i - offset) in
+  slot_s_find k slot
+
+val not_same_hash_key_not_found_in_slot
+  (#t : Type0) (len : usize{len > 0})
+  (k : key)
+  (i : usize)
+  (slot : slot_s t) :
+  Lemma
+  (requires (
+    hash_mod_key k len <> i /\
+    slot_s_inv len i slot))
+  (ensures (slot_s_find k slot == None))
+
+#push-options "--fuel 1"
+let rec not_same_hash_key_not_found_in_slot #t len k i slot =
+  match slot with
+  | [] -> ()
+  | (k',v) :: slot' -> not_same_hash_key_not_found_in_slot len k i slot'
+#pop-options
+
+/// Small variation of [binding_in_previous_slot_implies_neq]: if the hash of
+/// a key links it to a previous slot, it can't be found in the slots after.
+val key_in_previous_slot_implies_not_found
+  (#t : Type0) (len : usize{len > 0})
+  (k : key)
+  (offset : usize)
+  (slots : hashMap_s t{offset + length slots = len}) :
+  Lemma
+  (requires (
+    // The binding comes from a slot not in [slots]
+    hash_mod_key k len < offset /\
+    // The slots are the well-formed suffix of a hash map
+    partial_hashMap_s_inv len offset slots))
+  (ensures (
+    assoc_list_find k (flatten slots) == None))
+  (decreases slots)
+
+#push-options "--fuel 1"
+let rec key_in_previous_slot_implies_not_found #t len k offset slots =
+  match slots with
+  | [] -> ()
+  | slot :: slots' ->
+    find_append (same_key k) slot (flatten slots');
+    assert(index slots 0 == slot); // Triggers instantiations
+    not_same_hash_key_not_found_in_slot #t len k offset slot;
+    assert(assoc_list_find k slot == None);
+    assert(forall (i:nat{i < length slots'}). index slots' i == index slots (i+1)); // Triggers instantiations
+    key_in_previous_slot_implies_not_found len k (offset+1) slots'
+#pop-options  
+
+val partial_hashMap_s_is_assoc_list_lem
+  (#t : Type0) (len : usize{len > 0}) (offset : usize)
+  (hm : hashMap_s_nes t{offset + length hm = len})
+  (k : key{hash_mod_key k len >= offset}) :
+  Lemma
+  (requires (
+    partial_hashMap_s_inv len offset hm))
+  (ensures (
+    partial_hashMap_s_find len offset hm k == assoc_list_find k (flatten hm)))
+  (decreases hm)
+
+#push-options "--fuel 1"
+let rec partial_hashMap_s_is_assoc_list_lem #t len offset hm k =
+  match hm with
+  | [] -> ()
+  | slot :: hm' ->
+    let h = hash_mod_key k len in
+    let i = h - offset in
+    if i = 0 then
+      begin
+      // We must look in the current slot
+      assert(partial_hashMap_s_find len offset hm k == slot_s_find k slot);
+      find_append (same_key k) slot (flatten hm');
+      assert(forall (i:nat{i < length hm'}). index hm' i == index hm (i+1)); // Triggers instantiations
+      key_in_previous_slot_implies_not_found #t len k (offset+1) hm';
+      assert( // Of course, writing `== None` doesn't work...
+        match find (same_key k) (flatten hm') with
+        | None -> True
+        | Some _ -> False);
+      assert(
+        find (same_key k) (flatten hm) ==
+        begin match find (same_key k) slot with
+        | Some x -> Some x
+        | None -> find (same_key k) (flatten hm')
+        end);
+      ()
+      end
+    else
+      begin
+      // We must ignore the current slot
+      assert(partial_hashMap_s_find len offset hm k ==
+             partial_hashMap_s_find len (offset+1) hm' k);
+      find_append (same_key k) slot (flatten hm');
+      assert(index hm 0 == slot); // Triggers instantiations
+      not_same_hash_key_not_found_in_slot #t len k offset slot;
+      assert(forall (i:nat{i < length hm'}). index hm' i == index hm (i+1)); // Triggers instantiations
+      partial_hashMap_s_is_assoc_list_lem #t len (offset+1) hm' k
+      end
+#pop-options
+
+val hashMap_is_assoc_list_lem (#t : Type0) (hm : hashMap_t t) :
+  Lemma (requires (hashMap_t_base_inv hm))
+  (ensures (hashMap_is_assoc_list hm (hashMap_t_al_v hm)))
+
+let hashMap_is_assoc_list_lem #t hm =
+  let aux (k:key) :
+    Lemma (hashMap_t_find_s hm k == assoc_list_find k (hashMap_t_al_v hm))
+    [SMTPat (hashMap_t_find_s hm k)] =
+    let hm_v = hashMap_t_v hm in
+    let len = length hm_v in
+    partial_hashMap_s_is_assoc_list_lem #t len 0 hm_v k
+  in
+  ()
+
+/// The final lemma about [move_elements]: calling it on an empty hash table moves
+/// all the elements to this empty table.
+val hashMap_move_elements_lem
+  (t : Type0) (ntable : hashMap_t t) (slots : alloc_vec_Vec (list_t t)) :
+  Lemma
+  (requires (
+    let al = flatten (slots_t_v slots) in
+    hashMap_t_base_inv ntable /\
+    length al <= usize_max /\
+    assoc_list_inv al /\
+    // The table is empty
+    hashMap_t_len_s ntable = 0 /\
+    (forall (k:key). hashMap_t_find_s ntable k  == None)))
+  (ensures (
+    let al = flatten (slots_t_v slots) in
+    match hashMap_move_elements t ntable slots 0,
+          hashMap_move_elements_s_flat (hashMap_t_v ntable) al
+    with
+    | Return (ntable', _), Return ntable'_v ->
+      // The invariant is preserved
+      hashMap_t_base_inv ntable' /\
+      // We preserved the parameters
+      hashMap_t_same_params ntable' ntable /\
+      // The table has the same number of slots
+      length ntable'.slots = length ntable.slots /\
+      // The count is good
+      hashMap_t_len_s ntable' = length al /\
+      // The table can be linked to its model (we need this only to reveal
+      // "pretty" functional lemmas to the user in the fsti - so that we
+      // can write lemmas with SMT patterns - this is very F* specific)
+      hashMap_t_v ntable' == ntable'_v /\
+      // The new table contains exactly all the bindings from the slots
+      // Rk.: see the comment for [hashMap_is_assoc_list]
+      hashMap_is_assoc_list ntable' al
+    | _ -> False // We can only succeed
+    ))
+
+// Weird, dirty things happen below.
+// Manually unfolding some postconditions allowed to make the proof pass,
+// and also revealed the reason why some proofs failed with "Unknown assertion
+// failed" (resulting in the call to [flatten_0_is_flatten] for instance).
+// I think manually unfolding the postconditions allowed to account for the
+// lack of ifuel (this kind of proofs is annoying, really).
+#restart-solver
+#push-options "--z3rlimit 100"
+let hashMap_move_elements_lem t ntable slots =
+  let ntable_v = hashMap_t_v ntable in
+  let slots_v = slots_t_v slots in
+  let al = flatten slots_v in
+  hashMap_move_elements_lem_refin t ntable slots 0;
+  begin
+  match hashMap_move_elements t ntable slots 0,
+        hashMap_move_elements_s ntable_v slots_v 0
+  with
+  | Fail _, Fail _ -> ()
+  | Return (ntable', _), Return ntable'_v ->
+    assert(hashMap_t_base_inv ntable');
+    assert(hashMap_t_v ntable' == ntable'_v)
+  | _ -> assert(False)
+  end;
+  hashMap_move_elements_s_lem_refin_flat ntable_v slots_v 0;
+  begin
+  match hashMap_move_elements_s ntable_v slots_v 0,
+        hashMap_move_elements_s_flat ntable_v (flatten_i slots_v 0)
+  with
+  | Fail _, Fail _ -> ()
+  | Return hm, Return hm' -> assert(hm == hm')
+  | _ -> assert(False)
+  end;
+  flatten_0_is_flatten slots_v; // flatten_i slots_v 0 == flatten slots_v
+  hashMap_move_elements_s_flat_lem ntable_v al;
+  match hashMap_move_elements t ntable slots 0,
+        hashMap_move_elements_s_flat ntable_v al
+  with
+  | Return (ntable', _), Return ntable'_v ->
+    assert(hashMap_t_base_inv ntable');
+    assert(length ntable'.slots = length ntable.slots);
+    assert(hashMap_t_len_s ntable' = length al);
+    assert(hashMap_t_v ntable' == ntable'_v);
+    assert(hashMap_is_assoc_list ntable' al)
+  | _ -> assert(False)
+#pop-options
+
+(*** try_resize *)
+
+/// High-level model 1.
+/// This is one is slightly "crude": we just simplify a bit the function.
+
+let hashMap_try_resize_s_simpl
+  (#t : Type0)
+  (hm : hashMap_t t) :
+  Pure  (result (hashMap_t t))
+  (requires (
+    let (divid, divis) = hm.max_load_factor in
+    divid > 0 /\ divis > 0))
+  (ensures (fun _ -> True)) =
+  let capacity = length hm.slots in
+  let (divid, divis) = hm.max_load_factor in
+  if capacity <= (usize_max / 2) / divid then
+    let ncapacity : usize = capacity * 2 in
+    begin match hashMap_new_with_capacity t ncapacity divid divis with
+    | Fail e -> Fail e
+    | Return ntable ->
+      match hashMap_move_elements t ntable hm.slots 0 with
+      | Fail e -> Fail e
+      | Return (ntable', _) ->
+        let hm =
+          { hm with slots = ntable'.slots;
+                    max_load = ntable'.max_load }
+        in
+        Return hm
+    end
+  else Return hm
+
+val hashMap_try_resize_lem_refin
+  (t : Type0) (self : hashMap_t t) :
+  Lemma
+  (requires (
+    let (divid, divis) = self.max_load_factor in
+    divid > 0 /\ divis > 0))
+  (ensures (
+    match hashMap_try_resize t self,
+          hashMap_try_resize_s_simpl self
+    with
+    | Fail _, Fail _ -> True
+    | Return hm1, Return hm2 -> hm1 == hm2
+    | _ -> False))
+
+let hashMap_try_resize_lem_refin t self = ()
+
+/// Isolating arithmetic proofs
+
+let gt_lem0 (n m q : nat) :
+  Lemma (requires (m > 0 /\ n > q))
+  (ensures (n * m > q * m)) = ()
+
+let ge_lem0 (n m q : nat) :
+  Lemma (requires (m > 0 /\ n >= q))
+  (ensures (n * m >= q * m)) = ()
+
+let gt_ge_trans (n m p : nat) :
+  Lemma (requires (n > m /\ m >= p)) (ensures (n > p)) = ()
+
+let ge_trans (n m p : nat) :
+  Lemma (requires (n >= m /\ m >= p)) (ensures (n >= p)) = ()
+
+#push-options "--z3rlimit 200"
+let gt_lem1 (n m q : nat) :
+  Lemma (requires (m > 0 /\ n > q / m)) (ensures (n * m > q)) =
+  assert(n >= q / m + 1);
+  ge_lem0 n m (q / m + 1);
+  assert(n * m >= (q / m) * m + m)
+#pop-options
+
+let gt_lem2 (n m p q : nat) :
+  Lemma (requires (m > 0 /\ p > 0 /\ n > (q / m) / p)) (ensures (n * m * p > q)) =
+  gt_lem1 n p (q / m);
+  assert(n * p > q / m);
+  gt_lem1 (n * p) m q
+
+let ge_lem1 (n m q : nat) :
+  Lemma (requires (n >= m /\ q > 0))
+  (ensures (n / q >= m / q)) =
+  FStar.Math.Lemmas.lemma_div_le m n q
+
+#restart-solver
+#push-options "--z3rlimit 200"
+let times_divid_lem (n m p : pos) : Lemma ((n * m) / p >= n * (m / p))
+  =
+  FStar.Math.Lemmas.multiply_fractions m p;
+  assert(m >= (m / p) * p);
+  assert(n * m >= n * (m / p) * p); //
+  ge_lem1 (n * m) (n * (m / p) * p) p;
+  assert((n * m) / p >= (n * (m / p) * p) / p);
+  assert(n * (m / p) * p = (n * (m / p)) * p);
+  FStar.Math.Lemmas.cancel_mul_div (n * (m / p)) p;
+  assert(((n * (m / p)) * p) / p = n * (m / p))
+#pop-options
+
+/// The good old arithmetic proofs and their unstability...
+/// At some point I thought it was stable because it worked with `--quake 100`.
+/// Of course, it broke the next time I checked the file...
+/// It seems things are ok when we check this proof on its own, but not when
+/// it is sent at the same time as the one above (though we put #restart-solver!).
+/// I also tried `--quake 1/100` to no avail: it seems that when Z3 decides to
+/// fail the first one, it fails them all. I inserted #restart-solver before
+/// the previous lemma to see if it had an effect (of course not).
+val new_max_load_lem
+  (len : usize) (capacity : usize{capacity > 0})
+  (divid : usize{divid > 0}) (divis : usize{divis > 0}) :
+  Lemma
+  (requires (
+    let max_load = (capacity * divid) / divis in
+    let ncapacity = 2 * capacity in
+    let nmax_load = (ncapacity * divid) / divis in
+    capacity > 0 /\ 0 < divid /\ divid < divis /\
+    capacity * divid >= divis /\
+    len = max_load + 1))
+  (ensures (
+    let max_load = (capacity * divid) / divis in
+    let ncapacity = 2 * capacity in
+    let nmax_load = (ncapacity * divid) / divis in
+    len <= nmax_load))
+
+let mul_assoc (a b c : nat) : Lemma (a * b * c == a * (b * c)) = ()
+
+let ge_lem2 (a b c d : nat) : Lemma (requires (a >= b + c /\ c >= d)) (ensures (a >= b + d)) = ()
+let ge_div_lem1 (a b : nat) : Lemma (requires (a >= b /\ b > 0)) (ensures (a / b >= 1)) = ()
+
+#restart-solver
+#push-options "--z3rlimit 100 --z3cliopt smt.arith.nl=false"
+let new_max_load_lem len capacity divid divis =
+  FStar.Math.Lemmas.paren_mul_left 2 capacity divid;
+  mul_assoc 2 capacity divid;
+  // The following assertion often breaks though it is given by the above
+  // lemma. I really don't know what to do (I deactivated non-linear
+  // arithmetic and added the previous lemma call, moved the assertion up,
+  // boosted the rlimit...).
+  assert(2 * capacity * divid == 2 * (capacity * divid));
+  let max_load = (capacity * divid) / divis in
+  let ncapacity = 2 * capacity in
+  let nmax_load = (ncapacity * divid) / divis in
+  assert(nmax_load = (2 * capacity * divid) / divis);
+  times_divid_lem 2 (capacity * divid) divis;
+  assert((2 * (capacity * divid)) / divis >= 2 * ((capacity * divid) / divis));
+  assert(nmax_load >= 2 * ((capacity * divid) / divis));
+  assert(nmax_load >= 2 * max_load);
+  assert(nmax_load >= max_load + max_load);
+  ge_div_lem1 (capacity * divid) divis;
+  ge_lem2 nmax_load max_load max_load 1;
+  assert(nmax_load >= max_load + 1)
+#pop-options
+
+val hashMap_try_resize_s_simpl_lem (#t : Type0) (hm : hashMap_t t) :
+  Lemma
+  (requires (
+    // The base invariant is satisfied
+    hashMap_t_base_inv hm /\
+    // However, the "full" invariant is broken, as we call [try_resize]
+    // only if the current number of entries is > the max load.
+    // 
+    // There are two situations:
+    // - either we just reached the max load
+    // - or we were already saturated and can't resize
+    (let (dividend, divisor) = hm.max_load_factor in
+     hm.num_entries == hm.max_load + 1 \/
+     length hm.slots * 2 * dividend > usize_max)
+  ))
+  (ensures (
+    match hashMap_try_resize_s_simpl hm with
+    | Fail _ -> False
+    | Return hm' ->
+      // The full invariant is now satisfied (the full invariant is "base
+      // invariant" + the map is not overloaded (or can't be resized because
+      // already too big)
+      hashMap_t_inv hm' /\
+      // It contains the same bindings as the initial map
+      (forall (k:key). hashMap_t_find_s hm' k == hashMap_t_find_s hm k)))
+
+#restart-solver
+#push-options "--z3rlimit 400"
+let hashMap_try_resize_s_simpl_lem #t hm =
+  let capacity = length hm.slots in
+  let (divid, divis) = hm.max_load_factor in
+  if capacity <= (usize_max / 2) / divid then
+    begin
+    let ncapacity : usize = capacity * 2 in
+    assert(ncapacity * divid <= usize_max);
+    assert(hashMap_t_len_s hm = hm.max_load + 1);
+    new_max_load_lem (hashMap_t_len_s hm) capacity divid divis;
+    hashMap_new_with_capacity_lem t ncapacity divid divis;
+    match hashMap_new_with_capacity t ncapacity divid divis with
+    | Fail _ -> ()
+    | Return ntable ->
+      let slots = hm.slots in
+      let al = flatten (slots_t_v slots) in
+      // Proving that: length al = hm.num_entries
+      assert(al == flatten (map slot_t_v slots));
+      assert(al == flatten (map list_t_v slots));
+      assert(hashMap_t_al_v hm == flatten (hashMap_t_v hm));
+      assert(hashMap_t_al_v hm == flatten (map list_t_v hm.slots));
+      assert(al == hashMap_t_al_v hm);
+      assert(hashMap_t_base_inv ntable);
+      assert(length al = hm.num_entries);
+      assert(length al <= usize_max);
+      hashMap_t_base_inv_implies_assoc_list_lem hm;
+      assert(assoc_list_inv al);
+      assert(hashMap_t_len_s ntable = 0);
+      assert(forall (k:key). hashMap_t_find_s ntable k  == None);
+      hashMap_move_elements_lem t ntable hm.slots;
+      match hashMap_move_elements t ntable hm.slots 0 with
+      | Fail _ -> ()
+      | Return (ntable', _) ->
+        hashMap_is_assoc_list_lem hm;
+        assert(hashMap_is_assoc_list hm (hashMap_t_al_v hm));
+        let hm' =
+          { hm with slots = ntable'.slots;
+                    max_load = ntable'.max_load }
+        in
+        assert(hashMap_t_base_inv ntable');
+        assert(hashMap_t_base_inv hm');
+        assert(hashMap_t_len_s hm' = hashMap_t_len_s hm);
+        new_max_load_lem (hashMap_t_len_s hm') capacity divid divis;
+        assert(hashMap_t_len_s hm' <= hm'.max_load); // Requires a lemma
+        assert(hashMap_t_inv hm')
+    end
+  else
+    begin
+    gt_lem2 capacity 2 divid usize_max;
+    assert(capacity * 2 * divid > usize_max)
+    end
+#pop-options
+
+let hashMap_t_same_bindings  (#t : Type0) (hm hm' : hashMap_t_nes t) : Type0 =
+  forall (k:key). hashMap_t_find_s hm k == hashMap_t_find_s hm' k
+
+/// The final lemma about [try_resize]
+val hashMap_try_resize_lem (#t : Type0) (hm : hashMap_t t) :
+  Lemma
+  (requires (
+    hashMap_t_base_inv hm /\
+    // However, the "full" invariant is broken, as we call [try_resize]
+    // only if the current number of entries is > the max load.
+    // 
+    // There are two situations:
+    // - either we just reached the max load
+    // - or we were already saturated and can't resize
+    (let (dividend, divisor) = hm.max_load_factor in
+     hm.num_entries == hm.max_load + 1 \/
+     length hm.slots * 2 * dividend > usize_max)))
+  (ensures (
+    match hashMap_try_resize t hm with
+    | Fail _ -> False
+    | Return hm' ->
+      // The full invariant is now satisfied (the full invariant is "base
+      // invariant" + the map is not overloaded (or can't be resized because
+      // already too big)
+      hashMap_t_inv hm' /\
+      // The length is the same
+      hashMap_t_len_s hm' = hashMap_t_len_s hm /\
+      // It contains the same bindings as the initial map
+      hashMap_t_same_bindings hm' hm))
+
+let hashMap_try_resize_lem #t hm =
+  hashMap_try_resize_lem_refin t hm;
+  hashMap_try_resize_s_simpl_lem hm
+
+(*** insert *)
+
+/// The high-level model (very close to the original function: we don't need something
+/// very high level, just to clean it a bit)
+let hashMap_insert_s
+  (#t : Type0) (self : hashMap_t t) (key : usize) (value : t) :
+  result (hashMap_t t) =
+  match hashMap_insert_no_resize t self key value with
+  | Fail e -> Fail e
+  | Return hm' ->
+    if hashMap_t_len_s hm' > hm'.max_load then
+      hashMap_try_resize t hm'
+    else Return hm'
+
+val hashMap_insert_lem_refin
+  (t : Type0) (self : hashMap_t t) (key : usize) (value : t) :
+  Lemma (requires True)
+  (ensures (
+    match hashMap_insert t self key value,
+          hashMap_insert_s self key value
+    with
+    | Fail _, Fail _ -> True
+    | Return hm1, Return hm2 -> hm1 == hm2
+    | _ -> False))
+
+let hashMap_insert_lem_refin t self key value = ()
+
+/// Helper
+let hashMap_insert_bindings_lem
+  (t : Type0) (self : hashMap_t_nes t) (key : usize) (value : t)
+  (hm' hm'' : hashMap_t_nes t) :
+  Lemma
+  (requires (
+     hashMap_s_updated_binding (hashMap_t_v self) key
+                                (Some value) (hashMap_t_v hm') /\
+     hashMap_t_same_bindings hm' hm''))
+  (ensures (
+     hashMap_s_updated_binding (hashMap_t_v self) key
+                                (Some value) (hashMap_t_v hm'')))
+  = ()
+
+val hashMap_insert_lem_aux
+  (#t : Type0) (self : hashMap_t t) (key : usize) (value : t) :
+  Lemma (requires (hashMap_t_inv self))
+  (ensures (
+    match hashMap_insert t self key value with
+    | Fail _ ->
+      // We can fail only if:
+      // - the key is not in the map and we need to add it
+      // - we are already saturated
+      hashMap_t_len_s self = usize_max /\
+      None? (hashMap_t_find_s self key)
+    | Return hm' ->
+      // The invariant is preserved
+      hashMap_t_inv hm' /\
+      // [key] maps to [value] and the other bindings are preserved
+      hashMap_s_updated_binding (hashMap_t_v self) key (Some value) (hashMap_t_v hm') /\
+      // The length is incremented, iff we inserted a new key
+      (match hashMap_t_find_s self key with
+       | None -> hashMap_t_len_s hm' = hashMap_t_len_s self + 1
+       | Some _ -> hashMap_t_len_s hm' = hashMap_t_len_s self)))
+
+#restart-solver
+#push-options "--z3rlimit 200"
+let hashMap_insert_lem_aux #t self key value =
+  hashMap_insert_no_resize_lem_s t self key value;
+  hashMap_insert_no_resize_s_lem (hashMap_t_v self) key value;
+  match hashMap_insert_no_resize t self key value with
+  | Fail _ -> ()
+  | Return hm' ->
+    // Expanding the post of [hashMap_insert_no_resize_lem_s]
+    let self_v = hashMap_t_v self in
+    let hm'_v = Return?.v (hashMap_insert_no_resize_s self_v key value) in
+    assert(hashMap_t_base_inv hm');
+    assert(hashMap_t_same_params hm' self);
+    assert(hashMap_t_v hm' == hm'_v);
+    assert(hashMap_s_len hm'_v == hashMap_t_len_s hm');
+    // Expanding the post of [hashMap_insert_no_resize_s_lem]
+    assert(insert_post self_v key value hm'_v);
+    // Expanding [insert_post]
+    assert(hashMap_s_inv hm'_v);
+    assert(
+      match hashMap_s_find self_v key with
+      | None -> hashMap_s_len hm'_v = hashMap_s_len self_v + 1
+      | Some _ -> hashMap_s_len hm'_v = hashMap_s_len self_v);
+    if hashMap_t_len_s hm' > hm'.max_load then
+      begin
+      hashMap_try_resize_lem hm';
+      // Expanding the post of [hashMap_try_resize_lem]
+      let hm'' = Return?.v (hashMap_try_resize t hm') in
+      assert(hashMap_t_inv hm'');
+      let hm''_v = hashMap_t_v hm'' in
+      assert(forall k. hashMap_t_find_s hm'' k == hashMap_t_find_s hm' k);
+      assert(hashMap_t_len_s hm'' = hashMap_t_len_s hm'); // TODO
+      // Proving the post
+      assert(hashMap_t_inv hm'');
+      hashMap_insert_bindings_lem t self key value hm' hm'';
+      assert(
+        match hashMap_t_find_s self key with
+         | None -> hashMap_t_len_s hm'' = hashMap_t_len_s self + 1
+         | Some _ -> hashMap_t_len_s hm'' = hashMap_t_len_s self)
+      end
+    else ()
+#pop-options
+
+let hashMap_insert_lem #t self key value =
+  hashMap_insert_lem_aux #t self key value
+
+(*** contains_key *)
+
+(**** contains_key_in_list *)
+
+val hashMap_contains_key_in_list_lem
+  (#t : Type0) (key : usize) (ls : list_t t) :
+  Lemma
+  (ensures (
+    match hashMap_contains_key_in_list t key ls with
+    | Fail _ -> False
+    | Return b ->
+      b = Some? (slot_t_find_s key ls)))
+
+
+#push-options "--fuel 1"
+let rec hashMap_contains_key_in_list_lem #t key ls =
+  match ls with
+  | List_Cons ckey x ls0 ->
+    let b = ckey = key in
+    if b
+    then ()
+    else
+      begin
+      hashMap_contains_key_in_list_lem key ls0;
+      match hashMap_contains_key_in_list t key ls0 with
+      | Fail _ -> ()
+      | Return b0 -> ()
+      end
+  | List_Nil -> ()
+#pop-options
+
+(**** contains_key *)
+
+val hashMap_contains_key_lem_aux
+  (#t : Type0) (self : hashMap_t_nes t) (key : usize) :
+  Lemma
+  (ensures (
+    match hashMap_contains_key t self key with
+    | Fail _ -> False
+    | Return b -> b = Some? (hashMap_t_find_s self key)))
+
+let hashMap_contains_key_lem_aux #t self key =
+  begin match hash_key key with
+  | Fail _ -> ()
+  | Return i ->
+    let v = self.slots in
+    let i0 = alloc_vec_Vec_len (list_t t) v in
+    begin match usize_rem i i0 with
+    | Fail _ -> ()
+    | Return hash_mod ->
+      begin match alloc_vec_Vec_index_usize v hash_mod with
+      | Fail _ -> ()
+      | Return l ->
+        hashMap_contains_key_in_list_lem key l;
+        begin match hashMap_contains_key_in_list t key l with
+        | Fail _ -> ()
+        | Return b -> ()
+        end
+      end
+    end
+  end
+
+/// The lemma in the .fsti
+let hashMap_contains_key_lem #t self key =
+  hashMap_contains_key_lem_aux #t self key
+
+(*** get *)
+
+(**** get_in_list *)
+
+val hashMap_get_in_list_lem
+  (#t : Type0) (key : usize) (ls : list_t t) :
+  Lemma
+  (ensures (
+    match hashMap_get_in_list t key ls, slot_t_find_s key ls with
+    | Fail _, None -> True
+    | Return x, Some x' -> x == x'
+    | _ -> False))
+
+#push-options "--fuel 1"
+let rec hashMap_get_in_list_lem #t key ls =
+  begin match ls with
+  | List_Cons ckey cvalue ls0 ->
+    let b = ckey = key in
+    if b
+    then ()
+    else
+      begin
+      hashMap_get_in_list_lem key ls0;
+      match hashMap_get_in_list t key ls0 with
+      | Fail _ -> ()
+      | Return x -> ()
+      end
+  | List_Nil -> ()
+  end
+#pop-options
+
+(**** get *)
+
+val hashMap_get_lem_aux
+  (#t : Type0) (self : hashMap_t_nes t) (key : usize) :
+  Lemma
+  (ensures (
+    match hashMap_get t self key, hashMap_t_find_s self key with
+    | Fail _, None -> True
+    | Return x, Some x' -> x == x'
+    | _ -> False))
+
+let hashMap_get_lem_aux #t self key =
+  begin match hash_key key with
+  | Fail _ -> ()
+  | Return i ->
+    let v = self.slots in
+    let i0 = alloc_vec_Vec_len (list_t t) v in
+    begin match usize_rem i i0 with
+    | Fail _ -> ()
+    | Return hash_mod ->
+      begin match alloc_vec_Vec_index_usize v hash_mod with
+      | Fail _ -> ()
+      | Return l ->
+        begin
+        hashMap_get_in_list_lem key l;
+        match hashMap_get_in_list t key l with
+        | Fail _ -> ()
+        | Return x -> ()
+        end
+      end
+    end
+  end
+
+/// .fsti
+let hashMap_get_lem #t self key = hashMap_get_lem_aux #t self key
+
+(*** get_mut'fwd *)
+
+
+(**** get_mut_in_list'fwd *)
+
+val hashMap_get_mut_in_list_loop_lem
+  (#t : Type0) (ls : list_t t) (key : usize) :
+  Lemma
+  (ensures (
+    match hashMap_get_mut_in_list_loop t ls key, slot_t_find_s key ls with
+    | Fail _, None -> True
+    | Return x, Some x' -> x == x'
+    | _ -> False))
+
+#push-options "--fuel 1"
+let rec hashMap_get_mut_in_list_loop_lem #t ls key =
+  begin match ls with
+  | List_Cons ckey cvalue ls0 ->
+    let b = ckey = key in
+    if b
+    then ()
+    else
+      begin
+      hashMap_get_mut_in_list_loop_lem ls0 key;
+      match hashMap_get_mut_in_list_loop t ls0 key with
+      | Fail _ -> ()
+      | Return x -> ()
+      end
+  | List_Nil -> ()
+  end
+#pop-options
+
+(**** get_mut'fwd *)
+
+val hashMap_get_mut_lem_aux
+  (#t : Type0) (self : hashMap_t_nes t) (key : usize) :
+  Lemma
+  (ensures (
+    match hashMap_get_mut t self key, hashMap_t_find_s self key with
+    | Fail _, None -> True
+    | Return x, Some x' -> x == x'
+    | _ -> False))
+
+let hashMap_get_mut_lem_aux #t self key =
+  begin match hash_key key with
+  | Fail _ -> ()
+  | Return i ->
+    let v = self.slots in
+    let i0 = alloc_vec_Vec_len (list_t t) v in
+    begin match usize_rem i i0 with
+    | Fail _ -> ()
+    | Return hash_mod ->
+      begin match alloc_vec_Vec_index_usize v hash_mod with
+      | Fail _ -> ()
+      | Return l ->
+        begin
+        hashMap_get_mut_in_list_loop_lem l key;
+        match hashMap_get_mut_in_list_loop t l key with
+        | Fail _ -> ()
+        | Return x -> ()
+        end
+      end
+    end
+  end
+
+let hashMap_get_mut_lem #t self key =
+  hashMap_get_mut_lem_aux #t self key
+
+(*** get_mut'back *)
+
+(**** get_mut_in_list'back *)
+
+val hashMap_get_mut_in_list_loop_back_lem
+  (#t : Type0) (ls : list_t t) (key : usize) (ret : t) :
+  Lemma
+  (requires (Some? (slot_t_find_s key ls)))
+  (ensures (
+    match hashMap_get_mut_in_list_loop_back t ls key ret with
+    | Fail _ -> False
+    | Return ls' -> list_t_v ls' == find_update (same_key key) (list_t_v ls) (key,ret)
+    | _ -> False))
+
+#push-options "--fuel 1"
+let rec hashMap_get_mut_in_list_loop_back_lem #t ls key ret =
+  begin match ls with
+  | List_Cons ckey cvalue ls0 ->
+    let b = ckey = key in
+    if b
+    then let ls1 = List_Cons ckey ret ls0 in ()
+    else
+      begin
+      hashMap_get_mut_in_list_loop_back_lem ls0 key ret;
+      match hashMap_get_mut_in_list_loop_back t ls0 key ret with
+      | Fail _ -> ()
+      | Return l -> let ls1 = List_Cons ckey cvalue l in ()
+      end
+  | List_Nil -> ()
+  end
+#pop-options
+
+(**** get_mut'back *)
+
+/// Refinement lemma
+val hashMap_get_mut_back_lem_refin
+  (#t : Type0) (self : hashMap_t t{length self.slots > 0})
+  (key : usize) (ret : t) :
+  Lemma
+  (requires (Some? (hashMap_t_find_s self key)))
+  (ensures (
+    match hashMap_get_mut_back t self key ret with
+    | Fail _ -> False
+    | Return hm' ->
+      hashMap_t_v hm' == hashMap_insert_no_fail_s (hashMap_t_v self) key ret))
+
+let hashMap_get_mut_back_lem_refin #t self key ret =
+  begin match hash_key key with
+  | Fail _ -> ()
+  | Return i ->
+    let i0 = self.num_entries in
+    let p = self.max_load_factor in
+    let i1 = self.max_load in
+    let v = self.slots in
+    let i2 = alloc_vec_Vec_len (list_t t) v in
+    begin match usize_rem i i2 with
+    | Fail _ -> ()
+    | Return hash_mod ->
+      begin match alloc_vec_Vec_index_usize v hash_mod with
+      | Fail _ -> ()
+      | Return l ->
+        begin
+        hashMap_get_mut_in_list_loop_back_lem l key ret;
+        match hashMap_get_mut_in_list_loop_back t l key ret with
+        | Fail _ -> ()
+        | Return l0 ->
+          begin match alloc_vec_Vec_update_usize v hash_mod l0 with
+          | Fail _ -> ()
+          | Return v0 -> let self0 = MkhashMap_t i0 p i1 v0 in ()
+          end
+        end
+      end
+    end
+  end
+
+/// Final lemma
+val hashMap_get_mut_back_lem_aux
+  (#t : Type0) (hm : hashMap_t t)
+  (key : usize) (ret : t) :
+  Lemma
+  (requires (
+    hashMap_t_inv hm /\
+    Some? (hashMap_t_find_s hm key)))
+  (ensures (
+    match hashMap_get_mut_back t hm key ret with
+    | Fail _ -> False
+    | Return hm' ->
+      // Functional spec
+      hashMap_t_v hm' == hashMap_insert_no_fail_s (hashMap_t_v hm) key ret /\
+     // The invariant is preserved
+     hashMap_t_inv hm' /\
+     // The length is preserved
+     hashMap_t_len_s hm' = hashMap_t_len_s hm /\
+     // [key] maps to [value]
+     hashMap_t_find_s hm' key == Some ret /\
+     // The other bindings are preserved
+     (forall k'. k' <> key ==> hashMap_t_find_s hm' k' == hashMap_t_find_s hm k')))
+
+let hashMap_get_mut_back_lem_aux #t hm key ret =
+  let hm_v = hashMap_t_v hm in
+  hashMap_get_mut_back_lem_refin hm key ret;
+  match hashMap_get_mut_back t hm key ret with
+  | Fail _ -> assert(False)
+  | Return hm' ->
+    hashMap_insert_no_fail_s_lem hm_v key ret
+
+/// .fsti
+let hashMap_get_mut_back_lem #t hm key ret = hashMap_get_mut_back_lem_aux hm key ret
+
+(*** remove'fwd *)
+
+val hashMap_remove_from_list_lem
+  (#t : Type0) (key : usize) (ls : list_t t) :
+  Lemma
+  (ensures (
+    match hashMap_remove_from_list t key ls with
+    | Fail _ -> False
+    | Return opt_x ->
+      opt_x == slot_t_find_s key ls /\
+      (Some? opt_x ==> length (slot_t_v ls) > 0)))
+
+#push-options "--fuel 1"
+let rec hashMap_remove_from_list_lem #t key ls =
+  begin match ls with
+  | List_Cons ckey x tl ->
+    let b = ckey = key in
+    if b
+    then
+      let mv_ls = core_mem_replace (list_t t) (List_Cons ckey x tl) List_Nil in
+      begin match mv_ls with
+      | List_Cons i cvalue tl0 -> ()
+      | List_Nil -> ()
+      end
+    else
+      begin
+      hashMap_remove_from_list_lem key tl;
+      match hashMap_remove_from_list t key tl with
+      | Fail _ -> ()
+      | Return opt -> ()
+      end
+  | List_Nil -> ()
+  end
+#pop-options
+
+val hashMap_remove_lem_aux
+  (#t : Type0) (self : hashMap_t t) (key : usize) :
+  Lemma
+  (requires (
+    // We need the invariant to prove that upon decrementing the entries counter,
+    // the counter doesn't become negative
+    hashMap_t_inv self))
+  (ensures (
+    match hashMap_remove t self key with
+    | Fail _ -> False
+    | Return opt_x -> opt_x == hashMap_t_find_s self key))
+
+let hashMap_remove_lem_aux #t self key =
+  begin match hash_key key with
+  | Fail _ -> ()
+  | Return i ->
+    let i0 = self.num_entries in
+    let v = self.slots in
+    let i1 = alloc_vec_Vec_len (list_t t) v in
+    begin match usize_rem i i1 with
+    | Fail _ -> ()
+    | Return hash_mod ->
+      begin match alloc_vec_Vec_index_usize v hash_mod with
+      | Fail _ -> ()
+      | Return l ->
+        begin
+        hashMap_remove_from_list_lem key l;
+        match hashMap_remove_from_list t key l with
+        | Fail _ -> ()
+        | Return x ->
+          begin match x with
+          | None -> ()
+          | Some x0 ->
+            begin
+            assert(l == index v hash_mod);
+            assert(length (list_t_v #t l) > 0);
+            length_flatten_index (hashMap_t_v self) hash_mod;
+            match usize_sub i0 1 with
+            | Fail _ -> ()
+            | Return _ -> ()
+            end
+          end
+        end
+      end
+    end
+  end
+
+/// .fsti
+let hashMap_remove_lem #t self key = hashMap_remove_lem_aux #t self key
+
+(*** remove'back *)
+
+(**** Refinement proofs *)
+
+/// High-level model for [remove_from_list'back]
+let hashMap_remove_from_list_s
+  (#t : Type0) (key : usize) (ls : slot_s t) :
+  slot_s t =
+  filter_one (not_same_key key) ls
+
+/// Refinement lemma
+val hashMap_remove_from_list_back_lem_refin
+  (#t : Type0) (key : usize) (ls : list_t t) :
+  Lemma
+  (ensures (
+    match hashMap_remove_from_list_back t key ls with
+    | Fail _ -> False
+    | Return ls' ->
+      list_t_v ls' == hashMap_remove_from_list_s key (list_t_v ls) /\
+      // The length is decremented, iff the key was in the slot
+      (let len = length (list_t_v ls) in
+       let len' = length (list_t_v ls') in
+       match slot_s_find key (list_t_v ls) with
+       | None -> len = len'
+       | Some _ -> len = len' + 1)))
+
+#push-options "--fuel 1"
+let rec hashMap_remove_from_list_back_lem_refin #t key ls =
+  begin match ls with
+  | List_Cons ckey x tl ->
+    let b = ckey = key in
+    if b
+    then
+      let mv_ls = core_mem_replace (list_t t) (List_Cons ckey x tl) List_Nil in
+      begin match mv_ls with
+      | List_Cons i cvalue tl0 -> ()
+      | List_Nil -> ()
+      end
+    else
+      begin
+      hashMap_remove_from_list_back_lem_refin key tl;
+      match hashMap_remove_from_list_back t key tl with
+      | Fail _ -> ()
+      | Return l -> let ls0 = List_Cons ckey x l in ()
+      end
+  | List_Nil -> ()
+  end
+#pop-options
+
+/// High-level model for [remove_from_list'back]
+let hashMap_remove_s
+  (#t : Type0) (self : hashMap_s_nes t) (key : usize) :
+  hashMap_s t =
+  let len = length self in
+  let hash = hash_mod_key key len in
+  let slot = index self hash in
+  let slot' = hashMap_remove_from_list_s key slot in
+  list_update self hash slot'
+
+/// Refinement lemma
+val hashMap_remove_back_lem_refin
+  (#t : Type0) (self : hashMap_t_nes t) (key : usize) :
+  Lemma
+  (requires (
+    // We need the invariant to prove that upon decrementing the entries counter,
+    // the counter doesn't become negative
+    hashMap_t_inv self))
+  (ensures (
+    match hashMap_remove_back t self key with
+    | Fail _ -> False
+    | Return hm' ->
+      hashMap_t_same_params hm' self /\
+      hashMap_t_v hm' == hashMap_remove_s (hashMap_t_v self) key /\
+      // The length is decremented iff the key was in the map
+      (let len = hashMap_t_len_s self in
+       let len' = hashMap_t_len_s hm' in
+       match hashMap_t_find_s self key with
+       | None -> len = len'
+       | Some _ -> len = len' + 1)))
+
+let hashMap_remove_back_lem_refin #t self key =
+  begin match hash_key key with
+  | Fail _ -> ()
+  | Return i ->
+    let i0 = self.num_entries in
+    let p = self.max_load_factor in
+    let i1 = self.max_load in
+    let v = self.slots in
+    let i2 = alloc_vec_Vec_len (list_t t) v in
+    begin match usize_rem i i2 with
+    | Fail _ -> ()
+    | Return hash_mod ->
+      begin match alloc_vec_Vec_index_usize v hash_mod with
+      | Fail _ -> ()
+      | Return l ->
+        begin
+        hashMap_remove_from_list_lem key l;
+        match hashMap_remove_from_list t key l with
+        | Fail _ -> ()
+        | Return x ->
+          begin match x with
+          | None ->
+            begin
+            hashMap_remove_from_list_back_lem_refin key l;
+            match hashMap_remove_from_list_back t key l with
+            | Fail _ -> ()
+            | Return l0 ->
+              begin
+              length_flatten_update (slots_t_v v) hash_mod (list_t_v l0);
+              match alloc_vec_Vec_update_usize v hash_mod l0 with
+              | Fail _ -> ()
+              | Return v0 -> ()
+              end
+            end
+          | Some x0 ->
+            begin
+            assert(l == index v hash_mod);
+            assert(length (list_t_v #t l) > 0);
+            length_flatten_index (hashMap_t_v self) hash_mod;
+            match usize_sub i0 1 with
+            | Fail _ -> ()
+            | Return i3 ->
+              begin
+              hashMap_remove_from_list_back_lem_refin key l;
+              match hashMap_remove_from_list_back t key l with
+              | Fail _ -> ()
+              | Return l0 ->
+                begin
+                length_flatten_update (slots_t_v v) hash_mod (list_t_v l0);
+                match alloc_vec_Vec_update_usize v hash_mod l0 with
+                | Fail _ -> ()
+                | Return v0 -> ()
+                end
+              end
+            end
+          end
+        end
+      end
+    end
+  end
+
+(**** Invariants, high-level properties *)
+
+val hashMap_remove_from_list_s_lem
+  (#t : Type0) (k : usize) (slot : slot_s t) (len : usize{len > 0}) (i : usize) :
+  Lemma
+  (requires (slot_s_inv len i slot))
+  (ensures (
+    let slot' = hashMap_remove_from_list_s k slot in
+    slot_s_inv len i slot' /\
+    slot_s_find k slot' == None /\
+    (forall (k':key{k' <> k}). slot_s_find k' slot' == slot_s_find k' slot) /\
+    // This postcondition is necessary to prove that the invariant is preserved
+    // in the recursive calls. This allows us to do the proof in one go.
+    (forall (b:binding t). for_all (binding_neq b) slot ==> for_all (binding_neq b) slot')
+  ))
+
+#push-options "--fuel 1"
+let rec hashMap_remove_from_list_s_lem #t key slot len i =
+  match slot with
+  | [] -> ()
+  | (k',v) :: slot' ->
+    if k' <> key then
+      begin
+      hashMap_remove_from_list_s_lem key slot' len i;
+      let slot'' = hashMap_remove_from_list_s key slot' in
+      assert(for_all (same_hash_mod_key len i) ((k',v)::slot''));
+      assert(for_all (binding_neq (k',v)) slot'); // Triggers instanciation
+      assert(for_all (binding_neq (k',v)) slot'')
+      end
+    else
+      begin
+      assert(for_all (binding_neq (k',v)) slot');
+      for_all_binding_neq_find_lem key v slot'
+      end
+#pop-options
+
+val hashMap_remove_s_lem
+  (#t : Type0) (self : hashMap_s_nes t) (key : usize) :
+  Lemma
+  (requires (hashMap_s_inv self))
+  (ensures (
+    let hm' = hashMap_remove_s self key in
+    // The invariant is preserved
+    hashMap_s_inv hm' /\
+    // We updated the binding
+    hashMap_s_updated_binding self key None hm'))
+
+let hashMap_remove_s_lem #t self key =
+  let len = length self in
+  let hash = hash_mod_key key len in
+  let slot = index self hash in
+  hashMap_remove_from_list_s_lem key slot len hash;
+  let slot' = hashMap_remove_from_list_s key slot in
+  let hm' = list_update self hash slot' in
+  assert(hashMap_s_inv self)
+
+/// Final lemma about [remove'back]
+val hashMap_remove_back_lem_aux
+  (#t : Type0) (self : hashMap_t t) (key : usize) :
+  Lemma
+  (requires (hashMap_t_inv self))
+  (ensures (
+    match hashMap_remove_back t self key with
+    | Fail _ -> False
+    | Return hm' ->
+      hashMap_t_inv self /\
+      hashMap_t_same_params hm' self /\
+      // We updated the binding
+      hashMap_s_updated_binding (hashMap_t_v self) key None (hashMap_t_v hm') /\
+      hashMap_t_v hm' == hashMap_remove_s (hashMap_t_v self) key /\
+      // The length is decremented iff the key was in the map
+      (let len = hashMap_t_len_s self in
+       let len' = hashMap_t_len_s hm' in
+       match hashMap_t_find_s self key with
+       | None -> len = len'
+       | Some _ -> len = len' + 1)))
+
+let hashMap_remove_back_lem_aux #t self key =
+  hashMap_remove_back_lem_refin self key;
+  hashMap_remove_s_lem (hashMap_t_v self) key
+
+/// .fsti
+let hashMap_remove_back_lem #t self key =
+  hashMap_remove_back_lem_aux #t self key
diff --git a/tests/fstar-split/hashmap/Hashmap.Properties.fsti b/tests/fstar-split/hashmap/Hashmap.Properties.fsti
new file mode 100644
index 00000000..26c0ec06
--- /dev/null
+++ b/tests/fstar-split/hashmap/Hashmap.Properties.fsti
@@ -0,0 +1,267 @@
+(** Properties about the hashmap *)
+module Hashmap.Properties
+open Primitives
+open FStar.List.Tot
+open FStar.Mul
+open Hashmap.Types
+open Hashmap.Clauses
+open Hashmap.Funs
+
+#set-options "--z3rlimit 50 --fuel 0 --ifuel 1"
+
+// Small trick to align the .fst and the .fsti
+val _align_fsti : unit
+
+(*** Utilities *)
+
+type key : eqtype = usize
+
+type hash : eqtype = usize
+
+val hashMap_t_inv (#t : Type0) (hm : hashMap_t t) : Type0
+
+val len_s (#t : Type0) (hm : hashMap_t t) : nat
+
+val find_s (#t : Type0) (hm : hashMap_t t) (k : key) : option t
+
+(*** Overloading *)
+
+/// Upon inserting *new* entries in the hash map, the slots vector is resized
+/// whenever we reach the max load, unless we can't resize anymore because
+/// there are already too many entries. This way, we maintain performance by
+/// limiting the hash collisions.
+/// This is expressed by the following property, which is maintained in the hash
+/// map invariant.
+val hashMap_not_overloaded_lem (#t : Type0) (hm : hashMap_t t) :
+  Lemma
+  (requires (hashMap_t_inv hm))
+  (ensures (
+    // The capacity is the number of slots
+    let capacity = length hm.slots in
+    // The max load factor defines a threshold on the number of entries:
+    // if there are more entries than a given fraction of the number of slots,
+    // we resize the slots vector to limit the hash collisions
+    let (dividend, divisor) = hm.max_load_factor in
+    // technicality: this postcondition won't typecheck if we don't reveal
+    // that divisor > 0 (because of the division)
+    divisor > 0 /\
+    begin
+    // The max load, computed as a fraction of the capacity
+    let max_load = (capacity * dividend) / divisor in
+    // The number of entries inserted in the map is given by [len_s] (see
+    // the functional correctness lemmas, which state how this number evolves):
+    let len = len_s hm in
+    // We prove that:
+    // - either the number of entries is <= than the max load threshold
+    len <= max_load
+    // - or we couldn't resize the map, because then the arithmetic computations
+    //   would overflow (note that we always multiply the number of slots by 2)
+    || 2* capacity * dividend > usize_max
+    end))
+
+(*** Functional correctness *)
+(**** [new'fwd] *)
+
+/// [new] doesn't fail and returns an empty hash map
+val hashMap_new_lem (t : Type0) :
+  Lemma
+  (ensures (
+    match hashMap_new t with
+    | Fail _ -> False
+    | Return hm ->
+      // The hash map invariant is satisfied
+      hashMap_t_inv hm /\
+      // The hash map has a length of 0
+      len_s hm = 0 /\
+      // It contains no bindings
+      (forall k. find_s hm k == None)))
+
+(**** [clear] *)
+
+/// [clear] doesn't fail and turns the hash map into an empty map
+val hashMap_clear_lem
+  (#t : Type0) (self : hashMap_t t) :
+  Lemma
+  (requires (hashMap_t_inv self))
+  (ensures (
+    match hashMap_clear t self with
+    | Fail _ -> False
+    | Return hm ->
+      // The hash map invariant is satisfied
+      hashMap_t_inv hm /\
+      // The hash map has a length of 0
+      len_s hm = 0 /\
+      // It contains no bindings
+      (forall k. find_s hm k == None)))
+
+(**** [len] *)
+
+/// [len] can't fail and returns the length (the number of elements) of the hash map
+val hashMap_len_lem (#t : Type0) (self : hashMap_t t) :
+  Lemma
+  (requires (hashMap_t_inv self))
+  (ensures (
+    match hashMap_len t self with
+    | Fail _ -> False
+    | Return l -> l = len_s self))
+
+
+(**** [insert'fwd_back] *)
+
+/// The backward function for [insert] (note it is named "...insert'fwd_back" because
+/// the forward function doesn't return anything, and was thus filtered - in a
+/// sense the effect of applying the forward function then the backward function is
+/// entirely encompassed by the effect of the backward function alone).
+/// 
+/// [insert'fwd_back] simply inserts a binding.
+val hashMap_insert_lem
+  (#t : Type0) (self : hashMap_t t) (key : usize) (value : t) :
+  Lemma
+  (requires (hashMap_t_inv self))
+  (ensures (
+    match hashMap_insert t self key value with
+    | Fail _ ->
+      // We can fail only if:
+      // - the key is not in the map and we thus need to add it
+      None? (find_s self key) /\
+      // - and we are already saturated (we can't increment the internal counter)
+      len_s self = usize_max
+    | Return hm' ->
+      // The invariant is preserved
+      hashMap_t_inv hm' /\
+      // [key] maps to [value]
+      find_s hm' key == Some value /\
+      // The other bindings are preserved
+      (forall k'. k' <> key ==> find_s hm' k' == find_s self k') /\
+      begin
+      // The length is incremented, iff we inserted a new key
+      match find_s self key with
+      | None -> len_s hm' = len_s self + 1
+      | Some _ -> len_s hm' = len_s self
+      end))
+
+
+(**** [contains_key] *)
+
+/// [contains_key'fwd] can't fail and returns `true` if and only if there is
+/// a binding for key [key]
+val hashMap_contains_key_lem
+  (#t : Type0) (self : hashMap_t t) (key : usize) :
+  Lemma
+  (requires (hashMap_t_inv self))
+  (ensures (
+    match hashMap_contains_key t self key with
+    | Fail _ -> False
+    | Return b -> b = Some? (find_s self key)))
+
+(**** [get'fwd] *)
+
+/// [get] returns (a shared borrow to) the binding for key [key]
+val hashMap_get_lem
+  (#t : Type0) (self : hashMap_t t) (key : usize) :
+  Lemma
+  (requires (hashMap_t_inv self))
+  (ensures (
+    match hashMap_get t self key, find_s self key with
+    | Fail _, None -> True
+    | Return x, Some x' -> x == x'
+    | _ -> False))
+
+(**** [get_mut'fwd] *)
+
+/// [get_mut'fwd] returns (a mutable borrow to) the binding for key [key].
+/// 
+/// The *forward* function models the action of getting a borrow to an element
+/// in Rust, which gives the possibility of modifying this element in place. Then,
+/// upon ending the borrow, the effect of the modification is modelled in the
+/// translation through a call to the backward function.
+val hashMap_get_mut_lem
+  (#t : Type0) (self : hashMap_t t) (key : usize) :
+  Lemma
+  (requires (hashMap_t_inv self))
+  (ensures (
+    match hashMap_get_mut t self key, find_s self key with
+    | Fail _, None -> True
+    | Return x, Some x' -> x == x'
+    | _ -> False))
+
+
+(**** [get_mut'back] *)
+
+/// [get_mut'back] updates the binding for key [key], without failing.
+/// A call to [get_mut'back] must follow a call to [get_mut'fwd], which gives
+/// us that there must be a binding for key [key] in the map (otherwise we
+/// can't prove the absence of failure).
+val hashMap_get_mut_back_lem
+  (#t : Type0) (hm : hashMap_t t) (key : usize) (ret : t) :
+  Lemma
+  (requires (
+    hashMap_t_inv hm /\
+    // A call to the backward function must follow a call to the forward
+    // function, whose success gives us that there is a binding for the key.
+    // In the case of *forward* functions, "success" has to be understood as
+    // the absence of panics. When translating code from Rust to pure lambda
+    // calculus, we have the property that the generated calls to the backward
+    // functions can't fail (because their are preceded by calls to forward
+    // functions, which must then have succeeded before): for a backward function,
+    // "failure" is to be understood as the semantics getting stuck.
+    // This is of course true unless we filtered the call to the forward function
+    // because its effect is encompassed by the backward function, as with
+    // [hashMap_clear]).
+    Some? (find_s hm key)))
+  (ensures (
+    match hashMap_get_mut_back t hm key ret with
+    | Fail _ -> False // Can't fail
+    | Return hm' ->
+     // The invariant is preserved
+     hashMap_t_inv hm' /\
+     // The length is preserved
+     len_s hm' = len_s hm /\
+     // [key] maps to the update value, [ret]
+     find_s hm' key == Some ret /\
+     // The other bindings are preserved
+     (forall k'. k' <> key ==> find_s hm' k' == find_s hm k')))
+
+(**** [remove'fwd] *)
+
+/// [remove'fwd] returns the (optional) element which has been removed from the map
+/// (the rust function *moves* it out of the map). Note that the effect of the update
+/// on the map is modelles through the call to [remove'back] ([remove] takes a
+/// mutable borrow to the hash map as parameter).
+val hashMap_remove_lem
+  (#t : Type0) (self : hashMap_t t) (key : usize) :
+  Lemma
+  (requires (hashMap_t_inv self))
+  (ensures (
+    match hashMap_remove t self key with
+    | Fail _ -> False
+    | Return opt_x -> opt_x == find_s self key))
+
+
+(**** [remove'back] *)
+
+/// The hash map given as parameter to [remove] is given through a mutable borrow:
+/// hence the backward function which gives back the updated map, without the
+/// binding.
+val hashMap_remove_back_lem
+  (#t : Type0) (self : hashMap_t t) (key : usize) :
+  Lemma
+  (requires (hashMap_t_inv self))
+  (ensures (
+    match hashMap_remove_back t self key with
+    | Fail _ -> False
+    | Return hm' ->
+      // The invariant is preserved
+      hashMap_t_inv self /\
+      // The binding for [key] is not there anymore
+      find_s hm' key == None /\
+      // The other bindings are preserved
+      (forall k'. k' <> key ==> find_s hm' k' == find_s self k') /\
+      begin
+      // The length is decremented iff the key was in the map
+      let len = len_s self in
+      let len' = len_s hm' in
+      match find_s self key with
+      | None -> len = len'
+      | Some _ -> len = len' + 1
+      end))
diff --git a/tests/fstar-split/hashmap/Hashmap.Types.fst b/tests/fstar-split/hashmap/Hashmap.Types.fst
new file mode 100644
index 00000000..ef96b1e9
--- /dev/null
+++ b/tests/fstar-split/hashmap/Hashmap.Types.fst
@@ -0,0 +1,23 @@
+(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
+(** [hashmap]: type definitions *)
+module Hashmap.Types
+open Primitives
+
+#set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
+
+(** [hashmap::List]
+    Source: 'src/hashmap.rs', lines 19:0-19:16 *)
+type list_t (t : Type0) =
+| List_Cons : usize -> t -> list_t t -> list_t t
+| List_Nil : list_t t
+
+(** [hashmap::HashMap]
+    Source: 'src/hashmap.rs', lines 35:0-35:21 *)
+type hashMap_t (t : Type0) =
+{
+  num_entries : usize;
+  max_load_factor : (usize & usize);
+  max_load : usize;
+  slots : alloc_vec_Vec (list_t t);
+}
+
diff --git a/tests/fstar-split/hashmap/Makefile b/tests/fstar-split/hashmap/Makefile
new file mode 100644
index 00000000..fa7d1f36
--- /dev/null
+++ b/tests/fstar-split/hashmap/Makefile
@@ -0,0 +1,49 @@
+# This file was automatically generated - modify ../Makefile.template instead
+INCLUDE_DIRS = .
+
+FSTAR_INCLUDES = $(addprefix --include ,$(INCLUDE_DIRS))
+
+FSTAR_HINTS ?= --use_hints --use_hint_hashes --record_hints
+
+FSTAR_OPTIONS = $(FSTAR_HINTS) \
+  --cache_checked_modules $(FSTAR_INCLUDES) --cmi \
+  --warn_error '+241@247+285-274' \
+
+FSTAR_EXE ?= fstar.exe
+FSTAR_NO_FLAGS = $(FSTAR_EXE) --already_cached 'Prims FStar LowStar Steel' --odir obj --cache_dir obj
+
+FSTAR = $(FSTAR_NO_FLAGS) $(FSTAR_OPTIONS)
+
+# The F* roots are used to compute the dependency graph, and generate the .depend file
+FSTAR_ROOTS ?= $(wildcard *.fst *.fsti)
+
+# Build all the files
+all: $(addprefix obj/,$(addsuffix .checked,$(FSTAR_ROOTS)))
+
+# This is the right way to ensure the .depend file always gets re-built.
+ifeq (,$(filter %-in,$(MAKECMDGOALS)))
+ifndef NODEPEND
+ifndef MAKE_RESTARTS
+.depend: .FORCE
+	$(FSTAR_NO_FLAGS) --dep full $(notdir $(FSTAR_ROOTS)) > $@
+
+.PHONY: .FORCE
+.FORCE:
+endif
+endif
+
+include .depend
+endif
+
+# For the interactive mode
+%.fst-in %.fsti-in:
+	@echo $(FSTAR_OPTIONS)
+
+# Generete the .checked files in batch mode
+%.checked:
+	$(FSTAR) $(FSTAR_OPTIONS) $< && \
+	touch -c $@
+
+.PHONY: clean
+clean:
+	rm -f obj/*
diff --git a/tests/fstar-split/hashmap/Primitives.fst b/tests/fstar-split/hashmap/Primitives.fst
new file mode 100644
index 00000000..a3ffbde4
--- /dev/null
+++ b/tests/fstar-split/hashmap/Primitives.fst
@@ -0,0 +1,884 @@
+/// This file lists primitive and assumed functions and types
+module Primitives
+open FStar.Mul
+open FStar.List.Tot
+
+#set-options "--z3rlimit 15 --fuel 0 --ifuel 1"
+
+(*** Utilities *)
+val list_update (#a : Type0) (ls : list a) (i : nat{i < length ls}) (x : a) :
+  ls':list a{
+    length ls' = length ls /\
+    index ls' i == x
+  }
+#push-options "--fuel 1"
+let rec list_update #a ls i x =
+  match ls with
+  | x' :: ls -> if i = 0 then x :: ls else x' :: list_update ls (i-1) x
+#pop-options
+
+(*** Result *)
+type error : Type0 =
+| Failure
+| OutOfFuel
+
+type result (a : Type0) : Type0 =
+| Return : v:a -> result a
+| Fail : e:error -> result a
+
+// Monadic return operator
+unfold let return (#a : Type0) (x : a) : result a = Return x
+
+// Monadic bind operator.
+// Allows to use the notation:
+// ```
+// let* x = y in
+// ...
+// ```
+unfold let (let*) (#a #b : Type0) (m: result a)
+  (f: (x:a) -> Pure (result b) (requires (m == Return x)) (ensures fun _ -> True)) :
+  result b =
+  match m with
+  | Return x -> f x
+  | Fail e   -> Fail e
+
+// Monadic assert(...)
+let massert (b:bool) : result unit = if b then Return () else Fail Failure
+
+// Normalize and unwrap a successful result (used for globals).
+let eval_global (#a : Type0) (x : result a{Return? (normalize_term x)}) : a = Return?.v x
+
+(*** Misc *)
+type char = FStar.Char.char
+type string = string
+
+let is_zero (n: nat) : bool = n = 0
+let decrease (n: nat{n > 0}) : nat = n - 1
+
+let core_mem_replace (a : Type0) (x : a) (y : a) : a = x
+let core_mem_replace_back (a : Type0) (x : a) (y : a) : a = y
+
+// We don't really use raw pointers for now
+type mut_raw_ptr (t : Type0) = { v : t }
+type const_raw_ptr (t : Type0) = { v : t }
+
+(*** Scalars *)
+/// Rem.: most of the following code was partially generated
+
+assume val size_numbits : pos
+
+// TODO: we could use FStar.Int.int_t and FStar.UInt.int_t
+
+let isize_min : int = -9223372036854775808 // TODO: should be opaque
+let isize_max : int = 9223372036854775807 // TODO: should be opaque
+let i8_min : int = -128
+let i8_max : int = 127
+let i16_min : int = -32768
+let i16_max : int = 32767
+let i32_min : int = -2147483648
+let i32_max : int = 2147483647
+let i64_min : int = -9223372036854775808
+let i64_max : int = 9223372036854775807
+let i128_min : int = -170141183460469231731687303715884105728
+let i128_max : int = 170141183460469231731687303715884105727
+let usize_min : int = 0
+let usize_max : int = 4294967295 // TODO: should be opaque
+let u8_min : int = 0
+let u8_max : int = 255
+let u16_min : int = 0
+let u16_max : int = 65535
+let u32_min : int = 0
+let u32_max : int = 4294967295
+let u64_min : int = 0
+let u64_max : int = 18446744073709551615
+let u128_min : int = 0
+let u128_max : int = 340282366920938463463374607431768211455
+
+type scalar_ty =
+| Isize
+| I8
+| I16
+| I32
+| I64
+| I128
+| Usize
+| U8
+| U16
+| U32
+| U64
+| U128
+
+let is_unsigned = function
+  | Isize | I8 | I16 | I32 | I64 | I128 -> false
+  | Usize | U8 | U16 | U32 | U64 | U128 -> true
+
+let scalar_min (ty : scalar_ty) : int =
+  match ty with
+  | Isize -> isize_min
+  | I8 -> i8_min
+  | I16 -> i16_min
+  | I32 -> i32_min
+  | I64 -> i64_min
+  | I128 -> i128_min
+  | Usize -> usize_min
+  | U8 -> u8_min
+  | U16 -> u16_min
+  | U32 -> u32_min
+  | U64 -> u64_min
+  | U128 -> u128_min
+
+let scalar_max (ty : scalar_ty) : int =
+  match ty with
+  | Isize -> isize_max
+  | I8 -> i8_max
+  | I16 -> i16_max
+  | I32 -> i32_max
+  | I64 -> i64_max
+  | I128 -> i128_max
+  | Usize -> usize_max
+  | U8 -> u8_max
+  | U16 -> u16_max
+  | U32 -> u32_max
+  | U64 -> u64_max
+  | U128 -> u128_max
+
+type scalar (ty : scalar_ty) : eqtype = x:int{scalar_min ty <= x && x <= scalar_max ty}
+
+let mk_scalar (ty : scalar_ty) (x : int) : result (scalar ty) =
+  if scalar_min ty <= x && scalar_max ty >= x then Return x else Fail Failure
+
+let scalar_neg (#ty : scalar_ty) (x : scalar ty) : result (scalar ty) = mk_scalar ty (-x)
+
+let scalar_div (#ty : scalar_ty) (x : scalar ty) (y : scalar ty) : result (scalar ty) =
+  if y <> 0 then mk_scalar ty (x / y) else Fail Failure
+
+/// The remainder operation
+let int_rem (x : int) (y : int{y <> 0}) : int =
+  if x >= 0 then (x % y) else -(x % y)
+
+(* Checking consistency with Rust *)
+let _ = assert_norm(int_rem 1 2 = 1)
+let _ = assert_norm(int_rem (-1) 2 = -1)
+let _ = assert_norm(int_rem 1 (-2) = 1)
+let _ = assert_norm(int_rem (-1) (-2) = -1)
+
+let scalar_rem (#ty : scalar_ty) (x : scalar ty) (y : scalar ty) : result (scalar ty) =
+  if y <> 0 then mk_scalar ty (int_rem x y) else Fail Failure
+
+let scalar_add (#ty : scalar_ty) (x : scalar ty) (y : scalar ty) : result (scalar ty) =
+  mk_scalar ty (x + y)
+
+let scalar_sub (#ty : scalar_ty) (x : scalar ty) (y : scalar ty) : result (scalar ty) =
+  mk_scalar ty (x - y)
+
+let scalar_mul (#ty : scalar_ty) (x : scalar ty) (y : scalar ty) : result (scalar ty) =
+  mk_scalar ty (x * y)
+
+let scalar_xor (#ty : scalar_ty)
+    (x : scalar ty) (y : scalar ty) : scalar ty =
+  match ty with
+  | U8 -> FStar.UInt.logxor #8 x y
+  | U16 -> FStar.UInt.logxor #16 x y
+  | U32 -> FStar.UInt.logxor #32 x y
+  | U64 -> FStar.UInt.logxor #64 x y
+  | U128 -> FStar.UInt.logxor #128 x y
+  | Usize -> admit() // TODO
+  | I8 ->
+    // Encoding issues...
+    normalize_spec (FStar.Int.int_t 8);
+    normalize_spec (scalar I8);
+    FStar.Int.logxor #8 x y
+  | I16 ->
+    // Encoding issues...
+    normalize_spec (FStar.Int.int_t 16);
+    normalize_spec (scalar I16);
+    FStar.Int.logxor #16 x y
+  | I32 -> FStar.Int.logxor #32 x y
+  | I64 -> FStar.Int.logxor #64 x y
+  | I128 ->
+    // Encoding issues...
+    normalize_spec (FStar.Int.int_t 128);
+    normalize_spec (scalar I128);
+    FStar.Int.logxor #128 x y
+  | Isize -> admit() // TODO
+
+let scalar_or (#ty : scalar_ty)
+    (x : scalar ty) (y : scalar ty) : scalar ty =
+  match ty with
+  | U8 -> FStar.UInt.logor #8 x y
+  | U16 -> FStar.UInt.logor #16 x y
+  | U32 -> FStar.UInt.logor #32 x y
+  | U64 -> FStar.UInt.logor #64 x y
+  | U128 -> FStar.UInt.logor #128 x y
+  | Usize -> admit() // TODO
+  | I8 ->
+    // Encoding issues...
+    normalize_spec (FStar.Int.int_t 8);
+    normalize_spec (scalar I8);
+    FStar.Int.logor #8 x y
+  | I16 ->
+    // Encoding issues...
+    normalize_spec (FStar.Int.int_t 16);
+    normalize_spec (scalar I16);
+    FStar.Int.logor #16 x y
+  | I32 -> FStar.Int.logor #32 x y
+  | I64 -> FStar.Int.logor #64 x y
+  | I128 ->
+    // Encoding issues...
+    normalize_spec (FStar.Int.int_t 128);
+    normalize_spec (scalar I128);
+    FStar.Int.logor #128 x y
+  | Isize -> admit() // TODO
+
+let scalar_and (#ty : scalar_ty)
+    (x : scalar ty) (y : scalar ty) : scalar ty =
+  match ty with
+  | U8 -> FStar.UInt.logand #8 x y
+  | U16 -> FStar.UInt.logand #16 x y
+  | U32 -> FStar.UInt.logand #32 x y
+  | U64 -> FStar.UInt.logand #64 x y
+  | U128 -> FStar.UInt.logand #128 x y
+  | Usize -> admit() // TODO
+  | I8 ->
+    // Encoding issues...
+    normalize_spec (FStar.Int.int_t 8);
+    normalize_spec (scalar I8);
+    FStar.Int.logand #8 x y
+  | I16 ->
+    // Encoding issues...
+    normalize_spec (FStar.Int.int_t 16);
+    normalize_spec (scalar I16);
+    FStar.Int.logand #16 x y
+  | I32 -> FStar.Int.logand #32 x y
+  | I64 -> FStar.Int.logand #64 x y
+  | I128 ->
+    // Encoding issues...
+    normalize_spec (FStar.Int.int_t 128);
+    normalize_spec (scalar I128);
+    FStar.Int.logand #128 x y
+  | Isize -> admit() // TODO
+
+// Shift left
+let scalar_shl (#ty0 #ty1 : scalar_ty)
+    (x : scalar ty0) (y : scalar ty1) : result (scalar ty0) =
+  admit()
+
+// Shift right
+let scalar_shr (#ty0 #ty1 : scalar_ty)
+    (x : scalar ty0) (y : scalar ty1) : result (scalar ty0) =
+  admit()
+
+(** Cast an integer from a [src_ty] to a [tgt_ty] *)
+// TODO: check the semantics of casts in Rust
+let scalar_cast (src_ty : scalar_ty) (tgt_ty : scalar_ty) (x : scalar src_ty) : result (scalar tgt_ty) =
+  mk_scalar tgt_ty x
+
+// This can't fail, but for now we make all casts faillible (easier for the translation)
+let scalar_cast_bool (tgt_ty : scalar_ty) (x : bool) : result (scalar tgt_ty) =
+  mk_scalar tgt_ty (if x then 1 else 0)
+
+/// The scalar types
+type isize : eqtype = scalar Isize
+type i8    : eqtype = scalar I8
+type i16   : eqtype = scalar I16
+type i32   : eqtype = scalar I32
+type i64   : eqtype = scalar I64
+type i128  : eqtype = scalar I128
+type usize : eqtype = scalar Usize
+type u8    : eqtype = scalar U8
+type u16   : eqtype = scalar U16
+type u32   : eqtype = scalar U32
+type u64   : eqtype = scalar U64
+type u128  : eqtype = scalar U128
+
+
+let core_isize_min : isize = isize_min
+let core_isize_max : isize = isize_max
+let core_i8_min    : i8 = i8_min
+let core_i8_max    : i8 = i8_max
+let core_i16_min   : i16 = i16_min
+let core_i16_max   : i16 = i16_max
+let core_i32_min   : i32 = i32_min
+let core_i32_max   : i32 = i32_max
+let core_i64_min   : i64 = i64_min
+let core_i64_max   : i64 = i64_max
+let core_i128_min  : i128 = i128_min
+let core_i128_max  : i128 = i128_max
+
+let core_usize_min : usize = usize_min
+let core_usize_max : usize = usize_max
+let core_u8_min    : u8 = u8_min
+let core_u8_max    : u8 = u8_max
+let core_u16_min   : u16 = u16_min
+let core_u16_max   : u16 = u16_max
+let core_u32_min   : u32 = u32_min
+let core_u32_max   : u32 = u32_max
+let core_u64_min   : u64 = u64_min
+let core_u64_max   : u64 = u64_max
+let core_u128_min  : u128 = u128_min
+let core_u128_max  : u128 = u128_max
+
+/// Negation
+let isize_neg = scalar_neg #Isize
+let i8_neg = scalar_neg #I8
+let i16_neg = scalar_neg #I16
+let i32_neg = scalar_neg #I32
+let i64_neg = scalar_neg #I64
+let i128_neg = scalar_neg #I128
+
+/// Division
+let isize_div = scalar_div #Isize
+let i8_div = scalar_div #I8
+let i16_div = scalar_div #I16
+let i32_div = scalar_div #I32
+let i64_div = scalar_div #I64
+let i128_div = scalar_div #I128
+let usize_div = scalar_div #Usize
+let u8_div = scalar_div #U8
+let u16_div = scalar_div #U16
+let u32_div = scalar_div #U32
+let u64_div = scalar_div #U64
+let u128_div = scalar_div #U128
+
+/// Remainder
+let isize_rem = scalar_rem #Isize
+let i8_rem = scalar_rem #I8
+let i16_rem = scalar_rem #I16
+let i32_rem = scalar_rem #I32
+let i64_rem = scalar_rem #I64
+let i128_rem = scalar_rem #I128
+let usize_rem = scalar_rem #Usize
+let u8_rem = scalar_rem #U8
+let u16_rem = scalar_rem #U16
+let u32_rem = scalar_rem #U32
+let u64_rem = scalar_rem #U64
+let u128_rem = scalar_rem #U128
+
+/// Addition
+let isize_add = scalar_add #Isize
+let i8_add = scalar_add #I8
+let i16_add = scalar_add #I16
+let i32_add = scalar_add #I32
+let i64_add = scalar_add #I64
+let i128_add = scalar_add #I128
+let usize_add = scalar_add #Usize
+let u8_add = scalar_add #U8
+let u16_add = scalar_add #U16
+let u32_add = scalar_add #U32
+let u64_add = scalar_add #U64
+let u128_add = scalar_add #U128
+
+/// Subtraction
+let isize_sub = scalar_sub #Isize
+let i8_sub = scalar_sub #I8
+let i16_sub = scalar_sub #I16
+let i32_sub = scalar_sub #I32
+let i64_sub = scalar_sub #I64
+let i128_sub = scalar_sub #I128
+let usize_sub = scalar_sub #Usize
+let u8_sub = scalar_sub #U8
+let u16_sub = scalar_sub #U16
+let u32_sub = scalar_sub #U32
+let u64_sub = scalar_sub #U64
+let u128_sub = scalar_sub #U128
+
+/// Multiplication
+let isize_mul = scalar_mul #Isize
+let i8_mul = scalar_mul #I8
+let i16_mul = scalar_mul #I16
+let i32_mul = scalar_mul #I32
+let i64_mul = scalar_mul #I64
+let i128_mul = scalar_mul #I128
+let usize_mul = scalar_mul #Usize
+let u8_mul = scalar_mul #U8
+let u16_mul = scalar_mul #U16
+let u32_mul = scalar_mul #U32
+let u64_mul = scalar_mul #U64
+let u128_mul = scalar_mul #U128
+
+/// Xor
+let u8_xor = scalar_xor #U8
+let u16_xor = scalar_xor #U16
+let u32_xor = scalar_xor #U32
+let u64_xor = scalar_xor #U64
+let u128_xor = scalar_xor #U128
+let usize_xor = scalar_xor #Usize
+let i8_xor = scalar_xor #I8
+let i16_xor = scalar_xor #I16
+let i32_xor = scalar_xor #I32
+let i64_xor = scalar_xor #I64
+let i128_xor = scalar_xor #I128
+let isize_xor = scalar_xor #Isize
+
+/// Or
+let u8_or = scalar_or #U8
+let u16_or = scalar_or #U16
+let u32_or = scalar_or #U32
+let u64_or = scalar_or #U64
+let u128_or = scalar_or #U128
+let usize_or = scalar_or #Usize
+let i8_or = scalar_or #I8
+let i16_or = scalar_or #I16
+let i32_or = scalar_or #I32
+let i64_or = scalar_or #I64
+let i128_or = scalar_or #I128
+let isize_or = scalar_or #Isize
+
+/// And
+let u8_and = scalar_and #U8
+let u16_and = scalar_and #U16
+let u32_and = scalar_and #U32
+let u64_and = scalar_and #U64
+let u128_and = scalar_and #U128
+let usize_and = scalar_and #Usize
+let i8_and = scalar_and #I8
+let i16_and = scalar_and #I16
+let i32_and = scalar_and #I32
+let i64_and = scalar_and #I64
+let i128_and = scalar_and #I128
+let isize_and = scalar_and #Isize
+
+/// Shift left
+let u8_shl #ty = scalar_shl #U8 #ty
+let u16_shl #ty = scalar_shl #U16 #ty
+let u32_shl #ty = scalar_shl #U32 #ty
+let u64_shl #ty = scalar_shl #U64 #ty
+let u128_shl #ty = scalar_shl #U128 #ty
+let usize_shl #ty = scalar_shl #Usize #ty
+let i8_shl #ty = scalar_shl #I8 #ty
+let i16_shl #ty = scalar_shl #I16 #ty
+let i32_shl #ty = scalar_shl #I32 #ty
+let i64_shl #ty = scalar_shl #I64 #ty
+let i128_shl #ty = scalar_shl #I128 #ty
+let isize_shl #ty = scalar_shl #Isize #ty
+
+/// Shift right
+let u8_shr #ty = scalar_shr #U8 #ty
+let u16_shr #ty = scalar_shr #U16 #ty
+let u32_shr #ty = scalar_shr #U32 #ty
+let u64_shr #ty = scalar_shr #U64 #ty
+let u128_shr #ty = scalar_shr #U128 #ty
+let usize_shr #ty = scalar_shr #Usize #ty
+let i8_shr #ty = scalar_shr #I8 #ty
+let i16_shr #ty = scalar_shr #I16 #ty
+let i32_shr #ty = scalar_shr #I32 #ty
+let i64_shr #ty = scalar_shr #I64 #ty
+let i128_shr #ty = scalar_shr #I128 #ty
+let isize_shr #ty = scalar_shr #Isize #ty
+
+(*** core::ops *)
+
+// Trait declaration: [core::ops::index::Index]
+noeq type core_ops_index_Index (self idx : Type0) = {
+  output : Type0;
+  index : self → idx → result output
+}
+
+// Trait declaration: [core::ops::index::IndexMut]
+noeq type core_ops_index_IndexMut (self idx : Type0) = {
+  indexInst : core_ops_index_Index self idx;
+  index_mut : self → idx → result indexInst.output;
+  index_mut_back : self → idx → indexInst.output → result self;
+}
+
+// Trait declaration [core::ops::deref::Deref]
+noeq type core_ops_deref_Deref (self : Type0) = {
+  target : Type0;
+  deref : self → result target;
+}
+
+// Trait declaration [core::ops::deref::DerefMut]
+noeq type core_ops_deref_DerefMut (self : Type0) = {
+  derefInst : core_ops_deref_Deref self;
+  deref_mut : self → result derefInst.target;
+  deref_mut_back : self → derefInst.target → result self;
+}
+
+type core_ops_range_Range (a : Type0) = {
+  start : a;
+  end_ : a;
+}
+
+(*** [alloc] *)
+
+let alloc_boxed_Box_deref (t : Type0) (x : t) : result t = Return x
+let alloc_boxed_Box_deref_mut (t : Type0) (x : t) : result t = Return x
+let alloc_boxed_Box_deref_mut_back (t : Type) (_ : t) (x : t) : result t = Return x
+
+// Trait instance
+let alloc_boxed_Box_coreopsDerefInst (self : Type0) : core_ops_deref_Deref self = {
+  target = self;
+  deref = alloc_boxed_Box_deref self;
+}
+
+// Trait instance
+let alloc_boxed_Box_coreopsDerefMutInst (self : Type0) : core_ops_deref_DerefMut self = {
+  derefInst = alloc_boxed_Box_coreopsDerefInst self;
+  deref_mut = alloc_boxed_Box_deref_mut self;
+  deref_mut_back = alloc_boxed_Box_deref_mut_back self;
+}
+
+(*** Array *)
+type array (a : Type0) (n : usize) = s:list a{length s = n}
+
+// We tried putting the normalize_term condition as a refinement on the list
+// but it didn't work. It works with the requires clause.
+let mk_array (a : Type0) (n : usize)
+  (l : list a) :
+  Pure (array a n)
+  (requires (normalize_term(FStar.List.Tot.length l) = n))
+  (ensures (fun _ -> True)) =
+  normalize_term_spec (FStar.List.Tot.length l);
+  l
+
+let array_index_usize (a : Type0) (n : usize) (x : array a n) (i : usize) : result a =
+  if i < length x then Return (index x i)
+  else Fail Failure
+
+let array_update_usize (a : Type0) (n : usize) (x : array a n) (i : usize) (nx : a) : result (array a n) =
+  if i < length x then Return (list_update x i nx)
+  else Fail Failure
+
+(*** Slice *)
+type slice (a : Type0) = s:list a{length s <= usize_max}
+
+let slice_len (a : Type0) (s : slice a) : usize = length s
+
+let slice_index_usize (a : Type0) (x : slice a) (i : usize) : result a =
+  if i < length x then Return (index x i)
+  else Fail Failure
+
+let slice_update_usize (a : Type0) (x : slice a) (i : usize) (nx : a) : result (slice a) =
+  if i < length x then Return (list_update x i nx)
+  else Fail Failure
+
+(*** Subslices *)
+
+let array_to_slice (a : Type0) (n : usize) (x : array a n) : result (slice a) = Return x
+let array_from_slice (a : Type0) (n : usize) (x : array a n) (s : slice a) : result (array a n) =
+  if length s = n then Return s
+  else Fail Failure
+
+// TODO: finish the definitions below (there lacks [List.drop] and [List.take] in the standard library *)
+let array_subslice (a : Type0) (n : usize) (x : array a n) (r : core_ops_range_Range usize) : result (slice a) =
+  admit()
+
+let array_update_subslice (a : Type0) (n : usize) (x : array a n) (r : core_ops_range_Range usize) (ns : slice a) : result (array a n) =
+  admit()
+
+let array_repeat (a : Type0) (n : usize) (x : a) : array a n =
+  admit()
+
+let slice_subslice (a : Type0) (x : slice a) (r : core_ops_range_Range usize) : result (slice a) =
+  admit()
+
+let slice_update_subslice (a : Type0) (x : slice a) (r : core_ops_range_Range usize) (ns : slice a) : result (slice a) =
+  admit()
+
+(*** Vector *)
+type alloc_vec_Vec (a : Type0) = v:list a{length v <= usize_max}
+
+let alloc_vec_Vec_new (a  : Type0) : alloc_vec_Vec a = assert_norm(length #a [] == 0); []
+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) : 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) =
+  if i < length v then Return (list_update v i x) else Fail Failure
+
+// The **forward** function shouldn't be used
+let alloc_vec_Vec_push_fwd (a  : Type0) (v : alloc_vec_Vec a) (x : a) : unit = ()
+let alloc_vec_Vec_push (a  : Type0) (v : alloc_vec_Vec a) (x : a) :
+  Pure (result (alloc_vec_Vec a))
+  (requires True)
+  (ensures (fun res ->
+    match res with
+    | Fail e -> e == Failure
+    | Return v' -> length v' = length v + 1)) =
+  if length v < usize_max then begin
+    (**) assert_norm(length [x] == 1);
+    (**) append_length v [x];
+    (**) assert(length (append v [x]) = length v + 1);
+    Return (append v [x])
+    end
+  else Fail Failure
+
+// The **forward** function shouldn't be used
+let alloc_vec_Vec_insert_fwd (a : Type0) (v : alloc_vec_Vec a) (i : usize) (x : a) : result unit =
+  if i < length v then Return () else Fail Failure
+let alloc_vec_Vec_insert (a : Type0) (v : alloc_vec_Vec a) (i : usize) (x : a) : result (alloc_vec_Vec a) =
+  if i < length v then Return (list_update v i x) else Fail Failure
+
+// Trait declaration: [core::slice::index::private_slice_index::Sealed]
+type core_slice_index_private_slice_index_Sealed (self : Type0) = unit
+
+// Trait declaration: [core::slice::index::SliceIndex]
+noeq type core_slice_index_SliceIndex (self t : Type0) = {
+  sealedInst : core_slice_index_private_slice_index_Sealed self;
+  output : Type0;
+  get : self → t → result (option output);
+  get_mut : self → t → result (option output);
+  get_mut_back : self → t → option output → result t;
+  get_unchecked : self → const_raw_ptr t → result (const_raw_ptr output);
+  get_unchecked_mut : self → mut_raw_ptr t → result (mut_raw_ptr output);
+  index : self → t → result output;
+  index_mut : self → t → result output;
+  index_mut_back : self → t → output → result t;
+}
+
+// [core::slice::index::[T]::index]: forward function
+let core_slice_index_Slice_index
+  (t idx : Type0) (inst : core_slice_index_SliceIndex idx (slice t))
+  (s : slice t) (i : idx) : result inst.output =
+  let* x = inst.get i s in
+  match x with
+  | None -> Fail Failure
+  | Some x -> Return x
+
+// [core::slice::index::Range:::get]: forward function
+let core_slice_index_RangeUsize_get (t : Type0) (i : core_ops_range_Range usize) (s : slice t) :
+  result (option (slice t)) =
+  admit () // TODO
+
+// [core::slice::index::Range::get_mut]: forward function
+let core_slice_index_RangeUsize_get_mut
+  (t : Type0) : core_ops_range_Range usize → slice t → result (option (slice t)) =
+  admit () // TODO
+
+// [core::slice::index::Range::get_mut]: backward function 0
+let core_slice_index_RangeUsize_get_mut_back
+  (t : Type0) :
+  core_ops_range_Range usize → slice t → option (slice t) → result (slice t) =
+  admit () // TODO
+
+// [core::slice::index::Range::get_unchecked]: forward function
+let core_slice_index_RangeUsize_get_unchecked
+  (t : Type0) :
+  core_ops_range_Range usize → const_raw_ptr (slice t) → result (const_raw_ptr (slice t)) =
+  // Don't know what the model should be - for now we always fail to make
+  // sure code which uses it fails
+  fun _ _ -> Fail Failure
+
+// [core::slice::index::Range::get_unchecked_mut]: forward function
+let core_slice_index_RangeUsize_get_unchecked_mut
+  (t : Type0) :
+  core_ops_range_Range usize → mut_raw_ptr (slice t) → result (mut_raw_ptr (slice t)) =
+  // Don't know what the model should be - for now we always fail to make
+  // sure code which uses it fails
+  fun _ _ -> Fail Failure
+
+// [core::slice::index::Range::index]: forward function
+let core_slice_index_RangeUsize_index
+  (t : Type0) : core_ops_range_Range usize → slice t → result (slice t) =
+  admit () // TODO
+
+// [core::slice::index::Range::index_mut]: forward function
+let core_slice_index_RangeUsize_index_mut
+  (t : Type0) : core_ops_range_Range usize → slice t → result (slice t) =
+  admit () // TODO
+
+// [core::slice::index::Range::index_mut]: backward function 0
+let core_slice_index_RangeUsize_index_mut_back
+  (t : Type0) : core_ops_range_Range usize → slice t → slice t → result (slice t) =
+  admit () // TODO
+
+// [core::slice::index::[T]::index_mut]: forward function
+let core_slice_index_Slice_index_mut
+  (t idx : Type0) (inst : core_slice_index_SliceIndex idx (slice t)) :
+  slice t → idx → result inst.output =
+  admit () // 
+
+// [core::slice::index::[T]::index_mut]: backward function 0
+let core_slice_index_Slice_index_mut_back
+  (t idx : Type0) (inst : core_slice_index_SliceIndex idx (slice t)) :
+  slice t → idx → inst.output → result (slice t) =
+  admit () // TODO
+
+// [core::array::[T; N]::index]: forward function
+let core_array_Array_index
+  (t idx : Type0) (n : usize) (inst : core_ops_index_Index (slice t) idx)
+  (a : array t n) (i : idx) : result inst.output =
+  admit () // TODO
+
+// [core::array::[T; N]::index_mut]: forward function
+let core_array_Array_index_mut
+  (t idx : Type0) (n : usize) (inst : core_ops_index_IndexMut (slice t) idx)
+  (a : array t n) (i : idx) : result inst.indexInst.output =
+  admit () // TODO
+
+// [core::array::[T; N]::index_mut]: backward function 0
+let core_array_Array_index_mut_back
+  (t idx : Type0) (n : usize) (inst : core_ops_index_IndexMut (slice t) idx)
+  (a : array t n) (i : idx) (x : inst.indexInst.output) : result (array t n) =
+  admit () // TODO
+
+// Trait implementation: [core::slice::index::private_slice_index::Range]
+let core_slice_index_private_slice_index_SealedRangeUsizeInst
+  : core_slice_index_private_slice_index_Sealed (core_ops_range_Range usize) = ()
+
+// Trait implementation: [core::slice::index::Range]
+let core_slice_index_SliceIndexRangeUsizeSliceTInst (t : Type0) :
+  core_slice_index_SliceIndex (core_ops_range_Range usize) (slice t) = {
+  sealedInst = core_slice_index_private_slice_index_SealedRangeUsizeInst;
+  output = slice t;
+  get = core_slice_index_RangeUsize_get t;
+  get_mut = core_slice_index_RangeUsize_get_mut t;
+  get_mut_back = core_slice_index_RangeUsize_get_mut_back t;
+  get_unchecked = core_slice_index_RangeUsize_get_unchecked t;
+  get_unchecked_mut = core_slice_index_RangeUsize_get_unchecked_mut t;
+  index = core_slice_index_RangeUsize_index t;
+  index_mut = core_slice_index_RangeUsize_index_mut t;
+  index_mut_back = core_slice_index_RangeUsize_index_mut_back t;
+}
+
+// Trait implementation: [core::slice::index::[T]]
+let core_ops_index_IndexSliceTIInst (t idx : Type0)
+  (inst : core_slice_index_SliceIndex idx (slice t)) :
+  core_ops_index_Index (slice t) idx = {
+  output = inst.output;
+  index = core_slice_index_Slice_index t idx inst;
+}
+
+// Trait implementation: [core::slice::index::[T]]
+let core_ops_index_IndexMutSliceTIInst (t idx : Type0)
+  (inst : core_slice_index_SliceIndex idx (slice t)) :
+  core_ops_index_IndexMut (slice t) idx = {
+  indexInst = core_ops_index_IndexSliceTIInst t idx inst;
+  index_mut = core_slice_index_Slice_index_mut t idx inst;
+  index_mut_back = core_slice_index_Slice_index_mut_back t idx inst;
+}
+
+// Trait implementation: [core::array::[T; N]]
+let core_ops_index_IndexArrayInst (t idx : Type0) (n : usize)
+  (inst : core_ops_index_Index (slice t) idx) :
+  core_ops_index_Index (array t n) idx = {
+  output = inst.output;
+  index = core_array_Array_index t idx n inst;
+}
+
+// Trait implementation: [core::array::[T; N]]
+let core_ops_index_IndexMutArrayIInst (t idx : Type0) (n : usize)
+  (inst : core_ops_index_IndexMut (slice t) idx) :
+  core_ops_index_IndexMut (array t n) idx = {
+  indexInst = core_ops_index_IndexArrayInst t idx n inst.indexInst;
+  index_mut = core_array_Array_index_mut t idx n inst;
+  index_mut_back = core_array_Array_index_mut_back t idx n inst;
+}
+
+// [core::slice::index::usize::get]: forward function
+let core_slice_index_usize_get
+  (t : Type0) : usize → slice t → result (option t) =
+  admit () // TODO
+
+// [core::slice::index::usize::get_mut]: forward function
+let core_slice_index_usize_get_mut
+  (t : Type0) : usize → slice t → result (option t) =
+  admit () // TODO
+
+// [core::slice::index::usize::get_mut]: backward function 0
+let core_slice_index_usize_get_mut_back
+  (t : Type0) : usize → slice t → option t → result (slice t) =
+  admit () // TODO
+
+// [core::slice::index::usize::get_unchecked]: forward function
+let core_slice_index_usize_get_unchecked
+  (t : Type0) : usize → const_raw_ptr (slice t) → result (const_raw_ptr t) =
+  admit () // TODO
+
+// [core::slice::index::usize::get_unchecked_mut]: forward function
+let core_slice_index_usize_get_unchecked_mut
+  (t : Type0) : usize → mut_raw_ptr (slice t) → result (mut_raw_ptr t) =
+  admit () // TODO
+
+// [core::slice::index::usize::index]: forward function
+let core_slice_index_usize_index (t : Type0) : usize → slice t → result t =
+  admit () // TODO
+
+// [core::slice::index::usize::index_mut]: forward function
+let core_slice_index_usize_index_mut (t : Type0) : usize → slice t → result t =
+  admit () // TODO
+
+// [core::slice::index::usize::index_mut]: backward function 0
+let core_slice_index_usize_index_mut_back
+  (t : Type0) : usize → slice t → t → result (slice t) =
+  admit () // TODO
+
+// Trait implementation: [core::slice::index::private_slice_index::usize]
+let core_slice_index_private_slice_index_SealedUsizeInst
+  : core_slice_index_private_slice_index_Sealed usize = ()
+
+// Trait implementation: [core::slice::index::usize]
+let core_slice_index_SliceIndexUsizeSliceTInst (t : Type0) :
+  core_slice_index_SliceIndex usize (slice t) = {
+  sealedInst = core_slice_index_private_slice_index_SealedUsizeInst;
+  output = t;
+  get = core_slice_index_usize_get t;
+  get_mut = core_slice_index_usize_get_mut t;
+  get_mut_back = core_slice_index_usize_get_mut_back t;
+  get_unchecked = core_slice_index_usize_get_unchecked t;
+  get_unchecked_mut = core_slice_index_usize_get_unchecked_mut t;
+  index = core_slice_index_usize_index t;
+  index_mut = core_slice_index_usize_index_mut t;
+  index_mut_back = core_slice_index_usize_index_mut_back t;
+}
+
+// [alloc::vec::Vec::index]: forward function
+let alloc_vec_Vec_index (t idx : Type0) (inst : core_slice_index_SliceIndex idx (slice t))
+  (self : alloc_vec_Vec t) (i : idx) : result inst.output =
+  admit () // TODO
+
+// [alloc::vec::Vec::index_mut]: forward function
+let alloc_vec_Vec_index_mut (t idx : Type0) (inst : core_slice_index_SliceIndex idx (slice t))
+  (self : alloc_vec_Vec t) (i : idx) : result inst.output =
+  admit () // TODO
+
+// [alloc::vec::Vec::index_mut]: backward function 0
+let alloc_vec_Vec_index_mut_back
+  (t idx : Type0) (inst : core_slice_index_SliceIndex idx (slice t))
+  (self : alloc_vec_Vec t) (i : idx) (x : inst.output) : result (alloc_vec_Vec t) =
+  admit () // TODO
+
+// Trait implementation: [alloc::vec::Vec]
+let alloc_vec_Vec_coreopsindexIndexInst (t idx : Type0)
+  (inst : core_slice_index_SliceIndex idx (slice t)) :
+  core_ops_index_Index (alloc_vec_Vec t) idx = {
+  output = inst.output;
+  index = alloc_vec_Vec_index t idx inst;
+}
+
+// Trait implementation: [alloc::vec::Vec]
+let alloc_vec_Vec_coreopsindexIndexMutInst (t idx : Type0)
+  (inst : core_slice_index_SliceIndex idx (slice t)) :
+  core_ops_index_IndexMut (alloc_vec_Vec t) idx = {
+  indexInst = alloc_vec_Vec_coreopsindexIndexInst t idx inst;
+  index_mut = alloc_vec_Vec_index_mut t idx inst;
+  index_mut_back = alloc_vec_Vec_index_mut_back t idx inst;
+}
+
+(*** Theorems *)
+
+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_SliceIndexUsizeSliceTInst a) v i ==
+      alloc_vec_Vec_index_usize v i)
+  [SMTPat (alloc_vec_Vec_index a usize (core_slice_index_SliceIndexUsizeSliceTInst 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_SliceIndexUsizeSliceTInst a) v i ==
+      alloc_vec_Vec_index_usize v i)
+  [SMTPat (alloc_vec_Vec_index_mut a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i)]
+  =
+  admit()
+
+let alloc_vec_Vec_index_mut_back_eq (#a : Type0) (v : alloc_vec_Vec a) (i : usize) (x : a) :
+  Lemma (
+    alloc_vec_Vec_index_mut_back a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i x ==
+      alloc_vec_Vec_update_usize v i x)
+  [SMTPat (alloc_vec_Vec_index_mut_back a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i x)]
+  =
+  admit()