Merge pull request #206 from AeneasVerif/subdir

9 files changed, 1724 insertions, 0 deletions

diff --git a/tests/coq/hashmap_main/HashmapMain_Funs.v b/tests/coq/hashmap_main/HashmapMain_Funs.v
new file mode 100644
index 00000000..f6467d5a
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+++ b/tests/coq/hashmap_main/HashmapMain_Funs.v
@@ -0,0 +1,589 @@
+(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
+(** [hashmap_main]: function definitions *)
+Require Import Primitives.
+Import Primitives.
+Require Import Coq.ZArith.ZArith.
+Require Import List.
+Import ListNotations.
+Local Open Scope Primitives_scope.
+Require Import HashmapMain_Types.
+Include HashmapMain_Types.
+Require Import HashmapMain_FunsExternal.
+Include HashmapMain_FunsExternal.
+Module HashmapMain_Funs.
+
+(** [hashmap_main::hashmap::hash_key]:
+    Source: 'tests/src/hashmap.rs', lines 35:0-35:32 *)
+Definition hashmap_hash_key (k : usize) : result usize :=
+  Ok k.
+
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::allocate_slots]: loop 0:
+    Source: 'tests/src/hashmap.rs', lines 58:4-64:5 *)
+Fixpoint hashmap_HashMap_allocate_slots_loop
+  (T : Type) (n : nat) (slots : alloc_vec_Vec (hashmap_List_t T)) (n1 : usize)
+  :
+  result (alloc_vec_Vec (hashmap_List_t T))
+  :=
+  match n with
+  | O => Fail_ OutOfFuel
+  | S n2 =>
+    if n1 s> 0%usize
+    then (
+      slots1 <- alloc_vec_Vec_push (hashmap_List_t T) slots Hashmap_List_Nil;
+      n3 <- usize_sub n1 1%usize;
+      hashmap_HashMap_allocate_slots_loop T n2 slots1 n3)
+    else Ok slots
+  end
+.
+
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::allocate_slots]:
+    Source: 'tests/src/hashmap.rs', lines 58:4-58:76 *)
+Definition hashmap_HashMap_allocate_slots
+  (T : Type) (n : nat) (slots : alloc_vec_Vec (hashmap_List_t T)) (n1 : usize)
+  :
+  result (alloc_vec_Vec (hashmap_List_t T))
+  :=
+  hashmap_HashMap_allocate_slots_loop T n slots n1
+.
+
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::new_with_capacity]:
+    Source: 'tests/src/hashmap.rs', lines 67:4-71:13 *)
+Definition hashmap_HashMap_new_with_capacity
+  (T : Type) (n : nat) (capacity : usize) (max_load_dividend : usize)
+  (max_load_divisor : usize) :
+  result (hashmap_HashMap_t T)
+  :=
+  slots <-
+    hashmap_HashMap_allocate_slots T n (alloc_vec_Vec_new (hashmap_List_t T))
+      capacity;
+  i <- usize_mul capacity max_load_dividend;
+  i1 <- usize_div i max_load_divisor;
+  Ok
+    {|
+      hashmap_HashMap_num_entries := 0%usize;
+      hashmap_HashMap_max_load_factor := (max_load_dividend, max_load_divisor);
+      hashmap_HashMap_max_load := i1;
+      hashmap_HashMap_slots := slots
+    |}
+.
+
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::new]:
+    Source: 'tests/src/hashmap.rs', lines 83:4-83:24 *)
+Definition hashmap_HashMap_new
+  (T : Type) (n : nat) : result (hashmap_HashMap_t T) :=
+  hashmap_HashMap_new_with_capacity T n 32%usize 4%usize 5%usize
+.
+
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::clear]: loop 0:
+    Source: 'tests/src/hashmap.rs', lines 88:4-96:5 *)
+Fixpoint hashmap_HashMap_clear_loop
+  (T : Type) (n : nat) (slots : alloc_vec_Vec (hashmap_List_t T)) (i : usize) :
+  result (alloc_vec_Vec (hashmap_List_t T))
+  :=
+  match n with
+  | O => Fail_ OutOfFuel
+  | S n1 =>
+    let i1 := alloc_vec_Vec_len (hashmap_List_t T) slots in
+    if i s< i1
+    then (
+      p <-
+        alloc_vec_Vec_index_mut (hashmap_List_t T) usize
+          (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t T)) slots
+          i;
+      let (_, index_mut_back) := p in
+      i2 <- usize_add i 1%usize;
+      slots1 <- index_mut_back Hashmap_List_Nil;
+      hashmap_HashMap_clear_loop T n1 slots1 i2)
+    else Ok slots
+  end
+.
+
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::clear]:
+    Source: 'tests/src/hashmap.rs', lines 88:4-88:27 *)
+Definition hashmap_HashMap_clear
+  (T : Type) (n : nat) (self : hashmap_HashMap_t T) :
+  result (hashmap_HashMap_t T)
+  :=
+  hm <- hashmap_HashMap_clear_loop T n self.(hashmap_HashMap_slots) 0%usize;
+  Ok
+    {|
+      hashmap_HashMap_num_entries := 0%usize;
+      hashmap_HashMap_max_load_factor := self.(hashmap_HashMap_max_load_factor);
+      hashmap_HashMap_max_load := self.(hashmap_HashMap_max_load);
+      hashmap_HashMap_slots := hm
+    |}
+.
+
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::len]:
+    Source: 'tests/src/hashmap.rs', lines 98:4-98:30 *)
+Definition hashmap_HashMap_len
+  (T : Type) (self : hashmap_HashMap_t T) : result usize :=
+  Ok self.(hashmap_HashMap_num_entries)
+.
+
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::insert_in_list]: loop 0:
+    Source: 'tests/src/hashmap.rs', lines 105:4-122:5 *)
+Fixpoint hashmap_HashMap_insert_in_list_loop
+  (T : Type) (n : nat) (key : usize) (value : T) (ls : hashmap_List_t T) :
+  result (bool * (hashmap_List_t T))
+  :=
+  match n with
+  | O => Fail_ OutOfFuel
+  | S n1 =>
+    match ls with
+    | Hashmap_List_Cons ckey cvalue tl =>
+      if ckey s= key
+      then Ok (false, Hashmap_List_Cons ckey value tl)
+      else (
+        p <- hashmap_HashMap_insert_in_list_loop T n1 key value tl;
+        let (b, tl1) := p in
+        Ok (b, Hashmap_List_Cons ckey cvalue tl1))
+    | Hashmap_List_Nil =>
+      Ok (true, Hashmap_List_Cons key value Hashmap_List_Nil)
+    end
+  end
+.
+
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::insert_in_list]:
+    Source: 'tests/src/hashmap.rs', lines 105:4-105:71 *)
+Definition hashmap_HashMap_insert_in_list
+  (T : Type) (n : nat) (key : usize) (value : T) (ls : hashmap_List_t T) :
+  result (bool * (hashmap_List_t T))
+  :=
+  hashmap_HashMap_insert_in_list_loop T n key value ls
+.
+
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::insert_no_resize]:
+    Source: 'tests/src/hashmap.rs', lines 125:4-125:54 *)
+Definition hashmap_HashMap_insert_no_resize
+  (T : Type) (n : nat) (self : hashmap_HashMap_t T) (key : usize) (value : T) :
+  result (hashmap_HashMap_t T)
+  :=
+  hash <- hashmap_hash_key key;
+  let i := alloc_vec_Vec_len (hashmap_List_t T) self.(hashmap_HashMap_slots) in
+  hash_mod <- usize_rem hash i;
+  p <-
+    alloc_vec_Vec_index_mut (hashmap_List_t T) usize
+      (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t T))
+      self.(hashmap_HashMap_slots) hash_mod;
+  let (l, index_mut_back) := p in
+  p1 <- hashmap_HashMap_insert_in_list T n key value l;
+  let (inserted, l1) := p1 in
+  if inserted
+  then (
+    i1 <- usize_add self.(hashmap_HashMap_num_entries) 1%usize;
+    v <- index_mut_back l1;
+    Ok
+      {|
+        hashmap_HashMap_num_entries := i1;
+        hashmap_HashMap_max_load_factor :=
+          self.(hashmap_HashMap_max_load_factor);
+        hashmap_HashMap_max_load := self.(hashmap_HashMap_max_load);
+        hashmap_HashMap_slots := v
+      |})
+  else (
+    v <- index_mut_back l1;
+    Ok
+      {|
+        hashmap_HashMap_num_entries := self.(hashmap_HashMap_num_entries);
+        hashmap_HashMap_max_load_factor :=
+          self.(hashmap_HashMap_max_load_factor);
+        hashmap_HashMap_max_load := self.(hashmap_HashMap_max_load);
+        hashmap_HashMap_slots := v
+      |})
+.
+
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::move_elements_from_list]: loop 0:
+    Source: 'tests/src/hashmap.rs', lines 191:4-204:5 *)
+Fixpoint hashmap_HashMap_move_elements_from_list_loop
+  (T : Type) (n : nat) (ntable : hashmap_HashMap_t T) (ls : hashmap_List_t T) :
+  result (hashmap_HashMap_t T)
+  :=
+  match n with
+  | O => Fail_ OutOfFuel
+  | S n1 =>
+    match ls with
+    | Hashmap_List_Cons k v tl =>
+      ntable1 <- hashmap_HashMap_insert_no_resize T n1 ntable k v;
+      hashmap_HashMap_move_elements_from_list_loop T n1 ntable1 tl
+    | Hashmap_List_Nil => Ok ntable
+    end
+  end
+.
+
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::move_elements_from_list]:
+    Source: 'tests/src/hashmap.rs', lines 191:4-191:72 *)
+Definition hashmap_HashMap_move_elements_from_list
+  (T : Type) (n : nat) (ntable : hashmap_HashMap_t T) (ls : hashmap_List_t T) :
+  result (hashmap_HashMap_t T)
+  :=
+  hashmap_HashMap_move_elements_from_list_loop T n ntable ls
+.
+
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::move_elements]: loop 0:
+    Source: 'tests/src/hashmap.rs', lines 179:4-188:5 *)
+Fixpoint hashmap_HashMap_move_elements_loop
+  (T : Type) (n : nat) (ntable : hashmap_HashMap_t T)
+  (slots : alloc_vec_Vec (hashmap_List_t T)) (i : usize) :
+  result ((hashmap_HashMap_t T) * (alloc_vec_Vec (hashmap_List_t T)))
+  :=
+  match n with
+  | O => Fail_ OutOfFuel
+  | S n1 =>
+    let i1 := alloc_vec_Vec_len (hashmap_List_t T) slots in
+    if i s< i1
+    then (
+      p <-
+        alloc_vec_Vec_index_mut (hashmap_List_t T) usize
+          (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t T)) slots
+          i;
+      let (l, index_mut_back) := p in
+      let (ls, l1) := core_mem_replace (hashmap_List_t T) l Hashmap_List_Nil in
+      ntable1 <- hashmap_HashMap_move_elements_from_list T n1 ntable ls;
+      i2 <- usize_add i 1%usize;
+      slots1 <- index_mut_back l1;
+      hashmap_HashMap_move_elements_loop T n1 ntable1 slots1 i2)
+    else Ok (ntable, slots)
+  end
+.
+
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::move_elements]:
+    Source: 'tests/src/hashmap.rs', lines 179:4-179:95 *)
+Definition hashmap_HashMap_move_elements
+  (T : Type) (n : nat) (ntable : hashmap_HashMap_t T)
+  (slots : alloc_vec_Vec (hashmap_List_t T)) (i : usize) :
+  result ((hashmap_HashMap_t T) * (alloc_vec_Vec (hashmap_List_t T)))
+  :=
+  hashmap_HashMap_move_elements_loop T n ntable slots i
+.
+
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::try_resize]:
+    Source: 'tests/src/hashmap.rs', lines 148:4-148:28 *)
+Definition hashmap_HashMap_try_resize
+  (T : Type) (n : nat) (self : hashmap_HashMap_t T) :
+  result (hashmap_HashMap_t T)
+  :=
+  max_usize <- scalar_cast U32 Usize core_u32_max;
+  let capacity :=
+    alloc_vec_Vec_len (hashmap_List_t T) self.(hashmap_HashMap_slots) in
+  n1 <- usize_div max_usize 2%usize;
+  let (i, i1) := self.(hashmap_HashMap_max_load_factor) in
+  i2 <- usize_div n1 i;
+  if capacity s<= i2
+  then (
+    i3 <- usize_mul capacity 2%usize;
+    ntable <- hashmap_HashMap_new_with_capacity T n i3 i i1;
+    p <-
+      hashmap_HashMap_move_elements T n ntable self.(hashmap_HashMap_slots)
+        0%usize;
+    let (ntable1, _) := p in
+    Ok
+      {|
+        hashmap_HashMap_num_entries := self.(hashmap_HashMap_num_entries);
+        hashmap_HashMap_max_load_factor := (i, i1);
+        hashmap_HashMap_max_load := ntable1.(hashmap_HashMap_max_load);
+        hashmap_HashMap_slots := ntable1.(hashmap_HashMap_slots)
+      |})
+  else
+    Ok
+      {|
+        hashmap_HashMap_num_entries := self.(hashmap_HashMap_num_entries);
+        hashmap_HashMap_max_load_factor := (i, i1);
+        hashmap_HashMap_max_load := self.(hashmap_HashMap_max_load);
+        hashmap_HashMap_slots := self.(hashmap_HashMap_slots)
+      |}
+.
+
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::insert]:
+    Source: 'tests/src/hashmap.rs', lines 137:4-137:48 *)
+Definition hashmap_HashMap_insert
+  (T : Type) (n : nat) (self : hashmap_HashMap_t T) (key : usize) (value : T) :
+  result (hashmap_HashMap_t T)
+  :=
+  self1 <- hashmap_HashMap_insert_no_resize T n self key value;
+  i <- hashmap_HashMap_len T self1;
+  if i s> self1.(hashmap_HashMap_max_load)
+  then hashmap_HashMap_try_resize T n self1
+  else Ok self1
+.
+
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::contains_key_in_list]: loop 0:
+    Source: 'tests/src/hashmap.rs', lines 214:4-227:5 *)
+Fixpoint hashmap_HashMap_contains_key_in_list_loop
+  (T : Type) (n : nat) (key : usize) (ls : hashmap_List_t T) : result bool :=
+  match n with
+  | O => Fail_ OutOfFuel
+  | S n1 =>
+    match ls with
+    | Hashmap_List_Cons ckey _ tl =>
+      if ckey s= key
+      then Ok true
+      else hashmap_HashMap_contains_key_in_list_loop T n1 key tl
+    | Hashmap_List_Nil => Ok false
+    end
+  end
+.
+
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::contains_key_in_list]:
+    Source: 'tests/src/hashmap.rs', lines 214:4-214:68 *)
+Definition hashmap_HashMap_contains_key_in_list
+  (T : Type) (n : nat) (key : usize) (ls : hashmap_List_t T) : result bool :=
+  hashmap_HashMap_contains_key_in_list_loop T n key ls
+.
+
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::contains_key]:
+    Source: 'tests/src/hashmap.rs', lines 207:4-207:49 *)
+Definition hashmap_HashMap_contains_key
+  (T : Type) (n : nat) (self : hashmap_HashMap_t T) (key : usize) :
+  result bool
+  :=
+  hash <- hashmap_hash_key key;
+  let i := alloc_vec_Vec_len (hashmap_List_t T) self.(hashmap_HashMap_slots) in
+  hash_mod <- usize_rem hash i;
+  l <-
+    alloc_vec_Vec_index (hashmap_List_t T) usize
+      (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t T))
+      self.(hashmap_HashMap_slots) hash_mod;
+  hashmap_HashMap_contains_key_in_list T n key l
+.
+
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_in_list]: loop 0:
+    Source: 'tests/src/hashmap.rs', lines 232:4-245:5 *)
+Fixpoint hashmap_HashMap_get_in_list_loop
+  (T : Type) (n : nat) (key : usize) (ls : hashmap_List_t T) : result T :=
+  match n with
+  | O => Fail_ OutOfFuel
+  | S n1 =>
+    match ls with
+    | Hashmap_List_Cons ckey cvalue tl =>
+      if ckey s= key
+      then Ok cvalue
+      else hashmap_HashMap_get_in_list_loop T n1 key tl
+    | Hashmap_List_Nil => Fail_ Failure
+    end
+  end
+.
+
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_in_list]:
+    Source: 'tests/src/hashmap.rs', lines 232:4-232:70 *)
+Definition hashmap_HashMap_get_in_list
+  (T : Type) (n : nat) (key : usize) (ls : hashmap_List_t T) : result T :=
+  hashmap_HashMap_get_in_list_loop T n key ls
+.
+
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get]:
+    Source: 'tests/src/hashmap.rs', lines 247:4-247:55 *)
+Definition hashmap_HashMap_get
+  (T : Type) (n : nat) (self : hashmap_HashMap_t T) (key : usize) : result T :=
+  hash <- hashmap_hash_key key;
+  let i := alloc_vec_Vec_len (hashmap_List_t T) self.(hashmap_HashMap_slots) in
+  hash_mod <- usize_rem hash i;
+  l <-
+    alloc_vec_Vec_index (hashmap_List_t T) usize
+      (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t T))
+      self.(hashmap_HashMap_slots) hash_mod;
+  hashmap_HashMap_get_in_list T n key l
+.
+
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_mut_in_list]: loop 0:
+    Source: 'tests/src/hashmap.rs', lines 253:4-262:5 *)
+Fixpoint hashmap_HashMap_get_mut_in_list_loop
+  (T : Type) (n : nat) (ls : hashmap_List_t T) (key : usize) :
+  result (T * (T -> result (hashmap_List_t T)))
+  :=
+  match n with
+  | O => Fail_ OutOfFuel
+  | S n1 =>
+    match ls with
+    | Hashmap_List_Cons ckey cvalue tl =>
+      if ckey s= key
+      then
+        let back := fun (ret : T) => Ok (Hashmap_List_Cons ckey ret tl) in
+        Ok (cvalue, back)
+      else (
+        p <- hashmap_HashMap_get_mut_in_list_loop T n1 tl key;
+        let (t, back) := p in
+        let back1 :=
+          fun (ret : T) =>
+            tl1 <- back ret; Ok (Hashmap_List_Cons ckey cvalue tl1) in
+        Ok (t, back1))
+    | Hashmap_List_Nil => Fail_ Failure
+    end
+  end
+.
+
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_mut_in_list]:
+    Source: 'tests/src/hashmap.rs', lines 253:4-253:86 *)
+Definition hashmap_HashMap_get_mut_in_list
+  (T : Type) (n : nat) (ls : hashmap_List_t T) (key : usize) :
+  result (T * (T -> result (hashmap_List_t T)))
+  :=
+  hashmap_HashMap_get_mut_in_list_loop T n ls key
+.
+
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_mut]:
+    Source: 'tests/src/hashmap.rs', lines 265:4-265:67 *)
+Definition hashmap_HashMap_get_mut
+  (T : Type) (n : nat) (self : hashmap_HashMap_t T) (key : usize) :
+  result (T * (T -> result (hashmap_HashMap_t T)))
+  :=
+  hash <- hashmap_hash_key key;
+  let i := alloc_vec_Vec_len (hashmap_List_t T) self.(hashmap_HashMap_slots) in
+  hash_mod <- usize_rem hash i;
+  p <-
+    alloc_vec_Vec_index_mut (hashmap_List_t T) usize
+      (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t T))
+      self.(hashmap_HashMap_slots) hash_mod;
+  let (l, index_mut_back) := p in
+  p1 <- hashmap_HashMap_get_mut_in_list T n l key;
+  let (t, get_mut_in_list_back) := p1 in
+  let back :=
+    fun (ret : T) =>
+      l1 <- get_mut_in_list_back ret;
+      v <- index_mut_back l1;
+      Ok
+        {|
+          hashmap_HashMap_num_entries := self.(hashmap_HashMap_num_entries);
+          hashmap_HashMap_max_load_factor :=
+            self.(hashmap_HashMap_max_load_factor);
+          hashmap_HashMap_max_load := self.(hashmap_HashMap_max_load);
+          hashmap_HashMap_slots := v
+        |} in
+  Ok (t, back)
+.
+
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::remove_from_list]: loop 0:
+    Source: 'tests/src/hashmap.rs', lines 273:4-299:5 *)
+Fixpoint hashmap_HashMap_remove_from_list_loop
+  (T : Type) (n : nat) (key : usize) (ls : hashmap_List_t T) :
+  result ((option T) * (hashmap_List_t T))
+  :=
+  match n with
+  | O => Fail_ OutOfFuel
+  | S n1 =>
+    match ls with
+    | Hashmap_List_Cons ckey t tl =>
+      if ckey s= key
+      then
+        let (mv_ls, _) :=
+          core_mem_replace (hashmap_List_t T) (Hashmap_List_Cons ckey t tl)
+            Hashmap_List_Nil in
+        match mv_ls with
+        | Hashmap_List_Cons _ cvalue tl1 => Ok (Some cvalue, tl1)
+        | Hashmap_List_Nil => Fail_ Failure
+        end
+      else (
+        p <- hashmap_HashMap_remove_from_list_loop T n1 key tl;
+        let (o, tl1) := p in
+        Ok (o, Hashmap_List_Cons ckey t tl1))
+    | Hashmap_List_Nil => Ok (None, Hashmap_List_Nil)
+    end
+  end
+.
+
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::remove_from_list]:
+    Source: 'tests/src/hashmap.rs', lines 273:4-273:69 *)
+Definition hashmap_HashMap_remove_from_list
+  (T : Type) (n : nat) (key : usize) (ls : hashmap_List_t T) :
+  result ((option T) * (hashmap_List_t T))
+  :=
+  hashmap_HashMap_remove_from_list_loop T n key ls
+.
+
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::remove]:
+    Source: 'tests/src/hashmap.rs', lines 302:4-302:52 *)
+Definition hashmap_HashMap_remove
+  (T : Type) (n : nat) (self : hashmap_HashMap_t T) (key : usize) :
+  result ((option T) * (hashmap_HashMap_t T))
+  :=
+  hash <- hashmap_hash_key key;
+  let i := alloc_vec_Vec_len (hashmap_List_t T) self.(hashmap_HashMap_slots) in
+  hash_mod <- usize_rem hash i;
+  p <-
+    alloc_vec_Vec_index_mut (hashmap_List_t T) usize
+      (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t T))
+      self.(hashmap_HashMap_slots) hash_mod;
+  let (l, index_mut_back) := p in
+  p1 <- hashmap_HashMap_remove_from_list T n key l;
+  let (x, l1) := p1 in
+  match x with
+  | None =>
+    v <- index_mut_back l1;
+    Ok (None,
+      {|
+        hashmap_HashMap_num_entries := self.(hashmap_HashMap_num_entries);
+        hashmap_HashMap_max_load_factor :=
+          self.(hashmap_HashMap_max_load_factor);
+        hashmap_HashMap_max_load := self.(hashmap_HashMap_max_load);
+        hashmap_HashMap_slots := v
+      |})
+  | Some x1 =>
+    i1 <- usize_sub self.(hashmap_HashMap_num_entries) 1%usize;
+    v <- index_mut_back l1;
+    Ok (Some x1,
+      {|
+        hashmap_HashMap_num_entries := i1;
+        hashmap_HashMap_max_load_factor :=
+          self.(hashmap_HashMap_max_load_factor);
+        hashmap_HashMap_max_load := self.(hashmap_HashMap_max_load);
+        hashmap_HashMap_slots := v
+      |})
+  end
+.
+
+(** [hashmap_main::hashmap::test1]:
+    Source: 'tests/src/hashmap.rs', lines 323:0-323:10 *)
+Definition hashmap_test1 (n : nat) : result unit :=
+  hm <- hashmap_HashMap_new u64 n;
+  hm1 <- hashmap_HashMap_insert u64 n hm 0%usize 42%u64;
+  hm2 <- hashmap_HashMap_insert u64 n hm1 128%usize 18%u64;
+  hm3 <- hashmap_HashMap_insert u64 n hm2 1024%usize 138%u64;
+  hm4 <- hashmap_HashMap_insert u64 n hm3 1056%usize 256%u64;
+  i <- hashmap_HashMap_get u64 n hm4 128%usize;
+  if negb (i s= 18%u64)
+  then Fail_ Failure
+  else (
+    p <- hashmap_HashMap_get_mut u64 n hm4 1024%usize;
+    let (_, get_mut_back) := p in
+    hm5 <- get_mut_back 56%u64;
+    i1 <- hashmap_HashMap_get u64 n hm5 1024%usize;
+    if negb (i1 s= 56%u64)
+    then Fail_ Failure
+    else (
+      p1 <- hashmap_HashMap_remove u64 n hm5 1024%usize;
+      let (x, hm6) := p1 in
+      match x with
+      | None => Fail_ Failure
+      | Some x1 =>
+        if negb (x1 s= 56%u64)
+        then Fail_ Failure
+        else (
+          i2 <- hashmap_HashMap_get u64 n hm6 0%usize;
+          if negb (i2 s= 42%u64)
+          then Fail_ Failure
+          else (
+            i3 <- hashmap_HashMap_get u64 n hm6 128%usize;
+            if negb (i3 s= 18%u64)
+            then Fail_ Failure
+            else (
+              i4 <- hashmap_HashMap_get u64 n hm6 1056%usize;
+              if negb (i4 s= 256%u64) then Fail_ Failure else Ok tt)))
+      end))
+.
+
+(** [hashmap_main::insert_on_disk]:
+    Source: 'tests/src/hashmap_main.rs', lines 13:0-13:43 *)
+Definition insert_on_disk
+  (n : nat) (key : usize) (value : u64) (st : state) : result (state * unit) :=
+  p <- hashmap_utils_deserialize st;
+  let (st1, hm) := p in
+  hm1 <- hashmap_HashMap_insert u64 n hm key value;
+  hashmap_utils_serialize hm1 st1
+.
+
+(** [hashmap_main::main]:
+    Source: 'tests/src/hashmap_main.rs', lines 22:0-22:13 *)
+Definition main : result unit :=
+  Ok tt.
+
+End HashmapMain_Funs.
diff --git a/tests/coq/hashmap_main/HashmapMain_FunsExternal.v b/tests/coq/hashmap_main/HashmapMain_FunsExternal.v
new file mode 100644
index 00000000..fb5f23cd
--- /dev/null
+++ b/tests/coq/hashmap_main/HashmapMain_FunsExternal.v
@@ -0,0 +1,24 @@
+(** [hashmap_main]: external function declarations *)
+Require Import Primitives.
+Import Primitives.
+Require Import Coq.ZArith.ZArith.
+Require Import List.
+Import ListNotations.
+Local Open Scope Primitives_scope.
+Require Export HashmapMain_Types.
+Import HashmapMain_Types.
+Module HashmapMain_FunsExternal.
+
+(** [hashmap_main::hashmap_utils::deserialize]: forward function
+    Source: 'src/hashmap_utils.rs', lines 10:0-10:43 *)
+Axiom hashmap_utils_deserialize
+  : state -> result (state * (hashmap_HashMap_t u64))
+.
+
+(** [hashmap_main::hashmap_utils::serialize]: forward function
+    Source: 'src/hashmap_utils.rs', lines 5:0-5:42 *)
+Axiom hashmap_utils_serialize
+  : hashmap_HashMap_t u64 -> state -> result (state * unit)
+.
+
+End HashmapMain_FunsExternal.
diff --git a/tests/coq/hashmap_main/HashmapMain_FunsExternal_Template.v b/tests/coq/hashmap_main/HashmapMain_FunsExternal_Template.v
new file mode 100644
index 00000000..66835e8c
--- /dev/null
+++ b/tests/coq/hashmap_main/HashmapMain_FunsExternal_Template.v
@@ -0,0 +1,26 @@
+(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
+(** [hashmap_main]: external functions.
+-- This is a template file: rename it to "FunsExternal.lean" and fill the holes. *)
+Require Import Primitives.
+Import Primitives.
+Require Import Coq.ZArith.ZArith.
+Require Import List.
+Import ListNotations.
+Local Open Scope Primitives_scope.
+Require Import HashmapMain_Types.
+Include HashmapMain_Types.
+Module HashmapMain_FunsExternal_Template.
+
+(** [hashmap_main::hashmap_utils::deserialize]:
+    Source: 'tests/src/hashmap_utils.rs', lines 11:0-11:43 *)
+Axiom hashmap_utils_deserialize
+  : state -> result (state * (hashmap_HashMap_t u64))
+.
+
+(** [hashmap_main::hashmap_utils::serialize]:
+    Source: 'tests/src/hashmap_utils.rs', lines 6:0-6:42 *)
+Axiom hashmap_utils_serialize
+  : hashmap_HashMap_t u64 -> state -> result (state * unit)
+.
+
+End HashmapMain_FunsExternal_Template.
diff --git a/tests/coq/hashmap_main/HashmapMain_Types.v b/tests/coq/hashmap_main/HashmapMain_Types.v
new file mode 100644
index 00000000..5656bd9c
--- /dev/null
+++ b/tests/coq/hashmap_main/HashmapMain_Types.v
@@ -0,0 +1,40 @@
+(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
+(** [hashmap_main]: type definitions *)
+Require Import Primitives.
+Import Primitives.
+Require Import Coq.ZArith.ZArith.
+Require Import List.
+Import ListNotations.
+Local Open Scope Primitives_scope.
+Require Import HashmapMain_TypesExternal.
+Include HashmapMain_TypesExternal.
+Module HashmapMain_Types.
+
+(** [hashmap_main::hashmap::List]
+    Source: 'tests/src/hashmap.rs', lines 27:0-27:16 *)
+Inductive hashmap_List_t (T : Type) :=
+| Hashmap_List_Cons : usize -> T -> hashmap_List_t T -> hashmap_List_t T
+| Hashmap_List_Nil : hashmap_List_t T
+.
+
+Arguments Hashmap_List_Cons { _ }.
+Arguments Hashmap_List_Nil { _ }.
+
+(** [hashmap_main::hashmap::HashMap]
+    Source: 'tests/src/hashmap.rs', lines 43:0-43:21 *)
+Record hashmap_HashMap_t (T : Type) :=
+mkhashmap_HashMap_t {
+  hashmap_HashMap_num_entries : usize;
+  hashmap_HashMap_max_load_factor : (usize * usize);
+  hashmap_HashMap_max_load : usize;
+  hashmap_HashMap_slots : alloc_vec_Vec (hashmap_List_t T);
+}
+.
+
+Arguments mkhashmap_HashMap_t { _ }.
+Arguments hashmap_HashMap_num_entries { _ }.
+Arguments hashmap_HashMap_max_load_factor { _ }.
+Arguments hashmap_HashMap_max_load { _ }.
+Arguments hashmap_HashMap_slots { _ }.
+
+End HashmapMain_Types.
diff --git a/tests/coq/hashmap_main/HashmapMain_TypesExternal.v b/tests/coq/hashmap_main/HashmapMain_TypesExternal.v
new file mode 100644
index 00000000..28651c14
--- /dev/null
+++ b/tests/coq/hashmap_main/HashmapMain_TypesExternal.v
@@ -0,0 +1,14 @@
+(** [hashmap_main]: external types.
+-- This is a template file: rename it to "TypesExternal.lean" and fill the holes. *)
+Require Import Primitives.
+Import Primitives.
+Require Import Coq.ZArith.ZArith.
+Require Import List.
+Import ListNotations.
+Local Open Scope Primitives_scope.
+Module HashmapMain_TypesExternal.
+
+(** The state type used in the state-error monad *)
+Axiom state : Type.
+
+End HashmapMain_TypesExternal.
diff --git a/tests/coq/hashmap_main/HashmapMain_TypesExternal_Template.v b/tests/coq/hashmap_main/HashmapMain_TypesExternal_Template.v
new file mode 100644
index 00000000..391b2775
--- /dev/null
+++ b/tests/coq/hashmap_main/HashmapMain_TypesExternal_Template.v
@@ -0,0 +1,15 @@
+(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
+(** [hashmap_main]: external types.
+-- This is a template file: rename it to "TypesExternal.lean" and fill the holes. *)
+Require Import Primitives.
+Import Primitives.
+Require Import Coq.ZArith.ZArith.
+Require Import List.
+Import ListNotations.
+Local Open Scope Primitives_scope.
+Module HashmapMain_TypesExternal_Template.
+
+(** The state type used in the state-error monad *)
+Axiom state : Type.
+
+End HashmapMain_TypesExternal_Template.
diff --git a/tests/coq/hashmap_main/Makefile b/tests/coq/hashmap_main/Makefile
new file mode 100644
index 00000000..1a5aee4a
--- /dev/null
+++ b/tests/coq/hashmap_main/Makefile
@@ -0,0 +1,23 @@
+# This file was automatically generated - modify ../Makefile.template instead
+# Makefile originally taken from coq-club
+
+%: Makefile.coq phony
+	+make -f Makefile.coq $@
+
+all: Makefile.coq
+	+make -f Makefile.coq all
+
+clean: Makefile.coq
+	+make -f Makefile.coq clean
+	rm -f Makefile.coq
+
+Makefile.coq: _CoqProject Makefile
+	coq_makefile -f _CoqProject | sed 's/$$(COQCHK) $$(COQCHKFLAGS) $$(COQLIBS)/$$(COQCHK) $$(COQCHKFLAGS) $$(subst -Q,-R,$$(COQLIBS))/' > Makefile.coq
+
+_CoqProject: ;
+
+Makefile: ;
+
+phony: ;
+
+.PHONY: all clean phony
diff --git a/tests/coq/hashmap_main/Primitives.v b/tests/coq/hashmap_main/Primitives.v
new file mode 100644
index 00000000..b29fce43
--- /dev/null
+++ b/tests/coq/hashmap_main/Primitives.v
@@ -0,0 +1,981 @@
+Require Import Lia.
+Require Coq.Strings.Ascii.
+Require Coq.Strings.String.
+Require Import Coq.Program.Equality.
+Require Import Coq.ZArith.ZArith.
+Require Import Coq.ZArith.Znat.
+Require Import List.
+Import ListNotations.
+
+Module Primitives.
+
+  (* TODO: use more *)
+Declare Scope Primitives_scope.
+
+(*** Result *)
+
+Inductive error :=
+  | Failure
+  | OutOfFuel.
+
+Inductive result A :=
+  | Ok : A -> result A
+  | Fail_ : error -> result A.
+
+Arguments Ok {_} a.
+Arguments Fail_ {_}.
+
+Definition bind {A B} (m: result A) (f: A -> result B) : result B :=
+  match m with
+  | Fail_ e => Fail_ e
+  | Ok x => f x
+  end.
+
+Definition return_ {A: Type} (x: A) : result A := Ok x.
+Definition fail_ {A: Type} (e: error) : result A := Fail_ e.
+
+Notation "x <- c1 ; c2" := (bind c1 (fun x => c2))
+  (at level 61, c1 at next level, right associativity).
+
+(** Monadic assert *)
+Definition massert (b: bool) : result unit :=
+  if b then Ok tt else Fail_ Failure.
+
+(** Normalize and unwrap a successful result (used for globals) *)
+Definition eval_result_refl {A} {x} (a: result A) (p: a = Ok x) : A :=
+  match a as r return (r = Ok x -> A) with
+  | Ok a' => fun _  => a'
+  | Fail_ e   => fun p' =>
+      False_rect _ (eq_ind (Fail_ e)
+          (fun e : result A =>
+          match e with
+          | Ok _ => False
+          | Fail_ e => True
+          end)
+        I (Ok x) p')
+  end p.
+
+Notation "x %global" := (eval_result_refl x eq_refl) (at level 40).
+Notation "x %return" := (eval_result_refl x eq_refl) (at level 40).
+
+(* Sanity check *)
+Check (if true then Ok (1 + 2) else Fail_ Failure)%global = 3.
+
+(*** Misc *)
+
+Definition string := Coq.Strings.String.string.
+Definition char := Coq.Strings.Ascii.ascii.
+Definition char_of_byte := Coq.Strings.Ascii.ascii_of_byte.
+
+Definition core_mem_replace (a : Type) (x : a) (y : a) : a * a := (x, x) .
+
+Record mut_raw_ptr (T : Type) := { mut_raw_ptr_v : T }.
+Record const_raw_ptr (T : Type) := { const_raw_ptr_v : T }.
+
+(*** Scalars *)
+
+Definition i8_min   : Z := -128%Z.
+Definition i8_max   : Z := 127%Z.
+Definition i16_min  : Z := -32768%Z.
+Definition i16_max  : Z := 32767%Z.
+Definition i32_min  : Z := -2147483648%Z.
+Definition i32_max  : Z := 2147483647%Z.
+Definition i64_min  : Z := -9223372036854775808%Z.
+Definition i64_max  : Z := 9223372036854775807%Z.
+Definition i128_min : Z := -170141183460469231731687303715884105728%Z.
+Definition i128_max : Z := 170141183460469231731687303715884105727%Z.
+Definition u8_min   : Z := 0%Z.
+Definition u8_max   : Z := 255%Z.
+Definition u16_min  : Z := 0%Z.
+Definition u16_max  : Z := 65535%Z.
+Definition u32_min  : Z := 0%Z.
+Definition u32_max  : Z := 4294967295%Z.
+Definition u64_min  : Z := 0%Z.
+Definition u64_max  : Z := 18446744073709551615%Z.
+Definition u128_min : Z := 0%Z.
+Definition u128_max : Z := 340282366920938463463374607431768211455%Z.
+
+(** The bounds of [isize] and [usize] vary with the architecture. *)
+Axiom isize_min : Z.
+Axiom isize_max : Z.
+Definition usize_min : Z := 0%Z.
+Axiom usize_max : Z.
+
+Open Scope Z_scope.
+
+(** We provide those lemmas to reason about the bounds of [isize] and [usize] *)
+Axiom isize_min_bound : isize_min <= i32_min.
+Axiom isize_max_bound : i32_max <= isize_max.
+Axiom usize_max_bound : u32_max <= usize_max.
+
+Inductive scalar_ty :=
+  | Isize
+  | I8
+  | I16
+  | I32
+  | I64
+  | I128
+  | Usize
+  | U8
+  | U16
+  | U32
+  | U64
+  | U128
+.
+
+Definition scalar_min (ty: scalar_ty) : Z :=
+  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
+end.
+
+Definition scalar_max (ty: scalar_ty) : Z :=
+  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
+end.
+
+(** We use the following conservative bounds to make sure we can compute bound
+    checks in most situations *)
+Definition scalar_min_cons (ty: scalar_ty) : Z :=
+  match ty with
+  | Isize => i32_min
+  | Usize => u32_min
+  | _ => scalar_min ty
+end.
+
+Definition scalar_max_cons (ty: scalar_ty) : Z :=
+  match ty with
+  | Isize => i32_max
+  | Usize => u32_max
+  | _ => scalar_max ty
+end.
+
+Lemma scalar_min_cons_valid : forall ty, scalar_min ty <= scalar_min_cons ty .
+Proof.
+  destruct ty; unfold scalar_min_cons, scalar_min; try lia.
+  - pose isize_min_bound; lia.
+  - apply Z.le_refl.
+Qed.
+
+Lemma scalar_max_cons_valid : forall ty, scalar_max ty >= scalar_max_cons ty .
+Proof.
+  destruct ty; unfold scalar_max_cons, scalar_max; try lia.
+  - pose isize_max_bound; lia.
+  - pose usize_max_bound. lia.
+Qed.
+
+Definition scalar (ty: scalar_ty) : Type :=
+ { x: Z | scalar_min ty <= x <= scalar_max ty }.
+
+Definition to_Z {ty} (x: scalar ty) : Z := proj1_sig x.
+
+(** Bounds checks: we start by using the conservative bounds, to make sure we
+    can compute in most situations, then we use the real bounds (for [isize]
+    and [usize]). *)
+Definition scalar_ge_min (ty: scalar_ty) (x: Z) : bool :=
+  Z.leb (scalar_min_cons ty) x || Z.leb (scalar_min ty) x.
+
+Definition scalar_le_max (ty: scalar_ty) (x: Z) : bool :=
+  Z.leb x (scalar_max_cons ty) || Z.leb x (scalar_max ty).
+
+Lemma scalar_ge_min_valid (ty: scalar_ty) (x: Z) :
+  scalar_ge_min ty x = true -> scalar_min ty <= x .
+Proof.
+  unfold scalar_ge_min.
+  pose (scalar_min_cons_valid ty).
+  lia.
+Qed.
+
+Lemma scalar_le_max_valid (ty: scalar_ty) (x: Z) :
+  scalar_le_max ty x = true -> x <= scalar_max ty .
+Proof.
+  unfold scalar_le_max.
+  pose (scalar_max_cons_valid ty).
+  lia.
+Qed.
+
+Definition scalar_in_bounds (ty: scalar_ty) (x: Z) : bool :=
+  scalar_ge_min ty x && scalar_le_max ty x .
+
+Lemma scalar_in_bounds_valid (ty: scalar_ty) (x: Z) :
+  scalar_in_bounds ty x = true -> scalar_min ty <= x <= scalar_max ty .
+Proof.
+  unfold scalar_in_bounds.
+  intros H.
+  destruct (scalar_ge_min ty x) eqn:Hmin.
+  - destruct (scalar_le_max ty x) eqn:Hmax.
+    + pose (scalar_ge_min_valid ty x Hmin).
+      pose (scalar_le_max_valid ty x Hmax).
+      lia.
+    + inversion H.
+  - inversion H.
+Qed.
+
+Import Sumbool.
+
+Definition mk_scalar (ty: scalar_ty) (x: Z) : result (scalar ty) :=
+  match sumbool_of_bool (scalar_in_bounds ty x) with
+  | left H => Ok (exist _ x (scalar_in_bounds_valid _ _ H))
+  | right _ => Fail_ Failure
+  end.
+
+Definition scalar_add {ty} (x y: scalar ty) : result (scalar ty) := mk_scalar ty (to_Z x + to_Z y).
+
+Definition scalar_sub {ty} (x y: scalar ty) : result (scalar ty) := mk_scalar ty (to_Z x - to_Z y).
+
+Definition scalar_mul {ty} (x y: scalar ty) : result (scalar ty) := mk_scalar ty (to_Z x * to_Z y).
+
+Definition scalar_div {ty} (x y: scalar ty) : result (scalar ty) :=
+  if to_Z y =? 0 then Fail_ Failure else
+  mk_scalar ty (to_Z x / to_Z y).
+
+Definition scalar_rem {ty} (x y: scalar ty) : result (scalar ty) := mk_scalar ty (Z.rem (to_Z x) (to_Z y)).
+  
+Definition scalar_neg {ty} (x: scalar ty) : result (scalar ty) := mk_scalar ty (-(to_Z x)).
+
+Axiom scalar_xor : forall ty, scalar ty -> scalar ty -> scalar ty. (* TODO *)
+Axiom scalar_or : forall ty, scalar ty -> scalar ty -> scalar ty. (* TODO *)
+Axiom scalar_and : forall ty, scalar ty -> scalar ty -> scalar ty. (* TODO *)
+Axiom scalar_shl : forall ty0 ty1, scalar ty0 -> scalar ty1 -> result (scalar ty0). (* TODO *)
+Axiom scalar_shr : forall ty0 ty1, scalar ty0 -> scalar ty1 -> result (scalar ty0). (* TODO *)
+
+(** Cast an integer from a [src_ty] to a [tgt_ty] *)
+(* TODO: check the semantics of casts in Rust *)
+Definition scalar_cast (src_ty tgt_ty : scalar_ty) (x : scalar src_ty) : result (scalar tgt_ty) :=
+  mk_scalar tgt_ty (to_Z x).
+
+(* This can't fail, but for now we make all casts faillible (easier for the translation) *)
+Definition scalar_cast_bool (tgt_ty : scalar_ty) (x : bool) : result (scalar tgt_ty) :=
+  mk_scalar tgt_ty (if x then 1 else 0).
+
+(** Comparisons *)
+Definition scalar_leb {ty : scalar_ty} (x : scalar ty) (y : scalar ty) : bool :=
+  Z.leb (to_Z x) (to_Z y) .
+
+Definition scalar_ltb {ty : scalar_ty} (x : scalar ty) (y : scalar ty) : bool :=
+  Z.ltb (to_Z x) (to_Z y) .
+
+Definition scalar_geb {ty : scalar_ty} (x : scalar ty) (y : scalar ty) : bool :=
+  Z.geb (to_Z x) (to_Z y) .
+
+Definition scalar_gtb {ty : scalar_ty} (x : scalar ty) (y : scalar ty) : bool :=
+  Z.gtb (to_Z x) (to_Z y) .
+
+Definition scalar_eqb {ty : scalar_ty} (x : scalar ty) (y : scalar ty) : bool :=
+  Z.eqb (to_Z x) (to_Z y) .
+
+Definition scalar_neqb {ty : scalar_ty} (x : scalar ty) (y : scalar ty) : bool :=
+  negb (Z.eqb (to_Z x) (to_Z y)) .
+
+
+(** The scalar types *)
+Definition isize := scalar Isize.
+Definition i8    := scalar I8.
+Definition i16   := scalar I16.
+Definition i32   := scalar I32.
+Definition i64   := scalar I64.
+Definition i128  := scalar I128.
+Definition usize := scalar Usize.
+Definition u8    := scalar U8.
+Definition u16   := scalar U16.
+Definition u32   := scalar U32.
+Definition u64   := scalar U64.
+Definition u128  := scalar U128.
+
+(** Negaion *)
+Definition isize_neg := @scalar_neg Isize.
+Definition i8_neg    := @scalar_neg I8.
+Definition i16_neg   := @scalar_neg I16.
+Definition i32_neg   := @scalar_neg I32.
+Definition i64_neg   := @scalar_neg I64.
+Definition i128_neg  := @scalar_neg I128.
+
+(** Division *)
+Definition isize_div := @scalar_div Isize.
+Definition i8_div    := @scalar_div I8.
+Definition i16_div   := @scalar_div I16.
+Definition i32_div   := @scalar_div I32.
+Definition i64_div   := @scalar_div I64.
+Definition i128_div  := @scalar_div I128.
+Definition usize_div := @scalar_div Usize.
+Definition u8_div    := @scalar_div U8.
+Definition u16_div   := @scalar_div U16.
+Definition u32_div   := @scalar_div U32.
+Definition u64_div   := @scalar_div U64.
+Definition u128_div  := @scalar_div U128.
+
+(** Remainder *)
+Definition isize_rem := @scalar_rem Isize.
+Definition i8_rem    := @scalar_rem I8.
+Definition i16_rem   := @scalar_rem I16.
+Definition i32_rem   := @scalar_rem I32.
+Definition i64_rem   := @scalar_rem I64.
+Definition i128_rem  := @scalar_rem I128.
+Definition usize_rem := @scalar_rem Usize.
+Definition u8_rem    := @scalar_rem U8.
+Definition u16_rem   := @scalar_rem U16.
+Definition u32_rem   := @scalar_rem U32.
+Definition u64_rem   := @scalar_rem U64.
+Definition u128_rem  := @scalar_rem U128.
+
+(** Addition *)
+Definition isize_add := @scalar_add Isize.
+Definition i8_add    := @scalar_add I8.
+Definition i16_add   := @scalar_add I16.
+Definition i32_add   := @scalar_add I32.
+Definition i64_add   := @scalar_add I64.
+Definition i128_add  := @scalar_add I128.
+Definition usize_add := @scalar_add Usize.
+Definition u8_add    := @scalar_add U8.
+Definition u16_add   := @scalar_add U16.
+Definition u32_add   := @scalar_add U32.
+Definition u64_add   := @scalar_add U64.
+Definition u128_add  := @scalar_add U128.
+
+(** Substraction *)
+Definition isize_sub := @scalar_sub Isize.
+Definition i8_sub    := @scalar_sub I8.
+Definition i16_sub   := @scalar_sub I16.
+Definition i32_sub   := @scalar_sub I32.
+Definition i64_sub   := @scalar_sub I64.
+Definition i128_sub  := @scalar_sub I128.
+Definition usize_sub := @scalar_sub Usize.
+Definition u8_sub    := @scalar_sub U8.
+Definition u16_sub   := @scalar_sub U16.
+Definition u32_sub   := @scalar_sub U32.
+Definition u64_sub   := @scalar_sub U64.
+Definition u128_sub  := @scalar_sub U128.
+
+(** Multiplication *)
+Definition isize_mul := @scalar_mul Isize.
+Definition i8_mul    := @scalar_mul I8.
+Definition i16_mul   := @scalar_mul I16.
+Definition i32_mul   := @scalar_mul I32.
+Definition i64_mul   := @scalar_mul I64.
+Definition i128_mul  := @scalar_mul I128.
+Definition usize_mul := @scalar_mul Usize.
+Definition u8_mul    := @scalar_mul U8.
+Definition u16_mul   := @scalar_mul U16.
+Definition u32_mul   := @scalar_mul U32.
+Definition u64_mul   := @scalar_mul U64.
+Definition u128_mul  := @scalar_mul U128.
+
+(** Xor *)
+Definition u8_xor := @scalar_xor U8.
+Definition u16_xor := @scalar_xor U16.
+Definition u32_xor := @scalar_xor U32.
+Definition u64_xor := @scalar_xor U64.
+Definition u128_xor := @scalar_xor U128.
+Definition usize_xor := @scalar_xor Usize.
+Definition i8_xor := @scalar_xor I8.
+Definition i16_xor := @scalar_xor I16.
+Definition i32_xor := @scalar_xor I32.
+Definition i64_xor := @scalar_xor I64.
+Definition i128_xor := @scalar_xor I128.
+Definition isize_xor := @scalar_xor Isize.
+
+(** Or *)
+Definition u8_or := @scalar_or U8.
+Definition u16_or := @scalar_or U16.
+Definition u32_or := @scalar_or U32.
+Definition u64_or := @scalar_or U64.
+Definition u128_or := @scalar_or U128.
+Definition usize_or := @scalar_or Usize.
+Definition i8_or := @scalar_or I8.
+Definition i16_or := @scalar_or I16.
+Definition i32_or := @scalar_or I32.
+Definition i64_or := @scalar_or I64.
+Definition i128_or := @scalar_or I128.
+Definition isize_or := @scalar_or Isize.
+
+(** And *)
+Definition u8_and := @scalar_and U8.
+Definition u16_and := @scalar_and U16.
+Definition u32_and := @scalar_and U32.
+Definition u64_and := @scalar_and U64.
+Definition u128_and := @scalar_and U128.
+Definition usize_and := @scalar_and Usize.
+Definition i8_and := @scalar_and I8.
+Definition i16_and := @scalar_and I16.
+Definition i32_and := @scalar_and I32.
+Definition i64_and := @scalar_and I64.
+Definition i128_and := @scalar_and I128.
+Definition isize_and := @scalar_and Isize.
+
+(** Shift left *)
+Definition u8_shl {ty} := @scalar_shl U8 ty.
+Definition u16_shl {ty} := @scalar_shl U16 ty.
+Definition u32_shl {ty} := @scalar_shl U32 ty.
+Definition u64_shl {ty} := @scalar_shl U64 ty.
+Definition u128_shl {ty} := @scalar_shl U128 ty.
+Definition usize_shl {ty} := @scalar_shl Usize ty.
+Definition i8_shl {ty} := @scalar_shl I8 ty.
+Definition i16_shl {ty} := @scalar_shl I16 ty.
+Definition i32_shl {ty} := @scalar_shl I32 ty.
+Definition i64_shl {ty} := @scalar_shl I64 ty.
+Definition i128_shl {ty} := @scalar_shl I128 ty.
+Definition isize_shl {ty} := @scalar_shl Isize ty.
+
+(** Shift right *)
+Definition u8_shr {ty} := @scalar_shr U8 ty.
+Definition u16_shr {ty} := @scalar_shr U16 ty.
+Definition u32_shr {ty} := @scalar_shr U32 ty.
+Definition u64_shr {ty} := @scalar_shr U64 ty.
+Definition u128_shr {ty} := @scalar_shr U128 ty.
+Definition usize_shr {ty} := @scalar_shr Usize ty.
+Definition i8_shr {ty} := @scalar_shr I8 ty.
+Definition i16_shr {ty} := @scalar_shr I16 ty.
+Definition i32_shr {ty} := @scalar_shr I32 ty.
+Definition i64_shr {ty} := @scalar_shr I64 ty.
+Definition i128_shr {ty} := @scalar_shr I128 ty.
+Definition isize_shr {ty} := @scalar_shr Isize ty.
+
+(** Small utility *)
+Definition usize_to_nat (x: usize) : nat := Z.to_nat (to_Z x).
+
+(** Notations *)
+Notation "x %isize" := ((mk_scalar Isize x)%return) (at level 9).
+Notation "x %i8"    := ((mk_scalar I8    x)%return) (at level 9).
+Notation "x %i16"   := ((mk_scalar I16   x)%return) (at level 9).
+Notation "x %i32"   := ((mk_scalar I32   x)%return) (at level 9).
+Notation "x %i64"   := ((mk_scalar I64   x)%return) (at level 9).
+Notation "x %i128"  := ((mk_scalar I128  x)%return) (at level 9).
+Notation "x %usize" := ((mk_scalar Usize x)%return) (at level 9).
+Notation "x %u8"    := ((mk_scalar U8    x)%return) (at level 9).
+Notation "x %u16"   := ((mk_scalar U16   x)%return) (at level 9).
+Notation "x %u32"   := ((mk_scalar U32   x)%return) (at level 9).
+Notation "x %u64"   := ((mk_scalar U64   x)%return) (at level 9).
+Notation "x %u128"  := ((mk_scalar U128  x)%return) (at level 9).
+
+Notation "x s= y" := (scalar_eqb x y)  (at level 80) : Primitives_scope.
+Notation "x s<> y" := (scalar_neqb x y) (at level 80) : Primitives_scope.
+Notation "x s<= y" := (scalar_leb x y)  (at level 80) : Primitives_scope.
+Notation "x s< y" := (scalar_ltb x y)  (at level 80) : Primitives_scope.
+Notation "x s>= y" := (scalar_geb x y)  (at level 80) : Primitives_scope.
+Notation "x s> y" := (scalar_gtb x y)  (at level 80) : Primitives_scope.
+
+(** Constants *)
+Definition core_u8_max    := u8_max %u32.
+Definition core_u16_max   := u16_max %u32.
+Definition core_u32_max   := u32_max %u32.
+Definition core_u64_max   := u64_max %u64.
+Definition core_u128_max  := u64_max %u128.
+Axiom core_usize_max : usize. (** TODO *)
+Definition core_i8_max    := i8_max %i32.
+Definition core_i16_max   := i16_max %i32.
+Definition core_i32_max   := i32_max %i32.
+Definition core_i64_max   := i64_max %i64.
+Definition core_i128_max  := i64_max %i128.
+Axiom core_isize_max : isize. (** TODO *)
+
+(*** core *)
+
+(** Trait declaration: [core::clone::Clone] *)
+Record core_clone_Clone (self : Type) := {
+  clone : self -> result self
+}.
+
+Definition core_clone_impls_CloneBool_clone (b : bool) : bool := b.
+
+Definition core_clone_CloneBool : core_clone_Clone bool := {|
+  clone := fun b => Ok (core_clone_impls_CloneBool_clone b)
+|}.
+
+Definition core_clone_impls_CloneUsize_clone (x : usize) : usize := x.
+Definition core_clone_impls_CloneU8_clone (x : u8) : u8 := x.
+Definition core_clone_impls_CloneU16_clone (x : u16) : u16 := x.
+Definition core_clone_impls_CloneU32_clone (x : u32) : u32 := x.
+Definition core_clone_impls_CloneU64_clone (x : u64) : u64 := x.
+Definition core_clone_impls_CloneU128_clone (x : u128) : u128 := x.
+
+Definition core_clone_impls_CloneIsize_clone (x : isize) : isize := x.
+Definition core_clone_impls_CloneI8_clone (x : i8) : i8 := x.
+Definition core_clone_impls_CloneI16_clone (x : i16) : i16 := x.
+Definition core_clone_impls_CloneI32_clone (x : i32) : i32 := x.
+Definition core_clone_impls_CloneI64_clone (x : i64) : i64 := x.
+Definition core_clone_impls_CloneI128_clone (x : i128) : i128 := x.
+
+Definition core_clone_CloneUsize : core_clone_Clone usize := {|
+  clone := fun x => Ok (core_clone_impls_CloneUsize_clone x)
+|}.
+
+Definition core_clone_CloneU8 : core_clone_Clone u8 := {|
+  clone := fun x => Ok (core_clone_impls_CloneU8_clone x)
+|}.
+
+Definition core_clone_CloneU16 : core_clone_Clone u16 := {|
+  clone := fun x => Ok (core_clone_impls_CloneU16_clone x)
+|}.
+
+Definition core_clone_CloneU32 : core_clone_Clone u32 := {|
+  clone := fun x => Ok (core_clone_impls_CloneU32_clone x)
+|}.
+
+Definition core_clone_CloneU64 : core_clone_Clone u64 := {|
+  clone := fun x => Ok (core_clone_impls_CloneU64_clone x)
+|}.
+
+Definition core_clone_CloneU128 : core_clone_Clone u128 := {|
+  clone := fun x => Ok (core_clone_impls_CloneU128_clone x)
+|}.
+
+Definition core_clone_CloneIsize : core_clone_Clone isize := {|
+  clone := fun x => Ok (core_clone_impls_CloneIsize_clone x)
+|}.
+
+Definition core_clone_CloneI8 : core_clone_Clone i8 := {|
+  clone := fun x => Ok (core_clone_impls_CloneI8_clone x)
+|}.
+
+Definition core_clone_CloneI16 : core_clone_Clone i16 := {|
+  clone := fun x => Ok (core_clone_impls_CloneI16_clone x)
+|}.
+
+Definition core_clone_CloneI32 : core_clone_Clone i32 := {|
+  clone := fun x => Ok (core_clone_impls_CloneI32_clone x)
+|}.
+
+Definition core_clone_CloneI64 : core_clone_Clone i64 := {|
+  clone := fun x => Ok (core_clone_impls_CloneI64_clone x)
+|}.
+
+Definition core_clone_CloneI128 : core_clone_Clone i128 := {|
+  clone := fun x => Ok (core_clone_impls_CloneI128_clone x)
+|}.
+
+(** [core::option::{core::option::Option<T>}::unwrap] *)
+Definition core_option_Option_unwrap (T : Type) (x : option T) : result T :=
+  match x with
+  | None => Fail_ Failure
+  | Some x => Ok x
+  end.
+
+(*** core::ops *)
+
+(* Trait declaration: [core::ops::index::Index] *)
+Record core_ops_index_Index (Self Idx : Type) := mk_core_ops_index_Index {
+  core_ops_index_Index_Output : Type;
+  core_ops_index_Index_index : Self -> Idx -> result core_ops_index_Index_Output;
+}.
+Arguments mk_core_ops_index_Index {_ _}.
+Arguments core_ops_index_Index_Output {_ _}.
+Arguments core_ops_index_Index_index {_ _}.
+
+(* Trait declaration: [core::ops::index::IndexMut] *)
+Record core_ops_index_IndexMut (Self Idx : Type) := mk_core_ops_index_IndexMut {
+  core_ops_index_IndexMut_indexInst : core_ops_index_Index Self Idx;
+  core_ops_index_IndexMut_index_mut :
+    Self ->
+    Idx ->
+    result (core_ops_index_IndexMut_indexInst.(core_ops_index_Index_Output) *
+            (core_ops_index_IndexMut_indexInst.(core_ops_index_Index_Output) -> result Self));
+}.
+Arguments mk_core_ops_index_IndexMut {_ _}.
+Arguments core_ops_index_IndexMut_indexInst {_ _}.
+Arguments core_ops_index_IndexMut_index_mut {_ _}.
+
+(* Trait declaration [core::ops::deref::Deref] *)
+Record core_ops_deref_Deref (Self : Type) := mk_core_ops_deref_Deref {
+  core_ops_deref_Deref_target : Type;
+  core_ops_deref_Deref_deref : Self -> result core_ops_deref_Deref_target;
+}.
+Arguments mk_core_ops_deref_Deref {_}.
+Arguments core_ops_deref_Deref_target {_}.
+Arguments core_ops_deref_Deref_deref {_}.
+
+(* Trait declaration [core::ops::deref::DerefMut] *)
+Record core_ops_deref_DerefMut (Self : Type) := mk_core_ops_deref_DerefMut {
+  core_ops_deref_DerefMut_derefInst : core_ops_deref_Deref Self;
+  core_ops_deref_DerefMut_deref_mut :
+    Self ->
+    result (core_ops_deref_DerefMut_derefInst.(core_ops_deref_Deref_target) *
+            (core_ops_deref_DerefMut_derefInst.(core_ops_deref_Deref_target) -> result Self));
+}.
+Arguments mk_core_ops_deref_DerefMut {_}.
+Arguments core_ops_deref_DerefMut_derefInst {_}.
+Arguments core_ops_deref_DerefMut_deref_mut {_}.
+
+Record core_ops_range_Range (T : Type) := mk_core_ops_range_Range {
+  core_ops_range_Range_start : T;
+  core_ops_range_Range_end_ : T;
+}.
+Arguments mk_core_ops_range_Range {_}.
+Arguments core_ops_range_Range_start {_}.
+Arguments core_ops_range_Range_end_ {_}.
+
+(*** [alloc] *)
+
+Definition alloc_boxed_Box_deref (T : Type) (x : T) : result T := Ok x.
+Definition alloc_boxed_Box_deref_mut (T : Type) (x : T) : result (T * (T -> result T)) :=
+  Ok (x, fun x => Ok x).
+
+(* Trait instance *)
+Definition alloc_boxed_Box_coreopsDerefInst (Self : Type) : core_ops_deref_Deref Self := {|
+  core_ops_deref_Deref_target := Self;
+  core_ops_deref_Deref_deref := alloc_boxed_Box_deref Self;
+|}.
+
+(* Trait instance *)
+Definition alloc_boxed_Box_coreopsDerefMutInst (Self : Type) : core_ops_deref_DerefMut Self := {|
+  core_ops_deref_DerefMut_derefInst := alloc_boxed_Box_coreopsDerefInst Self;
+  core_ops_deref_DerefMut_deref_mut := alloc_boxed_Box_deref_mut Self;
+|}.
+
+
+(*** Arrays *)
+Definition array T (n : usize) := { l: list T | Z.of_nat (length l) = to_Z n}.
+
+Lemma le_0_usize_max : 0 <= usize_max.
+Proof.
+  pose (H := usize_max_bound).
+  unfold u32_max in H.
+  lia.
+Qed.
+
+Lemma eqb_imp_eq (x y : Z) : Z.eqb x y = true -> x = y.
+Proof.
+  lia.
+Qed.
+
+(* TODO: finish the definitions *)
+Axiom mk_array : forall (T : Type) (n : usize) (l : list T), array T n.
+
+(* For initialization *)
+Axiom array_repeat : forall (T : Type) (n : usize) (x : T), array T n.
+
+Axiom array_index_usize : forall (T : Type) (n : usize) (x : array T n) (i : usize), result T.
+Axiom array_update_usize : forall (T : Type) (n : usize) (x : array T n) (i : usize) (nx : T), result (array T n).
+
+Definition array_index_mut_usize (T : Type) (n : usize) (a : array T n) (i : usize) :
+  result (T * (T -> result (array T n))) :=
+  match array_index_usize T n a i with
+  | Fail_ e => Fail_ e
+  | Ok x => Ok (x, array_update_usize T n a i)
+  end.
+
+(*** Slice *)
+Definition slice T := { l: list T | Z.of_nat (length l) <= usize_max}.
+
+Axiom slice_len : forall (T : Type) (s : slice T), usize.
+Axiom slice_index_usize : forall (T : Type) (x : slice T) (i : usize), result T.
+Axiom slice_update_usize : forall (T : Type) (x : slice T) (i : usize) (nx : T), result (slice T).
+
+Definition slice_index_mut_usize (T : Type) (s : slice T) (i : usize) :
+  result (T * (T -> result (slice T))) :=
+  match slice_index_usize T s i with
+  | Fail_ e => Fail_ e
+  | Ok x => Ok (x, slice_update_usize T s i)
+  end.
+
+(*** Subslices *)
+
+Axiom array_to_slice : forall (T : Type) (n : usize) (x : array T n), result (slice T).
+Axiom array_from_slice : forall (T : Type) (n : usize) (x : array T n) (s : slice T), result (array T n).
+
+Definition array_to_slice_mut (T : Type) (n : usize) (a : array T n) :
+  result (slice T * (slice T -> result (array T n))) :=
+  match array_to_slice T n a with
+  | Fail_ e => Fail_ e
+  | Ok x => Ok (x, array_from_slice T n a)
+  end.
+
+Axiom array_subslice: forall (T : Type) (n : usize) (x : array T n) (r : core_ops_range_Range usize), result (slice T).
+Axiom array_update_subslice: forall (T : Type) (n : usize) (x : array T n) (r : core_ops_range_Range usize) (ns : slice T), result (array T n).
+
+Axiom slice_subslice: forall (T : Type) (x : slice T) (r : core_ops_range_Range usize), result (slice T).
+Axiom slice_update_subslice: forall (T : Type) (x : slice T) (r : core_ops_range_Range usize) (ns : slice T), result (slice T).
+
+(*** Vectors *)
+
+Definition alloc_vec_Vec T := { l: list T | Z.of_nat (length l) <= usize_max }.
+
+Definition alloc_vec_Vec_to_list {T: Type} (v: alloc_vec_Vec T) : list T := proj1_sig v.
+
+Definition alloc_vec_Vec_length {T: Type} (v: alloc_vec_Vec T) : Z := Z.of_nat (length (alloc_vec_Vec_to_list v)).
+
+Definition alloc_vec_Vec_new (T: Type) : alloc_vec_Vec T := (exist _ [] le_0_usize_max).
+
+Lemma alloc_vec_Vec_len_in_usize {T} (v: alloc_vec_Vec T) : usize_min <= alloc_vec_Vec_length v <= usize_max.
+Proof.
+  unfold alloc_vec_Vec_length, usize_min.
+  split.
+  - lia.
+  - apply (proj2_sig v).
+Qed.
+
+Definition alloc_vec_Vec_len (T: Type) (v: alloc_vec_Vec T) : usize :=
+  exist _ (alloc_vec_Vec_length v) (alloc_vec_Vec_len_in_usize v).
+
+Fixpoint list_update {A} (l: list A) (n: nat) (a: A)
+  : list A :=
+  match l with
+  | []     => []
+  | x :: t => match n with
+    | 0%nat => a :: t
+    | S m => x :: (list_update t m a)
+end end.
+
+Definition alloc_vec_Vec_bind {A B} (v: alloc_vec_Vec A) (f: list A -> result (list B)) : result (alloc_vec_Vec B) :=
+  l <- f (alloc_vec_Vec_to_list v) ;
+  match sumbool_of_bool (scalar_le_max Usize (Z.of_nat (length l))) with
+  | left H => Ok (exist _ l (scalar_le_max_valid _ _ H))
+  | right _ => Fail_ Failure
+  end.
+
+Definition alloc_vec_Vec_push (T: Type) (v: alloc_vec_Vec T) (x: T) : result (alloc_vec_Vec T) :=
+  alloc_vec_Vec_bind v (fun l => Ok (l ++ [x])).
+
+Definition alloc_vec_Vec_insert (T: Type) (v: alloc_vec_Vec T) (i: usize) (x: T) : result (alloc_vec_Vec T) :=
+  alloc_vec_Vec_bind v (fun l =>
+    if to_Z i <? Z.of_nat (length l)
+    then Ok (list_update l (usize_to_nat i) x)
+    else Fail_ Failure).
+
+(* Helper *)
+Axiom alloc_vec_Vec_index_usize : forall {T : Type} (v : alloc_vec_Vec T) (i : usize), result T.
+
+(* Helper *)
+Axiom alloc_vec_Vec_update_usize : forall {T : Type} (v : alloc_vec_Vec T) (i : usize) (x : T), result (alloc_vec_Vec T).
+
+Definition alloc_vec_Vec_index_mut_usize {T : Type} (v: alloc_vec_Vec T) (i: usize) :
+  result (T * (T -> result (alloc_vec_Vec T))) :=
+  match alloc_vec_Vec_index_usize v i with
+  | Ok x =>
+    Ok (x, alloc_vec_Vec_update_usize v i)
+  | Fail_ e => Fail_ e
+  end.
+
+(* Trait declaration: [core::slice::index::private_slice_index::Sealed] *)
+Definition core_slice_index_private_slice_index_Sealed (self : Type) := unit.
+
+(* Trait declaration: [core::slice::index::SliceIndex] *)
+Record core_slice_index_SliceIndex (Self T : Type) := mk_core_slice_index_SliceIndex {
+  core_slice_index_SliceIndex_sealedInst : core_slice_index_private_slice_index_Sealed Self;
+  core_slice_index_SliceIndex_Output : Type;
+  core_slice_index_SliceIndex_get : Self -> T -> result (option core_slice_index_SliceIndex_Output);
+  core_slice_index_SliceIndex_get_mut :
+    Self -> T -> result (option core_slice_index_SliceIndex_Output * (option core_slice_index_SliceIndex_Output -> result T));
+  core_slice_index_SliceIndex_get_unchecked : Self -> const_raw_ptr T -> result (const_raw_ptr core_slice_index_SliceIndex_Output);
+  core_slice_index_SliceIndex_get_unchecked_mut : Self -> mut_raw_ptr T -> result (mut_raw_ptr core_slice_index_SliceIndex_Output);
+  core_slice_index_SliceIndex_index : Self -> T -> result core_slice_index_SliceIndex_Output;
+  core_slice_index_SliceIndex_index_mut :
+    Self -> T -> result (core_slice_index_SliceIndex_Output * (core_slice_index_SliceIndex_Output -> result T));
+}.
+Arguments mk_core_slice_index_SliceIndex {_ _}.
+Arguments core_slice_index_SliceIndex_sealedInst {_ _}.
+Arguments core_slice_index_SliceIndex_Output {_ _}.
+Arguments core_slice_index_SliceIndex_get {_ _}.
+Arguments core_slice_index_SliceIndex_get_mut {_ _}.
+Arguments core_slice_index_SliceIndex_get_unchecked {_ _}.
+Arguments core_slice_index_SliceIndex_get_unchecked_mut {_ _}.
+Arguments core_slice_index_SliceIndex_index {_ _}.
+Arguments core_slice_index_SliceIndex_index_mut {_ _}.
+
+(* [core::slice::index::[T]::index]: forward function *)
+Definition core_slice_index_Slice_index
+  (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T))
+  (s : slice T) (i : Idx) : result inst.(core_slice_index_SliceIndex_Output) :=
+  x <- inst.(core_slice_index_SliceIndex_get) i s;
+  match x with
+  | None => Fail_ Failure
+  | Some x => Ok x
+  end.
+
+(* [core::slice::index::Range:::get]: forward function *)
+Axiom core_slice_index_RangeUsize_get : forall (T : Type) (i : core_ops_range_Range usize) (s : slice T), result (option (slice T)).
+
+(* [core::slice::index::Range::get_mut]: forward function *)
+Axiom core_slice_index_RangeUsize_get_mut :
+  forall (T : Type),
+    core_ops_range_Range usize -> slice T ->
+    result (option (slice T) * (option (slice T) -> result (slice T))).
+
+(* [core::slice::index::Range::get_unchecked]: forward function *)
+Definition core_slice_index_RangeUsize_get_unchecked
+  (T : Type) :
+  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 *)
+Definition core_slice_index_RangeUsize_get_unchecked_mut
+  (T : Type) :
+  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 *)
+Axiom core_slice_index_RangeUsize_index :
+  forall (T : Type), core_ops_range_Range usize -> slice T -> result (slice T).
+
+(* [core::slice::index::Range::index_mut]: forward function *)
+Axiom core_slice_index_RangeUsize_index_mut :
+  forall (T : Type), core_ops_range_Range usize -> slice T -> result (slice T * (slice T -> result (slice T))).
+
+(* [core::slice::index::[T]::index_mut]: forward function *)
+Axiom core_slice_index_Slice_index_mut :
+  forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T)),
+  slice T -> Idx ->
+  result (inst.(core_slice_index_SliceIndex_Output) *
+          (inst.(core_slice_index_SliceIndex_Output) -> result (slice T))).
+
+(* [core::array::[T; N]::index]: forward function *)
+Axiom core_array_Array_index :
+  forall (T Idx : Type) (N : usize) (inst : core_ops_index_Index (slice T) Idx)
+  (a : array T N) (i : Idx), result inst.(core_ops_index_Index_Output).
+
+(* [core::array::[T; N]::index_mut]: forward function *)
+Axiom core_array_Array_index_mut :
+  forall (T Idx : Type) (N : usize) (inst : core_ops_index_IndexMut (slice T) Idx)
+  (a : array T N) (i : Idx),
+  result (inst.(core_ops_index_IndexMut_indexInst).(core_ops_index_Index_Output) *
+          (inst.(core_ops_index_IndexMut_indexInst).(core_ops_index_Index_Output) -> result (array T N))).
+
+(* Trait implementation: [core::slice::index::private_slice_index::Range] *)
+Definition core_slice_index_private_slice_index_SealedRangeUsizeInst
+  : core_slice_index_private_slice_index_Sealed (core_ops_range_Range usize) := tt.
+
+(* Trait implementation: [core::slice::index::Range] *)
+Definition core_slice_index_SliceIndexRangeUsizeSliceTInst (T : Type) :
+  core_slice_index_SliceIndex (core_ops_range_Range usize) (slice T) := {|
+  core_slice_index_SliceIndex_sealedInst := core_slice_index_private_slice_index_SealedRangeUsizeInst;
+  core_slice_index_SliceIndex_Output := slice T;
+  core_slice_index_SliceIndex_get := core_slice_index_RangeUsize_get T;
+  core_slice_index_SliceIndex_get_mut := core_slice_index_RangeUsize_get_mut T;
+  core_slice_index_SliceIndex_get_unchecked := core_slice_index_RangeUsize_get_unchecked T;
+  core_slice_index_SliceIndex_get_unchecked_mut := core_slice_index_RangeUsize_get_unchecked_mut T;
+  core_slice_index_SliceIndex_index := core_slice_index_RangeUsize_index T;
+  core_slice_index_SliceIndex_index_mut := core_slice_index_RangeUsize_index_mut T;
+|}.
+
+(* Trait implementation: [core::slice::index::[T]] *)
+Definition core_ops_index_IndexSliceTIInst (T Idx : Type)
+  (inst : core_slice_index_SliceIndex Idx (slice T)) :
+  core_ops_index_Index (slice T) Idx := {|
+  core_ops_index_Index_Output := inst.(core_slice_index_SliceIndex_Output);
+  core_ops_index_Index_index := core_slice_index_Slice_index T Idx inst;
+|}.
+
+(* Trait implementation: [core::slice::index::[T]] *)
+Definition core_ops_index_IndexMutSliceTIInst (T Idx : Type)
+  (inst : core_slice_index_SliceIndex Idx (slice T)) :
+  core_ops_index_IndexMut (slice T) Idx := {|
+  core_ops_index_IndexMut_indexInst := core_ops_index_IndexSliceTIInst T Idx inst;
+  core_ops_index_IndexMut_index_mut := core_slice_index_Slice_index_mut T Idx inst;
+|}.
+
+(* Trait implementation: [core::array::[T; N]] *)
+Definition core_ops_index_IndexArrayInst (T Idx : Type) (N : usize)
+  (inst : core_ops_index_Index (slice T) Idx) :
+  core_ops_index_Index (array T N) Idx := {|
+  core_ops_index_Index_Output := inst.(core_ops_index_Index_Output);
+  core_ops_index_Index_index := core_array_Array_index T Idx N inst;
+|}.
+
+(* Trait implementation: [core::array::[T; N]] *)
+Definition core_ops_index_IndexMutArrayInst (T Idx : Type) (N : usize)
+  (inst : core_ops_index_IndexMut (slice T) Idx) :
+  core_ops_index_IndexMut (array T N) Idx := {|
+  core_ops_index_IndexMut_indexInst := core_ops_index_IndexArrayInst T Idx N inst.(core_ops_index_IndexMut_indexInst);
+  core_ops_index_IndexMut_index_mut := core_array_Array_index_mut T Idx N inst;
+|}.
+
+(* [core::slice::index::usize::get]: forward function *)
+Axiom core_slice_index_usize_get : forall (T : Type), usize -> slice T -> result (option T).
+
+(* [core::slice::index::usize::get_mut]: forward function *)
+Axiom core_slice_index_usize_get_mut :
+  forall (T : Type), usize -> slice T -> result (option T * (option T -> result (slice T))).
+
+(* [core::slice::index::usize::get_unchecked]: forward function *)
+Axiom core_slice_index_usize_get_unchecked :
+  forall (T : Type), usize -> const_raw_ptr (slice T) -> result (const_raw_ptr T).
+
+(* [core::slice::index::usize::get_unchecked_mut]: forward function *)
+Axiom core_slice_index_usize_get_unchecked_mut :
+  forall (T : Type), usize -> mut_raw_ptr (slice T) -> result (mut_raw_ptr T).
+
+(* [core::slice::index::usize::index]: forward function *)
+Axiom core_slice_index_usize_index : forall (T : Type), usize -> slice T -> result T.
+
+(* [core::slice::index::usize::index_mut]: forward function *)
+Axiom core_slice_index_usize_index_mut :
+  forall (T : Type), usize -> slice T -> result (T * (T -> result (slice T))).
+
+(* Trait implementation: [core::slice::index::private_slice_index::usize] *)
+Definition core_slice_index_private_slice_index_SealedUsizeInst
+  : core_slice_index_private_slice_index_Sealed usize := tt.
+
+(* Trait implementation: [core::slice::index::usize] *)
+Definition core_slice_index_SliceIndexUsizeSliceTInst (T : Type) :
+  core_slice_index_SliceIndex usize (slice T) := {|
+  core_slice_index_SliceIndex_sealedInst := core_slice_index_private_slice_index_SealedUsizeInst;
+  core_slice_index_SliceIndex_Output := T;
+  core_slice_index_SliceIndex_get := core_slice_index_usize_get T;
+  core_slice_index_SliceIndex_get_mut := core_slice_index_usize_get_mut T;
+  core_slice_index_SliceIndex_get_unchecked := core_slice_index_usize_get_unchecked T;
+  core_slice_index_SliceIndex_get_unchecked_mut := core_slice_index_usize_get_unchecked_mut T;
+  core_slice_index_SliceIndex_index := core_slice_index_usize_index T;
+  core_slice_index_SliceIndex_index_mut := core_slice_index_usize_index_mut T;
+|}.
+
+(* [alloc::vec::Vec::index]: forward function *)
+Axiom alloc_vec_Vec_index : forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T))
+  (Self : alloc_vec_Vec T) (i : Idx), result inst.(core_slice_index_SliceIndex_Output).
+
+(* [alloc::vec::Vec::index_mut]: forward function *)
+Axiom alloc_vec_Vec_index_mut : forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T))
+  (Self : alloc_vec_Vec T) (i : Idx),
+  result (inst.(core_slice_index_SliceIndex_Output) *
+          (inst.(core_slice_index_SliceIndex_Output) -> result (alloc_vec_Vec T))).
+
+(* Trait implementation: [alloc::vec::Vec] *)
+Definition alloc_vec_Vec_coreopsindexIndexInst (T Idx : Type)
+  (inst : core_slice_index_SliceIndex Idx (slice T)) :
+  core_ops_index_Index (alloc_vec_Vec T) Idx := {|
+  core_ops_index_Index_Output := inst.(core_slice_index_SliceIndex_Output);
+  core_ops_index_Index_index := alloc_vec_Vec_index T Idx inst;
+|}.
+
+(* Trait implementation: [alloc::vec::Vec] *)
+Definition alloc_vec_Vec_coreopsindexIndexMutInst (T Idx : Type)
+  (inst : core_slice_index_SliceIndex Idx (slice T)) :
+  core_ops_index_IndexMut (alloc_vec_Vec T) Idx := {|
+  core_ops_index_IndexMut_indexInst := alloc_vec_Vec_coreopsindexIndexInst T Idx inst;
+  core_ops_index_IndexMut_index_mut := alloc_vec_Vec_index_mut T Idx inst;
+|}.
+
+(*** Theorems *)
+
+Axiom alloc_vec_Vec_index_eq : forall {a : Type} (v : alloc_vec_Vec a) (i : usize) (x : a),
+  alloc_vec_Vec_index a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i =
+    alloc_vec_Vec_index_usize v i.
+
+Axiom alloc_vec_Vec_index_mut_eq : forall {a : Type} (v : alloc_vec_Vec a) (i : usize) (x : a),
+  alloc_vec_Vec_index_mut a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i =
+    alloc_vec_Vec_index_mut_usize v i.
+
+End Primitives.
diff --git a/tests/coq/hashmap_main/_CoqProject b/tests/coq/hashmap_main/_CoqProject
new file mode 100644
index 00000000..d73541d9
--- /dev/null
+++ b/tests/coq/hashmap_main/_CoqProject
@@ -0,0 +1,12 @@
+# This file was automatically generated - see ../Makefile
+-R . Lib
+-arg -w
+-arg all
+
+HashmapMain_Types.v
+HashmapMain_FunsExternal_Template.v
+Primitives.v
+HashmapMain_Funs.v
+HashmapMain_TypesExternal.v
+HashmapMain_FunsExternal.v
+HashmapMain_TypesExternal_Template.v