Make minor fixes, improve formatting for Lean and generate code for all the test suite

38 files changed, 5661 insertions, 358 deletions

diff --git a/Makefile b/Makefile
index 1533668c..4c5a12e8 100644
--- a/Makefile
+++ b/Makefile
@@ -115,43 +115,57 @@ AENEAS_CMD = $(AENEAS_EXE) $(CHARON_TEST_DIR)/llbc/$(FILE).llbc -dest tests/$(BA
 # Add specific options to some tests
 trans-no_nested_borrows trans-paper: \
 	OPTIONS += -test-units -test-trans-units -no-split-files -no-state
-trans-no_nested_borrows trans-paper: SUBDIR:=misc
+trans-no_nested_borrows trans-paper: SUBDIR := misc
 tfstar-no_nested_borrows tfstar-paper:
+tlean-no_nested_borrows: SUBDIR := misc/no_nested_borrows
+tlean-paper: SUBDIR := misc/paper
 
 trans-loops: OPTIONS += -no-state
 trans-loops: SUBDIR := misc
 tfstar-loops: OPTIONS += -decreases-clauses -template-clauses
 tcoq-loops: OPTIONS += -use-fuel -no-split-files
+tlean-loops: SUBDIR := misc/loops
+tlean-loops: OPTIONS += -decreases-clauses -template-clauses
 
 trans-hashmap: OPTIONS += -no-state
-trans-hashmap: SUBDIR:=hashmap
+trans-hashmap: SUBDIR := hashmap
 tfstar-hashmap: OPTIONS += -decreases-clauses -template-clauses
 tcoq-hashmap: OPTIONS += -use-fuel
+tlean-hashmap: OPTIONS += -decreases-clauses -template-clauses
 
 trans-hashmap_main: OPTIONS +=
-trans-hashmap_main: SUBDIR:=hashmap_on_disk
+trans-hashmap_main: SUBDIR := hashmap_on_disk
 tfstar-hashmap_main: OPTIONS += -decreases-clauses -template-clauses
 tcoq-hashmap_main: OPTIONS += -use-fuel
+tlean-hashmap_main: OPTIONS += -decreases-clauses -template-clauses
 
 transp-polonius_list: OPTIONS += -test-units -test-trans-units -no-split-files -no-state
-transp-polonius_list: SUBDIR:=misc
+transp-polonius_list: SUBDIR := misc
 tfstarp-polonius_list: OPTIONS +=
 tcoqp-polonius_list: OPTIONS +=
+tleanp-polonius_list: SUBDIR := misc/polonius_list
+tleanp-polonius_list: OPTIONS +=
 
 trans-constants: OPTIONS += -test-units -test-trans-units -no-split-files -no-state
-trans-constants: SUBDIR:=misc
+trans-constants: SUBDIR := misc
 tfstar-constants: OPTIONS +=
 tcoq-constants: OPTIONS +=
+tlean-constants: SUBDIR := misc/constants
+tlean-constants: OPTIONS +=
 
 trans-external: OPTIONS +=
-trans-external: SUBDIR:=misc
+trans-external: SUBDIR := misc
 tfstar-external: OPTIONS +=
+tcoq-external: OPTIONS +=
+tlean-external: SUBDIR := misc/external
+tlean-external: OPTIONS +=
 
 BETREE_FSTAR_OPTIONS = -decreases-clauses -template-clauses
 transp-betree_main: OPTIONS += -backward-no-state-update
 transp-betree_main: SUBDIR:=betree
 tfstarp-betree_main: OPTIONS += $(BETREE_FSTAR_OPTIONS)
 tcoqp-betree_main: OPTIONS += -use-fuel
+tleanp-betree_main: OPTIONS += $(BETREE_FSTAR_OPTIONS)
 
 # Additional test on the betree: translate it without `-backward-no-state-update`.
 # This generates very ugly code, but is good to test the translation.
@@ -228,6 +242,13 @@ tlean-%: BACKEND_SUBDIR := lean
 tlean-%:
 	$(AENEAS_CMD)
 
+# "p" stands for "Polonius"
+.PHONY: tleanp-%
+tleanp-%: OPTIONS += -backend lean -test-trans-units
+tleanp-%: BACKEND_SUBDIR := lean
+tleanp-%:
+	$(AENEAS_CMD)
+
 # Nix
 .PHONY: nix
 nix: nix-aeneas-tests nix-aeneas-verify-fstar nix-aeneas-verify-coq
diff --git a/compiler/Extract.ml b/compiler/Extract.ml
index 24f8d141..1057cc3b 100644
--- a/compiler/Extract.ml
+++ b/compiler/Extract.ml
@@ -17,9 +17,9 @@ let int_name (int_ty : integer_type) =
   let isize, usize, i_format, u_format =
     match !backend with
     | FStar | Coq ->
-        "isize", "usize", format_of_string "i%d", format_of_string "u%d"
+        ("isize", "usize", format_of_string "i%d", format_of_string "u%d")
     | Lean ->
-        "ISize", "USize", format_of_string "Int%d", format_of_string "UInt%d"
+        ("ISize", "USize", format_of_string "Int%d", format_of_string "UInt%d")
   in
   match int_ty with
   | Isize -> isize
@@ -39,11 +39,10 @@ let int_name (int_ty : integer_type) =
 let unop_name (unop : unop) : string =
   match unop with
   | Not -> ( match !backend with FStar | Lean -> "not" | Coq -> "negb")
-  | Neg (int_ty: integer_type) ->
-      begin match !backend with
+  | Neg (int_ty : integer_type) -> (
+      match !backend with
       | Lean -> int_name int_ty ^ ".checked_neg"
-      | _ -> int_name int_ty ^ "_neg"
-      end
+      | _ -> int_name int_ty ^ "_neg")
   | Cast _ -> raise (Failure "Unsupported")
 
 (** Small helper to compute the name of a binary operation (note that many
@@ -74,8 +73,8 @@ let keywords () =
   let named_binops = [ E.Div; Rem; Add; Sub; Mul ] in
   let named_binops =
     List.concat_map
-       (fun bn -> List.map (fun it -> named_binop_name bn it) T.all_int_types)
-       named_binops
+      (fun bn -> List.map (fun it -> named_binop_name bn it) T.all_int_types)
+      named_binops
   in
   let misc =
     match !backend with
@@ -132,8 +131,7 @@ let keywords () =
           "tt";
           "char_of_byte";
         ]
-    | Lean ->
-        [] (* TODO *)
+    | Lean -> [] (* TODO *)
   in
   List.concat [ named_unops; named_binops; misc ]
 
@@ -202,7 +200,7 @@ let assumed_llbc_functions :
     (VecIndexMut, rg0, "vec_index_mut_back");
   ]
 
-let assumed_pure_functions (): (pure_assumed_fun_id * string) list =
+let assumed_pure_functions () : (pure_assumed_fun_id * string) list =
   match !backend with
   | FStar ->
       [
@@ -251,14 +249,12 @@ let extract_unop (extract_expr : bool -> texpression -> unit)
       if inside then F.pp_print_string fmt "(";
       F.pp_print_string fmt "scalar_cast";
       F.pp_print_space fmt ();
-      if !backend <> Lean then begin
+      if !backend <> Lean then (
         F.pp_print_string fmt
           (StringUtils.capitalize_first_letter
              (PrintPure.integer_type_to_string src));
-        F.pp_print_space fmt ()
-      end;
-      if !backend = Lean then
-        F.pp_print_string fmt (int_name tgt)
+        F.pp_print_space fmt ());
+      if !backend = Lean then F.pp_print_string fmt (int_name tgt)
       else
         F.pp_print_string fmt
           (StringUtils.capitalize_first_letter
@@ -284,7 +280,9 @@ let extract_binop (extract_expr : bool -> texpression -> unit)
         | Gt -> ">"
         | _ -> raise (Failure "Unreachable")
       in
-      let binop = match !backend with FStar | Lean -> binop | Coq -> "s" ^ binop in
+      let binop =
+        match !backend with FStar | Lean -> binop | Coq -> "s" ^ binop
+      in
       extract_expr false arg0;
       F.pp_print_space fmt ();
       F.pp_print_string fmt binop;
@@ -301,7 +299,7 @@ let extract_binop (extract_expr : bool -> texpression -> unit)
   if inside then F.pp_print_string fmt ")"
 
 let type_decl_kind_to_qualif (kind : decl_kind)
-    (type_kind : type_decl_kind option): string =
+    (type_kind : type_decl_kind option) : string =
   match !backend with
   | FStar -> (
       match kind with
@@ -326,7 +324,8 @@ let type_decl_kind_to_qualif (kind : decl_kind)
       | _ -> raise (Failure "Unexpected"))
   | Lean -> (
       match kind with
-      | SingleNonRec -> if type_kind = Some Struct then "structure" else "inductive"
+      | SingleNonRec ->
+          if type_kind = Some Struct then "structure" else "inductive"
       | SingleRec -> "inductive"
       | MutRecFirst -> "mutual inductive"
       | MutRecInner -> "inductive"
@@ -364,7 +363,6 @@ let fun_decl_kind_to_qualif (kind : decl_kind) =
       | Assumed -> "axiom"
       | Declared -> "axiom")
 
-
 (**
    [ctx]: we use the context to lookup type definitions, to retrieve type names.
    This is used to compute variable names, when they have no basenames: in this
@@ -439,7 +437,9 @@ let mk_formatter (ctx : trans_ctx) (crate_name : string)
     let name = get_type_name name in
     let name = List.map to_snake_case name in
     let name = String.concat "_" name in
-    match !backend with FStar | Lean -> name | Coq -> capitalize_first_letter name
+    match !backend with
+    | FStar | Lean -> name
+    | Coq -> capitalize_first_letter name
   in
   let type_name name = type_name_to_snake_case name ^ "_t" in
   let field_name (def_name : name) (field_id : FieldId.id)
@@ -587,7 +587,7 @@ let mk_formatter (ctx : trans_ctx) (crate_name : string)
             F.pp_print_string fmt (int_name sv.int_ty);
             F.pp_print_string fmt ".ofNatCore ";
             Z.pp_print fmt sv.value;
-            F.pp_print_string fmt (" (by intlit))"))
+            F.pp_print_string fmt " (by intlit))")
     | Bool b ->
         let b = if b then "true" else "false" in
         F.pp_print_string fmt b
@@ -607,7 +607,6 @@ let mk_formatter (ctx : trans_ctx) (crate_name : string)
             in
             F.pp_print_string fmt c;
             if inside then F.pp_print_string fmt ")")
-
     | String s ->
         (* We need to replace all the line breaks *)
         let s =
@@ -655,8 +654,7 @@ let print_decl_end_delimiter (fmt : F.formatter) (kind : decl_kind) =
     F.pp_print_cut fmt ();
     F.pp_print_string fmt ".")
 
-let unit_name () =
-  match !backend with | Lean -> "Unit" | Coq | FStar -> "unit"
+let unit_name () = match !backend with Lean -> "Unit" | Coq | FStar -> "unit"
 
 (** [inside] constrols whether we should add parentheses or not around type
     applications (if [true] we add parentheses).
@@ -675,7 +673,9 @@ let rec extract_ty (ctx : extraction_ctx) (fmt : F.formatter) (inside : bool)
             Collections.List.iter_link
               (fun () ->
                 F.pp_print_space fmt ();
-                let product = match !backend with FStar -> "&" | Coq -> "*" | Lean -> "×" in
+                let product =
+                  match !backend with FStar -> "&" | Coq -> "*" | Lean -> "×"
+                in
                 F.pp_print_string fmt product;
                 F.pp_print_space fmt ())
               (extract_ty ctx fmt true) tys;
@@ -906,8 +906,7 @@ let extract_type_decl_struct_body (ctx : extraction_ctx) (fmt : F.formatter)
       if !backend = Coq && not is_rec then (
         F.pp_print_string fmt (ctx_get_struct (AdtId def.def_id) ctx);
         F.pp_print_string fmt " ");
-      if !backend <> Lean then
-        F.pp_print_string fmt "{";
+      if !backend <> Lean then F.pp_print_string fmt "{";
       F.pp_print_break fmt 1 ctx.indent_incr;
       (* The body itself *)
       F.pp_open_hvbox fmt 0;
@@ -920,8 +919,7 @@ let extract_type_decl_struct_body (ctx : extraction_ctx) (fmt : F.formatter)
         F.pp_print_string fmt ":";
         F.pp_print_space fmt ();
         extract_ty ctx fmt false f.field_ty;
-        if !backend <> Lean then
-          F.pp_print_string fmt ";";
+        if !backend <> Lean then F.pp_print_string fmt ";";
         F.pp_close_box fmt ()
       in
       let fields = FieldId.mapi (fun fid f -> (fid, f)) fields in
@@ -931,8 +929,7 @@ let extract_type_decl_struct_body (ctx : extraction_ctx) (fmt : F.formatter)
       (* Close *)
       F.pp_close_box fmt ();
       F.pp_print_space fmt ();
-      if !backend <> Lean then
-        F.pp_print_string fmt "}")
+      if !backend <> Lean then F.pp_print_string fmt "}")
     else (
       (* We extract for Coq, and we have a recursive record, or a record in
          a group of mutually recursive types: we extract it as an inductive type
@@ -945,12 +942,12 @@ let extract_type_decl_struct_body (ctx : extraction_ctx) (fmt : F.formatter)
   ()
 
 (** Extract a nestable, muti-line comment *)
-let extract_comment (fmt: F.formatter) (s: string): unit =
+let extract_comment (fmt : F.formatter) (s : string) : unit =
   match !backend with
   | Coq | FStar ->
       F.pp_print_string fmt "(** ";
       F.pp_print_string fmt s;
-      F.pp_print_string fmt " *)";
+      F.pp_print_string fmt " *)"
   | Lean ->
       F.pp_print_string fmt "/- ";
       F.pp_print_string fmt s;
@@ -1002,7 +999,9 @@ let extract_type_decl (ctx : extraction_ctx) (fmt : F.formatter)
   let qualif = ctx.fmt.type_decl_kind_to_qualif kind type_kind in
   F.pp_print_string fmt (qualif ^ " " ^ def_name);
   (* Print the type parameters *)
-  let type_keyword = match !backend with FStar -> "Type0" | Coq | Lean -> "Type" in
+  let type_keyword =
+    match !backend with FStar -> "Type0" | Coq | Lean -> "Type"
+  in
   if def.type_params <> [] then (
     if use_forall then (
       F.pp_print_space fmt ();
@@ -1023,10 +1022,13 @@ let extract_type_decl (ctx : extraction_ctx) (fmt : F.formatter)
   (* Print the "=" if we extract the body*)
   if extract_body then (
     F.pp_print_space fmt ();
-    let eq = match !backend with
+    let eq =
+      match !backend with
       | FStar -> "="
       | Coq -> ":="
-      | Lean -> if type_kind = Some Struct && kind = SingleNonRec then "where" else ":="
+      | Lean ->
+          if type_kind = Some Struct && kind = SingleNonRec then "where"
+          else ":="
     in
     F.pp_print_string fmt eq)
   else (
@@ -1307,18 +1309,15 @@ let extract_state_type (fmt : F.formatter) (ctx : extraction_ctx)
   let state_name = ctx_get_assumed_type State ctx in
   (* The syntax for Lean and Coq is almost identical. *)
   let print_axiom () =
-    if !backend = Coq then
-      F.pp_print_string fmt "Axiom"
-    else
-      F.pp_print_string fmt "axiom";
+    if !backend = Coq then F.pp_print_string fmt "Axiom"
+    else F.pp_print_string fmt "axiom";
     F.pp_print_space fmt ();
     F.pp_print_string fmt state_name;
     F.pp_print_space fmt ();
     F.pp_print_string fmt ":";
     F.pp_print_space fmt ();
     F.pp_print_string fmt "Type";
-    if !backend = Coq then
-      F.pp_print_string fmt "."
+    if !backend = Coq then F.pp_print_string fmt "."
   in
   (* The kind should be [Assumed] or [Declared] *)
   (match kind with
@@ -1336,8 +1335,7 @@ let extract_state_type (fmt : F.formatter) (ctx : extraction_ctx)
           F.pp_print_string fmt ":";
           F.pp_print_space fmt ();
           F.pp_print_string fmt "Type0"
-      | Coq | Lean ->
-          print_axiom ())
+      | Coq | Lean -> print_axiom ())
   | Declared -> (
       match !backend with
       | FStar ->
@@ -1348,8 +1346,7 @@ let extract_state_type (fmt : F.formatter) (ctx : extraction_ctx)
           F.pp_print_string fmt ":";
           F.pp_print_space fmt ();
           F.pp_print_string fmt "Type0"
-      | Coq | Lean ->
-          print_axiom ()));
+      | Coq | Lean -> print_axiom ()));
   (* Close the box for the definition *)
   F.pp_close_box fmt ();
   (* Add breaks to insert new lines between definitions *)
@@ -1367,8 +1364,7 @@ let extract_fun_decl_register_names (ctx : extraction_ctx) (keep_fwd : bool)
     if has_decreases_clause def then
       let ctx = ctx_add_decreases_clause def ctx in
       ctx_add_terminates_clause def ctx
-    else
-      ctx
+    else ctx
   in
   let ctx = List.fold_left register_decreases ctx (fwd :: loop_fwds) in
   let register_fun ctx f = ctx_add_fun_decl (keep_fwd, def) f ctx in
@@ -1439,8 +1435,7 @@ let extract_adt_g_value
         | Some vid ->
             if !backend = Lean then
               ctx_get_type adt_id ctx ^ "." ^ ctx_get_variant adt_id vid ctx
-            else
-              ctx_get_variant adt_id vid ctx
+            else ctx_get_variant adt_id vid ctx
         | None -> ctx_get_struct adt_id ctx
       in
       if inside && field_values <> [] then F.pp_print_string fmt "(";
@@ -1579,9 +1574,10 @@ and extract_function_call (ctx : extraction_ctx) (fmt : F.formatter)
       (* Open a box for the function call *)
       F.pp_open_hovbox fmt ctx.indent_incr;
       (* Print the function name *)
-      let fun_name = Option.value
-        ~default:(ctx_get_function fun_id ctx)
-        (ctx_maybe_get (DeclaredId fun_id) ctx)
+      let fun_name =
+        Option.value
+          ~default:(ctx_get_function fun_id ctx)
+          (ctx_maybe_get (DeclaredId fun_id) ctx)
       in
       F.pp_print_string fmt fun_name;
       (* Print the type parameters *)
@@ -1641,18 +1637,26 @@ and extract_adt_cons (ctx : extraction_ctx) (fmt : F.formatter) (inside : bool)
         match adt_cons.variant_id with
         | Some vid ->
             if !backend = Lean then
-              ctx_get_type adt_cons.adt_id ctx ^ "." ^ ctx_get_variant adt_cons.adt_id vid ctx
-            else
-              ctx_get_variant adt_cons.adt_id vid ctx
+              ctx_get_type adt_cons.adt_id ctx
+              ^ "."
+              ^ ctx_get_variant adt_cons.adt_id vid ctx
+            else ctx_get_variant adt_cons.adt_id vid ctx
         | None -> ctx_get_struct adt_cons.adt_id ctx
       in
       let is_lean_struct = !backend = Lean && adt_cons.variant_id = None in
-      if is_lean_struct then
+      if is_lean_struct then (
         (* TODO: when only one or two fields differ, considering using the with
            syntax (peephole optimization) *)
-        let decl_id = match adt_cons.adt_id with | AdtId id -> id | _ -> assert false in
-        let def_kind = (TypeDeclId.Map.find decl_id ctx.trans_ctx.type_context.type_decls).kind in
-        let fields = match def_kind with | T.Struct fields -> fields | _ -> assert false in
+        let decl_id =
+          match adt_cons.adt_id with AdtId id -> id | _ -> assert false
+        in
+        let def_kind =
+          (TypeDeclId.Map.find decl_id ctx.trans_ctx.type_context.type_decls)
+            .kind
+        in
+        let fields =
+          match def_kind with T.Struct fields -> fields | _ -> assert false
+        in
         let fields = FieldId.mapi (fun fid f -> (fid, f)) fields in
         F.pp_open_hvbox fmt 0;
         F.pp_open_hvbox fmt ctx.indent_incr;
@@ -1663,8 +1667,7 @@ and extract_adt_cons (ctx : extraction_ctx) (fmt : F.formatter) (inside : bool)
         Collections.List.iter_link
           (fun () ->
             F.pp_print_string fmt ",";
-            F.pp_print_space fmt ()
-          )
+            F.pp_print_space fmt ())
           (fun ((fid, _), e) ->
             F.pp_open_hvbox fmt ctx.indent_incr;
             let f = ctx_get_field adt_cons.adt_id fid ctx in
@@ -1673,15 +1676,14 @@ and extract_adt_cons (ctx : extraction_ctx) (fmt : F.formatter) (inside : bool)
             F.pp_open_hvbox fmt ctx.indent_incr;
             extract_texpression ctx fmt true e;
             F.pp_close_box fmt ();
-            F.pp_close_box fmt ()
-          )
+            F.pp_close_box fmt ())
           (List.combine fields args);
         F.pp_close_box fmt ();
         F.pp_close_box fmt ();
         F.pp_close_box fmt ();
         F.pp_print_space fmt ();
         F.pp_print_string fmt "}";
-        F.pp_close_box fmt ()
+        F.pp_close_box fmt ())
       else
         let use_parentheses = inside && args <> [] in
         if use_parentheses then F.pp_print_string fmt "(";
@@ -1708,15 +1710,13 @@ and extract_field_projector (ctx : extraction_ctx) (fmt : F.formatter)
       (* Extract the expression *)
       extract_texpression ctx fmt true arg;
       (* We allow to break where the "." appears (except Lean, it's a syntax error) *)
-      if !backend <> Lean then
-        F.pp_print_break fmt 0 0;
+      if !backend <> Lean then F.pp_print_break fmt 0 0;
       F.pp_print_string fmt ".";
       (* If in Coq, the field projection has to be parenthesized *)
       (match !backend with
       | FStar -> F.pp_print_string fmt field_name
       | Coq -> F.pp_print_string fmt ("(" ^ field_name ^ ")")
-      | Lean -> F.pp_print_string fmt field_name
-      );
+      | Lean -> F.pp_print_string fmt field_name);
       (* Close the box *)
       F.pp_close_box fmt ()
   | arg :: args ->
@@ -1780,7 +1780,11 @@ and extract_lets (ctx : extraction_ctx) (fmt : F.formatter) (inside : bool)
       if monadic && !backend = Coq then (
         let ctx = extract_typed_pattern ctx fmt true lv in
         F.pp_print_space fmt ();
-        let arrow = match !backend with FStar -> "<--" | Coq -> "<-" | Lean -> failwith "impossible" in
+        let arrow =
+          match !backend with
+          | Coq -> "<-"
+          | FStar | Lean -> failwith "impossible"
+        in
         F.pp_print_string fmt arrow;
         F.pp_print_space fmt ();
         extract_texpression ctx fmt false re;
@@ -1791,13 +1795,24 @@ and extract_lets (ctx : extraction_ctx) (fmt : F.formatter) (inside : bool)
         F.pp_print_space fmt ();
         let ctx = extract_typed_pattern ctx fmt true lv in
         F.pp_print_space fmt ();
-        let eq = match !backend with FStar -> "=" | Coq -> ":=" | Lean -> if monadic then "<-" else ":=" in
+        let eq =
+          match !backend with
+          | FStar -> "="
+          | Coq -> ":="
+          | Lean -> if monadic then "<-" else ":="
+        in
         F.pp_print_string fmt eq;
         F.pp_print_space fmt ();
         extract_texpression ctx fmt false re;
-        F.pp_print_space fmt ();
-        if !backend <> Lean then
-          F.pp_print_string fmt "in";
+        (* In Lean, monadic let-bindings don't require to end with "in".
+
+           TODO: does this work because we add a line break? This is very annoying,
+           because we need to enforce there will be a line break. In order to fix
+           this, we should open a vbox instead of an hov_box.
+        *)
+        if !backend <> Lean then (
+          F.pp_print_space fmt ();
+          F.pp_print_string fmt "in");
         ctx)
     in
     (* Close the box for the let-binding *)
@@ -1809,11 +1824,10 @@ and extract_lets (ctx : extraction_ctx) (fmt : F.formatter) (inside : bool)
   let exists_monadic = List.exists (fun (m, _, _) -> m) lets in
   (* If Lean, we rely on monadic blocks, so we insert a do and open a new box
      immediately *)
-  if !backend = Lean && exists_monadic then begin
+  if !backend = Lean && exists_monadic then (
     F.pp_open_vbox fmt ctx.indent_incr;
     F.pp_print_string fmt "do";
-    F.pp_print_space fmt ();
-  end;
+    F.pp_print_space fmt ());
   let ctx =
     List.fold_left
       (fun ctx (monadic, lv, re) -> extract_let ctx monadic lv re)
@@ -1826,8 +1840,7 @@ and extract_lets (ctx : extraction_ctx) (fmt : F.formatter) (inside : bool)
   (* Close the box for the next expression *)
   F.pp_close_box fmt ();
   (* do-box (Lean only) *)
-  if !backend = Lean && exists_monadic then
-    F.pp_close_box fmt ();
+  if !backend = Lean && exists_monadic then F.pp_close_box fmt ();
   (* Close parentheses *)
   if inside && !backend <> Lean then F.pp_print_string fmt ")";
   (* Close the box for the whole expression *)
@@ -1874,9 +1887,7 @@ and extract_Switch (ctx : extraction_ctx) (fmt : F.formatter) (inside : bool)
          | Coq ->
              F.pp_print_string fmt " (";
              F.pp_print_cut fmt ()
-         | Lean ->
-             F.pp_print_cut fmt ()
-        );
+         | Lean -> F.pp_print_cut fmt ());
         (* Print the branch expression *)
         extract_texpression ctx fmt false e_branch;
         (* Close the parenthesized expression *)
@@ -1886,8 +1897,7 @@ and extract_Switch (ctx : extraction_ctx) (fmt : F.formatter) (inside : bool)
              F.pp_print_space fmt ();
              F.pp_print_string fmt "end"
          | Coq -> F.pp_print_string fmt ")"
-         | Lean -> ()
-        );
+         | Lean -> ());
         (* Close the box for the branch *)
         if not parenth then F.pp_close_box fmt ();
         (* Close the box for the then/else+branch *)
@@ -1940,8 +1950,7 @@ and extract_Switch (ctx : extraction_ctx) (fmt : F.formatter) (inside : bool)
       (* End the match *)
       F.pp_print_space fmt ();
       (* Relying on indentation in Lean *)
-      if !backend <> Lean then
-        F.pp_print_string fmt "end");
+      if !backend <> Lean then F.pp_print_string fmt "end");
   (* Close parentheses *)
   if inside then F.pp_print_string fmt ")";
   (* Close the box for the whole expression *)
@@ -1978,7 +1987,9 @@ let extract_fun_parameters (space : bool ref) (ctx : extraction_ctx)
       def.signature.type_params;
     F.pp_print_string fmt ":";
     F.pp_print_space fmt ();
-    let type_keyword = match !backend with FStar -> "Type0" | Coq | Lean -> "Type" in
+    let type_keyword =
+      match !backend with FStar -> "Type0" | Coq | Lean -> "Type"
+    in
     F.pp_print_string fmt (type_keyword ^ ")");
     (* Close the box for the type parameters *)
     F.pp_close_box fmt ());
@@ -2053,7 +2064,8 @@ let extract_template_decreases_clause (ctx : extraction_ctx) (fmt : F.formatter)
   (* Add a break before *)
   F.pp_print_break fmt 0 0;
   (* Print a comment to link the extracted type to its original rust definition *)
-  extract_comment fmt ("[" ^ Print.fun_name_to_string def.basename ^ "]: decreases clause");
+  extract_comment fmt
+    ("[" ^ Print.fun_name_to_string def.basename ^ "]: decreases clause");
   F.pp_print_space fmt ();
   (* Open a box for the definition, so that whenever possible it gets printed on
    * one line *)
@@ -2102,7 +2114,8 @@ let extract_template_decreases_clause (ctx : extraction_ctx) (fmt : F.formatter)
     defines a proof script (allowed to refer to function arguments) that proves
     termination.
 *)
-let extract_termination_and_decreasing (ctx: extraction_ctx) (fmt: F.formatter) (def: fun_decl): unit =
+let extract_termination_and_decreasing (ctx : extraction_ctx)
+    (fmt : F.formatter) (def : fun_decl) : unit =
   assert (!backend = Lean);
 
   (* Retrieve the function name *)
@@ -2111,7 +2124,8 @@ let extract_termination_and_decreasing (ctx: extraction_ctx) (fmt: F.formatter)
   (* Add a break before *)
   F.pp_print_break fmt 0 0;
   (* Print a comment to link the extracted type to its original rust definition *)
-  extract_comment fmt ("[" ^ Print.fun_name_to_string def.basename ^ "]: termination measure");
+  extract_comment fmt
+    ("[" ^ Print.fun_name_to_string def.basename ^ "]: termination measure");
   F.pp_print_space fmt ();
   (* Open a box for the definition, so that whenever possible it gets printed on
    * one line *)
@@ -2136,11 +2150,11 @@ let extract_termination_and_decreasing (ctx: extraction_ctx) (fmt: F.formatter)
   F.pp_close_box fmt ();
   F.pp_print_space fmt ();
   (* Tuple of the arguments *)
-  let vars = List.map (fun (v: var) -> v.id) def_body.inputs in
+  let vars = List.map (fun (v : var) -> v.id) def_body.inputs in
 
   if List.length vars = 1 then
     F.pp_print_string fmt (ctx_get_var (List.hd vars) ctx_body)
-  else begin
+  else (
     F.pp_open_hovbox fmt 0;
     F.pp_print_string fmt "(";
     Collections.List.iter_link
@@ -2150,8 +2164,7 @@ let extract_termination_and_decreasing (ctx: extraction_ctx) (fmt: F.formatter)
       (fun v -> F.pp_print_string fmt (ctx_get_var v ctx_body))
       vars;
     F.pp_print_string fmt ")";
-    F.pp_close_box fmt ();
-  end;
+    F.pp_close_box fmt ());
   (* Close the box for "let FUN_NAME (PARAMS) : EFFECT = admit()" *)
   F.pp_close_box fmt ();
   (* Close the box for the whole definition *)
@@ -2176,9 +2189,9 @@ let extract_termination_and_decreasing (ctx: extraction_ctx) (fmt: F.formatter)
   F.pp_open_hovbox fmt 0;
   F.pp_print_string fmt "| `(tactic| ";
   F.pp_print_string fmt def_name;
-  F.pp_print_space fmt ();
-  Collections.List.iter_link (F.pp_print_space fmt)
+  List.iter
     (fun v ->
+      F.pp_print_space fmt ();
       F.pp_print_string fmt "$";
       F.pp_print_string fmt (ctx_get_var v ctx_body))
     vars;
@@ -2230,10 +2243,9 @@ let extract_fun_decl (ctx : extraction_ctx) (fmt : F.formatter)
   (* *)
   let qualif = ctx.fmt.fun_decl_kind_to_qualif kind in
   (* For Lean: we generate a record of assumed functions *)
-  if not (!backend = Lean && (kind = Assumed || kind = Declared)) then begin
+  if not (!backend = Lean && (kind = Assumed || kind = Declared)) then (
     F.pp_print_string fmt qualif;
-    F.pp_print_space fmt ()
-  end;
+    F.pp_print_space fmt ());
   F.pp_print_string fmt def_name;
   F.pp_print_space fmt ();
   if use_forall then (
@@ -2271,10 +2283,9 @@ let extract_fun_decl (ctx : extraction_ctx) (fmt : F.formatter)
     (* [Tot] *)
     if has_decreases_clause then (
       assert_backend_supports_decreases_clauses ();
-      if !backend = FStar then begin
+      if !backend = FStar then (
         F.pp_print_string fmt "Tot";
-        F.pp_print_space fmt ()
-      end);
+        F.pp_print_space fmt ()));
     extract_ty ctx fmt has_decreases_clause def.signature.output;
     (* Close the box for the return type *)
     F.pp_close_box fmt ();
@@ -2355,26 +2366,28 @@ let extract_fun_decl (ctx : extraction_ctx) (fmt : F.formatter)
   (* Close the outer box for the definition *)
   F.pp_close_box fmt ();
   (* Termination clause *)
-  if has_decreases_clause && !backend = Lean then begin
+  if has_decreases_clause && !backend = Lean then (
     let def_body = Option.get def.body in
-    let all_vars = List.map (fun (v: var) -> v.id) def_body.inputs in
+    let all_vars = List.map (fun (v : var) -> v.id) def_body.inputs in
     let num_fwd_inputs =
       def.signature.info.num_fwd_inputs_with_fuel_with_state
     in
     let vars = Collections.List.prefix num_fwd_inputs all_vars in
 
     (* terminates_by *)
-    let terminates_name = ctx_get_terminates_clause def.def_id def.loop_id ctx in
+    let terminates_name =
+      ctx_get_terminates_clause def.def_id def.loop_id ctx
+    in
     F.pp_print_break fmt 0 0;
     F.pp_open_hovbox fmt ctx.indent_incr;
     F.pp_print_string fmt "termination_by";
     F.pp_open_hovbox fmt 0;
     F.pp_print_space fmt ();
     F.pp_print_string fmt def_name;
-    F.pp_print_space fmt ();
-    Collections.List.iter_link
-      (F.pp_print_space fmt)
-      (fun v -> F.pp_print_string fmt (ctx_get_var v ctx_body))
+    List.iter
+      (fun v ->
+        F.pp_print_space fmt ();
+        F.pp_print_string fmt (ctx_get_var v ctx_body))
       all_vars;
     F.pp_print_space fmt ();
     F.pp_print_string fmt "=>";
@@ -2382,17 +2395,16 @@ let extract_fun_decl (ctx : extraction_ctx) (fmt : F.formatter)
     F.pp_open_hovbox fmt 0;
     F.pp_print_space fmt ();
     F.pp_print_string fmt terminates_name;
-    F.pp_print_space fmt ();
     List.iter
       (fun (p : type_var) ->
         let pname = ctx_get_type_var p.index ctx in
-        F.pp_print_string fmt pname;
-        F.pp_print_space fmt ())
+        F.pp_print_space fmt ();
+        F.pp_print_string fmt pname)
       def.signature.type_params;
     List.iter
       (fun v ->
-        F.pp_print_string fmt (ctx_get_var v ctx_body);
-        F.pp_print_space fmt ())
+        F.pp_print_space fmt ();
+        F.pp_print_string fmt (ctx_get_var v ctx_body))
       vars;
     F.pp_close_box fmt ();
     F.pp_close_box fmt ();
@@ -2404,14 +2416,13 @@ let extract_fun_decl (ctx : extraction_ctx) (fmt : F.formatter)
     F.pp_print_space fmt ();
     F.pp_open_hvbox fmt ctx.indent_incr;
     F.pp_print_string fmt decreases_name;
-    F.pp_print_space fmt ();
-    Collections.List.iter_link
-      (F.pp_print_space fmt)
-      (fun v -> F.pp_print_string fmt (ctx_get_var v ctx_body))
+    List.iter
+      (fun v ->
+        F.pp_print_space fmt ();
+        F.pp_print_string fmt (ctx_get_var v ctx_body))
       vars;
     F.pp_close_box fmt ();
-    F.pp_close_box fmt ()
-  end;
+    F.pp_close_box fmt ());
   (* Add breaks to insert new lines between definitions *)
   F.pp_print_break fmt 0 0
 
@@ -2561,7 +2572,8 @@ let extract_unit_test_if_unit_fun (ctx : extraction_ctx) (fmt : F.formatter)
     (* Add a break before *)
     F.pp_print_break fmt 0 0;
     (* Print a comment *)
-    extract_comment fmt ("Unit test for [" ^ Print.fun_name_to_string def.basename ^ "]");
+    extract_comment fmt
+      ("Unit test for [" ^ Print.fun_name_to_string def.basename ^ "]");
     F.pp_print_space fmt ();
     (* Open a box for the test *)
     F.pp_open_hovbox fmt ctx.indent_incr;
@@ -2613,8 +2625,7 @@ let extract_unit_test_if_unit_fun (ctx : extraction_ctx) (fmt : F.formatter)
         F.pp_print_string fmt "=";
         F.pp_print_space fmt ();
         let success = ctx_get_variant (Assumed Result) result_return_id ctx in
-        F.pp_print_string fmt ("." ^ success ^ " ())")
-    );
+        F.pp_print_string fmt ("." ^ success ^ " ())"));
     (* Close the box for the test *)
     F.pp_close_box fmt ();
     (* Add a break after *)
diff --git a/compiler/ExtractBase.ml b/compiler/ExtractBase.ml
index 4c4a9959..e96a80f9 100644
--- a/compiler/ExtractBase.ml
+++ b/compiler/ExtractBase.ml
@@ -51,7 +51,7 @@ type decl_kind =
       (** The first definition of a group of mutually-recursive definitions.
 
           F*:  [type x0 = ... and x1 = ...]
-          Coq: [Fixpoing x0 := ... with x1 := ...]
+          Coq: [Fixpoint x0 := ... with x1 := ...]
        *)
   | MutRecInner
       (** An inner definition in a group of mutually-recursive definitions. *)
@@ -217,7 +217,6 @@ type formatter = {
             the same purpose as in {!field:fun_name}.
           - loop identifier, if this is for a loop
        *)
-
   var_basename : StringSet.t -> string option -> ty -> string;
       (** Generates a variable basename.
 
@@ -471,8 +470,7 @@ let id_to_string (id : id) (ctx : extraction_ctx) : string =
   | GlobalId gid ->
       let name = (A.GlobalDeclId.Map.find gid global_decls).name in
       "global name: " ^ Print.global_name_to_string name
-  | DeclaredId fid
-  | FunId fid -> (
+  | DeclaredId fid | FunId fid -> (
       match fid with
       | FromLlbc (fid, lp_id, rg_id) ->
           let fun_name =
@@ -781,12 +779,12 @@ let ctx_add_fun_decl (trans_group : bool * pure_fun_translation)
     ctx.fmt.fun_name def.basename def.num_loops def.loop_id num_rgs rg_info
       (keep_fwd, num_backs)
   in
-  let ctx = if def.body = None && !Config.backend = Lean then
-    ctx_add
-      (DeclaredId (FromLlbc (A.Regular def_id, def.loop_id, def.back_id)))
-      ("opaque_defs." ^ name) ctx
-  else
-    ctx
+  let ctx =
+    if def.body = None && !Config.backend = Lean then
+      ctx_add
+        (DeclaredId (FromLlbc (A.Regular def_id, def.loop_id, def.back_id)))
+        ("opaque_defs." ^ name) ctx
+    else ctx
   in
   ctx_add
     (FunId (FromLlbc (A.Regular def_id, def.loop_id, def.back_id)))
diff --git a/compiler/Translate.ml b/compiler/Translate.ml
index df7a750d..1c0bcf73 100644
--- a/compiler/Translate.ml
+++ b/compiler/Translate.ml
@@ -466,10 +466,9 @@ let export_global (fmt : Format.formatter) (config : gen_config) (ctx : gen_ctx)
 
   let is_opaque = Option.is_none body.Pure.body in
   if
-    config.extract_globals && (
-      ((not is_opaque) && config.extract_transparent)
-      || (is_opaque && config.extract_opaque)
-    )
+    config.extract_globals
+    && (((not is_opaque) && config.extract_transparent)
+       || (is_opaque && config.extract_opaque))
   then
     Extract.extract_global_decl ctx.extract_ctx fmt global body config.interface
 
@@ -564,7 +563,8 @@ let export_functions_group (fmt : Format.formatter) (config : gen_config)
           let has_decr_clause = has_decreases_clause decl in
           if has_decr_clause then
             if !Config.backend = Lean then
-              Extract.extract_termination_and_decreasing ctx.extract_ctx fmt decl
+              Extract.extract_termination_and_decreasing ctx.extract_ctx fmt
+                decl
             else
               Extract.extract_template_decreases_clause ctx.extract_ctx fmt decl
         in
@@ -661,24 +661,22 @@ let extract_definitions (fmt : Format.formatter) (config : gen_config)
    *)
   if config.extract_state_type && config.extract_fun_decls then
     export_state_type ();
-  if config.extract_opaque && config.extract_fun_decls && !Config.backend = Lean then begin
+  if config.extract_opaque && config.extract_fun_decls && !Config.backend = Lean
+  then (
     Format.pp_print_break fmt 0 0;
     Format.pp_open_vbox fmt ctx.extract_ctx.indent_incr;
     Format.pp_print_string fmt "structure OpaqueDefs where";
-    Format.pp_print_break fmt 0 0
-  end;
+    Format.pp_print_break fmt 0 0);
   List.iter export_decl_group ctx.crate.declarations;
-  if config.extract_opaque && !Config.backend = Lean then begin
-    Format.pp_close_box fmt ()
-  end;
+  if config.extract_opaque && !Config.backend = Lean then
+    Format.pp_close_box fmt ();
   if config.extract_state_type && not config.extract_fun_decls then
     export_state_type ()
 
 let extract_file (config : gen_config) (ctx : gen_ctx) (filename : string)
     (rust_module_name : string) (module_name : string) (custom_msg : string)
-    ?(custom_variables: string list = [])
-    (custom_imports : string list) (custom_includes : string list)
-    : unit =
+    ?(custom_variables : string list = []) (custom_imports : string list)
+    (custom_includes : string list) : unit =
   (* Open the file and create the formatter *)
   let out = open_out filename in
   let fmt = Format.formatter_of_out_channel out in
@@ -691,14 +689,14 @@ let extract_file (config : gen_config) (ctx : gen_ctx) (filename : string)
    * internal count is consistent with the state of the file.
    *)
   (* Create the header *)
-  begin match !Config.backend with
+  (match !Config.backend with
   | Lean ->
       Printf.fprintf out "-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS\n";
-      Printf.fprintf out "-- [%s]%s\n" rust_module_name custom_msg;
+      Printf.fprintf out "-- [%s]%s\n" rust_module_name custom_msg
   | Coq | FStar ->
-      Printf.fprintf out "(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)\n";
-      Printf.fprintf out "(** [%s]%s *)\n" rust_module_name custom_msg
-  end;
+      Printf.fprintf out
+        "(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)\n";
+      Printf.fprintf out "(** [%s]%s *)\n" rust_module_name custom_msg);
   (match !Config.backend with
   | FStar ->
       Printf.fprintf out "module %s\n" module_name;
@@ -732,11 +730,9 @@ let extract_file (config : gen_config) (ctx : gen_ctx) (filename : string)
       List.iter (fun m -> Printf.fprintf out "import %s\n" m) custom_imports;
       (* Add the custom includes *)
       List.iter (fun m -> Printf.fprintf out "import %s\n" m) custom_includes;
-      if custom_variables <> [] then begin
+      if custom_variables <> [] then (
         Printf.fprintf out "\n";
-        List.iter (fun m -> Printf.fprintf out "%s\n" m) custom_variables
-      end
-  );
+        List.iter (fun m -> Printf.fprintf out "%s\n" m) custom_variables));
   (* From now onwards, we use the formatter *)
   (* Set the margin *)
   Format.pp_set_margin fmt 80;
@@ -885,13 +881,11 @@ let translate_module (filename : string) (dest_dir : string) (crate : A.crate) :
 
   (* Lean reflects the module hierarchy within the filesystem, so we need to
      create more directories *)
-  if !Config.backend = Lean then begin
-    let (^^) = Filename.concat in
+  if !Config.backend = Lean then (
+    let ( ^^ ) = Filename.concat in
     mkdir_if (dest_dir ^^ "Base");
     mkdir_if (dest_dir ^^ module_name);
-    if needs_clauses_module then
-      mkdir_if (dest_dir ^^ module_name ^^ "Clauses");
-  end;
+    if needs_clauses_module then mkdir_if (dest_dir ^^ module_name ^^ "Clauses"));
 
   (* Copy the "Primitives" file *)
   let _ =
@@ -936,7 +930,17 @@ let translate_module (filename : string) (dest_dir : string) (crate : A.crate) :
   let file_delimiter =
     if !Config.backend = Lean then "/" else module_delimiter
   in
-  let ext = match !Config.backend with FStar -> ".fst" | Coq -> ".v" | Lean -> ".lean" in
+  (* File extension for the "regular" modules *)
+  let ext =
+    match !Config.backend with FStar -> ".fst" | Coq -> ".v" | Lean -> ".lean"
+  in
+  (* File extension for the opaque module *)
+  let opaque_ext =
+    match !Config.backend with
+    | FStar -> ".fsti"
+    | Coq -> ".v"
+    | Lean -> ".lean"
+  in
 
   (* Extract one or several files, depending on the configuration *)
   if !Config.split_files then (
@@ -985,20 +989,28 @@ let translate_module (filename : string) (dest_dir : string) (crate : A.crate) :
       ": type definitions" [] [];
 
     (* Extract the template clauses *)
-    if needs_clauses_module && !Config.extract_template_decreases_clauses then (
-      let clauses_filename = extract_filebasename ^ file_delimiter ^ "Clauses" ^ file_delimiter ^ "Template" ^ ext in
-      let clauses_module = module_name ^ module_delimiter ^ "Clauses" ^ module_delimiter ^ "Template" in
-      let clauses_config =
-        { base_gen_config with extract_template_decreases_clauses = true }
-      in
-      extract_file clauses_config gen_ctx clauses_filename crate.A.name
-        clauses_module ": templates for the decreases clauses" [ types_module ]
-        []);
+    (if needs_clauses_module && !Config.extract_template_decreases_clauses then
+     let template_clauses_filename =
+       extract_filebasename ^ file_delimiter ^ "Clauses" ^ file_delimiter
+       ^ "Template" ^ ext
+     in
+     let template_clauses_module =
+       module_name ^ module_delimiter ^ "Clauses" ^ module_delimiter
+       ^ "Template"
+     in
+     let template_clauses_config =
+       { base_gen_config with extract_template_decreases_clauses = true }
+     in
+     extract_file template_clauses_config gen_ctx template_clauses_filename
+       crate.A.name template_clauses_module
+       ": templates for the decreases clauses" [ types_module ] []);
 
     (* Extract the opaque functions, if needed *)
     let opaque_funs_module =
       if has_opaque_funs then (
-        let opaque_filename = extract_filebasename ^ file_delimiter ^ "Opaque" ^ ext in
+        let opaque_filename =
+          extract_filebasename ^ file_delimiter ^ "Opaque" ^ opaque_ext
+        in
         let opaque_module = module_name ^ module_delimiter ^ "Opaque" in
         let opaque_config =
           {
@@ -1028,13 +1040,18 @@ let translate_module (filename : string) (dest_dir : string) (crate : A.crate) :
     in
     let clauses_module =
       if needs_clauses_module then
-        [ module_name ^ module_delimiter ^ "Clauses" ^ module_delimiter ^ "Template"]
+        let clauses_submodule =
+          if !Config.backend = Lean then module_delimiter ^ "Clauses" else ""
+        in
+        [ module_name ^ clauses_submodule ^ module_delimiter ^ "Clauses" ]
+      else []
+    in
+    let custom_variables =
+      if has_opaque_funs then [ "section variable (opaque_defs: OpaqueDefs)" ]
       else []
     in
-    let custom_variables = if has_opaque_funs then [ "section variable (opaque_defs: OpaqueDefs)" ] else [] in
     extract_file fun_config gen_ctx fun_filename crate.A.name fun_module
-      ": function definitions" []
-      ~custom_variables
+      ": function definitions" [] ~custom_variables
       ([ types_module ] @ opaque_funs_module @ clauses_module))
   else
     let gen_config =
diff --git a/tests/coq/betree/BetreeMain_Types.v b/tests/coq/betree/BetreeMain_Types.v
index d02289de..25f280dd 100644
--- a/tests/coq/betree/BetreeMain_Types.v
+++ b/tests/coq/betree/BetreeMain_Types.v
@@ -102,12 +102,6 @@ mkBetree_be_tree_t {
 }
 .
 
-(** [core::num::u64::{10}::MAX] *)
-Definition core_num_u64_max_body : result u64 :=
-  Return (18446744073709551615%u64)
-.
-Definition core_num_u64_max_c : u64 := core_num_u64_max_body%global.
-
 (** The state type used in the state-error monad *)
 Axiom state : Type.
 
diff --git a/tests/coq/hashmap/Hashmap_Types.v b/tests/coq/hashmap/Hashmap_Types.v
index a3b68f9a..ce6e7dab 100644
--- a/tests/coq/hashmap/Hashmap_Types.v
+++ b/tests/coq/hashmap/Hashmap_Types.v
@@ -31,8 +31,4 @@ Arguments Hash_map_max_load_factor {T}.
 Arguments Hash_map_max_load {T}.
 Arguments Hash_map_slots {T}.
 
-(** [core::num::u32::{9}::MAX] *)
-Definition core_num_u32_max_body : result u32 := Return (4294967295%u32).
-Definition core_num_u32_max_c : u32 := core_num_u32_max_body%global.
-
 End Hashmap_Types .
diff --git a/tests/coq/hashmap_on_disk/HashmapMain_Types.v b/tests/coq/hashmap_on_disk/HashmapMain_Types.v
index 01243baf..b92cbf3a 100644
--- a/tests/coq/hashmap_on_disk/HashmapMain_Types.v
+++ b/tests/coq/hashmap_on_disk/HashmapMain_Types.v
@@ -31,10 +31,6 @@ Arguments Hashmap_hash_map_max_load_factor {T}.
 Arguments Hashmap_hash_map_max_load {T}.
 Arguments Hashmap_hash_map_slots {T}.
 
-(** [core::num::u32::{9}::MAX] *)
-Definition core_num_u32_max_body : result u32 := Return (4294967295%u32).
-Definition core_num_u32_max_c : u32 := core_num_u32_max_body%global.
-
 (** The state type used in the state-error monad *)
 Axiom state : Type.
 
diff --git a/tests/fstar/betree/BetreeMain.Clauses.Template.fst b/tests/fstar/betree/BetreeMain.Clauses.Template.fst
index d48213d3..5a9776ab 100644
--- a/tests/fstar/betree/BetreeMain.Clauses.Template.fst
+++ b/tests/fstar/betree/BetreeMain.Clauses.Template.fst
@@ -6,10 +6,6 @@ open BetreeMain.Types
 
 #set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
 
-(** [core::num::u64::{10}::MAX] *)
-let core_num_u64_max_body : result u64 = Return 18446744073709551615
-let core_num_u64_max_c : u64 = eval_global core_num_u64_max_body
-
 (** [betree_main::betree::List::{1}::len]: decreases clause *)
 unfold
 let betree_list_len_decreases (t : Type0) (self : betree_list_t t) : nat =
diff --git a/tests/fstar/betree/BetreeMain.Types.fsti b/tests/fstar/betree/BetreeMain.Types.fsti
index c81e3302..aad9cb43 100644
--- a/tests/fstar/betree/BetreeMain.Types.fsti
+++ b/tests/fstar/betree/BetreeMain.Types.fsti
@@ -55,10 +55,6 @@ type betree_be_tree_t =
   betree_be_tree_root : betree_node_t;
 }
 
-(** [core::num::u64::{10}::MAX] *)
-let core_num_u64_max_body : result u64 = Return 18446744073709551615
-let core_num_u64_max_c : u64 = eval_global core_num_u64_max_body
-
 (** The state type used in the state-error monad *)
 val state : Type0
 
diff --git a/tests/fstar/betree_back_stateful/BetreeMain.Clauses.Template.fst b/tests/fstar/betree_back_stateful/BetreeMain.Clauses.Template.fst
index d48213d3..5a9776ab 100644
--- a/tests/fstar/betree_back_stateful/BetreeMain.Clauses.Template.fst
+++ b/tests/fstar/betree_back_stateful/BetreeMain.Clauses.Template.fst
@@ -6,10 +6,6 @@ open BetreeMain.Types
 
 #set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
 
-(** [core::num::u64::{10}::MAX] *)
-let core_num_u64_max_body : result u64 = Return 18446744073709551615
-let core_num_u64_max_c : u64 = eval_global core_num_u64_max_body
-
 (** [betree_main::betree::List::{1}::len]: decreases clause *)
 unfold
 let betree_list_len_decreases (t : Type0) (self : betree_list_t t) : nat =
diff --git a/tests/fstar/betree_back_stateful/BetreeMain.Types.fsti b/tests/fstar/betree_back_stateful/BetreeMain.Types.fsti
index c81e3302..aad9cb43 100644
--- a/tests/fstar/betree_back_stateful/BetreeMain.Types.fsti
+++ b/tests/fstar/betree_back_stateful/BetreeMain.Types.fsti
@@ -55,10 +55,6 @@ type betree_be_tree_t =
   betree_be_tree_root : betree_node_t;
 }
 
-(** [core::num::u64::{10}::MAX] *)
-let core_num_u64_max_body : result u64 = Return 18446744073709551615
-let core_num_u64_max_c : u64 = eval_global core_num_u64_max_body
-
 (** The state type used in the state-error monad *)
 val state : Type0
 
diff --git a/tests/fstar/hashmap/Hashmap.Clauses.Template.fst b/tests/fstar/hashmap/Hashmap.Clauses.Template.fst
index aef5e25e..640ae783 100644
--- a/tests/fstar/hashmap/Hashmap.Clauses.Template.fst
+++ b/tests/fstar/hashmap/Hashmap.Clauses.Template.fst
@@ -24,10 +24,6 @@ let hash_map_insert_in_list_loop_decreases (t : Type0) (key : usize)
   (value : t) (ls : list_t t) : nat =
   admit ()
 
-(** [core::num::u32::{9}::MAX] *)
-let core_num_u32_max_body : result u32 = Return 4294967295
-let core_num_u32_max_c : u32 = eval_global core_num_u32_max_body
-
 (** [hashmap::HashMap::{0}::move_elements_from_list]: decreases clause *)
 unfold
 let hash_map_move_elements_from_list_loop_decreases (t : Type0)
diff --git a/tests/fstar/hashmap/Hashmap.Types.fst b/tests/fstar/hashmap/Hashmap.Types.fst
index d53b8a42..91ee26c6 100644
--- a/tests/fstar/hashmap/Hashmap.Types.fst
+++ b/tests/fstar/hashmap/Hashmap.Types.fst
@@ -19,7 +19,3 @@ type hash_map_t (t : Type0) =
   hash_map_slots : vec (list_t t);
 }
 
-(** [core::num::u32::{9}::MAX] *)
-let core_num_u32_max_body : result u32 = Return 4294967295
-let core_num_u32_max_c : u32 = eval_global core_num_u32_max_body
-
diff --git a/tests/fstar/hashmap_on_disk/HashmapMain.Clauses.Template.fst b/tests/fstar/hashmap_on_disk/HashmapMain.Clauses.Template.fst
index 1e15d1f9..615c670d 100644
--- a/tests/fstar/hashmap_on_disk/HashmapMain.Clauses.Template.fst
+++ b/tests/fstar/hashmap_on_disk/HashmapMain.Clauses.Template.fst
@@ -24,10 +24,6 @@ let hashmap_hash_map_insert_in_list_loop_decreases (t : Type0) (key : usize)
   (value : t) (ls : hashmap_list_t t) : nat =
   admit ()
 
-(** [core::num::u32::{9}::MAX] *)
-let core_num_u32_max_body : result u32 = Return 4294967295
-let core_num_u32_max_c : u32 = eval_global core_num_u32_max_body
-
 (** [hashmap_main::hashmap::HashMap::{0}::move_elements_from_list]: decreases clause *)
 unfold
 let hashmap_hash_map_move_elements_from_list_loop_decreases (t : Type0)
diff --git a/tests/fstar/hashmap_on_disk/HashmapMain.Types.fsti b/tests/fstar/hashmap_on_disk/HashmapMain.Types.fsti
index ce4d6485..e289174b 100644
--- a/tests/fstar/hashmap_on_disk/HashmapMain.Types.fsti
+++ b/tests/fstar/hashmap_on_disk/HashmapMain.Types.fsti
@@ -19,10 +19,6 @@ type hashmap_hash_map_t (t : Type0) =
   hashmap_hash_map_slots : vec (hashmap_list_t t);
 }
 
-(** [core::num::u32::{9}::MAX] *)
-let core_num_u32_max_body : result u32 = Return 4294967295
-let core_num_u32_max_c : u32 = eval_global core_num_u32_max_body
-
 (** The state type used in the state-error monad *)
 val state : Type0
 
diff --git a/tests/lean/hashmap/Base/Primitives.lean b/tests/lean/hashmap/Base/Primitives.lean
new file mode 100644
index 00000000..79958d94
--- /dev/null
+++ b/tests/lean/hashmap/Base/Primitives.lean
@@ -0,0 +1,373 @@
+import Lean
+import Lean.Meta.Tactic.Simp
+import Init.Data.List.Basic
+import Mathlib.Tactic.RunCmd
+
+-------------
+-- PRELUDE --
+-------------
+
+-- Results & monadic combinators
+
+-- TODO: use syntactic conventions and capitalize error, result, etc.
+
+inductive error where
+   | assertionFailure: error
+   | integerOverflow: error
+   | arrayOutOfBounds: error
+   | maximumSizeExceeded: error
+   | panic: error
+deriving Repr, BEq
+
+open error
+
+inductive result (α : Type u) where
+  | ret (v: α): result α
+  | fail (e: error): result α 
+deriving Repr, BEq
+
+open result
+
+/- HELPERS -/
+
+-- TODO: is there automated syntax for these discriminators?
+def is_ret {α: Type} (r: result α): Bool :=
+  match r with
+  | result.ret _ => true
+  | result.fail _ => false
+
+def massert (b:Bool) : result Unit :=
+  if b then .ret () else fail assertionFailure
+
+def eval_global {α: Type} (x: result α) (_: is_ret x): α :=
+  match x with
+  | result.fail _ => by contradiction
+  | result.ret x => x
+
+/- DO-DSL SUPPORT -/
+
+def bind (x: result α) (f: α -> result β) : result β :=
+  match x with
+  | ret v  => f v 
+  | fail v => fail v
+
+-- Allows using result in do-blocks
+instance : Bind result where
+  bind := bind
+
+-- Allows using return x in do-blocks
+instance : Pure result where
+  pure := fun x => ret x
+
+/- CUSTOM-DSL SUPPORT -/
+
+-- Let-binding the result of a monadic operation is oftentimes not sufficient,
+-- because we may need a hypothesis for equational reasoning in the scope. We
+-- rely on subtype, and a custom let-binding operator, in effect recreating our
+-- own variant of the do-dsl
+
+def result.attach : (o : result α) → result { x : α // o = ret x }
+  | .ret x => .ret ⟨x, rfl⟩
+  | .fail e   => .fail e
+
+macro "let" h:ident " : " e:term " <-- " f:term : doElem =>
+  `(doElem| let ⟨$e, $h⟩ ← result.attach $f)
+
+-- Silly example of the kind of reasoning that this notation enables
+#eval do
+  let h: y <-- .ret (0: Nat)
+  let _: y = 0 := by cases h; decide
+  let r: { x: Nat // x = 0 } := ⟨ y, by assumption ⟩
+  .ret r
+
+----------------------
+-- MACHINE INTEGERS --
+----------------------
+
+-- NOTE: we reuse the USize type from prelude.lean, because at least we know
+-- it's defined in an idiomatic style that is going to make proofs easy (and
+-- indeed, several proofs here are much shortened compared to Aymeric's earlier
+-- attempt.) This is not stricto sensu the *correct* thing to do, because one
+-- can query at run-time the value of USize, which we do *not* want to do (we
+-- don't know what target we'll run on!), but when the day comes, we'll just
+-- define our own USize.
+-- ANOTHER NOTE: there is USize.sub but it has wraparound semantics, which is
+-- not something we want to define (I think), so we use our own monadic sub (but
+-- is it in line with the Rust behavior?)
+
+-- TODO: I am somewhat under the impression that subtraction is defined as a
+-- total function over nats...? the hypothesis in the if condition is not used
+-- in the then-branch which confuses me quite a bit
+
+-- TODO: add a refinement for the result (just like vec_push_back below) that
+-- explains that the toNat of the result (in the case of success) is the sub of
+-- the toNat of the arguments (i.e. intrinsic specification)
+-- ... do we want intrinsic specifications for the builtins? that might require
+-- some careful type annotations in the monadic notation for clients, but may
+-- give us more "for free"
+
+-- Note from Chris Bailey: "If there's more than one salient property of your
+-- definition then the subtyping strategy might get messy, and the property part
+-- of a subtype is less discoverable by the simplifier or tactics like
+-- library_search." Try to settle this with a Lean expert on what is the most
+-- productive way to go about this?
+
+-- One needs to perform a little bit of reasoning in order to successfully
+-- inject constants into USize, so we provide a general-purpose macro
+
+syntax "intlit" : tactic
+
+macro_rules
+  | `(tactic| intlit) => `(tactic|
+    match USize.size, usize_size_eq with
+    | _, Or.inl rfl => decide
+    | _, Or.inr rfl => decide)
+
+-- This is how the macro is expected to be used
+#eval USize.ofNatCore 0 (by intlit)
+
+-- Also works for other integer types (at the expense of a needless disjunction)
+#eval UInt32.ofNatCore 0 (by intlit)
+
+-- Further thoughts: look at what has been done here:
+-- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/Fin/Basic.lean
+-- and
+-- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/UInt.lean
+-- which both contain a fair amount of reasoning already!
+def USize.checked_sub (n: USize) (m: USize): result USize :=
+  -- NOTE: the test USize.toNat n - m >= 0 seems to always succeed?
+  if n >= m then
+    let n' := USize.toNat n
+    let m' := USize.toNat n
+    let r := USize.ofNatCore (n' - m') (by
+      have h: n' - m' <= n' := by
+        apply Nat.sub_le_of_le_add
+        case h => rewrite [ Nat.add_comm ]; apply Nat.le_add_left
+      apply Nat.lt_of_le_of_lt h
+      apply n.val.isLt
+    )
+    return r
+  else
+    fail integerOverflow
+
+def USize.checked_add (n: USize) (m: USize): result USize :=
+  if h: n.val.val + m.val.val <= 4294967295 then
+    .ret ⟨ n.val.val + m.val.val, by
+      have h': 4294967295 < USize.size := by intlit
+      apply Nat.lt_of_le_of_lt h h'
+    ⟩
+  else if h: n.val + m.val < USize.size then
+    .ret ⟨ n.val + m.val, h ⟩
+  else
+    .fail integerOverflow
+
+def USize.checked_rem (n: USize) (m: USize): result USize :=
+  if h: m > 0 then
+    .ret ⟨ n.val % m.val, by
+      have h1: ↑m.val < USize.size := m.val.isLt
+      have h2: n.val.val % m.val.val < m.val.val := @Nat.mod_lt n.val m.val h
+      apply Nat.lt_trans h2 h1
+    ⟩
+  else
+    .fail integerOverflow
+
+def USize.checked_mul (n: USize) (m: USize): result USize :=
+    if h: n.val.val * m.val.val <= 4294967295 then
+    .ret ⟨ n.val.val * m.val.val, by
+      have h': 4294967295 < USize.size := by intlit
+      apply Nat.lt_of_le_of_lt h h'
+    ⟩
+  else if h: n.val * m.val < USize.size then
+    .ret ⟨ n.val * m.val, h ⟩
+  else
+    .fail integerOverflow
+
+def USize.checked_div (n: USize) (m: USize): result USize :=
+  if m > 0 then
+    .ret ⟨ n.val / m.val, by
+      have h1: ↑n.val < USize.size := n.val.isLt
+      have h2: n.val.val / m.val.val <= n.val.val := @Nat.div_le_self n.val m.val
+      apply Nat.lt_of_le_of_lt h2 h1
+    ⟩
+  else
+    .fail integerOverflow
+
+class MachineInteger (t: Type) where
+  size: Nat
+  val: t -> Fin size
+  ofNatCore: (n:Nat) -> LT.lt n size -> t
+
+set_option hygiene false in
+run_cmd
+  for typeName in [`UInt8, `UInt16, `UInt32, `UInt64, `USize].map Lean.mkIdent do
+  Lean.Elab.Command.elabCommand (← `(
+    namespace $typeName
+    instance: MachineInteger $typeName where
+      size := size
+      val := val
+      ofNatCore := ofNatCore
+    end $typeName
+  ))
+
+def scalar_cast { src: Type } (dst: Type) [ MachineInteger src ] [ MachineInteger dst ] (x: src): result dst :=
+  if h: MachineInteger.val x < MachineInteger.size dst then
+    .ret (MachineInteger.ofNatCore (MachineInteger.val x).val h)
+  else
+    .fail integerOverflow
+
+
+-- Test behavior...
+#eval assert! USize.checked_sub 10 20 == fail integerOverflow; 0
+
+#eval USize.checked_sub 20 10
+-- NOTE: compare with concrete behavior here, which I do not think we want
+#eval USize.sub 0 1
+#eval UInt8.add 255 255
+
+-------------
+-- VECTORS --
+-------------
+
+-- Note: unlike F*, Lean seems to use strict upper bounds (e.g. USize.size)
+-- rather than maximum values (usize_max).
+def vec (α : Type u) := { l : List α // List.length l < USize.size }
+
+def vec_new (α : Type u): vec α := ⟨ [], by {
+  match USize.size, usize_size_eq with
+  | _, Or.inl rfl => simp
+  | _, Or.inr rfl => simp
+  } ⟩
+
+#check vec_new
+
+def vec_len (α : Type u) (v : vec α) : USize :=
+  let ⟨ v, l ⟩ := v
+  USize.ofNatCore (List.length v) l
+
+#eval vec_len Nat (vec_new Nat)
+ 
+def vec_push_fwd (α : Type u) (_ : vec α) (_ : α) : Unit := ()
+
+-- NOTE: old version trying to use a subtype notation, but probably better to
+-- leave result elimination to auxiliary lemmas with suitable preconditions
+-- TODO: I originally wrote `List.length v.val < USize.size - 1`; how can one
+-- make the proof work in that case? Probably need to import tactics from
+-- mathlib to deal with inequalities... would love to see an example.
+def vec_push_back_old (α : Type u) (v : vec α) (x : α) : { res: result (vec α) //
+  match res with | fail _ => True | ret v' => List.length v'.val = List.length v.val + 1}
+  :=
+  if h : List.length v.val + 1 < USize.size then
+    ⟨ return ⟨List.concat v.val x,
+      by
+        rw [List.length_concat]
+        assumption
+     ⟩, by simp ⟩
+  else
+    ⟨ fail maximumSizeExceeded, by simp ⟩
+
+#eval do
+  -- NOTE: the // notation is syntactic sugar for Subtype, a refinement with
+  -- fields val and property. However, Lean's elaborator can automatically
+  -- select the `val` field if the context provides a type annotation. We
+  -- annotate `x`, which relieves us of having to write `.val` on the right-hand
+  -- side of the monadic let.
+  let v := vec_new Nat
+  let x: vec Nat ← (vec_push_back_old Nat v 1: result (vec Nat)) -- WHY do we need the type annotation here?
+  -- TODO: strengthen post-condition above and do a demo to show that we can
+  -- safely eliminate the `fail` case
+  return (vec_len Nat x)
+
+def vec_push_back (α : Type u) (v : vec α) (x : α) : result (vec α)
+  :=
+  if h : List.length v.val + 1 <= 4294967295 then
+    return ⟨ List.concat v.val x,
+      by
+        rw [List.length_concat]
+        have h': 4294967295 < USize.size := by intlit
+        apply Nat.lt_of_le_of_lt h h'
+    ⟩
+  else if h: List.length v.val + 1 < USize.size then
+    return ⟨List.concat v.val x,
+      by
+        rw [List.length_concat]
+        assumption
+     ⟩
+  else
+    fail maximumSizeExceeded
+
+def vec_insert_fwd (α : Type u) (v: vec α) (i: USize) (_: α): result Unit :=
+  if i.val < List.length v.val then
+    .ret ()
+  else
+    .fail arrayOutOfBounds
+
+def vec_insert_back (α : Type u) (v: vec α) (i: USize) (x: α): result (vec α) :=
+  if i.val < List.length v.val then
+    .ret ⟨ List.set v.val i.val x, by
+      have h: List.length v.val < USize.size := v.property
+      rewrite [ List.length_set v.val i.val x ]
+      assumption
+    ⟩
+  else
+    .fail arrayOutOfBounds
+
+def vec_index_fwd (α : Type u) (v: vec α) (i: USize): result α :=
+  if h: i.val < List.length v.val then
+    .ret (List.get v.val ⟨i.val, h⟩)
+  else
+    .fail arrayOutOfBounds
+
+def vec_index_back (α : Type u) (v: vec α) (i: USize) (_: α): result Unit :=
+  if i.val < List.length v.val then
+    .ret ()
+  else
+    .fail arrayOutOfBounds
+
+def vec_index_mut_fwd (α : Type u) (v: vec α) (i: USize): result α :=
+  if h: i.val < List.length v.val then
+    .ret (List.get v.val ⟨i.val, h⟩)
+  else
+    .fail arrayOutOfBounds
+
+def vec_index_mut_back (α : Type u) (v: vec α) (i: USize) (x: α): result (vec α) :=
+  if i.val < List.length v.val then
+    .ret ⟨ List.set v.val i.val x, by
+      have h: List.length v.val < USize.size := v.property
+      rewrite [ List.length_set v.val i.val x ]
+      assumption
+    ⟩
+  else
+    .fail arrayOutOfBounds
+
+----------
+-- MISC --
+----------
+
+def mem_replace_fwd (a : Type) (x : a) (_ : a) : a :=
+  x
+
+def mem_replace_back (a : Type) (_ : a) (y : a) : a :=
+  y
+
+--------------------
+-- ASSERT COMMAND --
+--------------------
+
+open Lean Elab Command Term Meta
+
+syntax (name := assert) "#assert" term: command
+
+@[command_elab assert]
+def assertImpl : CommandElab := fun (_stx: Syntax) => do
+  logInfo "Reducing and asserting: "
+  logInfo _stx[1]
+  runTermElabM (fun _ => do
+    let e ← Term.elabTerm _stx[1] none
+    logInfo (Expr.dbgToString e)
+    -- How to evaluate the term and compare the result to true?
+    pure ())
+  -- logInfo (Expr.dbgToString (``true))
+  -- throwError "TODO: assert"
+
+#eval 2 == 2
+#assert (2 == 2)
diff --git a/tests/lean/hashmap/Hashmap/Clauses/Clauses.lean b/tests/lean/hashmap/Hashmap/Clauses/Clauses.lean
new file mode 100644
index 00000000..eec8ef96
--- /dev/null
+++ b/tests/lean/hashmap/Hashmap/Clauses/Clauses.lean
@@ -0,0 +1,107 @@
+-- [hashmap]: the decreases clauses
+import Base.Primitives
+import Hashmap.Types
+
+/- [hashmap::HashMap::{0}::allocate_slots]: termination measure -/
+@[simp]
+def hash_map_allocate_slots_loop_terminates (T : Type) (slots : vec (list_t T))
+  (n : USize) :=
+  (slots, n)
+
+syntax "hash_map_allocate_slots_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| hash_map_allocate_slots_loop_decreases $slots $n) =>`(tactic| sorry)
+
+/- [hashmap::HashMap::{0}::clear]: termination measure -/
+@[simp]
+def hash_map_clear_loop_terminates (T : Type) (slots : vec (list_t T))
+  (i : USize) :=
+  (slots, i)
+
+syntax "hash_map_clear_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| hash_map_clear_loop_decreases $slots $i) =>`(tactic| sorry)
+
+/- [hashmap::HashMap::{0}::insert_in_list]: termination measure -/
+@[simp]
+def hash_map_insert_in_list_loop_terminates (T : Type) (key : USize)
+  (value : T) (ls : list_t T) :=
+  (key, value, ls)
+
+syntax "hash_map_insert_in_list_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| hash_map_insert_in_list_loop_decreases $key $value $ls) =>
+  `(tactic| sorry)
+
+/- [hashmap::HashMap::{0}::move_elements_from_list]: termination measure -/
+@[simp]
+def hash_map_move_elements_from_list_loop_terminates (T : Type)
+  (ntable : hash_map_t T) (ls : list_t T) :=
+  (ntable, ls)
+
+syntax "hash_map_move_elements_from_list_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| hash_map_move_elements_from_list_loop_decreases $ntable $ls) =>
+  `(tactic| sorry)
+
+/- [hashmap::HashMap::{0}::move_elements]: termination measure -/
+@[simp]
+def hash_map_move_elements_loop_terminates (T : Type) (ntable : hash_map_t T)
+  (slots : vec (list_t T)) (i : USize) :=
+  (ntable, slots, i)
+
+syntax "hash_map_move_elements_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| hash_map_move_elements_loop_decreases $ntable $slots $i) =>
+  `(tactic| sorry)
+
+/- [hashmap::HashMap::{0}::contains_key_in_list]: termination measure -/
+@[simp]
+def hash_map_contains_key_in_list_loop_terminates (T : Type) (key : USize)
+  (ls : list_t T) :=
+  (key, ls)
+
+syntax "hash_map_contains_key_in_list_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| hash_map_contains_key_in_list_loop_decreases $key $ls) =>
+  `(tactic| sorry)
+
+/- [hashmap::HashMap::{0}::get_in_list]: termination measure -/
+@[simp]
+def hash_map_get_in_list_loop_terminates (T : Type) (key : USize)
+  (ls : list_t T) :=
+  (key, ls)
+
+syntax "hash_map_get_in_list_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| hash_map_get_in_list_loop_decreases $key $ls) =>`(tactic| sorry)
+
+/- [hashmap::HashMap::{0}::get_mut_in_list]: termination measure -/
+@[simp]
+def hash_map_get_mut_in_list_loop_terminates (T : Type) (ls : list_t T)
+  (key : USize) :=
+  (ls, key)
+
+syntax "hash_map_get_mut_in_list_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| hash_map_get_mut_in_list_loop_decreases $ls $key) =>`(tactic| sorry)
+
+/- [hashmap::HashMap::{0}::remove_from_list]: termination measure -/
+@[simp]
+def hash_map_remove_from_list_loop_terminates (T : Type) (key : USize)
+  (ls : list_t T) :=
+  (key, ls)
+
+syntax "hash_map_remove_from_list_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| hash_map_remove_from_list_loop_decreases $key $ls) =>`(tactic| sorry)
+
diff --git a/tests/lean/hashmap/Hashmap/Clauses/Template.lean b/tests/lean/hashmap/Hashmap/Clauses/Template.lean
new file mode 100644
index 00000000..2bc92153
--- /dev/null
+++ b/tests/lean/hashmap/Hashmap/Clauses/Template.lean
@@ -0,0 +1,108 @@
+-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
+-- [hashmap]: templates for the decreases clauses
+import Base.Primitives
+import Hashmap.Types
+
+/- [hashmap::HashMap::{0}::allocate_slots]: termination measure -/
+@[simp]
+def hash_map_allocate_slots_loop_terminates (T : Type) (slots : vec (list_t T))
+  (n : USize) :=
+  (slots, n)
+
+syntax "hash_map_allocate_slots_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| hash_map_allocate_slots_loop_decreases $slots $n) =>`(tactic| sorry)
+
+/- [hashmap::HashMap::{0}::clear]: termination measure -/
+@[simp]
+def hash_map_clear_loop_terminates (T : Type) (slots : vec (list_t T))
+  (i : USize) :=
+  (slots, i)
+
+syntax "hash_map_clear_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| hash_map_clear_loop_decreases $slots $i) =>`(tactic| sorry)
+
+/- [hashmap::HashMap::{0}::insert_in_list]: termination measure -/
+@[simp]
+def hash_map_insert_in_list_loop_terminates (T : Type) (key : USize)
+  (value : T) (ls : list_t T) :=
+  (key, value, ls)
+
+syntax "hash_map_insert_in_list_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| hash_map_insert_in_list_loop_decreases $key $value $ls) =>
+  `(tactic| sorry)
+
+/- [hashmap::HashMap::{0}::move_elements_from_list]: termination measure -/
+@[simp]
+def hash_map_move_elements_from_list_loop_terminates (T : Type)
+  (ntable : hash_map_t T) (ls : list_t T) :=
+  (ntable, ls)
+
+syntax "hash_map_move_elements_from_list_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| hash_map_move_elements_from_list_loop_decreases $ntable $ls) =>
+  `(tactic| sorry)
+
+/- [hashmap::HashMap::{0}::move_elements]: termination measure -/
+@[simp]
+def hash_map_move_elements_loop_terminates (T : Type) (ntable : hash_map_t T)
+  (slots : vec (list_t T)) (i : USize) :=
+  (ntable, slots, i)
+
+syntax "hash_map_move_elements_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| hash_map_move_elements_loop_decreases $ntable $slots $i) =>
+  `(tactic| sorry)
+
+/- [hashmap::HashMap::{0}::contains_key_in_list]: termination measure -/
+@[simp]
+def hash_map_contains_key_in_list_loop_terminates (T : Type) (key : USize)
+  (ls : list_t T) :=
+  (key, ls)
+
+syntax "hash_map_contains_key_in_list_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| hash_map_contains_key_in_list_loop_decreases $key $ls) =>
+  `(tactic| sorry)
+
+/- [hashmap::HashMap::{0}::get_in_list]: termination measure -/
+@[simp]
+def hash_map_get_in_list_loop_terminates (T : Type) (key : USize)
+  (ls : list_t T) :=
+  (key, ls)
+
+syntax "hash_map_get_in_list_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| hash_map_get_in_list_loop_decreases $key $ls) =>`(tactic| sorry)
+
+/- [hashmap::HashMap::{0}::get_mut_in_list]: termination measure -/
+@[simp]
+def hash_map_get_mut_in_list_loop_terminates (T : Type) (ls : list_t T)
+  (key : USize) :=
+  (ls, key)
+
+syntax "hash_map_get_mut_in_list_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| hash_map_get_mut_in_list_loop_decreases $ls $key) =>`(tactic| sorry)
+
+/- [hashmap::HashMap::{0}::remove_from_list]: termination measure -/
+@[simp]
+def hash_map_remove_from_list_loop_terminates (T : Type) (key : USize)
+  (ls : list_t T) :=
+  (key, ls)
+
+syntax "hash_map_remove_from_list_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| hash_map_remove_from_list_loop_decreases $key $ls) =>`(tactic| sorry)
+
diff --git a/tests/lean/hashmap/Hashmap/Funs.lean b/tests/lean/hashmap/Hashmap/Funs.lean
new file mode 100644
index 00000000..030b335a
--- /dev/null
+++ b/tests/lean/hashmap/Hashmap/Funs.lean
@@ -0,0 +1,580 @@
+-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
+-- [hashmap]: function definitions
+import Base.Primitives
+import Hashmap.Types
+import Hashmap.Clauses.Clauses
+
+/- [hashmap::hash_key] -/
+def hash_key_fwd (k : USize) : result USize := result.ret k
+
+/- [hashmap::HashMap::{0}::allocate_slots] -/
+def hash_map_allocate_slots_loop_fwd
+  (T : Type) (slots : vec (list_t T)) (n : USize) :
+  (result (vec (list_t T)))
+  :=
+  if n > (USize.ofNatCore 0 (by intlit))
+  then
+    do
+      let slots0 <- vec_push_back (list_t T) slots list_t.ListNil
+      let n0 <- USize.checked_sub n (USize.ofNatCore 1 (by intlit))
+      hash_map_allocate_slots_loop_fwd T slots0 n0
+  else result.ret slots
+termination_by hash_map_allocate_slots_loop_fwd slots n =>
+                                                          hash_map_allocate_slots_loop_terminates
+                                                          T slots n
+decreasing_by hash_map_allocate_slots_loop_decreases slots n
+
+/- [hashmap::HashMap::{0}::allocate_slots] -/
+def hash_map_allocate_slots_fwd
+  (T : Type) (slots : vec (list_t T)) (n : USize) : result (vec (list_t T)) :=
+  hash_map_allocate_slots_loop_fwd T slots n
+
+/- [hashmap::HashMap::{0}::new_with_capacity] -/
+def hash_map_new_with_capacity_fwd
+  (T : Type) (capacity : USize) (max_load_dividend : USize)
+  (max_load_divisor : USize) :
+  result (hash_map_t T)
+  :=
+  do
+    let v := vec_new (list_t T)
+    let slots <- hash_map_allocate_slots_fwd T v capacity
+    let i <- USize.checked_mul capacity max_load_dividend
+    let i0 <- USize.checked_div i max_load_divisor
+    result.ret
+      {
+        hash_map_num_entries := (USize.ofNatCore 0 (by intlit)),
+        hash_map_max_load_factor := (max_load_dividend, max_load_divisor),
+        hash_map_max_load := i0,
+        hash_map_slots := slots
+      }
+
+/- [hashmap::HashMap::{0}::new] -/
+def hash_map_new_fwd (T : Type) : result (hash_map_t T) :=
+  hash_map_new_with_capacity_fwd T (USize.ofNatCore 32 (by intlit))
+    (USize.ofNatCore 4 (by intlit)) (USize.ofNatCore 5 (by intlit))
+
+/- [hashmap::HashMap::{0}::clear] -/
+def hash_map_clear_loop_fwd_back
+  (T : Type) (slots : vec (list_t T)) (i : USize) :
+  (result (vec (list_t T)))
+  :=
+  let i0 := vec_len (list_t T) slots
+  if i < i0
+  then
+    do
+      let i1 <- USize.checked_add i (USize.ofNatCore 1 (by intlit))
+      let slots0 <- vec_index_mut_back (list_t T) slots i list_t.ListNil
+      hash_map_clear_loop_fwd_back T slots0 i1
+  else result.ret slots
+termination_by hash_map_clear_loop_fwd_back slots i =>
+                                                      hash_map_clear_loop_terminates
+                                                      T slots i
+decreasing_by hash_map_clear_loop_decreases slots i
+
+/- [hashmap::HashMap::{0}::clear] -/
+def hash_map_clear_fwd_back
+  (T : Type) (self : hash_map_t T) : result (hash_map_t T) :=
+  do
+    let v <-
+      hash_map_clear_loop_fwd_back T self.hash_map_slots
+        (USize.ofNatCore 0 (by intlit))
+    result.ret
+      {
+        hash_map_num_entries := (USize.ofNatCore 0 (by intlit)),
+        hash_map_max_load_factor := self.hash_map_max_load_factor,
+        hash_map_max_load := self.hash_map_max_load,
+        hash_map_slots := v
+      }
+
+/- [hashmap::HashMap::{0}::len] -/
+def hash_map_len_fwd (T : Type) (self : hash_map_t T) : result USize :=
+  result.ret self.hash_map_num_entries
+
+/- [hashmap::HashMap::{0}::insert_in_list] -/
+def hash_map_insert_in_list_loop_fwd
+  (T : Type) (key : USize) (value : T) (ls : list_t T) : (result Bool) :=
+  match ls with
+  | list_t.ListCons ckey cvalue tl =>
+    if ckey = key
+    then result.ret false
+    else hash_map_insert_in_list_loop_fwd T key value tl
+  | list_t.ListNil => result.ret true
+  
+termination_by hash_map_insert_in_list_loop_fwd key value ls =>
+                                                               hash_map_insert_in_list_loop_terminates
+                                                               T key value ls
+decreasing_by hash_map_insert_in_list_loop_decreases key value ls
+
+/- [hashmap::HashMap::{0}::insert_in_list] -/
+def hash_map_insert_in_list_fwd
+  (T : Type) (key : USize) (value : T) (ls : list_t T) : result Bool :=
+  hash_map_insert_in_list_loop_fwd T key value ls
+
+/- [hashmap::HashMap::{0}::insert_in_list] -/
+def hash_map_insert_in_list_loop_back
+  (T : Type) (key : USize) (value : T) (ls : list_t T) : (result (list_t T)) :=
+  match ls with
+  | list_t.ListCons ckey cvalue tl =>
+    if ckey = key
+    then result.ret (list_t.ListCons ckey value tl)
+    else
+      do
+        let tl0 <- hash_map_insert_in_list_loop_back T key value tl
+        result.ret (list_t.ListCons ckey cvalue tl0)
+  | list_t.ListNil =>
+    let l := list_t.ListNil result.ret (list_t.ListCons key value l)
+  
+termination_by hash_map_insert_in_list_loop_back key value ls =>
+                                                                hash_map_insert_in_list_loop_terminates
+                                                                T key value ls
+decreasing_by hash_map_insert_in_list_loop_decreases key value ls
+
+/- [hashmap::HashMap::{0}::insert_in_list] -/
+def hash_map_insert_in_list_back
+  (T : Type) (key : USize) (value : T) (ls : list_t T) : result (list_t T) :=
+  hash_map_insert_in_list_loop_back T key value ls
+
+/- [hashmap::HashMap::{0}::insert_no_resize] -/
+def hash_map_insert_no_resize_fwd_back
+  (T : Type) (self : hash_map_t T) (key : USize) (value : T) :
+  result (hash_map_t T)
+  :=
+  do
+    let hash <- hash_key_fwd key
+    let i := vec_len (list_t T) self.hash_map_slots
+    let hash_mod <- USize.checked_rem hash i
+    let l <- vec_index_mut_fwd (list_t T) self.hash_map_slots hash_mod
+    let inserted <- hash_map_insert_in_list_fwd T key value l
+    if inserted
+    then
+      do
+        let i0 <- USize.checked_add self.hash_map_num_entries
+          (USize.ofNatCore 1 (by intlit))
+        let l0 <- hash_map_insert_in_list_back T key value l
+        let v <- vec_index_mut_back (list_t T) self.hash_map_slots hash_mod l0
+        result.ret
+          {
+            hash_map_num_entries := i0,
+            hash_map_max_load_factor := self.hash_map_max_load_factor,
+            hash_map_max_load := self.hash_map_max_load,
+            hash_map_slots := v
+          }
+    else
+      do
+        let l0 <- hash_map_insert_in_list_back T key value l
+        let v <- vec_index_mut_back (list_t T) self.hash_map_slots hash_mod l0
+        result.ret
+          {
+            hash_map_num_entries := self.hash_map_num_entries,
+            hash_map_max_load_factor := self.hash_map_max_load_factor,
+            hash_map_max_load := self.hash_map_max_load,
+            hash_map_slots := v
+          }
+
+/- [core::num::u32::{9}::MAX] -/
+def core_num_u32_max_body : result UInt32 :=
+  result.ret (UInt32.ofNatCore 4294967295 (by intlit))
+def core_num_u32_max_c : UInt32 := eval_global core_num_u32_max_body (by simp)
+
+/- [hashmap::HashMap::{0}::move_elements_from_list] -/
+def hash_map_move_elements_from_list_loop_fwd_back
+  (T : Type) (ntable : hash_map_t T) (ls : list_t T) :
+  (result (hash_map_t T))
+  :=
+  match ls with
+  | list_t.ListCons k v tl =>
+    do
+      let ntable0 <- hash_map_insert_no_resize_fwd_back T ntable k v
+      hash_map_move_elements_from_list_loop_fwd_back T ntable0 tl
+  | list_t.ListNil => result.ret ntable
+  
+termination_by hash_map_move_elements_from_list_loop_fwd_back ntable ls =>
+   hash_map_move_elements_from_list_loop_terminates T ntable ls
+decreasing_by hash_map_move_elements_from_list_loop_decreases ntable ls
+
+/- [hashmap::HashMap::{0}::move_elements_from_list] -/
+def hash_map_move_elements_from_list_fwd_back
+  (T : Type) (ntable : hash_map_t T) (ls : list_t T) : result (hash_map_t T) :=
+  hash_map_move_elements_from_list_loop_fwd_back T ntable ls
+
+/- [hashmap::HashMap::{0}::move_elements] -/
+def hash_map_move_elements_loop_fwd_back
+  (T : Type) (ntable : hash_map_t T) (slots : vec (list_t T)) (i : USize) :
+  (result ((hash_map_t T) × (vec (list_t T))))
+  :=
+  let i0 := vec_len (list_t T) slots
+  if i < i0
+  then
+    do
+      let l <- vec_index_mut_fwd (list_t T) slots i
+      let ls := mem_replace_fwd (list_t T) l list_t.ListNil
+      let ntable0 <- hash_map_move_elements_from_list_fwd_back T ntable ls
+      let i1 <- USize.checked_add i (USize.ofNatCore 1 (by intlit))
+      let l0 := mem_replace_back (list_t T) l list_t.ListNil
+      let slots0 <- vec_index_mut_back (list_t T) slots i l0
+      hash_map_move_elements_loop_fwd_back T ntable0 slots0 i1
+  else result.ret (ntable, slots)
+termination_by hash_map_move_elements_loop_fwd_back ntable slots i =>
+   hash_map_move_elements_loop_terminates T ntable slots i
+decreasing_by hash_map_move_elements_loop_decreases ntable slots i
+
+/- [hashmap::HashMap::{0}::move_elements] -/
+def hash_map_move_elements_fwd_back
+  (T : Type) (ntable : hash_map_t T) (slots : vec (list_t T)) (i : USize) :
+  result ((hash_map_t T) × (vec (list_t T)))
+  :=
+  hash_map_move_elements_loop_fwd_back T ntable slots i
+
+/- [hashmap::HashMap::{0}::try_resize] -/
+def hash_map_try_resize_fwd_back
+  (T : Type) (self : hash_map_t T) : result (hash_map_t T) :=
+  do
+    let max_usize <- scalar_cast USize core_num_u32_max_c
+    let capacity := vec_len (list_t T) self.hash_map_slots
+    let n1 <- USize.checked_div max_usize (USize.ofNatCore 2 (by intlit))
+    let (i, i0) := self.hash_map_max_load_factor
+    let i1 <- USize.checked_div n1 i
+    if capacity <= i1
+    then
+      do
+        let i2 <- USize.checked_mul capacity (USize.ofNatCore 2 (by intlit))
+        let ntable <- hash_map_new_with_capacity_fwd T i2 i i0
+        let (ntable0, _) <-
+          hash_map_move_elements_fwd_back T ntable self.hash_map_slots
+            (USize.ofNatCore 0 (by intlit))
+        result.ret
+          {
+            hash_map_num_entries := self.hash_map_num_entries,
+            hash_map_max_load_factor := (i, i0),
+            hash_map_max_load := ntable0.hash_map_max_load,
+            hash_map_slots := ntable0.hash_map_slots
+          }
+    else
+      result.ret
+        {
+          hash_map_num_entries := self.hash_map_num_entries,
+          hash_map_max_load_factor := (i, i0),
+          hash_map_max_load := self.hash_map_max_load,
+          hash_map_slots := self.hash_map_slots
+        }
+
+/- [hashmap::HashMap::{0}::insert] -/
+def hash_map_insert_fwd_back
+  (T : Type) (self : hash_map_t T) (key : USize) (value : T) :
+  result (hash_map_t T)
+  :=
+  do
+    let self0 <- hash_map_insert_no_resize_fwd_back T self key value
+    let i <- hash_map_len_fwd T self0
+    if i > self0.hash_map_max_load
+    then hash_map_try_resize_fwd_back T self0
+    else result.ret self0
+
+/- [hashmap::HashMap::{0}::contains_key_in_list] -/
+def hash_map_contains_key_in_list_loop_fwd
+  (T : Type) (key : USize) (ls : list_t T) : (result Bool) :=
+  match ls with
+  | list_t.ListCons ckey t tl =>
+    if ckey = key
+    then result.ret true
+    else hash_map_contains_key_in_list_loop_fwd T key tl
+  | list_t.ListNil => result.ret false
+  
+termination_by hash_map_contains_key_in_list_loop_fwd key ls =>
+                                                               hash_map_contains_key_in_list_loop_terminates
+                                                               T key ls
+decreasing_by hash_map_contains_key_in_list_loop_decreases key ls
+
+/- [hashmap::HashMap::{0}::contains_key_in_list] -/
+def hash_map_contains_key_in_list_fwd
+  (T : Type) (key : USize) (ls : list_t T) : result Bool :=
+  hash_map_contains_key_in_list_loop_fwd T key ls
+
+/- [hashmap::HashMap::{0}::contains_key] -/
+def hash_map_contains_key_fwd
+  (T : Type) (self : hash_map_t T) (key : USize) : result Bool :=
+  do
+    let hash <- hash_key_fwd key
+    let i := vec_len (list_t T) self.hash_map_slots
+    let hash_mod <- USize.checked_rem hash i
+    let l <- vec_index_fwd (list_t T) self.hash_map_slots hash_mod
+    hash_map_contains_key_in_list_fwd T key l
+
+/- [hashmap::HashMap::{0}::get_in_list] -/
+def hash_map_get_in_list_loop_fwd
+  (T : Type) (key : USize) (ls : list_t T) : (result T) :=
+  match ls with
+  | list_t.ListCons ckey cvalue tl =>
+    if ckey = key
+    then result.ret cvalue
+    else hash_map_get_in_list_loop_fwd T key tl
+  | list_t.ListNil => result.fail error.panic
+  
+termination_by hash_map_get_in_list_loop_fwd key ls =>
+                                                      hash_map_get_in_list_loop_terminates
+                                                      T key ls
+decreasing_by hash_map_get_in_list_loop_decreases key ls
+
+/- [hashmap::HashMap::{0}::get_in_list] -/
+def hash_map_get_in_list_fwd
+  (T : Type) (key : USize) (ls : list_t T) : result T :=
+  hash_map_get_in_list_loop_fwd T key ls
+
+/- [hashmap::HashMap::{0}::get] -/
+def hash_map_get_fwd
+  (T : Type) (self : hash_map_t T) (key : USize) : result T :=
+  do
+    let hash <- hash_key_fwd key
+    let i := vec_len (list_t T) self.hash_map_slots
+    let hash_mod <- USize.checked_rem hash i
+    let l <- vec_index_fwd (list_t T) self.hash_map_slots hash_mod
+    hash_map_get_in_list_fwd T key l
+
+/- [hashmap::HashMap::{0}::get_mut_in_list] -/
+def hash_map_get_mut_in_list_loop_fwd
+  (T : Type) (ls : list_t T) (key : USize) : (result T) :=
+  match ls with
+  | list_t.ListCons ckey cvalue tl =>
+    if ckey = key
+    then result.ret cvalue
+    else hash_map_get_mut_in_list_loop_fwd T tl key
+  | list_t.ListNil => result.fail error.panic
+  
+termination_by hash_map_get_mut_in_list_loop_fwd ls key =>
+                                                          hash_map_get_mut_in_list_loop_terminates
+                                                          T ls key
+decreasing_by hash_map_get_mut_in_list_loop_decreases ls key
+
+/- [hashmap::HashMap::{0}::get_mut_in_list] -/
+def hash_map_get_mut_in_list_fwd
+  (T : Type) (ls : list_t T) (key : USize) : result T :=
+  hash_map_get_mut_in_list_loop_fwd T ls key
+
+/- [hashmap::HashMap::{0}::get_mut_in_list] -/
+def hash_map_get_mut_in_list_loop_back
+  (T : Type) (ls : list_t T) (key : USize) (ret0 : T) : (result (list_t T)) :=
+  match ls with
+  | list_t.ListCons ckey cvalue tl =>
+    if ckey = key
+    then result.ret (list_t.ListCons ckey ret0 tl)
+    else
+      do
+        let tl0 <- hash_map_get_mut_in_list_loop_back T tl key ret0
+        result.ret (list_t.ListCons ckey cvalue tl0)
+  | list_t.ListNil => result.fail error.panic
+  
+termination_by hash_map_get_mut_in_list_loop_back ls key ret0 =>
+                                                                hash_map_get_mut_in_list_loop_terminates
+                                                                T ls key
+decreasing_by hash_map_get_mut_in_list_loop_decreases ls key
+
+/- [hashmap::HashMap::{0}::get_mut_in_list] -/
+def hash_map_get_mut_in_list_back
+  (T : Type) (ls : list_t T) (key : USize) (ret0 : T) : result (list_t T) :=
+  hash_map_get_mut_in_list_loop_back T ls key ret0
+
+/- [hashmap::HashMap::{0}::get_mut] -/
+def hash_map_get_mut_fwd
+  (T : Type) (self : hash_map_t T) (key : USize) : result T :=
+  do
+    let hash <- hash_key_fwd key
+    let i := vec_len (list_t T) self.hash_map_slots
+    let hash_mod <- USize.checked_rem hash i
+    let l <- vec_index_mut_fwd (list_t T) self.hash_map_slots hash_mod
+    hash_map_get_mut_in_list_fwd T l key
+
+/- [hashmap::HashMap::{0}::get_mut] -/
+def hash_map_get_mut_back
+  (T : Type) (self : hash_map_t T) (key : USize) (ret0 : T) :
+  result (hash_map_t T)
+  :=
+  do
+    let hash <- hash_key_fwd key
+    let i := vec_len (list_t T) self.hash_map_slots
+    let hash_mod <- USize.checked_rem hash i
+    let l <- vec_index_mut_fwd (list_t T) self.hash_map_slots hash_mod
+    let l0 <- hash_map_get_mut_in_list_back T l key ret0
+    let v <- vec_index_mut_back (list_t T) self.hash_map_slots hash_mod l0
+    result.ret
+      {
+        hash_map_num_entries := self.hash_map_num_entries,
+        hash_map_max_load_factor := self.hash_map_max_load_factor,
+        hash_map_max_load := self.hash_map_max_load,
+        hash_map_slots := v
+      }
+
+/- [hashmap::HashMap::{0}::remove_from_list] -/
+def hash_map_remove_from_list_loop_fwd
+  (T : Type) (key : USize) (ls : list_t T) : (result (Option T)) :=
+  match ls with
+  | list_t.ListCons ckey t tl =>
+    if ckey = key
+    then
+      let mv_ls :=
+        mem_replace_fwd (list_t T) (list_t.ListCons ckey t tl) list_t.ListNil
+      match mv_ls with
+      | list_t.ListCons i cvalue tl0 => result.ret (Option.some cvalue)
+      | list_t.ListNil => result.fail error.panic
+      
+    else hash_map_remove_from_list_loop_fwd T key tl
+  | list_t.ListNil => result.ret Option.none
+  
+termination_by hash_map_remove_from_list_loop_fwd key ls =>
+                                                           hash_map_remove_from_list_loop_terminates
+                                                           T key ls
+decreasing_by hash_map_remove_from_list_loop_decreases key ls
+
+/- [hashmap::HashMap::{0}::remove_from_list] -/
+def hash_map_remove_from_list_fwd
+  (T : Type) (key : USize) (ls : list_t T) : result (Option T) :=
+  hash_map_remove_from_list_loop_fwd T key ls
+
+/- [hashmap::HashMap::{0}::remove_from_list] -/
+def hash_map_remove_from_list_loop_back
+  (T : Type) (key : USize) (ls : list_t T) : (result (list_t T)) :=
+  match ls with
+  | list_t.ListCons ckey t tl =>
+    if ckey = key
+    then
+      let mv_ls :=
+        mem_replace_fwd (list_t T) (list_t.ListCons ckey t tl) list_t.ListNil
+      match mv_ls with
+      | list_t.ListCons i cvalue tl0 => result.ret tl0
+      | list_t.ListNil => result.fail error.panic
+      
+    else
+      do
+        let tl0 <- hash_map_remove_from_list_loop_back T key tl
+        result.ret (list_t.ListCons ckey t tl0)
+  | list_t.ListNil => result.ret list_t.ListNil
+  
+termination_by hash_map_remove_from_list_loop_back key ls =>
+                                                            hash_map_remove_from_list_loop_terminates
+                                                            T key ls
+decreasing_by hash_map_remove_from_list_loop_decreases key ls
+
+/- [hashmap::HashMap::{0}::remove_from_list] -/
+def hash_map_remove_from_list_back
+  (T : Type) (key : USize) (ls : list_t T) : result (list_t T) :=
+  hash_map_remove_from_list_loop_back T key ls
+
+/- [hashmap::HashMap::{0}::remove] -/
+def hash_map_remove_fwd
+  (T : Type) (self : hash_map_t T) (key : USize) : result (Option T) :=
+  do
+    let hash <- hash_key_fwd key
+    let i := vec_len (list_t T) self.hash_map_slots
+    let hash_mod <- USize.checked_rem hash i
+    let l <- vec_index_mut_fwd (list_t T) self.hash_map_slots hash_mod
+    let x <- hash_map_remove_from_list_fwd T key l
+    match x with
+    | Option.none => result.ret Option.none
+    | Option.some x0 =>
+      do
+        let _ <- USize.checked_sub self.hash_map_num_entries
+          (USize.ofNatCore 1 (by intlit))
+        result.ret (Option.some x0)
+    
+
+/- [hashmap::HashMap::{0}::remove] -/
+def hash_map_remove_back
+  (T : Type) (self : hash_map_t T) (key : USize) : result (hash_map_t T) :=
+  do
+    let hash <- hash_key_fwd key
+    let i := vec_len (list_t T) self.hash_map_slots
+    let hash_mod <- USize.checked_rem hash i
+    let l <- vec_index_mut_fwd (list_t T) self.hash_map_slots hash_mod
+    let x <- hash_map_remove_from_list_fwd T key l
+    match x with
+    | Option.none =>
+      do
+        let l0 <- hash_map_remove_from_list_back T key l
+        let v <- vec_index_mut_back (list_t T) self.hash_map_slots hash_mod l0
+        result.ret
+          {
+            hash_map_num_entries := self.hash_map_num_entries,
+            hash_map_max_load_factor := self.hash_map_max_load_factor,
+            hash_map_max_load := self.hash_map_max_load,
+            hash_map_slots := v
+          }
+    | Option.some x0 =>
+      do
+        let i0 <- USize.checked_sub self.hash_map_num_entries
+          (USize.ofNatCore 1 (by intlit))
+        let l0 <- hash_map_remove_from_list_back T key l
+        let v <- vec_index_mut_back (list_t T) self.hash_map_slots hash_mod l0
+        result.ret
+          {
+            hash_map_num_entries := i0,
+            hash_map_max_load_factor := self.hash_map_max_load_factor,
+            hash_map_max_load := self.hash_map_max_load,
+            hash_map_slots := v
+          }
+    
+
+/- [hashmap::test1] -/
+def test1_fwd : result Unit :=
+  do
+    let hm <- hash_map_new_fwd UInt64
+    let hm0 <-
+      hash_map_insert_fwd_back UInt64 hm (USize.ofNatCore 0 (by intlit))
+        (UInt64.ofNatCore 42 (by intlit))
+    let hm1 <-
+      hash_map_insert_fwd_back UInt64 hm0 (USize.ofNatCore 128 (by intlit))
+        (UInt64.ofNatCore 18 (by intlit))
+    let hm2 <-
+      hash_map_insert_fwd_back UInt64 hm1 (USize.ofNatCore 1024 (by intlit))
+        (UInt64.ofNatCore 138 (by intlit))
+    let hm3 <-
+      hash_map_insert_fwd_back UInt64 hm2 (USize.ofNatCore 1056 (by intlit))
+        (UInt64.ofNatCore 256 (by intlit))
+    let i <- hash_map_get_fwd UInt64 hm3 (USize.ofNatCore 128 (by intlit))
+    if not (i = (UInt64.ofNatCore 18 (by intlit)))
+    then result.fail error.panic
+    else
+      do
+        let hm4 <-
+          hash_map_get_mut_back UInt64 hm3 (USize.ofNatCore 1024 (by intlit))
+            (UInt64.ofNatCore 56 (by intlit))
+        let i0 <-
+          hash_map_get_fwd UInt64 hm4 (USize.ofNatCore 1024 (by intlit))
+        if not (i0 = (UInt64.ofNatCore 56 (by intlit)))
+        then result.fail error.panic
+        else
+          do
+            let x <-
+              hash_map_remove_fwd UInt64 hm4 (USize.ofNatCore 1024 (by intlit))
+            match x with
+            | Option.none => result.fail error.panic
+            | Option.some x0 =>
+              if not (x0 = (UInt64.ofNatCore 56 (by intlit)))
+              then result.fail error.panic
+              else
+                do
+                  let hm5 <-
+                    hash_map_remove_back UInt64 hm4
+                      (USize.ofNatCore 1024 (by intlit))
+                  let i1 <-
+                    hash_map_get_fwd UInt64 hm5 (USize.ofNatCore 0 (by intlit))
+                  if not (i1 = (UInt64.ofNatCore 42 (by intlit)))
+                  then result.fail error.panic
+                  else
+                    do
+                      let i2 <-
+                        hash_map_get_fwd UInt64 hm5
+                          (USize.ofNatCore 128 (by intlit))
+                      if not (i2 = (UInt64.ofNatCore 18 (by intlit)))
+                      then result.fail error.panic
+                      else
+                        do
+                          let i3 <-
+                            hash_map_get_fwd UInt64 hm5
+                              (USize.ofNatCore 1056 (by intlit))
+                          if not (i3 = (UInt64.ofNatCore 256 (by intlit)))
+                          then result.fail error.panic
+                          else result.ret ()
+            
+
+/- Unit test for [hashmap::test1] -/
+#assert (test1_fwd = .ret ())
+
diff --git a/tests/lean/hashmap/Hashmap/Types.lean b/tests/lean/hashmap/Hashmap/Types.lean
new file mode 100644
index 00000000..9f08bd60
--- /dev/null
+++ b/tests/lean/hashmap/Hashmap/Types.lean
@@ -0,0 +1,18 @@
+-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
+-- [hashmap]: type definitions
+import Base.Primitives
+
+/- [hashmap::List] -/
+inductive list_t (T : Type) :=
+| ListCons : USize -> T -> list_t T -> list_t T
+| ListNil : list_t T
+
+/- [hashmap::HashMap] -/
+structure hash_map_t (T : Type) where
+
+  hash_map_num_entries : USize
+  hash_map_max_load_factor : (USize × USize)
+  hash_map_max_load : USize
+  hash_map_slots : vec (list_t T)
+
+
diff --git a/tests/lean/hashmap_on_disk/HashmapMain/Clauses/Clauses.lean b/tests/lean/hashmap_on_disk/HashmapMain/Clauses/Clauses.lean
new file mode 100644
index 00000000..16a4ea4c
--- /dev/null
+++ b/tests/lean/hashmap_on_disk/HashmapMain/Clauses/Clauses.lean
@@ -0,0 +1,111 @@
+-- [hashmap_main]: decreases clauses
+import Base.Primitives
+import HashmapMain.Types
+
+/- [hashmap_main::hashmap::HashMap::{0}::allocate_slots]: termination measure -/
+@[simp]
+def hashmap_hash_map_allocate_slots_loop_terminates (T : Type)
+  (slots : vec (hashmap_list_t T)) (n : USize) :=
+  (slots, n)
+
+syntax "hashmap_hash_map_allocate_slots_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| hashmap_hash_map_allocate_slots_loop_decreases $slots $n) =>
+  `(tactic| sorry)
+
+/- [hashmap_main::hashmap::HashMap::{0}::clear]: termination measure -/
+@[simp]
+def hashmap_hash_map_clear_loop_terminates (T : Type)
+  (slots : vec (hashmap_list_t T)) (i : USize) :=
+  (slots, i)
+
+syntax "hashmap_hash_map_clear_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| hashmap_hash_map_clear_loop_decreases $slots $i) =>`(tactic| sorry)
+
+/- [hashmap_main::hashmap::HashMap::{0}::insert_in_list]: termination measure -/
+@[simp]
+def hashmap_hash_map_insert_in_list_loop_terminates (T : Type) (key : USize)
+  (value : T) (ls : hashmap_list_t T) :=
+  (key, value, ls)
+
+syntax "hashmap_hash_map_insert_in_list_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| hashmap_hash_map_insert_in_list_loop_decreases $key $value $ls) =>
+  `(tactic| sorry)
+
+/- [hashmap_main::hashmap::HashMap::{0}::move_elements_from_list]: termination measure -/
+@[simp]
+def hashmap_hash_map_move_elements_from_list_loop_terminates (T : Type)
+  (ntable : hashmap_hash_map_t T) (ls : hashmap_list_t T) :=
+  (ntable, ls)
+
+syntax "hashmap_hash_map_move_elements_from_list_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| hashmap_hash_map_move_elements_from_list_loop_decreases $ntable
+$ls) =>`(tactic| sorry)
+
+/- [hashmap_main::hashmap::HashMap::{0}::move_elements]: termination measure -/
+@[simp]
+def hashmap_hash_map_move_elements_loop_terminates (T : Type)
+  (ntable : hashmap_hash_map_t T) (slots : vec (hashmap_list_t T)) (i : USize)
+  :=
+  (ntable, slots, i)
+
+syntax "hashmap_hash_map_move_elements_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| hashmap_hash_map_move_elements_loop_decreases $ntable $slots $i) =>
+  `(tactic| sorry)
+
+/- [hashmap_main::hashmap::HashMap::{0}::contains_key_in_list]: termination measure -/
+@[simp]
+def hashmap_hash_map_contains_key_in_list_loop_terminates (T : Type)
+  (key : USize) (ls : hashmap_list_t T) :=
+  (key, ls)
+
+syntax "hashmap_hash_map_contains_key_in_list_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| hashmap_hash_map_contains_key_in_list_loop_decreases $key $ls) =>
+  `(tactic| sorry)
+
+/- [hashmap_main::hashmap::HashMap::{0}::get_in_list]: termination measure -/
+@[simp]
+def hashmap_hash_map_get_in_list_loop_terminates (T : Type) (key : USize)
+  (ls : hashmap_list_t T) :=
+  (key, ls)
+
+syntax "hashmap_hash_map_get_in_list_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| hashmap_hash_map_get_in_list_loop_decreases $key $ls) =>`(tactic| sorry)
+
+/- [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list]: termination measure -/
+@[simp]
+def hashmap_hash_map_get_mut_in_list_loop_terminates (T : Type)
+  (ls : hashmap_list_t T) (key : USize) :=
+  (ls, key)
+
+syntax "hashmap_hash_map_get_mut_in_list_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| hashmap_hash_map_get_mut_in_list_loop_decreases $ls $key) =>
+  `(tactic| sorry)
+
+/- [hashmap_main::hashmap::HashMap::{0}::remove_from_list]: termination measure -/
+@[simp]
+def hashmap_hash_map_remove_from_list_loop_terminates (T : Type) (key : USize)
+  (ls : hashmap_list_t T) :=
+  (key, ls)
+
+syntax "hashmap_hash_map_remove_from_list_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| hashmap_hash_map_remove_from_list_loop_decreases $key $ls) =>
+  `(tactic| sorry)
+
diff --git a/tests/lean/hashmap_on_disk/HashmapMain/Clauses/Template.lean b/tests/lean/hashmap_on_disk/HashmapMain/Clauses/Template.lean
index bf331d6e..3466e7e0 100644
--- a/tests/lean/hashmap_on_disk/HashmapMain/Clauses/Template.lean
+++ b/tests/lean/hashmap_on_disk/HashmapMain/Clauses/Template.lean
@@ -15,17 +15,16 @@ macro_rules
 | `(tactic| hashmap_hash_map_allocate_slots_loop_decreases $slots $n) =>
   `(tactic| sorry)
 
-/- [hashmap_main::hashmap::HashMap::{0}::clear_slots]: termination measure -/
+/- [hashmap_main::hashmap::HashMap::{0}::clear]: termination measure -/
 @[simp]
-def hashmap_hash_map_clear_slots_loop_terminates (T : Type)
+def hashmap_hash_map_clear_loop_terminates (T : Type)
   (slots : vec (hashmap_list_t T)) (i : USize) :=
   (slots, i)
 
-syntax "hashmap_hash_map_clear_slots_loop_decreases" term+ : tactic
+syntax "hashmap_hash_map_clear_loop_decreases" term+ : tactic
 
 macro_rules
-| `(tactic| hashmap_hash_map_clear_slots_loop_decreases $slots $i) =>
-  `(tactic| sorry)
+| `(tactic| hashmap_hash_map_clear_loop_decreases $slots $i) =>`(tactic| sorry)
 
 /- [hashmap_main::hashmap::HashMap::{0}::insert_in_list]: termination measure -/
 @[simp]
diff --git a/tests/lean/hashmap_on_disk/HashmapMain/Funs.lean b/tests/lean/hashmap_on_disk/HashmapMain/Funs.lean
index b0c4d683..5134f483 100644
--- a/tests/lean/hashmap_on_disk/HashmapMain/Funs.lean
+++ b/tests/lean/hashmap_on_disk/HashmapMain/Funs.lean
@@ -3,7 +3,7 @@
 import Base.Primitives
 import HashmapMain.Types
 import HashmapMain.Opaque
-import HashmapMain.Clauses.Template
+import HashmapMain.Clauses.Clauses
 
 section variable (opaque_defs: OpaqueDefs)
 
@@ -19,13 +19,13 @@ def hashmap_hash_map_allocate_slots_loop_fwd
   then
     do
       let slots0 <-
-        vec_push_back (hashmap_list_t T) slots hashmap_list_t.HashmapListNil 
-      let n0 <- USize.checked_sub n (USize.ofNatCore 1 (by intlit)) 
+        vec_push_back (hashmap_list_t T) slots hashmap_list_t.HashmapListNil
+      let n0 <- USize.checked_sub n (USize.ofNatCore 1 (by intlit))
       hashmap_hash_map_allocate_slots_loop_fwd T slots0 n0
   else result.ret slots
 termination_by hashmap_hash_map_allocate_slots_loop_fwd slots n =>
                                                                   hashmap_hash_map_allocate_slots_loop_terminates
-                                                                  T slots n 
+                                                                  T slots n
 decreasing_by hashmap_hash_map_allocate_slots_loop_decreases slots n
 
 /- [hashmap_main::hashmap::HashMap::{0}::allocate_slots] -/
@@ -42,10 +42,10 @@ def hashmap_hash_map_new_with_capacity_fwd
   result (hashmap_hash_map_t T)
   :=
   do
-    let v := vec_new (hashmap_list_t T) 
-    let slots <- hashmap_hash_map_allocate_slots_fwd T v capacity 
-    let i <- USize.checked_mul capacity max_load_dividend 
-    let i0 <- USize.checked_div i max_load_divisor 
+    let v := vec_new (hashmap_list_t T)
+    let slots <- hashmap_hash_map_allocate_slots_fwd T v capacity
+    let i <- USize.checked_mul capacity max_load_dividend
+    let i0 <- USize.checked_div i max_load_divisor
     result.ret
       {
         hashmap_hash_map_num_entries := (USize.ofNatCore 0 (by intlit)),
@@ -60,40 +60,33 @@ def hashmap_hash_map_new_fwd (T : Type) : result (hashmap_hash_map_t T) :=
   hashmap_hash_map_new_with_capacity_fwd T (USize.ofNatCore 32 (by intlit))
     (USize.ofNatCore 4 (by intlit)) (USize.ofNatCore 5 (by intlit))
 
-/- [hashmap_main::hashmap::HashMap::{0}::clear_slots] -/
-def hashmap_hash_map_clear_slots_loop_fwd_back
+/- [hashmap_main::hashmap::HashMap::{0}::clear] -/
+def hashmap_hash_map_clear_loop_fwd_back
   (T : Type) (slots : vec (hashmap_list_t T)) (i : USize) :
   (result (vec (hashmap_list_t T)))
   :=
-  let i0 := vec_len (hashmap_list_t T) slots 
+  let i0 := vec_len (hashmap_list_t T) slots
   if i < i0
   then
     do
-      let i1 <- USize.checked_add i (USize.ofNatCore 1 (by intlit)) 
+      let i1 <- USize.checked_add i (USize.ofNatCore 1 (by intlit))
       let slots0 <-
         vec_index_mut_back (hashmap_list_t T) slots i
-          hashmap_list_t.HashmapListNil 
-      hashmap_hash_map_clear_slots_loop_fwd_back T slots0 i1
+          hashmap_list_t.HashmapListNil
+      hashmap_hash_map_clear_loop_fwd_back T slots0 i1
   else result.ret slots
-termination_by hashmap_hash_map_clear_slots_loop_fwd_back slots i =>
-                                                                    hashmap_hash_map_clear_slots_loop_terminates
-                                                                    T slots i 
-decreasing_by hashmap_hash_map_clear_slots_loop_decreases slots i
-
-/- [hashmap_main::hashmap::HashMap::{0}::clear_slots] -/
-def hashmap_hash_map_clear_slots_fwd_back
-  (T : Type) (slots : vec (hashmap_list_t T)) :
-  result (vec (hashmap_list_t T))
-  :=
-  hashmap_hash_map_clear_slots_loop_fwd_back T slots
-    (USize.ofNatCore 0 (by intlit))
+termination_by hashmap_hash_map_clear_loop_fwd_back slots i =>
+                                                              hashmap_hash_map_clear_loop_terminates
+                                                              T slots i
+decreasing_by hashmap_hash_map_clear_loop_decreases slots i
 
 /- [hashmap_main::hashmap::HashMap::{0}::clear] -/
 def hashmap_hash_map_clear_fwd_back
   (T : Type) (self : hashmap_hash_map_t T) : result (hashmap_hash_map_t T) :=
   do
     let v <-
-      hashmap_hash_map_clear_slots_fwd_back T self.hashmap_hash_map_slots 
+      hashmap_hash_map_clear_loop_fwd_back T self.hashmap_hash_map_slots
+        (USize.ofNatCore 0 (by intlit))
     result.ret
       {
         hashmap_hash_map_num_entries := (USize.ofNatCore 0 (by intlit)),
@@ -120,7 +113,7 @@ def hashmap_hash_map_insert_in_list_loop_fwd
   | hashmap_list_t.HashmapListNil => result.ret true
   
 termination_by hashmap_hash_map_insert_in_list_loop_fwd key value ls =>
-   hashmap_hash_map_insert_in_list_loop_terminates T key value ls 
+   hashmap_hash_map_insert_in_list_loop_terminates T key value ls
 decreasing_by hashmap_hash_map_insert_in_list_loop_decreases key value ls
 
 /- [hashmap_main::hashmap::HashMap::{0}::insert_in_list] -/
@@ -139,14 +132,14 @@ def hashmap_hash_map_insert_in_list_loop_back
     then result.ret (hashmap_list_t.HashmapListCons ckey value tl)
     else
       do
-        let l <- hashmap_hash_map_insert_in_list_loop_back T key value tl 
-        result.ret (hashmap_list_t.HashmapListCons ckey cvalue l)
+        let tl0 <- hashmap_hash_map_insert_in_list_loop_back T key value tl
+        result.ret (hashmap_list_t.HashmapListCons ckey cvalue tl0)
   | hashmap_list_t.HashmapListNil =>
-    let l := hashmap_list_t.HashmapListNil 
+    let l := hashmap_list_t.HashmapListNil
     result.ret (hashmap_list_t.HashmapListCons key value l)
   
 termination_by hashmap_hash_map_insert_in_list_loop_back key value ls =>
-   hashmap_hash_map_insert_in_list_loop_terminates T key value ls 
+   hashmap_hash_map_insert_in_list_loop_terminates T key value ls
 decreasing_by hashmap_hash_map_insert_in_list_loop_decreases key value ls
 
 /- [hashmap_main::hashmap::HashMap::{0}::insert_in_list] -/
@@ -162,21 +155,21 @@ def hashmap_hash_map_insert_no_resize_fwd_back
   result (hashmap_hash_map_t T)
   :=
   do
-    let hash <- hashmap_hash_key_fwd key 
-    let i := vec_len (hashmap_list_t T) self.hashmap_hash_map_slots 
-    let hash_mod <- USize.checked_rem hash i 
+    let hash <- hashmap_hash_key_fwd key
+    let i := vec_len (hashmap_list_t T) self.hashmap_hash_map_slots
+    let hash_mod <- USize.checked_rem hash i
     let l <-
-      vec_index_mut_fwd (hashmap_list_t T) self.hashmap_hash_map_slots hash_mod 
-    let inserted <- hashmap_hash_map_insert_in_list_fwd T key value l 
+      vec_index_mut_fwd (hashmap_list_t T) self.hashmap_hash_map_slots hash_mod
+    let inserted <- hashmap_hash_map_insert_in_list_fwd T key value l
     if inserted
     then
       do
         let i0 <- USize.checked_add self.hashmap_hash_map_num_entries
-          (USize.ofNatCore 1 (by intlit)) 
-        let l0 <- hashmap_hash_map_insert_in_list_back T key value l 
+          (USize.ofNatCore 1 (by intlit))
+        let l0 <- hashmap_hash_map_insert_in_list_back T key value l
         let v <-
           vec_index_mut_back (hashmap_list_t T) self.hashmap_hash_map_slots
-            hash_mod l0 
+            hash_mod l0
         result.ret
           {
             hashmap_hash_map_num_entries := i0,
@@ -186,10 +179,10 @@ def hashmap_hash_map_insert_no_resize_fwd_back
           }
     else
       do
-        let l0 <- hashmap_hash_map_insert_in_list_back T key value l 
+        let l0 <- hashmap_hash_map_insert_in_list_back T key value l
         let v <-
           vec_index_mut_back (hashmap_list_t T) self.hashmap_hash_map_slots
-            hash_mod l0 
+            hash_mod l0
         result.ret
           {
             hashmap_hash_map_num_entries := self.hashmap_hash_map_num_entries,
@@ -211,13 +204,13 @@ def hashmap_hash_map_move_elements_from_list_loop_fwd_back
   match ls with
   | hashmap_list_t.HashmapListCons k v tl =>
     do
-      let ntable0 <- hashmap_hash_map_insert_no_resize_fwd_back T ntable k v 
+      let ntable0 <- hashmap_hash_map_insert_no_resize_fwd_back T ntable k v
       hashmap_hash_map_move_elements_from_list_loop_fwd_back T ntable0 tl
   | hashmap_list_t.HashmapListNil => result.ret ntable
   
 termination_by hashmap_hash_map_move_elements_from_list_loop_fwd_back ntable ls
               => hashmap_hash_map_move_elements_from_list_loop_terminates T
-                ntable ls 
+                ntable ls
 decreasing_by hashmap_hash_map_move_elements_from_list_loop_decreases ntable ls
 
 /- [hashmap_main::hashmap::HashMap::{0}::move_elements_from_list] -/
@@ -233,23 +226,23 @@ def hashmap_hash_map_move_elements_loop_fwd_back
   (i : USize) :
   (result ((hashmap_hash_map_t T) × (vec (hashmap_list_t T))))
   :=
-  let i0 := vec_len (hashmap_list_t T) slots 
+  let i0 := vec_len (hashmap_list_t T) slots
   if i < i0
   then
     do
-      let l <- vec_index_mut_fwd (hashmap_list_t T) slots i 
+      let l <- vec_index_mut_fwd (hashmap_list_t T) slots i
       let ls :=
-        mem_replace_fwd (hashmap_list_t T) l hashmap_list_t.HashmapListNil 
+        mem_replace_fwd (hashmap_list_t T) l hashmap_list_t.HashmapListNil
       let ntable0 <-
-        hashmap_hash_map_move_elements_from_list_fwd_back T ntable ls 
-      let i1 <- USize.checked_add i (USize.ofNatCore 1 (by intlit)) 
+        hashmap_hash_map_move_elements_from_list_fwd_back T ntable ls
+      let i1 <- USize.checked_add i (USize.ofNatCore 1 (by intlit))
       let l0 :=
-        mem_replace_back (hashmap_list_t T) l hashmap_list_t.HashmapListNil 
-      let slots0 <- vec_index_mut_back (hashmap_list_t T) slots i l0 
+        mem_replace_back (hashmap_list_t T) l hashmap_list_t.HashmapListNil
+      let slots0 <- vec_index_mut_back (hashmap_list_t T) slots i l0
       hashmap_hash_map_move_elements_loop_fwd_back T ntable0 slots0 i1
   else result.ret (ntable, slots)
 termination_by hashmap_hash_map_move_elements_loop_fwd_back ntable slots i =>
-   hashmap_hash_map_move_elements_loop_terminates T ntable slots i 
+   hashmap_hash_map_move_elements_loop_terminates T ntable slots i
 decreasing_by hashmap_hash_map_move_elements_loop_decreases ntable slots i
 
 /- [hashmap_main::hashmap::HashMap::{0}::move_elements] -/
@@ -264,19 +257,19 @@ def hashmap_hash_map_move_elements_fwd_back
 def hashmap_hash_map_try_resize_fwd_back
   (T : Type) (self : hashmap_hash_map_t T) : result (hashmap_hash_map_t T) :=
   do
-    let max_usize <- scalar_cast USize core_num_u32_max_c 
-    let capacity := vec_len (hashmap_list_t T) self.hashmap_hash_map_slots 
-    let n1 <- USize.checked_div max_usize (USize.ofNatCore 2 (by intlit)) 
-    let (i, i0) := self.hashmap_hash_map_max_load_factor 
-    let i1 <- USize.checked_div n1 i 
+    let max_usize <- scalar_cast USize core_num_u32_max_c
+    let capacity := vec_len (hashmap_list_t T) self.hashmap_hash_map_slots
+    let n1 <- USize.checked_div max_usize (USize.ofNatCore 2 (by intlit))
+    let (i, i0) := self.hashmap_hash_map_max_load_factor
+    let i1 <- USize.checked_div n1 i
     if capacity <= i1
     then
       do
-        let i2 <- USize.checked_mul capacity (USize.ofNatCore 2 (by intlit)) 
-        let ntable <- hashmap_hash_map_new_with_capacity_fwd T i2 i i0 
+        let i2 <- USize.checked_mul capacity (USize.ofNatCore 2 (by intlit))
+        let ntable <- hashmap_hash_map_new_with_capacity_fwd T i2 i i0
         let (ntable0, _) <-
           hashmap_hash_map_move_elements_fwd_back T ntable
-            self.hashmap_hash_map_slots (USize.ofNatCore 0 (by intlit)) 
+            self.hashmap_hash_map_slots (USize.ofNatCore 0 (by intlit))
         result.ret
           {
             hashmap_hash_map_num_entries := self.hashmap_hash_map_num_entries,
@@ -299,8 +292,8 @@ def hashmap_hash_map_insert_fwd_back
   result (hashmap_hash_map_t T)
   :=
   do
-    let self0 <- hashmap_hash_map_insert_no_resize_fwd_back T self key value 
-    let i <- hashmap_hash_map_len_fwd T self0 
+    let self0 <- hashmap_hash_map_insert_no_resize_fwd_back T self key value
+    let i <- hashmap_hash_map_len_fwd T self0
     if i > self0.hashmap_hash_map_max_load
     then hashmap_hash_map_try_resize_fwd_back T self0
     else result.ret self0
@@ -316,7 +309,7 @@ def hashmap_hash_map_contains_key_in_list_loop_fwd
   | hashmap_list_t.HashmapListNil => result.ret false
   
 termination_by hashmap_hash_map_contains_key_in_list_loop_fwd key ls =>
-   hashmap_hash_map_contains_key_in_list_loop_terminates T key ls 
+   hashmap_hash_map_contains_key_in_list_loop_terminates T key ls
 decreasing_by hashmap_hash_map_contains_key_in_list_loop_decreases key ls
 
 /- [hashmap_main::hashmap::HashMap::{0}::contains_key_in_list] -/
@@ -328,11 +321,11 @@ def hashmap_hash_map_contains_key_in_list_fwd
 def hashmap_hash_map_contains_key_fwd
   (T : Type) (self : hashmap_hash_map_t T) (key : USize) : result Bool :=
   do
-    let hash <- hashmap_hash_key_fwd key 
-    let i := vec_len (hashmap_list_t T) self.hashmap_hash_map_slots 
-    let hash_mod <- USize.checked_rem hash i 
+    let hash <- hashmap_hash_key_fwd key
+    let i := vec_len (hashmap_list_t T) self.hashmap_hash_map_slots
+    let hash_mod <- USize.checked_rem hash i
     let l <-
-      vec_index_fwd (hashmap_list_t T) self.hashmap_hash_map_slots hash_mod 
+      vec_index_fwd (hashmap_list_t T) self.hashmap_hash_map_slots hash_mod
     hashmap_hash_map_contains_key_in_list_fwd T key l
 
 /- [hashmap_main::hashmap::HashMap::{0}::get_in_list] -/
@@ -347,7 +340,7 @@ def hashmap_hash_map_get_in_list_loop_fwd
   
 termination_by hashmap_hash_map_get_in_list_loop_fwd key ls =>
                                                               hashmap_hash_map_get_in_list_loop_terminates
-                                                              T key ls 
+                                                              T key ls
 decreasing_by hashmap_hash_map_get_in_list_loop_decreases key ls
 
 /- [hashmap_main::hashmap::HashMap::{0}::get_in_list] -/
@@ -359,11 +352,11 @@ def hashmap_hash_map_get_in_list_fwd
 def hashmap_hash_map_get_fwd
   (T : Type) (self : hashmap_hash_map_t T) (key : USize) : result T :=
   do
-    let hash <- hashmap_hash_key_fwd key 
-    let i := vec_len (hashmap_list_t T) self.hashmap_hash_map_slots 
-    let hash_mod <- USize.checked_rem hash i 
+    let hash <- hashmap_hash_key_fwd key
+    let i := vec_len (hashmap_list_t T) self.hashmap_hash_map_slots
+    let hash_mod <- USize.checked_rem hash i
     let l <-
-      vec_index_fwd (hashmap_list_t T) self.hashmap_hash_map_slots hash_mod 
+      vec_index_fwd (hashmap_list_t T) self.hashmap_hash_map_slots hash_mod
     hashmap_hash_map_get_in_list_fwd T key l
 
 /- [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list] -/
@@ -378,7 +371,7 @@ def hashmap_hash_map_get_mut_in_list_loop_fwd
   
 termination_by hashmap_hash_map_get_mut_in_list_loop_fwd ls key =>
                                                                   hashmap_hash_map_get_mut_in_list_loop_terminates
-                                                                  T ls key 
+                                                                  T ls key
 decreasing_by hashmap_hash_map_get_mut_in_list_loop_decreases ls key
 
 /- [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list] -/
@@ -397,12 +390,12 @@ def hashmap_hash_map_get_mut_in_list_loop_back
     then result.ret (hashmap_list_t.HashmapListCons ckey ret0 tl)
     else
       do
-        let l <- hashmap_hash_map_get_mut_in_list_loop_back T tl key ret0 
-        result.ret (hashmap_list_t.HashmapListCons ckey cvalue l)
+        let tl0 <- hashmap_hash_map_get_mut_in_list_loop_back T tl key ret0
+        result.ret (hashmap_list_t.HashmapListCons ckey cvalue tl0)
   | hashmap_list_t.HashmapListNil => result.fail error.panic
   
 termination_by hashmap_hash_map_get_mut_in_list_loop_back ls key ret0 =>
-   hashmap_hash_map_get_mut_in_list_loop_terminates T ls key 
+   hashmap_hash_map_get_mut_in_list_loop_terminates T ls key
 decreasing_by hashmap_hash_map_get_mut_in_list_loop_decreases ls key
 
 /- [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list] -/
@@ -416,11 +409,11 @@ def hashmap_hash_map_get_mut_in_list_back
 def hashmap_hash_map_get_mut_fwd
   (T : Type) (self : hashmap_hash_map_t T) (key : USize) : result T :=
   do
-    let hash <- hashmap_hash_key_fwd key 
-    let i := vec_len (hashmap_list_t T) self.hashmap_hash_map_slots 
-    let hash_mod <- USize.checked_rem hash i 
+    let hash <- hashmap_hash_key_fwd key
+    let i := vec_len (hashmap_list_t T) self.hashmap_hash_map_slots
+    let hash_mod <- USize.checked_rem hash i
     let l <-
-      vec_index_mut_fwd (hashmap_list_t T) self.hashmap_hash_map_slots hash_mod 
+      vec_index_mut_fwd (hashmap_list_t T) self.hashmap_hash_map_slots hash_mod
     hashmap_hash_map_get_mut_in_list_fwd T l key
 
 /- [hashmap_main::hashmap::HashMap::{0}::get_mut] -/
@@ -429,15 +422,15 @@ def hashmap_hash_map_get_mut_back
   result (hashmap_hash_map_t T)
   :=
   do
-    let hash <- hashmap_hash_key_fwd key 
-    let i := vec_len (hashmap_list_t T) self.hashmap_hash_map_slots 
-    let hash_mod <- USize.checked_rem hash i 
+    let hash <- hashmap_hash_key_fwd key
+    let i := vec_len (hashmap_list_t T) self.hashmap_hash_map_slots
+    let hash_mod <- USize.checked_rem hash i
     let l <-
-      vec_index_mut_fwd (hashmap_list_t T) self.hashmap_hash_map_slots hash_mod 
-    let l0 <- hashmap_hash_map_get_mut_in_list_back T l key ret0 
+      vec_index_mut_fwd (hashmap_list_t T) self.hashmap_hash_map_slots hash_mod
+    let l0 <- hashmap_hash_map_get_mut_in_list_back T l key ret0
     let v <-
       vec_index_mut_back (hashmap_list_t T) self.hashmap_hash_map_slots
-        hash_mod l0 
+        hash_mod l0
     result.ret
       {
         hashmap_hash_map_num_entries := self.hashmap_hash_map_num_entries,
@@ -455,7 +448,7 @@ def hashmap_hash_map_remove_from_list_loop_fwd
     then
       let mv_ls :=
         mem_replace_fwd (hashmap_list_t T) (hashmap_list_t.HashmapListCons ckey
-          t tl) hashmap_list_t.HashmapListNil 
+          t tl) hashmap_list_t.HashmapListNil
       match mv_ls with
       | hashmap_list_t.HashmapListCons i cvalue tl0 =>
         result.ret (Option.some cvalue)
@@ -466,7 +459,7 @@ def hashmap_hash_map_remove_from_list_loop_fwd
   
 termination_by hashmap_hash_map_remove_from_list_loop_fwd key ls =>
                                                                    hashmap_hash_map_remove_from_list_loop_terminates
-                                                                   T key ls 
+                                                                   T key ls
 decreasing_by hashmap_hash_map_remove_from_list_loop_decreases key ls
 
 /- [hashmap_main::hashmap::HashMap::{0}::remove_from_list] -/
@@ -485,20 +478,20 @@ def hashmap_hash_map_remove_from_list_loop_back
     then
       let mv_ls :=
         mem_replace_fwd (hashmap_list_t T) (hashmap_list_t.HashmapListCons ckey
-          t tl) hashmap_list_t.HashmapListNil 
+          t tl) hashmap_list_t.HashmapListNil
       match mv_ls with
       | hashmap_list_t.HashmapListCons i cvalue tl0 => result.ret tl0
       | hashmap_list_t.HashmapListNil => result.fail error.panic
       
     else
       do
-        let l <- hashmap_hash_map_remove_from_list_loop_back T key tl 
-        result.ret (hashmap_list_t.HashmapListCons ckey t l)
+        let tl0 <- hashmap_hash_map_remove_from_list_loop_back T key tl
+        result.ret (hashmap_list_t.HashmapListCons ckey t tl0)
   | hashmap_list_t.HashmapListNil => result.ret hashmap_list_t.HashmapListNil
   
 termination_by hashmap_hash_map_remove_from_list_loop_back key ls =>
                                                                     hashmap_hash_map_remove_from_list_loop_terminates
-                                                                    T key ls 
+                                                                    T key ls
 decreasing_by hashmap_hash_map_remove_from_list_loop_decreases key ls
 
 /- [hashmap_main::hashmap::HashMap::{0}::remove_from_list] -/
@@ -512,18 +505,18 @@ def hashmap_hash_map_remove_from_list_back
 def hashmap_hash_map_remove_fwd
   (T : Type) (self : hashmap_hash_map_t T) (key : USize) : result (Option T) :=
   do
-    let hash <- hashmap_hash_key_fwd key 
-    let i := vec_len (hashmap_list_t T) self.hashmap_hash_map_slots 
-    let hash_mod <- USize.checked_rem hash i 
+    let hash <- hashmap_hash_key_fwd key
+    let i := vec_len (hashmap_list_t T) self.hashmap_hash_map_slots
+    let hash_mod <- USize.checked_rem hash i
     let l <-
-      vec_index_mut_fwd (hashmap_list_t T) self.hashmap_hash_map_slots hash_mod 
-    let x <- hashmap_hash_map_remove_from_list_fwd T key l 
+      vec_index_mut_fwd (hashmap_list_t T) self.hashmap_hash_map_slots hash_mod
+    let x <- hashmap_hash_map_remove_from_list_fwd T key l
     match x with
     | Option.none => result.ret Option.none
     | Option.some x0 =>
       do
         let _ <- USize.checked_sub self.hashmap_hash_map_num_entries
-          (USize.ofNatCore 1 (by intlit)) 
+          (USize.ofNatCore 1 (by intlit))
         result.ret (Option.some x0)
     
 
@@ -533,19 +526,19 @@ def hashmap_hash_map_remove_back
   result (hashmap_hash_map_t T)
   :=
   do
-    let hash <- hashmap_hash_key_fwd key 
-    let i := vec_len (hashmap_list_t T) self.hashmap_hash_map_slots 
-    let hash_mod <- USize.checked_rem hash i 
+    let hash <- hashmap_hash_key_fwd key
+    let i := vec_len (hashmap_list_t T) self.hashmap_hash_map_slots
+    let hash_mod <- USize.checked_rem hash i
     let l <-
-      vec_index_mut_fwd (hashmap_list_t T) self.hashmap_hash_map_slots hash_mod 
-    let x <- hashmap_hash_map_remove_from_list_fwd T key l 
+      vec_index_mut_fwd (hashmap_list_t T) self.hashmap_hash_map_slots hash_mod
+    let x <- hashmap_hash_map_remove_from_list_fwd T key l
     match x with
     | Option.none =>
       do
-        let l0 <- hashmap_hash_map_remove_from_list_back T key l 
+        let l0 <- hashmap_hash_map_remove_from_list_back T key l
         let v <-
           vec_index_mut_back (hashmap_list_t T) self.hashmap_hash_map_slots
-            hash_mod l0 
+            hash_mod l0
         result.ret
           {
             hashmap_hash_map_num_entries := self.hashmap_hash_map_num_entries,
@@ -556,11 +549,11 @@ def hashmap_hash_map_remove_back
     | Option.some x0 =>
       do
         let i0 <- USize.checked_sub self.hashmap_hash_map_num_entries
-          (USize.ofNatCore 1 (by intlit)) 
-        let l0 <- hashmap_hash_map_remove_from_list_back T key l 
+          (USize.ofNatCore 1 (by intlit))
+        let l0 <- hashmap_hash_map_remove_from_list_back T key l
         let v <-
           vec_index_mut_back (hashmap_list_t T) self.hashmap_hash_map_slots
-            hash_mod l0 
+            hash_mod l0
         result.ret
           {
             hashmap_hash_map_num_entries := i0,
@@ -573,21 +566,21 @@ def hashmap_hash_map_remove_back
 /- [hashmap_main::hashmap::test1] -/
 def hashmap_test1_fwd : result Unit :=
   do
-    let hm <- hashmap_hash_map_new_fwd UInt64 
+    let hm <- hashmap_hash_map_new_fwd UInt64
     let hm0 <-
       hashmap_hash_map_insert_fwd_back UInt64 hm
-        (USize.ofNatCore 0 (by intlit)) (UInt64.ofNatCore 42 (by intlit)) 
+        (USize.ofNatCore 0 (by intlit)) (UInt64.ofNatCore 42 (by intlit))
     let hm1 <-
       hashmap_hash_map_insert_fwd_back UInt64 hm0
-        (USize.ofNatCore 128 (by intlit)) (UInt64.ofNatCore 18 (by intlit)) 
+        (USize.ofNatCore 128 (by intlit)) (UInt64.ofNatCore 18 (by intlit))
     let hm2 <-
       hashmap_hash_map_insert_fwd_back UInt64 hm1
-        (USize.ofNatCore 1024 (by intlit)) (UInt64.ofNatCore 138 (by intlit)) 
+        (USize.ofNatCore 1024 (by intlit)) (UInt64.ofNatCore 138 (by intlit))
     let hm3 <-
       hashmap_hash_map_insert_fwd_back UInt64 hm2
-        (USize.ofNatCore 1056 (by intlit)) (UInt64.ofNatCore 256 (by intlit)) 
+        (USize.ofNatCore 1056 (by intlit)) (UInt64.ofNatCore 256 (by intlit))
     let i <-
-      hashmap_hash_map_get_fwd UInt64 hm3 (USize.ofNatCore 128 (by intlit)) 
+      hashmap_hash_map_get_fwd UInt64 hm3 (USize.ofNatCore 128 (by intlit))
     if not (i = (UInt64.ofNatCore 18 (by intlit)))
     then result.fail error.panic
     else
@@ -595,17 +588,17 @@ def hashmap_test1_fwd : result Unit :=
         let hm4 <-
           hashmap_hash_map_get_mut_back UInt64 hm3
             (USize.ofNatCore 1024 (by intlit))
-            (UInt64.ofNatCore 56 (by intlit)) 
+            (UInt64.ofNatCore 56 (by intlit))
         let i0 <-
           hashmap_hash_map_get_fwd UInt64 hm4
-            (USize.ofNatCore 1024 (by intlit)) 
+            (USize.ofNatCore 1024 (by intlit))
         if not (i0 = (UInt64.ofNatCore 56 (by intlit)))
         then result.fail error.panic
         else
           do
             let x <-
               hashmap_hash_map_remove_fwd UInt64 hm4
-                (USize.ofNatCore 1024 (by intlit)) 
+                (USize.ofNatCore 1024 (by intlit))
             match x with
             | Option.none => result.fail error.panic
             | Option.some x0 =>
@@ -615,24 +608,24 @@ def hashmap_test1_fwd : result Unit :=
                 do
                   let hm5 <-
                     hashmap_hash_map_remove_back UInt64 hm4
-                      (USize.ofNatCore 1024 (by intlit)) 
+                      (USize.ofNatCore 1024 (by intlit))
                   let i1 <-
                     hashmap_hash_map_get_fwd UInt64 hm5
-                      (USize.ofNatCore 0 (by intlit)) 
+                      (USize.ofNatCore 0 (by intlit))
                   if not (i1 = (UInt64.ofNatCore 42 (by intlit)))
                   then result.fail error.panic
                   else
                     do
                       let i2 <-
                         hashmap_hash_map_get_fwd UInt64 hm5
-                          (USize.ofNatCore 128 (by intlit)) 
+                          (USize.ofNatCore 128 (by intlit))
                       if not (i2 = (UInt64.ofNatCore 18 (by intlit)))
                       then result.fail error.panic
                       else
                         do
                           let i3 <-
                             hashmap_hash_map_get_fwd UInt64 hm5
-                              (USize.ofNatCore 1056 (by intlit)) 
+                              (USize.ofNatCore 1056 (by intlit))
                           if not (i3 = (UInt64.ofNatCore 256 (by intlit)))
                           then result.fail error.panic
                           else result.ret ()
@@ -645,9 +638,9 @@ def hashmap_test1_fwd : result Unit :=
 def insert_on_disk_fwd
   (key : USize) (value : UInt64) (st : state) : result (state × Unit) :=
   do
-    let (st0, hm) <- opaque_defs.hashmap_utils_deserialize_fwd st 
-    let hm0 <- hashmap_hash_map_insert_fwd_back UInt64 hm key value 
-    let (st1, _) <- opaque_defs.hashmap_utils_serialize_fwd hm0 st0 
+    let (st0, hm) <- opaque_defs.hashmap_utils_deserialize_fwd st
+    let hm0 <- hashmap_hash_map_insert_fwd_back UInt64 hm key value
+    let (st1, _) <- opaque_defs.hashmap_utils_serialize_fwd hm0 st0
     result.ret (st1, ())
 
 /- [hashmap_main::main] -/
diff --git a/tests/lean/misc/constants/Base/Primitives.lean b/tests/lean/misc/constants/Base/Primitives.lean
new file mode 100644
index 00000000..79958d94
--- /dev/null
+++ b/tests/lean/misc/constants/Base/Primitives.lean
@@ -0,0 +1,373 @@
+import Lean
+import Lean.Meta.Tactic.Simp
+import Init.Data.List.Basic
+import Mathlib.Tactic.RunCmd
+
+-------------
+-- PRELUDE --
+-------------
+
+-- Results & monadic combinators
+
+-- TODO: use syntactic conventions and capitalize error, result, etc.
+
+inductive error where
+   | assertionFailure: error
+   | integerOverflow: error
+   | arrayOutOfBounds: error
+   | maximumSizeExceeded: error
+   | panic: error
+deriving Repr, BEq
+
+open error
+
+inductive result (α : Type u) where
+  | ret (v: α): result α
+  | fail (e: error): result α 
+deriving Repr, BEq
+
+open result
+
+/- HELPERS -/
+
+-- TODO: is there automated syntax for these discriminators?
+def is_ret {α: Type} (r: result α): Bool :=
+  match r with
+  | result.ret _ => true
+  | result.fail _ => false
+
+def massert (b:Bool) : result Unit :=
+  if b then .ret () else fail assertionFailure
+
+def eval_global {α: Type} (x: result α) (_: is_ret x): α :=
+  match x with
+  | result.fail _ => by contradiction
+  | result.ret x => x
+
+/- DO-DSL SUPPORT -/
+
+def bind (x: result α) (f: α -> result β) : result β :=
+  match x with
+  | ret v  => f v 
+  | fail v => fail v
+
+-- Allows using result in do-blocks
+instance : Bind result where
+  bind := bind
+
+-- Allows using return x in do-blocks
+instance : Pure result where
+  pure := fun x => ret x
+
+/- CUSTOM-DSL SUPPORT -/
+
+-- Let-binding the result of a monadic operation is oftentimes not sufficient,
+-- because we may need a hypothesis for equational reasoning in the scope. We
+-- rely on subtype, and a custom let-binding operator, in effect recreating our
+-- own variant of the do-dsl
+
+def result.attach : (o : result α) → result { x : α // o = ret x }
+  | .ret x => .ret ⟨x, rfl⟩
+  | .fail e   => .fail e
+
+macro "let" h:ident " : " e:term " <-- " f:term : doElem =>
+  `(doElem| let ⟨$e, $h⟩ ← result.attach $f)
+
+-- Silly example of the kind of reasoning that this notation enables
+#eval do
+  let h: y <-- .ret (0: Nat)
+  let _: y = 0 := by cases h; decide
+  let r: { x: Nat // x = 0 } := ⟨ y, by assumption ⟩
+  .ret r
+
+----------------------
+-- MACHINE INTEGERS --
+----------------------
+
+-- NOTE: we reuse the USize type from prelude.lean, because at least we know
+-- it's defined in an idiomatic style that is going to make proofs easy (and
+-- indeed, several proofs here are much shortened compared to Aymeric's earlier
+-- attempt.) This is not stricto sensu the *correct* thing to do, because one
+-- can query at run-time the value of USize, which we do *not* want to do (we
+-- don't know what target we'll run on!), but when the day comes, we'll just
+-- define our own USize.
+-- ANOTHER NOTE: there is USize.sub but it has wraparound semantics, which is
+-- not something we want to define (I think), so we use our own monadic sub (but
+-- is it in line with the Rust behavior?)
+
+-- TODO: I am somewhat under the impression that subtraction is defined as a
+-- total function over nats...? the hypothesis in the if condition is not used
+-- in the then-branch which confuses me quite a bit
+
+-- TODO: add a refinement for the result (just like vec_push_back below) that
+-- explains that the toNat of the result (in the case of success) is the sub of
+-- the toNat of the arguments (i.e. intrinsic specification)
+-- ... do we want intrinsic specifications for the builtins? that might require
+-- some careful type annotations in the monadic notation for clients, but may
+-- give us more "for free"
+
+-- Note from Chris Bailey: "If there's more than one salient property of your
+-- definition then the subtyping strategy might get messy, and the property part
+-- of a subtype is less discoverable by the simplifier or tactics like
+-- library_search." Try to settle this with a Lean expert on what is the most
+-- productive way to go about this?
+
+-- One needs to perform a little bit of reasoning in order to successfully
+-- inject constants into USize, so we provide a general-purpose macro
+
+syntax "intlit" : tactic
+
+macro_rules
+  | `(tactic| intlit) => `(tactic|
+    match USize.size, usize_size_eq with
+    | _, Or.inl rfl => decide
+    | _, Or.inr rfl => decide)
+
+-- This is how the macro is expected to be used
+#eval USize.ofNatCore 0 (by intlit)
+
+-- Also works for other integer types (at the expense of a needless disjunction)
+#eval UInt32.ofNatCore 0 (by intlit)
+
+-- Further thoughts: look at what has been done here:
+-- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/Fin/Basic.lean
+-- and
+-- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/UInt.lean
+-- which both contain a fair amount of reasoning already!
+def USize.checked_sub (n: USize) (m: USize): result USize :=
+  -- NOTE: the test USize.toNat n - m >= 0 seems to always succeed?
+  if n >= m then
+    let n' := USize.toNat n
+    let m' := USize.toNat n
+    let r := USize.ofNatCore (n' - m') (by
+      have h: n' - m' <= n' := by
+        apply Nat.sub_le_of_le_add
+        case h => rewrite [ Nat.add_comm ]; apply Nat.le_add_left
+      apply Nat.lt_of_le_of_lt h
+      apply n.val.isLt
+    )
+    return r
+  else
+    fail integerOverflow
+
+def USize.checked_add (n: USize) (m: USize): result USize :=
+  if h: n.val.val + m.val.val <= 4294967295 then
+    .ret ⟨ n.val.val + m.val.val, by
+      have h': 4294967295 < USize.size := by intlit
+      apply Nat.lt_of_le_of_lt h h'
+    ⟩
+  else if h: n.val + m.val < USize.size then
+    .ret ⟨ n.val + m.val, h ⟩
+  else
+    .fail integerOverflow
+
+def USize.checked_rem (n: USize) (m: USize): result USize :=
+  if h: m > 0 then
+    .ret ⟨ n.val % m.val, by
+      have h1: ↑m.val < USize.size := m.val.isLt
+      have h2: n.val.val % m.val.val < m.val.val := @Nat.mod_lt n.val m.val h
+      apply Nat.lt_trans h2 h1
+    ⟩
+  else
+    .fail integerOverflow
+
+def USize.checked_mul (n: USize) (m: USize): result USize :=
+    if h: n.val.val * m.val.val <= 4294967295 then
+    .ret ⟨ n.val.val * m.val.val, by
+      have h': 4294967295 < USize.size := by intlit
+      apply Nat.lt_of_le_of_lt h h'
+    ⟩
+  else if h: n.val * m.val < USize.size then
+    .ret ⟨ n.val * m.val, h ⟩
+  else
+    .fail integerOverflow
+
+def USize.checked_div (n: USize) (m: USize): result USize :=
+  if m > 0 then
+    .ret ⟨ n.val / m.val, by
+      have h1: ↑n.val < USize.size := n.val.isLt
+      have h2: n.val.val / m.val.val <= n.val.val := @Nat.div_le_self n.val m.val
+      apply Nat.lt_of_le_of_lt h2 h1
+    ⟩
+  else
+    .fail integerOverflow
+
+class MachineInteger (t: Type) where
+  size: Nat
+  val: t -> Fin size
+  ofNatCore: (n:Nat) -> LT.lt n size -> t
+
+set_option hygiene false in
+run_cmd
+  for typeName in [`UInt8, `UInt16, `UInt32, `UInt64, `USize].map Lean.mkIdent do
+  Lean.Elab.Command.elabCommand (← `(
+    namespace $typeName
+    instance: MachineInteger $typeName where
+      size := size
+      val := val
+      ofNatCore := ofNatCore
+    end $typeName
+  ))
+
+def scalar_cast { src: Type } (dst: Type) [ MachineInteger src ] [ MachineInteger dst ] (x: src): result dst :=
+  if h: MachineInteger.val x < MachineInteger.size dst then
+    .ret (MachineInteger.ofNatCore (MachineInteger.val x).val h)
+  else
+    .fail integerOverflow
+
+
+-- Test behavior...
+#eval assert! USize.checked_sub 10 20 == fail integerOverflow; 0
+
+#eval USize.checked_sub 20 10
+-- NOTE: compare with concrete behavior here, which I do not think we want
+#eval USize.sub 0 1
+#eval UInt8.add 255 255
+
+-------------
+-- VECTORS --
+-------------
+
+-- Note: unlike F*, Lean seems to use strict upper bounds (e.g. USize.size)
+-- rather than maximum values (usize_max).
+def vec (α : Type u) := { l : List α // List.length l < USize.size }
+
+def vec_new (α : Type u): vec α := ⟨ [], by {
+  match USize.size, usize_size_eq with
+  | _, Or.inl rfl => simp
+  | _, Or.inr rfl => simp
+  } ⟩
+
+#check vec_new
+
+def vec_len (α : Type u) (v : vec α) : USize :=
+  let ⟨ v, l ⟩ := v
+  USize.ofNatCore (List.length v) l
+
+#eval vec_len Nat (vec_new Nat)
+ 
+def vec_push_fwd (α : Type u) (_ : vec α) (_ : α) : Unit := ()
+
+-- NOTE: old version trying to use a subtype notation, but probably better to
+-- leave result elimination to auxiliary lemmas with suitable preconditions
+-- TODO: I originally wrote `List.length v.val < USize.size - 1`; how can one
+-- make the proof work in that case? Probably need to import tactics from
+-- mathlib to deal with inequalities... would love to see an example.
+def vec_push_back_old (α : Type u) (v : vec α) (x : α) : { res: result (vec α) //
+  match res with | fail _ => True | ret v' => List.length v'.val = List.length v.val + 1}
+  :=
+  if h : List.length v.val + 1 < USize.size then
+    ⟨ return ⟨List.concat v.val x,
+      by
+        rw [List.length_concat]
+        assumption
+     ⟩, by simp ⟩
+  else
+    ⟨ fail maximumSizeExceeded, by simp ⟩
+
+#eval do
+  -- NOTE: the // notation is syntactic sugar for Subtype, a refinement with
+  -- fields val and property. However, Lean's elaborator can automatically
+  -- select the `val` field if the context provides a type annotation. We
+  -- annotate `x`, which relieves us of having to write `.val` on the right-hand
+  -- side of the monadic let.
+  let v := vec_new Nat
+  let x: vec Nat ← (vec_push_back_old Nat v 1: result (vec Nat)) -- WHY do we need the type annotation here?
+  -- TODO: strengthen post-condition above and do a demo to show that we can
+  -- safely eliminate the `fail` case
+  return (vec_len Nat x)
+
+def vec_push_back (α : Type u) (v : vec α) (x : α) : result (vec α)
+  :=
+  if h : List.length v.val + 1 <= 4294967295 then
+    return ⟨ List.concat v.val x,
+      by
+        rw [List.length_concat]
+        have h': 4294967295 < USize.size := by intlit
+        apply Nat.lt_of_le_of_lt h h'
+    ⟩
+  else if h: List.length v.val + 1 < USize.size then
+    return ⟨List.concat v.val x,
+      by
+        rw [List.length_concat]
+        assumption
+     ⟩
+  else
+    fail maximumSizeExceeded
+
+def vec_insert_fwd (α : Type u) (v: vec α) (i: USize) (_: α): result Unit :=
+  if i.val < List.length v.val then
+    .ret ()
+  else
+    .fail arrayOutOfBounds
+
+def vec_insert_back (α : Type u) (v: vec α) (i: USize) (x: α): result (vec α) :=
+  if i.val < List.length v.val then
+    .ret ⟨ List.set v.val i.val x, by
+      have h: List.length v.val < USize.size := v.property
+      rewrite [ List.length_set v.val i.val x ]
+      assumption
+    ⟩
+  else
+    .fail arrayOutOfBounds
+
+def vec_index_fwd (α : Type u) (v: vec α) (i: USize): result α :=
+  if h: i.val < List.length v.val then
+    .ret (List.get v.val ⟨i.val, h⟩)
+  else
+    .fail arrayOutOfBounds
+
+def vec_index_back (α : Type u) (v: vec α) (i: USize) (_: α): result Unit :=
+  if i.val < List.length v.val then
+    .ret ()
+  else
+    .fail arrayOutOfBounds
+
+def vec_index_mut_fwd (α : Type u) (v: vec α) (i: USize): result α :=
+  if h: i.val < List.length v.val then
+    .ret (List.get v.val ⟨i.val, h⟩)
+  else
+    .fail arrayOutOfBounds
+
+def vec_index_mut_back (α : Type u) (v: vec α) (i: USize) (x: α): result (vec α) :=
+  if i.val < List.length v.val then
+    .ret ⟨ List.set v.val i.val x, by
+      have h: List.length v.val < USize.size := v.property
+      rewrite [ List.length_set v.val i.val x ]
+      assumption
+    ⟩
+  else
+    .fail arrayOutOfBounds
+
+----------
+-- MISC --
+----------
+
+def mem_replace_fwd (a : Type) (x : a) (_ : a) : a :=
+  x
+
+def mem_replace_back (a : Type) (_ : a) (y : a) : a :=
+  y
+
+--------------------
+-- ASSERT COMMAND --
+--------------------
+
+open Lean Elab Command Term Meta
+
+syntax (name := assert) "#assert" term: command
+
+@[command_elab assert]
+def assertImpl : CommandElab := fun (_stx: Syntax) => do
+  logInfo "Reducing and asserting: "
+  logInfo _stx[1]
+  runTermElabM (fun _ => do
+    let e ← Term.elabTerm _stx[1] none
+    logInfo (Expr.dbgToString e)
+    -- How to evaluate the term and compare the result to true?
+    pure ())
+  -- logInfo (Expr.dbgToString (``true))
+  -- throwError "TODO: assert"
+
+#eval 2 == 2
+#assert (2 == 2)
diff --git a/tests/lean/misc/constants/Constants.lean b/tests/lean/misc/constants/Constants.lean
new file mode 100644
index 00000000..a5cbe363
--- /dev/null
+++ b/tests/lean/misc/constants/Constants.lean
@@ -0,0 +1,138 @@
+-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
+-- [constants]
+import Base.Primitives
+
+structure OpaqueDefs where
+  
+  /- [constants::X0] -/
+  def x0_body : result UInt32 := result.ret (UInt32.ofNatCore 0 (by intlit))
+  def x0_c : UInt32 := eval_global x0_body (by simp)
+  
+  /- [core::num::u32::{9}::MAX] -/
+  def core_num_u32_max_body : result UInt32 :=
+    result.ret (UInt32.ofNatCore 4294967295 (by intlit))
+  def core_num_u32_max_c : UInt32 :=
+    eval_global core_num_u32_max_body (by simp)
+  
+  /- [constants::X1] -/
+  def x1_body : result UInt32 := result.ret core_num_u32_max_c
+  def x1_c : UInt32 := eval_global x1_body (by simp)
+  
+  /- [constants::X2] -/
+  def x2_body : result UInt32 := result.ret (UInt32.ofNatCore 3 (by intlit))
+  def x2_c : UInt32 := eval_global x2_body (by simp)
+  
+  /- [constants::incr] -/
+  def incr_fwd (n : UInt32) : result UInt32 :=
+    UInt32.checked_add n (UInt32.ofNatCore 1 (by intlit))
+  
+  /- [constants::X3] -/
+  def x3_body : result UInt32 := incr_fwd (UInt32.ofNatCore 32 (by intlit))
+  def x3_c : UInt32 := eval_global x3_body (by simp)
+  
+  /- [constants::mk_pair0] -/
+  def mk_pair0_fwd (x : UInt32) (y : UInt32) : result (UInt32 × UInt32) :=
+    result.ret (x, y)
+  
+  /- [constants::Pair] -/
+  structure pair_t (T1 T2 : Type) where  pair_x : T1 pair_y : T2 
+  
+  /- [constants::mk_pair1] -/
+  def mk_pair1_fwd (x : UInt32) (y : UInt32) : result (pair_t UInt32 UInt32) :=
+    result.ret { pair_x := x, pair_y := y }
+  
+  /- [constants::P0] -/
+  def p0_body : result (UInt32 × UInt32) :=
+    mk_pair0_fwd (UInt32.ofNatCore 0 (by intlit))
+      (UInt32.ofNatCore 1 (by intlit))
+  def p0_c : (UInt32 × UInt32) := eval_global p0_body (by simp)
+  
+  /- [constants::P1] -/
+  def p1_body : result (pair_t UInt32 UInt32) :=
+    mk_pair1_fwd (UInt32.ofNatCore 0 (by intlit))
+      (UInt32.ofNatCore 1 (by intlit))
+  def p1_c : pair_t UInt32 UInt32 := eval_global p1_body (by simp)
+  
+  /- [constants::P2] -/
+  def p2_body : result (UInt32 × UInt32) :=
+    result.ret
+    ((UInt32.ofNatCore 0 (by intlit)),
+    (UInt32.ofNatCore 1 (by intlit)))
+  def p2_c : (UInt32 × UInt32) := eval_global p2_body (by simp)
+  
+  /- [constants::P3] -/
+  def p3_body : result (pair_t UInt32 UInt32) :=
+    result.ret
+    {
+      pair_x := (UInt32.ofNatCore 0 (by intlit)),
+      pair_y := (UInt32.ofNatCore 1 (by intlit))
+    }
+  def p3_c : pair_t UInt32 UInt32 := eval_global p3_body (by simp)
+  
+  /- [constants::Wrap] -/
+  structure wrap_t (T : Type) where  wrap_val : T 
+  
+  /- [constants::Wrap::{0}::new] -/
+  def wrap_new_fwd (T : Type) (val : T) : result (wrap_t T) :=
+    result.ret { wrap_val := val }
+  
+  /- [constants::Y] -/
+  def y_body : result (wrap_t Int32) :=
+    wrap_new_fwd Int32 (Int32.ofNatCore 2 (by intlit))
+  def y_c : wrap_t Int32 := eval_global y_body (by simp)
+  
+  /- [constants::unwrap_y] -/
+  def unwrap_y_fwd : result Int32 := result.ret y_c.wrap_val
+  
+  /- [constants::YVAL] -/
+  def yval_body : result Int32 := unwrap_y_fwd
+  def yval_c : Int32 := eval_global yval_body (by simp)
+  
+  /- [constants::get_z1::Z1] -/
+  def get_z1_z1_body : result Int32 :=
+    result.ret (Int32.ofNatCore 3 (by intlit))
+  def get_z1_z1_c : Int32 := eval_global get_z1_z1_body (by simp)
+  
+  /- [constants::get_z1] -/
+  def get_z1_fwd : result Int32 := result.ret get_z1_z1_c
+  
+  /- [constants::add] -/
+  def add_fwd (a : Int32) (b : Int32) : result Int32 := Int32.checked_add a b
+  
+  /- [constants::Q1] -/
+  def q1_body : result Int32 := result.ret (Int32.ofNatCore 5 (by intlit))
+  def q1_c : Int32 := eval_global q1_body (by simp)
+  
+  /- [constants::Q2] -/
+  def q2_body : result Int32 := result.ret q1_c
+  def q2_c : Int32 := eval_global q2_body (by simp)
+  
+  /- [constants::Q3] -/
+  def q3_body : result Int32 := add_fwd q2_c (Int32.ofNatCore 3 (by intlit))
+  def q3_c : Int32 := eval_global q3_body (by simp)
+  
+  /- [constants::get_z2] -/
+  def get_z2_fwd : result Int32 :=
+    do
+      let i <- get_z1_fwd
+      let i0 <- add_fwd i q3_c
+      add_fwd q1_c i0
+  
+  /- [constants::S1] -/
+  def s1_body : result UInt32 := result.ret (UInt32.ofNatCore 6 (by intlit))
+  def s1_c : UInt32 := eval_global s1_body (by simp)
+  
+  /- [constants::S2] -/
+  def s2_body : result UInt32 := incr_fwd s1_c
+  def s2_c : UInt32 := eval_global s2_body (by simp)
+  
+  /- [constants::S3] -/
+  def s3_body : result (pair_t UInt32 UInt32) := result.ret p3_c
+  def s3_c : pair_t UInt32 UInt32 := eval_global s3_body (by simp)
+  
+  /- [constants::S4] -/
+  def s4_body : result (pair_t UInt32 UInt32) :=
+    mk_pair1_fwd (UInt32.ofNatCore 7 (by intlit))
+      (UInt32.ofNatCore 8 (by intlit))
+  def s4_c : pair_t UInt32 UInt32 := eval_global s4_body (by simp)
+  
diff --git a/tests/lean/misc/external/Base/Primitives.lean b/tests/lean/misc/external/Base/Primitives.lean
new file mode 100644
index 00000000..79958d94
--- /dev/null
+++ b/tests/lean/misc/external/Base/Primitives.lean
@@ -0,0 +1,373 @@
+import Lean
+import Lean.Meta.Tactic.Simp
+import Init.Data.List.Basic
+import Mathlib.Tactic.RunCmd
+
+-------------
+-- PRELUDE --
+-------------
+
+-- Results & monadic combinators
+
+-- TODO: use syntactic conventions and capitalize error, result, etc.
+
+inductive error where
+   | assertionFailure: error
+   | integerOverflow: error
+   | arrayOutOfBounds: error
+   | maximumSizeExceeded: error
+   | panic: error
+deriving Repr, BEq
+
+open error
+
+inductive result (α : Type u) where
+  | ret (v: α): result α
+  | fail (e: error): result α 
+deriving Repr, BEq
+
+open result
+
+/- HELPERS -/
+
+-- TODO: is there automated syntax for these discriminators?
+def is_ret {α: Type} (r: result α): Bool :=
+  match r with
+  | result.ret _ => true
+  | result.fail _ => false
+
+def massert (b:Bool) : result Unit :=
+  if b then .ret () else fail assertionFailure
+
+def eval_global {α: Type} (x: result α) (_: is_ret x): α :=
+  match x with
+  | result.fail _ => by contradiction
+  | result.ret x => x
+
+/- DO-DSL SUPPORT -/
+
+def bind (x: result α) (f: α -> result β) : result β :=
+  match x with
+  | ret v  => f v 
+  | fail v => fail v
+
+-- Allows using result in do-blocks
+instance : Bind result where
+  bind := bind
+
+-- Allows using return x in do-blocks
+instance : Pure result where
+  pure := fun x => ret x
+
+/- CUSTOM-DSL SUPPORT -/
+
+-- Let-binding the result of a monadic operation is oftentimes not sufficient,
+-- because we may need a hypothesis for equational reasoning in the scope. We
+-- rely on subtype, and a custom let-binding operator, in effect recreating our
+-- own variant of the do-dsl
+
+def result.attach : (o : result α) → result { x : α // o = ret x }
+  | .ret x => .ret ⟨x, rfl⟩
+  | .fail e   => .fail e
+
+macro "let" h:ident " : " e:term " <-- " f:term : doElem =>
+  `(doElem| let ⟨$e, $h⟩ ← result.attach $f)
+
+-- Silly example of the kind of reasoning that this notation enables
+#eval do
+  let h: y <-- .ret (0: Nat)
+  let _: y = 0 := by cases h; decide
+  let r: { x: Nat // x = 0 } := ⟨ y, by assumption ⟩
+  .ret r
+
+----------------------
+-- MACHINE INTEGERS --
+----------------------
+
+-- NOTE: we reuse the USize type from prelude.lean, because at least we know
+-- it's defined in an idiomatic style that is going to make proofs easy (and
+-- indeed, several proofs here are much shortened compared to Aymeric's earlier
+-- attempt.) This is not stricto sensu the *correct* thing to do, because one
+-- can query at run-time the value of USize, which we do *not* want to do (we
+-- don't know what target we'll run on!), but when the day comes, we'll just
+-- define our own USize.
+-- ANOTHER NOTE: there is USize.sub but it has wraparound semantics, which is
+-- not something we want to define (I think), so we use our own monadic sub (but
+-- is it in line with the Rust behavior?)
+
+-- TODO: I am somewhat under the impression that subtraction is defined as a
+-- total function over nats...? the hypothesis in the if condition is not used
+-- in the then-branch which confuses me quite a bit
+
+-- TODO: add a refinement for the result (just like vec_push_back below) that
+-- explains that the toNat of the result (in the case of success) is the sub of
+-- the toNat of the arguments (i.e. intrinsic specification)
+-- ... do we want intrinsic specifications for the builtins? that might require
+-- some careful type annotations in the monadic notation for clients, but may
+-- give us more "for free"
+
+-- Note from Chris Bailey: "If there's more than one salient property of your
+-- definition then the subtyping strategy might get messy, and the property part
+-- of a subtype is less discoverable by the simplifier or tactics like
+-- library_search." Try to settle this with a Lean expert on what is the most
+-- productive way to go about this?
+
+-- One needs to perform a little bit of reasoning in order to successfully
+-- inject constants into USize, so we provide a general-purpose macro
+
+syntax "intlit" : tactic
+
+macro_rules
+  | `(tactic| intlit) => `(tactic|
+    match USize.size, usize_size_eq with
+    | _, Or.inl rfl => decide
+    | _, Or.inr rfl => decide)
+
+-- This is how the macro is expected to be used
+#eval USize.ofNatCore 0 (by intlit)
+
+-- Also works for other integer types (at the expense of a needless disjunction)
+#eval UInt32.ofNatCore 0 (by intlit)
+
+-- Further thoughts: look at what has been done here:
+-- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/Fin/Basic.lean
+-- and
+-- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/UInt.lean
+-- which both contain a fair amount of reasoning already!
+def USize.checked_sub (n: USize) (m: USize): result USize :=
+  -- NOTE: the test USize.toNat n - m >= 0 seems to always succeed?
+  if n >= m then
+    let n' := USize.toNat n
+    let m' := USize.toNat n
+    let r := USize.ofNatCore (n' - m') (by
+      have h: n' - m' <= n' := by
+        apply Nat.sub_le_of_le_add
+        case h => rewrite [ Nat.add_comm ]; apply Nat.le_add_left
+      apply Nat.lt_of_le_of_lt h
+      apply n.val.isLt
+    )
+    return r
+  else
+    fail integerOverflow
+
+def USize.checked_add (n: USize) (m: USize): result USize :=
+  if h: n.val.val + m.val.val <= 4294967295 then
+    .ret ⟨ n.val.val + m.val.val, by
+      have h': 4294967295 < USize.size := by intlit
+      apply Nat.lt_of_le_of_lt h h'
+    ⟩
+  else if h: n.val + m.val < USize.size then
+    .ret ⟨ n.val + m.val, h ⟩
+  else
+    .fail integerOverflow
+
+def USize.checked_rem (n: USize) (m: USize): result USize :=
+  if h: m > 0 then
+    .ret ⟨ n.val % m.val, by
+      have h1: ↑m.val < USize.size := m.val.isLt
+      have h2: n.val.val % m.val.val < m.val.val := @Nat.mod_lt n.val m.val h
+      apply Nat.lt_trans h2 h1
+    ⟩
+  else
+    .fail integerOverflow
+
+def USize.checked_mul (n: USize) (m: USize): result USize :=
+    if h: n.val.val * m.val.val <= 4294967295 then
+    .ret ⟨ n.val.val * m.val.val, by
+      have h': 4294967295 < USize.size := by intlit
+      apply Nat.lt_of_le_of_lt h h'
+    ⟩
+  else if h: n.val * m.val < USize.size then
+    .ret ⟨ n.val * m.val, h ⟩
+  else
+    .fail integerOverflow
+
+def USize.checked_div (n: USize) (m: USize): result USize :=
+  if m > 0 then
+    .ret ⟨ n.val / m.val, by
+      have h1: ↑n.val < USize.size := n.val.isLt
+      have h2: n.val.val / m.val.val <= n.val.val := @Nat.div_le_self n.val m.val
+      apply Nat.lt_of_le_of_lt h2 h1
+    ⟩
+  else
+    .fail integerOverflow
+
+class MachineInteger (t: Type) where
+  size: Nat
+  val: t -> Fin size
+  ofNatCore: (n:Nat) -> LT.lt n size -> t
+
+set_option hygiene false in
+run_cmd
+  for typeName in [`UInt8, `UInt16, `UInt32, `UInt64, `USize].map Lean.mkIdent do
+  Lean.Elab.Command.elabCommand (← `(
+    namespace $typeName
+    instance: MachineInteger $typeName where
+      size := size
+      val := val
+      ofNatCore := ofNatCore
+    end $typeName
+  ))
+
+def scalar_cast { src: Type } (dst: Type) [ MachineInteger src ] [ MachineInteger dst ] (x: src): result dst :=
+  if h: MachineInteger.val x < MachineInteger.size dst then
+    .ret (MachineInteger.ofNatCore (MachineInteger.val x).val h)
+  else
+    .fail integerOverflow
+
+
+-- Test behavior...
+#eval assert! USize.checked_sub 10 20 == fail integerOverflow; 0
+
+#eval USize.checked_sub 20 10
+-- NOTE: compare with concrete behavior here, which I do not think we want
+#eval USize.sub 0 1
+#eval UInt8.add 255 255
+
+-------------
+-- VECTORS --
+-------------
+
+-- Note: unlike F*, Lean seems to use strict upper bounds (e.g. USize.size)
+-- rather than maximum values (usize_max).
+def vec (α : Type u) := { l : List α // List.length l < USize.size }
+
+def vec_new (α : Type u): vec α := ⟨ [], by {
+  match USize.size, usize_size_eq with
+  | _, Or.inl rfl => simp
+  | _, Or.inr rfl => simp
+  } ⟩
+
+#check vec_new
+
+def vec_len (α : Type u) (v : vec α) : USize :=
+  let ⟨ v, l ⟩ := v
+  USize.ofNatCore (List.length v) l
+
+#eval vec_len Nat (vec_new Nat)
+ 
+def vec_push_fwd (α : Type u) (_ : vec α) (_ : α) : Unit := ()
+
+-- NOTE: old version trying to use a subtype notation, but probably better to
+-- leave result elimination to auxiliary lemmas with suitable preconditions
+-- TODO: I originally wrote `List.length v.val < USize.size - 1`; how can one
+-- make the proof work in that case? Probably need to import tactics from
+-- mathlib to deal with inequalities... would love to see an example.
+def vec_push_back_old (α : Type u) (v : vec α) (x : α) : { res: result (vec α) //
+  match res with | fail _ => True | ret v' => List.length v'.val = List.length v.val + 1}
+  :=
+  if h : List.length v.val + 1 < USize.size then
+    ⟨ return ⟨List.concat v.val x,
+      by
+        rw [List.length_concat]
+        assumption
+     ⟩, by simp ⟩
+  else
+    ⟨ fail maximumSizeExceeded, by simp ⟩
+
+#eval do
+  -- NOTE: the // notation is syntactic sugar for Subtype, a refinement with
+  -- fields val and property. However, Lean's elaborator can automatically
+  -- select the `val` field if the context provides a type annotation. We
+  -- annotate `x`, which relieves us of having to write `.val` on the right-hand
+  -- side of the monadic let.
+  let v := vec_new Nat
+  let x: vec Nat ← (vec_push_back_old Nat v 1: result (vec Nat)) -- WHY do we need the type annotation here?
+  -- TODO: strengthen post-condition above and do a demo to show that we can
+  -- safely eliminate the `fail` case
+  return (vec_len Nat x)
+
+def vec_push_back (α : Type u) (v : vec α) (x : α) : result (vec α)
+  :=
+  if h : List.length v.val + 1 <= 4294967295 then
+    return ⟨ List.concat v.val x,
+      by
+        rw [List.length_concat]
+        have h': 4294967295 < USize.size := by intlit
+        apply Nat.lt_of_le_of_lt h h'
+    ⟩
+  else if h: List.length v.val + 1 < USize.size then
+    return ⟨List.concat v.val x,
+      by
+        rw [List.length_concat]
+        assumption
+     ⟩
+  else
+    fail maximumSizeExceeded
+
+def vec_insert_fwd (α : Type u) (v: vec α) (i: USize) (_: α): result Unit :=
+  if i.val < List.length v.val then
+    .ret ()
+  else
+    .fail arrayOutOfBounds
+
+def vec_insert_back (α : Type u) (v: vec α) (i: USize) (x: α): result (vec α) :=
+  if i.val < List.length v.val then
+    .ret ⟨ List.set v.val i.val x, by
+      have h: List.length v.val < USize.size := v.property
+      rewrite [ List.length_set v.val i.val x ]
+      assumption
+    ⟩
+  else
+    .fail arrayOutOfBounds
+
+def vec_index_fwd (α : Type u) (v: vec α) (i: USize): result α :=
+  if h: i.val < List.length v.val then
+    .ret (List.get v.val ⟨i.val, h⟩)
+  else
+    .fail arrayOutOfBounds
+
+def vec_index_back (α : Type u) (v: vec α) (i: USize) (_: α): result Unit :=
+  if i.val < List.length v.val then
+    .ret ()
+  else
+    .fail arrayOutOfBounds
+
+def vec_index_mut_fwd (α : Type u) (v: vec α) (i: USize): result α :=
+  if h: i.val < List.length v.val then
+    .ret (List.get v.val ⟨i.val, h⟩)
+  else
+    .fail arrayOutOfBounds
+
+def vec_index_mut_back (α : Type u) (v: vec α) (i: USize) (x: α): result (vec α) :=
+  if i.val < List.length v.val then
+    .ret ⟨ List.set v.val i.val x, by
+      have h: List.length v.val < USize.size := v.property
+      rewrite [ List.length_set v.val i.val x ]
+      assumption
+    ⟩
+  else
+    .fail arrayOutOfBounds
+
+----------
+-- MISC --
+----------
+
+def mem_replace_fwd (a : Type) (x : a) (_ : a) : a :=
+  x
+
+def mem_replace_back (a : Type) (_ : a) (y : a) : a :=
+  y
+
+--------------------
+-- ASSERT COMMAND --
+--------------------
+
+open Lean Elab Command Term Meta
+
+syntax (name := assert) "#assert" term: command
+
+@[command_elab assert]
+def assertImpl : CommandElab := fun (_stx: Syntax) => do
+  logInfo "Reducing and asserting: "
+  logInfo _stx[1]
+  runTermElabM (fun _ => do
+    let e ← Term.elabTerm _stx[1] none
+    logInfo (Expr.dbgToString e)
+    -- How to evaluate the term and compare the result to true?
+    pure ())
+  -- logInfo (Expr.dbgToString (``true))
+  -- throwError "TODO: assert"
+
+#eval 2 == 2
+#assert (2 == 2)
diff --git a/tests/lean/misc/external/External/Funs.lean b/tests/lean/misc/external/External/Funs.lean
new file mode 100644
index 00000000..bb1e296d
--- /dev/null
+++ b/tests/lean/misc/external/External/Funs.lean
@@ -0,0 +1,93 @@
+-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
+-- [external]: function definitions
+import Base.Primitives
+import External.Types
+import External.Opaque
+
+section variable (opaque_defs: OpaqueDefs)
+
+/- [external::swap] -/
+def swap_fwd
+  (T : Type) (x : T) (y : T) (st : state) : result (state × Unit) :=
+  do
+    let (st0, _) <- opaque_defs.core_mem_swap_fwd T x y st
+    let (st1, _) <- opaque_defs.core_mem_swap_back0 T x y st st0
+    let (st2, _) <- opaque_defs.core_mem_swap_back1 T x y st st1
+    result.ret (st2, ())
+
+/- [external::swap] -/
+def swap_back
+  (T : Type) (x : T) (y : T) (st : state) (st0 : state) :
+  result (state × (T × T))
+  :=
+  do
+    let (st1, _) <- opaque_defs.core_mem_swap_fwd T x y st
+    let (st2, x0) <- opaque_defs.core_mem_swap_back0 T x y st st1
+    let (_, y0) <- opaque_defs.core_mem_swap_back1 T x y st st2
+    result.ret (st0, (x0, y0))
+
+/- [external::test_new_non_zero_u32] -/
+def test_new_non_zero_u32_fwd
+  (x : UInt32) (st : state) :
+  result (state × core_num_nonzero_non_zero_u32_t)
+  :=
+  do
+    let (st0, opt) <- opaque_defs.core_num_nonzero_non_zero_u32_new_fwd x st
+    opaque_defs.core_option_option_unwrap_fwd core_num_nonzero_non_zero_u32_t
+      opt st0
+
+/- [external::test_vec] -/
+def test_vec_fwd : result Unit :=
+  do
+    let v := vec_new UInt32
+    let _ <- vec_push_back UInt32 v (UInt32.ofNatCore 0 (by intlit))
+    result.ret ()
+
+/- Unit test for [external::test_vec] -/
+#assert (test_vec_fwd = .ret ())
+
+/- [external::custom_swap] -/
+def custom_swap_fwd
+  (T : Type) (x : T) (y : T) (st : state) : result (state × T) :=
+  do
+    let (st0, _) <- opaque_defs.core_mem_swap_fwd T x y st
+    let (st1, x0) <- opaque_defs.core_mem_swap_back0 T x y st st0
+    let (st2, _) <- opaque_defs.core_mem_swap_back1 T x y st st1
+    result.ret (st2, x0)
+
+/- [external::custom_swap] -/
+def custom_swap_back
+  (T : Type) (x : T) (y : T) (st : state) (ret0 : T) (st0 : state) :
+  result (state × (T × T))
+  :=
+  do
+    let (st1, _) <- opaque_defs.core_mem_swap_fwd T x y st
+    let (st2, _) <- opaque_defs.core_mem_swap_back0 T x y st st1
+    let (_, y0) <- opaque_defs.core_mem_swap_back1 T x y st st2
+    result.ret (st0, (ret0, y0))
+
+/- [external::test_custom_swap] -/
+def test_custom_swap_fwd
+  (x : UInt32) (y : UInt32) (st : state) : result (state × Unit) :=
+  do
+    let (st0, _) <- custom_swap_fwd UInt32 x y st
+    result.ret (st0, ())
+
+/- [external::test_custom_swap] -/
+def test_custom_swap_back
+  (x : UInt32) (y : UInt32) (st : state) (st0 : state) :
+  result (state × (UInt32 × UInt32))
+  :=
+  custom_swap_back UInt32 x y st (UInt32.ofNatCore 1 (by intlit)) st0
+
+/- [external::test_swap_non_zero] -/
+def test_swap_non_zero_fwd
+  (x : UInt32) (st : state) : result (state × UInt32) :=
+  do
+    let (st0, _) <- swap_fwd UInt32 x (UInt32.ofNatCore 0 (by intlit)) st
+    let (st1, (x0, _)) <-
+      swap_back UInt32 x (UInt32.ofNatCore 0 (by intlit)) st st0
+    if x0 = (UInt32.ofNatCore 0 (by intlit))
+    then result.fail error.panic
+    else result.ret (st1, x0)
+
diff --git a/tests/lean/misc/external/External/Opaque.lean b/tests/lean/misc/external/External/Opaque.lean
new file mode 100644
index 00000000..40ccc313
--- /dev/null
+++ b/tests/lean/misc/external/External/Opaque.lean
@@ -0,0 +1,28 @@
+-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
+-- [external]: opaque function definitions
+import Base.Primitives
+import External.Types
+
+structure OpaqueDefs where
+  
+  /- [core::mem::swap] -/
+  core_mem_swap_fwd (T : Type) : T -> T -> state -> result (state × Unit)
+  
+  /- [core::mem::swap] -/
+  core_mem_swap_back0
+    (T : Type) : T -> T -> state -> state -> result (state × T)
+  
+  /- [core::mem::swap] -/
+  core_mem_swap_back1
+    (T : Type) : T -> T -> state -> state -> result (state × T)
+  
+  /- [core::num::nonzero::NonZeroU32::{14}::new] -/
+  core_num_nonzero_non_zero_u32_new_fwd
+    :
+    UInt32 -> state -> result (state × (Option
+      core_num_nonzero_non_zero_u32_t))
+  
+  /- [core::option::Option::{0}::unwrap] -/
+  core_option_option_unwrap_fwd
+    (T : Type) : Option T -> state -> result (state × T)
+  
diff --git a/tests/lean/misc/external/External/Types.lean b/tests/lean/misc/external/External/Types.lean
new file mode 100644
index 00000000..b6fa292b
--- /dev/null
+++ b/tests/lean/misc/external/External/Types.lean
@@ -0,0 +1,8 @@
+-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
+-- [external]: type definitions
+import Base.Primitives
+
+/- [core::num::nonzero::NonZeroU32] -/
+axiom core_num_nonzero_non_zero_u32_t : Type
+/- The state type used in the state-error monad -/ axiom state : Type
+
diff --git a/tests/lean/misc/loops/Base/Primitives.lean b/tests/lean/misc/loops/Base/Primitives.lean
new file mode 100644
index 00000000..79958d94
--- /dev/null
+++ b/tests/lean/misc/loops/Base/Primitives.lean
@@ -0,0 +1,373 @@
+import Lean
+import Lean.Meta.Tactic.Simp
+import Init.Data.List.Basic
+import Mathlib.Tactic.RunCmd
+
+-------------
+-- PRELUDE --
+-------------
+
+-- Results & monadic combinators
+
+-- TODO: use syntactic conventions and capitalize error, result, etc.
+
+inductive error where
+   | assertionFailure: error
+   | integerOverflow: error
+   | arrayOutOfBounds: error
+   | maximumSizeExceeded: error
+   | panic: error
+deriving Repr, BEq
+
+open error
+
+inductive result (α : Type u) where
+  | ret (v: α): result α
+  | fail (e: error): result α 
+deriving Repr, BEq
+
+open result
+
+/- HELPERS -/
+
+-- TODO: is there automated syntax for these discriminators?
+def is_ret {α: Type} (r: result α): Bool :=
+  match r with
+  | result.ret _ => true
+  | result.fail _ => false
+
+def massert (b:Bool) : result Unit :=
+  if b then .ret () else fail assertionFailure
+
+def eval_global {α: Type} (x: result α) (_: is_ret x): α :=
+  match x with
+  | result.fail _ => by contradiction
+  | result.ret x => x
+
+/- DO-DSL SUPPORT -/
+
+def bind (x: result α) (f: α -> result β) : result β :=
+  match x with
+  | ret v  => f v 
+  | fail v => fail v
+
+-- Allows using result in do-blocks
+instance : Bind result where
+  bind := bind
+
+-- Allows using return x in do-blocks
+instance : Pure result where
+  pure := fun x => ret x
+
+/- CUSTOM-DSL SUPPORT -/
+
+-- Let-binding the result of a monadic operation is oftentimes not sufficient,
+-- because we may need a hypothesis for equational reasoning in the scope. We
+-- rely on subtype, and a custom let-binding operator, in effect recreating our
+-- own variant of the do-dsl
+
+def result.attach : (o : result α) → result { x : α // o = ret x }
+  | .ret x => .ret ⟨x, rfl⟩
+  | .fail e   => .fail e
+
+macro "let" h:ident " : " e:term " <-- " f:term : doElem =>
+  `(doElem| let ⟨$e, $h⟩ ← result.attach $f)
+
+-- Silly example of the kind of reasoning that this notation enables
+#eval do
+  let h: y <-- .ret (0: Nat)
+  let _: y = 0 := by cases h; decide
+  let r: { x: Nat // x = 0 } := ⟨ y, by assumption ⟩
+  .ret r
+
+----------------------
+-- MACHINE INTEGERS --
+----------------------
+
+-- NOTE: we reuse the USize type from prelude.lean, because at least we know
+-- it's defined in an idiomatic style that is going to make proofs easy (and
+-- indeed, several proofs here are much shortened compared to Aymeric's earlier
+-- attempt.) This is not stricto sensu the *correct* thing to do, because one
+-- can query at run-time the value of USize, which we do *not* want to do (we
+-- don't know what target we'll run on!), but when the day comes, we'll just
+-- define our own USize.
+-- ANOTHER NOTE: there is USize.sub but it has wraparound semantics, which is
+-- not something we want to define (I think), so we use our own monadic sub (but
+-- is it in line with the Rust behavior?)
+
+-- TODO: I am somewhat under the impression that subtraction is defined as a
+-- total function over nats...? the hypothesis in the if condition is not used
+-- in the then-branch which confuses me quite a bit
+
+-- TODO: add a refinement for the result (just like vec_push_back below) that
+-- explains that the toNat of the result (in the case of success) is the sub of
+-- the toNat of the arguments (i.e. intrinsic specification)
+-- ... do we want intrinsic specifications for the builtins? that might require
+-- some careful type annotations in the monadic notation for clients, but may
+-- give us more "for free"
+
+-- Note from Chris Bailey: "If there's more than one salient property of your
+-- definition then the subtyping strategy might get messy, and the property part
+-- of a subtype is less discoverable by the simplifier or tactics like
+-- library_search." Try to settle this with a Lean expert on what is the most
+-- productive way to go about this?
+
+-- One needs to perform a little bit of reasoning in order to successfully
+-- inject constants into USize, so we provide a general-purpose macro
+
+syntax "intlit" : tactic
+
+macro_rules
+  | `(tactic| intlit) => `(tactic|
+    match USize.size, usize_size_eq with
+    | _, Or.inl rfl => decide
+    | _, Or.inr rfl => decide)
+
+-- This is how the macro is expected to be used
+#eval USize.ofNatCore 0 (by intlit)
+
+-- Also works for other integer types (at the expense of a needless disjunction)
+#eval UInt32.ofNatCore 0 (by intlit)
+
+-- Further thoughts: look at what has been done here:
+-- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/Fin/Basic.lean
+-- and
+-- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/UInt.lean
+-- which both contain a fair amount of reasoning already!
+def USize.checked_sub (n: USize) (m: USize): result USize :=
+  -- NOTE: the test USize.toNat n - m >= 0 seems to always succeed?
+  if n >= m then
+    let n' := USize.toNat n
+    let m' := USize.toNat n
+    let r := USize.ofNatCore (n' - m') (by
+      have h: n' - m' <= n' := by
+        apply Nat.sub_le_of_le_add
+        case h => rewrite [ Nat.add_comm ]; apply Nat.le_add_left
+      apply Nat.lt_of_le_of_lt h
+      apply n.val.isLt
+    )
+    return r
+  else
+    fail integerOverflow
+
+def USize.checked_add (n: USize) (m: USize): result USize :=
+  if h: n.val.val + m.val.val <= 4294967295 then
+    .ret ⟨ n.val.val + m.val.val, by
+      have h': 4294967295 < USize.size := by intlit
+      apply Nat.lt_of_le_of_lt h h'
+    ⟩
+  else if h: n.val + m.val < USize.size then
+    .ret ⟨ n.val + m.val, h ⟩
+  else
+    .fail integerOverflow
+
+def USize.checked_rem (n: USize) (m: USize): result USize :=
+  if h: m > 0 then
+    .ret ⟨ n.val % m.val, by
+      have h1: ↑m.val < USize.size := m.val.isLt
+      have h2: n.val.val % m.val.val < m.val.val := @Nat.mod_lt n.val m.val h
+      apply Nat.lt_trans h2 h1
+    ⟩
+  else
+    .fail integerOverflow
+
+def USize.checked_mul (n: USize) (m: USize): result USize :=
+    if h: n.val.val * m.val.val <= 4294967295 then
+    .ret ⟨ n.val.val * m.val.val, by
+      have h': 4294967295 < USize.size := by intlit
+      apply Nat.lt_of_le_of_lt h h'
+    ⟩
+  else if h: n.val * m.val < USize.size then
+    .ret ⟨ n.val * m.val, h ⟩
+  else
+    .fail integerOverflow
+
+def USize.checked_div (n: USize) (m: USize): result USize :=
+  if m > 0 then
+    .ret ⟨ n.val / m.val, by
+      have h1: ↑n.val < USize.size := n.val.isLt
+      have h2: n.val.val / m.val.val <= n.val.val := @Nat.div_le_self n.val m.val
+      apply Nat.lt_of_le_of_lt h2 h1
+    ⟩
+  else
+    .fail integerOverflow
+
+class MachineInteger (t: Type) where
+  size: Nat
+  val: t -> Fin size
+  ofNatCore: (n:Nat) -> LT.lt n size -> t
+
+set_option hygiene false in
+run_cmd
+  for typeName in [`UInt8, `UInt16, `UInt32, `UInt64, `USize].map Lean.mkIdent do
+  Lean.Elab.Command.elabCommand (← `(
+    namespace $typeName
+    instance: MachineInteger $typeName where
+      size := size
+      val := val
+      ofNatCore := ofNatCore
+    end $typeName
+  ))
+
+def scalar_cast { src: Type } (dst: Type) [ MachineInteger src ] [ MachineInteger dst ] (x: src): result dst :=
+  if h: MachineInteger.val x < MachineInteger.size dst then
+    .ret (MachineInteger.ofNatCore (MachineInteger.val x).val h)
+  else
+    .fail integerOverflow
+
+
+-- Test behavior...
+#eval assert! USize.checked_sub 10 20 == fail integerOverflow; 0
+
+#eval USize.checked_sub 20 10
+-- NOTE: compare with concrete behavior here, which I do not think we want
+#eval USize.sub 0 1
+#eval UInt8.add 255 255
+
+-------------
+-- VECTORS --
+-------------
+
+-- Note: unlike F*, Lean seems to use strict upper bounds (e.g. USize.size)
+-- rather than maximum values (usize_max).
+def vec (α : Type u) := { l : List α // List.length l < USize.size }
+
+def vec_new (α : Type u): vec α := ⟨ [], by {
+  match USize.size, usize_size_eq with
+  | _, Or.inl rfl => simp
+  | _, Or.inr rfl => simp
+  } ⟩
+
+#check vec_new
+
+def vec_len (α : Type u) (v : vec α) : USize :=
+  let ⟨ v, l ⟩ := v
+  USize.ofNatCore (List.length v) l
+
+#eval vec_len Nat (vec_new Nat)
+ 
+def vec_push_fwd (α : Type u) (_ : vec α) (_ : α) : Unit := ()
+
+-- NOTE: old version trying to use a subtype notation, but probably better to
+-- leave result elimination to auxiliary lemmas with suitable preconditions
+-- TODO: I originally wrote `List.length v.val < USize.size - 1`; how can one
+-- make the proof work in that case? Probably need to import tactics from
+-- mathlib to deal with inequalities... would love to see an example.
+def vec_push_back_old (α : Type u) (v : vec α) (x : α) : { res: result (vec α) //
+  match res with | fail _ => True | ret v' => List.length v'.val = List.length v.val + 1}
+  :=
+  if h : List.length v.val + 1 < USize.size then
+    ⟨ return ⟨List.concat v.val x,
+      by
+        rw [List.length_concat]
+        assumption
+     ⟩, by simp ⟩
+  else
+    ⟨ fail maximumSizeExceeded, by simp ⟩
+
+#eval do
+  -- NOTE: the // notation is syntactic sugar for Subtype, a refinement with
+  -- fields val and property. However, Lean's elaborator can automatically
+  -- select the `val` field if the context provides a type annotation. We
+  -- annotate `x`, which relieves us of having to write `.val` on the right-hand
+  -- side of the monadic let.
+  let v := vec_new Nat
+  let x: vec Nat ← (vec_push_back_old Nat v 1: result (vec Nat)) -- WHY do we need the type annotation here?
+  -- TODO: strengthen post-condition above and do a demo to show that we can
+  -- safely eliminate the `fail` case
+  return (vec_len Nat x)
+
+def vec_push_back (α : Type u) (v : vec α) (x : α) : result (vec α)
+  :=
+  if h : List.length v.val + 1 <= 4294967295 then
+    return ⟨ List.concat v.val x,
+      by
+        rw [List.length_concat]
+        have h': 4294967295 < USize.size := by intlit
+        apply Nat.lt_of_le_of_lt h h'
+    ⟩
+  else if h: List.length v.val + 1 < USize.size then
+    return ⟨List.concat v.val x,
+      by
+        rw [List.length_concat]
+        assumption
+     ⟩
+  else
+    fail maximumSizeExceeded
+
+def vec_insert_fwd (α : Type u) (v: vec α) (i: USize) (_: α): result Unit :=
+  if i.val < List.length v.val then
+    .ret ()
+  else
+    .fail arrayOutOfBounds
+
+def vec_insert_back (α : Type u) (v: vec α) (i: USize) (x: α): result (vec α) :=
+  if i.val < List.length v.val then
+    .ret ⟨ List.set v.val i.val x, by
+      have h: List.length v.val < USize.size := v.property
+      rewrite [ List.length_set v.val i.val x ]
+      assumption
+    ⟩
+  else
+    .fail arrayOutOfBounds
+
+def vec_index_fwd (α : Type u) (v: vec α) (i: USize): result α :=
+  if h: i.val < List.length v.val then
+    .ret (List.get v.val ⟨i.val, h⟩)
+  else
+    .fail arrayOutOfBounds
+
+def vec_index_back (α : Type u) (v: vec α) (i: USize) (_: α): result Unit :=
+  if i.val < List.length v.val then
+    .ret ()
+  else
+    .fail arrayOutOfBounds
+
+def vec_index_mut_fwd (α : Type u) (v: vec α) (i: USize): result α :=
+  if h: i.val < List.length v.val then
+    .ret (List.get v.val ⟨i.val, h⟩)
+  else
+    .fail arrayOutOfBounds
+
+def vec_index_mut_back (α : Type u) (v: vec α) (i: USize) (x: α): result (vec α) :=
+  if i.val < List.length v.val then
+    .ret ⟨ List.set v.val i.val x, by
+      have h: List.length v.val < USize.size := v.property
+      rewrite [ List.length_set v.val i.val x ]
+      assumption
+    ⟩
+  else
+    .fail arrayOutOfBounds
+
+----------
+-- MISC --
+----------
+
+def mem_replace_fwd (a : Type) (x : a) (_ : a) : a :=
+  x
+
+def mem_replace_back (a : Type) (_ : a) (y : a) : a :=
+  y
+
+--------------------
+-- ASSERT COMMAND --
+--------------------
+
+open Lean Elab Command Term Meta
+
+syntax (name := assert) "#assert" term: command
+
+@[command_elab assert]
+def assertImpl : CommandElab := fun (_stx: Syntax) => do
+  logInfo "Reducing and asserting: "
+  logInfo _stx[1]
+  runTermElabM (fun _ => do
+    let e ← Term.elabTerm _stx[1] none
+    logInfo (Expr.dbgToString e)
+    -- How to evaluate the term and compare the result to true?
+    pure ())
+  -- logInfo (Expr.dbgToString (``true))
+  -- throwError "TODO: assert"
+
+#eval 2 == 2
+#assert (2 == 2)
diff --git a/tests/lean/misc/loops/Loops/Clauses/Clauses.lean b/tests/lean/misc/loops/Loops/Clauses/Clauses.lean
new file mode 100644
index 00000000..5ddb65ca
--- /dev/null
+++ b/tests/lean/misc/loops/Loops/Clauses/Clauses.lean
@@ -0,0 +1,209 @@
+-- [loops]: decreases clauses
+import Base.Primitives
+import Loops.Types
+
+/- [loops::sum]: termination measure -/
+@[simp]
+def sum_loop_terminates (max : UInt32) (i : UInt32) (s : UInt32) := (max, i, s)
+
+syntax "sum_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| sum_loop_decreases $max $i $s) =>`(tactic| sorry)
+
+/- [loops::sum_with_mut_borrows]: termination measure -/
+@[simp]
+def sum_with_mut_borrows_loop_terminates (max : UInt32) (mi : UInt32)
+  (ms : UInt32) :=
+  (max, mi, ms)
+
+syntax "sum_with_mut_borrows_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| sum_with_mut_borrows_loop_decreases $max $mi $ms) =>`(tactic| sorry)
+
+/- [loops::sum_with_shared_borrows]: termination measure -/
+@[simp]
+def sum_with_shared_borrows_loop_terminates (max : UInt32) (i : UInt32)
+  (s : UInt32) :=
+  (max, i, s)
+
+syntax "sum_with_shared_borrows_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| sum_with_shared_borrows_loop_decreases $max $i $s) =>`(tactic| sorry)
+
+/- [loops::clear]: termination measure -/
+@[simp] def clear_loop_terminates (v : vec UInt32) (i : USize) := (v, i)
+
+syntax "clear_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| clear_loop_decreases $v $i) =>`(tactic| sorry)
+
+/- [loops::list_mem]: termination measure -/
+@[simp]
+def list_mem_loop_terminates (x : UInt32) (ls : list_t UInt32) := (x, ls)
+
+syntax "list_mem_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| list_mem_loop_decreases $x $ls) =>`(tactic| sorry)
+
+/- [loops::list_nth_mut_loop]: termination measure -/
+@[simp]
+def list_nth_mut_loop_loop_terminates (T : Type) (ls : list_t T) (i : UInt32)
+  :=
+  (ls, i)
+
+syntax "list_nth_mut_loop_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| list_nth_mut_loop_loop_decreases $ls $i) =>`(tactic| sorry)
+
+/- [loops::list_nth_shared_loop]: termination measure -/
+@[simp]
+def list_nth_shared_loop_loop_terminates (T : Type) (ls : list_t T)
+  (i : UInt32) :=
+  (ls, i)
+
+syntax "list_nth_shared_loop_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| list_nth_shared_loop_loop_decreases $ls $i) =>`(tactic| sorry)
+
+/- [loops::get_elem_mut]: termination measure -/
+@[simp]
+def get_elem_mut_loop_terminates (x : USize) (ls : list_t USize) := (x, ls)
+
+syntax "get_elem_mut_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| get_elem_mut_loop_decreases $x $ls) =>`(tactic| sorry)
+
+/- [loops::get_elem_shared]: termination measure -/
+@[simp]
+def get_elem_shared_loop_terminates (x : USize) (ls : list_t USize) := (x, ls)
+
+syntax "get_elem_shared_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| get_elem_shared_loop_decreases $x $ls) =>`(tactic| sorry)
+
+/- [loops::list_nth_mut_loop_with_id]: termination measure -/
+@[simp]
+def list_nth_mut_loop_with_id_loop_terminates (T : Type) (i : UInt32)
+  (ls : list_t T) :=
+  (i, ls)
+
+syntax "list_nth_mut_loop_with_id_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| list_nth_mut_loop_with_id_loop_decreases $i $ls) =>`(tactic| sorry)
+
+/- [loops::list_nth_shared_loop_with_id]: termination measure -/
+@[simp]
+def list_nth_shared_loop_with_id_loop_terminates (T : Type) (i : UInt32)
+  (ls : list_t T) :=
+  (i, ls)
+
+syntax "list_nth_shared_loop_with_id_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| list_nth_shared_loop_with_id_loop_decreases $i $ls) =>`(tactic| sorry)
+
+/- [loops::list_nth_mut_loop_pair]: termination measure -/
+@[simp]
+def list_nth_mut_loop_pair_loop_terminates (T : Type) (ls0 : list_t T)
+  (ls1 : list_t T) (i : UInt32) :=
+  (ls0, ls1, i)
+
+syntax "list_nth_mut_loop_pair_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| list_nth_mut_loop_pair_loop_decreases $ls0 $ls1 $i) =>`(tactic| sorry)
+
+/- [loops::list_nth_shared_loop_pair]: termination measure -/
+@[simp]
+def list_nth_shared_loop_pair_loop_terminates (T : Type) (ls0 : list_t T)
+  (ls1 : list_t T) (i : UInt32) :=
+  (ls0, ls1, i)
+
+syntax "list_nth_shared_loop_pair_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| list_nth_shared_loop_pair_loop_decreases $ls0 $ls1 $i) =>
+  `(tactic| sorry)
+
+/- [loops::list_nth_mut_loop_pair_merge]: termination measure -/
+@[simp]
+def list_nth_mut_loop_pair_merge_loop_terminates (T : Type) (ls0 : list_t T)
+  (ls1 : list_t T) (i : UInt32) :=
+  (ls0, ls1, i)
+
+syntax "list_nth_mut_loop_pair_merge_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| list_nth_mut_loop_pair_merge_loop_decreases $ls0 $ls1 $i) =>
+  `(tactic| sorry)
+
+/- [loops::list_nth_shared_loop_pair_merge]: termination measure -/
+@[simp]
+def list_nth_shared_loop_pair_merge_loop_terminates (T : Type) (ls0 : list_t T)
+  (ls1 : list_t T) (i : UInt32) :=
+  (ls0, ls1, i)
+
+syntax "list_nth_shared_loop_pair_merge_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| list_nth_shared_loop_pair_merge_loop_decreases $ls0 $ls1 $i) =>
+  `(tactic| sorry)
+
+/- [loops::list_nth_mut_shared_loop_pair]: termination measure -/
+@[simp]
+def list_nth_mut_shared_loop_pair_loop_terminates (T : Type) (ls0 : list_t T)
+  (ls1 : list_t T) (i : UInt32) :=
+  (ls0, ls1, i)
+
+syntax "list_nth_mut_shared_loop_pair_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| list_nth_mut_shared_loop_pair_loop_decreases $ls0 $ls1 $i) =>
+  `(tactic| sorry)
+
+/- [loops::list_nth_mut_shared_loop_pair_merge]: termination measure -/
+@[simp]
+def list_nth_mut_shared_loop_pair_merge_loop_terminates (T : Type)
+  (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) :=
+  (ls0, ls1, i)
+
+syntax "list_nth_mut_shared_loop_pair_merge_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| list_nth_mut_shared_loop_pair_merge_loop_decreases $ls0 $ls1 $i) =>
+  `(tactic| sorry)
+
+/- [loops::list_nth_shared_mut_loop_pair]: termination measure -/
+@[simp]
+def list_nth_shared_mut_loop_pair_loop_terminates (T : Type) (ls0 : list_t T)
+  (ls1 : list_t T) (i : UInt32) :=
+  (ls0, ls1, i)
+
+syntax "list_nth_shared_mut_loop_pair_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| list_nth_shared_mut_loop_pair_loop_decreases $ls0 $ls1 $i) =>
+  `(tactic| sorry)
+
+/- [loops::list_nth_shared_mut_loop_pair_merge]: termination measure -/
+@[simp]
+def list_nth_shared_mut_loop_pair_merge_loop_terminates (T : Type)
+  (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) :=
+  (ls0, ls1, i)
+
+syntax "list_nth_shared_mut_loop_pair_merge_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| list_nth_shared_mut_loop_pair_merge_loop_decreases $ls0 $ls1 $i) =>
+  `(tactic| sorry)
+
diff --git a/tests/lean/misc/loops/Loops/Clauses/Template.lean b/tests/lean/misc/loops/Loops/Clauses/Template.lean
new file mode 100644
index 00000000..3c0f2f7c
--- /dev/null
+++ b/tests/lean/misc/loops/Loops/Clauses/Template.lean
@@ -0,0 +1,210 @@
+-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
+-- [loops]: templates for the decreases clauses
+import Base.Primitives
+import Loops.Types
+
+/- [loops::sum]: termination measure -/
+@[simp]
+def sum_loop_terminates (max : UInt32) (i : UInt32) (s : UInt32) := (max, i, s)
+
+syntax "sum_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| sum_loop_decreases $max $i $s) =>`(tactic| sorry)
+
+/- [loops::sum_with_mut_borrows]: termination measure -/
+@[simp]
+def sum_with_mut_borrows_loop_terminates (max : UInt32) (mi : UInt32)
+  (ms : UInt32) :=
+  (max, mi, ms)
+
+syntax "sum_with_mut_borrows_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| sum_with_mut_borrows_loop_decreases $max $mi $ms) =>`(tactic| sorry)
+
+/- [loops::sum_with_shared_borrows]: termination measure -/
+@[simp]
+def sum_with_shared_borrows_loop_terminates (max : UInt32) (i : UInt32)
+  (s : UInt32) :=
+  (max, i, s)
+
+syntax "sum_with_shared_borrows_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| sum_with_shared_borrows_loop_decreases $max $i $s) =>`(tactic| sorry)
+
+/- [loops::clear]: termination measure -/
+@[simp] def clear_loop_terminates (v : vec UInt32) (i : USize) := (v, i)
+
+syntax "clear_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| clear_loop_decreases $v $i) =>`(tactic| sorry)
+
+/- [loops::list_mem]: termination measure -/
+@[simp]
+def list_mem_loop_terminates (x : UInt32) (ls : list_t UInt32) := (x, ls)
+
+syntax "list_mem_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| list_mem_loop_decreases $x $ls) =>`(tactic| sorry)
+
+/- [loops::list_nth_mut_loop]: termination measure -/
+@[simp]
+def list_nth_mut_loop_loop_terminates (T : Type) (ls : list_t T) (i : UInt32)
+  :=
+  (ls, i)
+
+syntax "list_nth_mut_loop_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| list_nth_mut_loop_loop_decreases $ls $i) =>`(tactic| sorry)
+
+/- [loops::list_nth_shared_loop]: termination measure -/
+@[simp]
+def list_nth_shared_loop_loop_terminates (T : Type) (ls : list_t T)
+  (i : UInt32) :=
+  (ls, i)
+
+syntax "list_nth_shared_loop_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| list_nth_shared_loop_loop_decreases $ls $i) =>`(tactic| sorry)
+
+/- [loops::get_elem_mut]: termination measure -/
+@[simp]
+def get_elem_mut_loop_terminates (x : USize) (ls : list_t USize) := (x, ls)
+
+syntax "get_elem_mut_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| get_elem_mut_loop_decreases $x $ls) =>`(tactic| sorry)
+
+/- [loops::get_elem_shared]: termination measure -/
+@[simp]
+def get_elem_shared_loop_terminates (x : USize) (ls : list_t USize) := (x, ls)
+
+syntax "get_elem_shared_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| get_elem_shared_loop_decreases $x $ls) =>`(tactic| sorry)
+
+/- [loops::list_nth_mut_loop_with_id]: termination measure -/
+@[simp]
+def list_nth_mut_loop_with_id_loop_terminates (T : Type) (i : UInt32)
+  (ls : list_t T) :=
+  (i, ls)
+
+syntax "list_nth_mut_loop_with_id_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| list_nth_mut_loop_with_id_loop_decreases $i $ls) =>`(tactic| sorry)
+
+/- [loops::list_nth_shared_loop_with_id]: termination measure -/
+@[simp]
+def list_nth_shared_loop_with_id_loop_terminates (T : Type) (i : UInt32)
+  (ls : list_t T) :=
+  (i, ls)
+
+syntax "list_nth_shared_loop_with_id_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| list_nth_shared_loop_with_id_loop_decreases $i $ls) =>`(tactic| sorry)
+
+/- [loops::list_nth_mut_loop_pair]: termination measure -/
+@[simp]
+def list_nth_mut_loop_pair_loop_terminates (T : Type) (ls0 : list_t T)
+  (ls1 : list_t T) (i : UInt32) :=
+  (ls0, ls1, i)
+
+syntax "list_nth_mut_loop_pair_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| list_nth_mut_loop_pair_loop_decreases $ls0 $ls1 $i) =>`(tactic| sorry)
+
+/- [loops::list_nth_shared_loop_pair]: termination measure -/
+@[simp]
+def list_nth_shared_loop_pair_loop_terminates (T : Type) (ls0 : list_t T)
+  (ls1 : list_t T) (i : UInt32) :=
+  (ls0, ls1, i)
+
+syntax "list_nth_shared_loop_pair_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| list_nth_shared_loop_pair_loop_decreases $ls0 $ls1 $i) =>
+  `(tactic| sorry)
+
+/- [loops::list_nth_mut_loop_pair_merge]: termination measure -/
+@[simp]
+def list_nth_mut_loop_pair_merge_loop_terminates (T : Type) (ls0 : list_t T)
+  (ls1 : list_t T) (i : UInt32) :=
+  (ls0, ls1, i)
+
+syntax "list_nth_mut_loop_pair_merge_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| list_nth_mut_loop_pair_merge_loop_decreases $ls0 $ls1 $i) =>
+  `(tactic| sorry)
+
+/- [loops::list_nth_shared_loop_pair_merge]: termination measure -/
+@[simp]
+def list_nth_shared_loop_pair_merge_loop_terminates (T : Type) (ls0 : list_t T)
+  (ls1 : list_t T) (i : UInt32) :=
+  (ls0, ls1, i)
+
+syntax "list_nth_shared_loop_pair_merge_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| list_nth_shared_loop_pair_merge_loop_decreases $ls0 $ls1 $i) =>
+  `(tactic| sorry)
+
+/- [loops::list_nth_mut_shared_loop_pair]: termination measure -/
+@[simp]
+def list_nth_mut_shared_loop_pair_loop_terminates (T : Type) (ls0 : list_t T)
+  (ls1 : list_t T) (i : UInt32) :=
+  (ls0, ls1, i)
+
+syntax "list_nth_mut_shared_loop_pair_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| list_nth_mut_shared_loop_pair_loop_decreases $ls0 $ls1 $i) =>
+  `(tactic| sorry)
+
+/- [loops::list_nth_mut_shared_loop_pair_merge]: termination measure -/
+@[simp]
+def list_nth_mut_shared_loop_pair_merge_loop_terminates (T : Type)
+  (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) :=
+  (ls0, ls1, i)
+
+syntax "list_nth_mut_shared_loop_pair_merge_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| list_nth_mut_shared_loop_pair_merge_loop_decreases $ls0 $ls1 $i) =>
+  `(tactic| sorry)
+
+/- [loops::list_nth_shared_mut_loop_pair]: termination measure -/
+@[simp]
+def list_nth_shared_mut_loop_pair_loop_terminates (T : Type) (ls0 : list_t T)
+  (ls1 : list_t T) (i : UInt32) :=
+  (ls0, ls1, i)
+
+syntax "list_nth_shared_mut_loop_pair_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| list_nth_shared_mut_loop_pair_loop_decreases $ls0 $ls1 $i) =>
+  `(tactic| sorry)
+
+/- [loops::list_nth_shared_mut_loop_pair_merge]: termination measure -/
+@[simp]
+def list_nth_shared_mut_loop_pair_merge_loop_terminates (T : Type)
+  (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) :=
+  (ls0, ls1, i)
+
+syntax "list_nth_shared_mut_loop_pair_merge_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| list_nth_shared_mut_loop_pair_merge_loop_decreases $ls0 $ls1 $i) =>
+  `(tactic| sorry)
+
diff --git a/tests/lean/misc/loops/Loops/Funs.lean b/tests/lean/misc/loops/Loops/Funs.lean
new file mode 100644
index 00000000..5fe5b4ff
--- /dev/null
+++ b/tests/lean/misc/loops/Loops/Funs.lean
@@ -0,0 +1,786 @@
+-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
+-- [loops]: function definitions
+import Base.Primitives
+import Loops.Types
+import Loops.Clauses.Clauses
+
+/- [loops::sum] -/
+def sum_loop_fwd (max : UInt32) (i : UInt32) (s : UInt32) : (result UInt32) :=
+  if i < max
+  then
+    do
+      let s0 <- UInt32.checked_add s i
+      let i0 <- UInt32.checked_add i (UInt32.ofNatCore 1 (by intlit))
+      sum_loop_fwd max i0 s0
+  else UInt32.checked_mul s (UInt32.ofNatCore 2 (by intlit))
+termination_by sum_loop_fwd max i s => sum_loop_terminates max i s
+decreasing_by sum_loop_decreases max i s
+
+/- [loops::sum] -/
+def sum_fwd (max : UInt32) : result UInt32 :=
+  sum_loop_fwd max (UInt32.ofNatCore 0 (by intlit))
+    (UInt32.ofNatCore 0 (by intlit))
+
+/- [loops::sum_with_mut_borrows] -/
+def sum_with_mut_borrows_loop_fwd
+  (max : UInt32) (mi : UInt32) (ms : UInt32) : (result UInt32) :=
+  if mi < max
+  then
+    do
+      let ms0 <- UInt32.checked_add ms mi
+      let mi0 <- UInt32.checked_add mi (UInt32.ofNatCore 1 (by intlit))
+      sum_with_mut_borrows_loop_fwd max mi0 ms0
+  else UInt32.checked_mul ms (UInt32.ofNatCore 2 (by intlit))
+termination_by sum_with_mut_borrows_loop_fwd max mi ms =>
+                                                         sum_with_mut_borrows_loop_terminates
+                                                         max mi ms
+decreasing_by sum_with_mut_borrows_loop_decreases max mi ms
+
+/- [loops::sum_with_mut_borrows] -/
+def sum_with_mut_borrows_fwd (max : UInt32) : result UInt32 :=
+  sum_with_mut_borrows_loop_fwd max (UInt32.ofNatCore 0 (by intlit))
+    (UInt32.ofNatCore 0 (by intlit))
+
+/- [loops::sum_with_shared_borrows] -/
+def sum_with_shared_borrows_loop_fwd
+  (max : UInt32) (i : UInt32) (s : UInt32) : (result UInt32) :=
+  if i < max
+  then
+    do
+      let i0 <- UInt32.checked_add i (UInt32.ofNatCore 1 (by intlit))
+      let s0 <- UInt32.checked_add s i0
+      sum_with_shared_borrows_loop_fwd max i0 s0
+  else UInt32.checked_mul s (UInt32.ofNatCore 2 (by intlit))
+termination_by sum_with_shared_borrows_loop_fwd max i s =>
+                                                          sum_with_shared_borrows_loop_terminates
+                                                          max i s
+decreasing_by sum_with_shared_borrows_loop_decreases max i s
+
+/- [loops::sum_with_shared_borrows] -/
+def sum_with_shared_borrows_fwd (max : UInt32) : result UInt32 :=
+  sum_with_shared_borrows_loop_fwd max (UInt32.ofNatCore 0 (by intlit))
+    (UInt32.ofNatCore 0 (by intlit))
+
+/- [loops::clear] -/
+def clear_loop_fwd_back (v : vec UInt32) (i : USize) : (result (vec UInt32)) :=
+  let i0 := vec_len UInt32 v
+  if i < i0
+  then
+    do
+      let i1 <- USize.checked_add i (USize.ofNatCore 1 (by intlit))
+      let v0 <- vec_index_mut_back UInt32 v i (UInt32.ofNatCore 0 (by intlit))
+      clear_loop_fwd_back v0 i1
+  else result.ret v
+termination_by clear_loop_fwd_back v i => clear_loop_terminates v i
+decreasing_by clear_loop_decreases v i
+
+/- [loops::clear] -/
+def clear_fwd_back (v : vec UInt32) : result (vec UInt32) :=
+  clear_loop_fwd_back v (USize.ofNatCore 0 (by intlit))
+
+/- [loops::list_mem] -/
+def list_mem_loop_fwd (x : UInt32) (ls : list_t UInt32) : (result Bool) :=
+  match ls with
+  | list_t.ListCons y tl =>
+    if y = x then result.ret true else list_mem_loop_fwd x tl
+  | list_t.ListNil => result.ret false
+  
+termination_by list_mem_loop_fwd x ls => list_mem_loop_terminates x ls
+decreasing_by list_mem_loop_decreases x ls
+
+/- [loops::list_mem] -/
+def list_mem_fwd (x : UInt32) (ls : list_t UInt32) : result Bool :=
+  list_mem_loop_fwd x ls
+
+/- [loops::list_nth_mut_loop] -/
+def list_nth_mut_loop_loop_fwd
+  (T : Type) (ls : list_t T) (i : UInt32) : (result T) :=
+  match ls with
+  | list_t.ListCons x tl =>
+    if i = (UInt32.ofNatCore 0 (by intlit))
+    then result.ret x
+    else
+      do
+        let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+        list_nth_mut_loop_loop_fwd T tl i0
+  | list_t.ListNil => result.fail error.panic
+  
+termination_by list_nth_mut_loop_loop_fwd ls i =>
+                                                 list_nth_mut_loop_loop_terminates
+                                                 T ls i
+decreasing_by list_nth_mut_loop_loop_decreases ls i
+
+/- [loops::list_nth_mut_loop] -/
+def list_nth_mut_loop_fwd (T : Type) (ls : list_t T) (i : UInt32) : result T :=
+  list_nth_mut_loop_loop_fwd T ls i
+
+/- [loops::list_nth_mut_loop] -/
+def list_nth_mut_loop_loop_back
+  (T : Type) (ls : list_t T) (i : UInt32) (ret0 : T) : (result (list_t T)) :=
+  match ls with
+  | list_t.ListCons x tl =>
+    if i = (UInt32.ofNatCore 0 (by intlit))
+    then result.ret (list_t.ListCons ret0 tl)
+    else
+      do
+        let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+        let tl0 <- list_nth_mut_loop_loop_back T tl i0 ret0
+        result.ret (list_t.ListCons x tl0)
+  | list_t.ListNil => result.fail error.panic
+  
+termination_by list_nth_mut_loop_loop_back ls i ret0 =>
+                                                       list_nth_mut_loop_loop_terminates
+                                                       T ls i
+decreasing_by list_nth_mut_loop_loop_decreases ls i
+
+/- [loops::list_nth_mut_loop] -/
+def list_nth_mut_loop_back
+  (T : Type) (ls : list_t T) (i : UInt32) (ret0 : T) : result (list_t T) :=
+  list_nth_mut_loop_loop_back T ls i ret0
+
+/- [loops::list_nth_shared_loop] -/
+def list_nth_shared_loop_loop_fwd
+  (T : Type) (ls : list_t T) (i : UInt32) : (result T) :=
+  match ls with
+  | list_t.ListCons x tl =>
+    if i = (UInt32.ofNatCore 0 (by intlit))
+    then result.ret x
+    else
+      do
+        let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+        list_nth_shared_loop_loop_fwd T tl i0
+  | list_t.ListNil => result.fail error.panic
+  
+termination_by list_nth_shared_loop_loop_fwd ls i =>
+                                                    list_nth_shared_loop_loop_terminates
+                                                    T ls i
+decreasing_by list_nth_shared_loop_loop_decreases ls i
+
+/- [loops::list_nth_shared_loop] -/
+def list_nth_shared_loop_fwd
+  (T : Type) (ls : list_t T) (i : UInt32) : result T :=
+  list_nth_shared_loop_loop_fwd T ls i
+
+/- [loops::get_elem_mut] -/
+def get_elem_mut_loop_fwd (x : USize) (ls : list_t USize) : (result USize) :=
+  match ls with
+  | list_t.ListCons y tl =>
+    if y = x then result.ret y else get_elem_mut_loop_fwd x tl
+  | list_t.ListNil => result.fail error.panic
+  
+termination_by get_elem_mut_loop_fwd x ls => get_elem_mut_loop_terminates x ls
+decreasing_by get_elem_mut_loop_decreases x ls
+
+/- [loops::get_elem_mut] -/
+def get_elem_mut_fwd (slots : vec (list_t USize)) (x : USize) : result USize :=
+  do
+    let l <-
+      vec_index_mut_fwd (list_t USize) slots (USize.ofNatCore 0 (by intlit))
+    get_elem_mut_loop_fwd x l
+
+/- [loops::get_elem_mut] -/
+def get_elem_mut_loop_back
+  (x : USize) (ls : list_t USize) (ret0 : USize) : (result (list_t USize)) :=
+  match ls with
+  | list_t.ListCons y tl =>
+    if y = x
+    then result.ret (list_t.ListCons ret0 tl)
+    else
+      do
+        let tl0 <- get_elem_mut_loop_back x tl ret0
+        result.ret (list_t.ListCons y tl0)
+  | list_t.ListNil => result.fail error.panic
+  
+termination_by get_elem_mut_loop_back x ls ret0 => get_elem_mut_loop_terminates
+                                                  x ls
+decreasing_by get_elem_mut_loop_decreases x ls
+
+/- [loops::get_elem_mut] -/
+def get_elem_mut_back
+  (slots : vec (list_t USize)) (x : USize) (ret0 : USize) :
+  result (vec (list_t USize))
+  :=
+  do
+    let l <-
+      vec_index_mut_fwd (list_t USize) slots (USize.ofNatCore 0 (by intlit))
+    let l0 <- get_elem_mut_loop_back x l ret0
+    vec_index_mut_back (list_t USize) slots (USize.ofNatCore 0 (by intlit)) l0
+
+/- [loops::get_elem_shared] -/
+def get_elem_shared_loop_fwd
+  (x : USize) (ls : list_t USize) : (result USize) :=
+  match ls with
+  | list_t.ListCons y tl =>
+    if y = x then result.ret y else get_elem_shared_loop_fwd x tl
+  | list_t.ListNil => result.fail error.panic
+  
+termination_by get_elem_shared_loop_fwd x ls => get_elem_shared_loop_terminates
+                                               x ls
+decreasing_by get_elem_shared_loop_decreases x ls
+
+/- [loops::get_elem_shared] -/
+def get_elem_shared_fwd
+  (slots : vec (list_t USize)) (x : USize) : result USize :=
+  do
+    let l <- vec_index_fwd (list_t USize) slots (USize.ofNatCore 0 (by intlit))
+    get_elem_shared_loop_fwd x l
+
+/- [loops::id_mut] -/
+def id_mut_fwd (T : Type) (ls : list_t T) : result (list_t T) := result.ret ls
+
+/- [loops::id_mut] -/
+def id_mut_back
+  (T : Type) (ls : list_t T) (ret0 : list_t T) : result (list_t T) :=
+  result.ret ret0
+
+/- [loops::id_shared] -/
+def id_shared_fwd (T : Type) (ls : list_t T) : result (list_t T) :=
+  result.ret ls
+
+/- [loops::list_nth_mut_loop_with_id] -/
+def list_nth_mut_loop_with_id_loop_fwd
+  (T : Type) (i : UInt32) (ls : list_t T) : (result T) :=
+  match ls with
+  | list_t.ListCons x tl =>
+    if i = (UInt32.ofNatCore 0 (by intlit))
+    then result.ret x
+    else
+      do
+        let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+        list_nth_mut_loop_with_id_loop_fwd T i0 tl
+  | list_t.ListNil => result.fail error.panic
+  
+termination_by list_nth_mut_loop_with_id_loop_fwd i ls =>
+                                                         list_nth_mut_loop_with_id_loop_terminates
+                                                         T i ls
+decreasing_by list_nth_mut_loop_with_id_loop_decreases i ls
+
+/- [loops::list_nth_mut_loop_with_id] -/
+def list_nth_mut_loop_with_id_fwd
+  (T : Type) (ls : list_t T) (i : UInt32) : result T :=
+  do
+    let ls0 <- id_mut_fwd T ls
+    list_nth_mut_loop_with_id_loop_fwd T i ls0
+
+/- [loops::list_nth_mut_loop_with_id] -/
+def list_nth_mut_loop_with_id_loop_back
+  (T : Type) (i : UInt32) (ls : list_t T) (ret0 : T) : (result (list_t T)) :=
+  match ls with
+  | list_t.ListCons x tl =>
+    if i = (UInt32.ofNatCore 0 (by intlit))
+    then result.ret (list_t.ListCons ret0 tl)
+    else
+      do
+        let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+        let tl0 <- list_nth_mut_loop_with_id_loop_back T i0 tl ret0
+        result.ret (list_t.ListCons x tl0)
+  | list_t.ListNil => result.fail error.panic
+  
+termination_by list_nth_mut_loop_with_id_loop_back i ls ret0 =>
+                                                               list_nth_mut_loop_with_id_loop_terminates
+                                                               T i ls
+decreasing_by list_nth_mut_loop_with_id_loop_decreases i ls
+
+/- [loops::list_nth_mut_loop_with_id] -/
+def list_nth_mut_loop_with_id_back
+  (T : Type) (ls : list_t T) (i : UInt32) (ret0 : T) : result (list_t T) :=
+  do
+    let ls0 <- id_mut_fwd T ls
+    let l <- list_nth_mut_loop_with_id_loop_back T i ls0 ret0
+    id_mut_back T ls l
+
+/- [loops::list_nth_shared_loop_with_id] -/
+def list_nth_shared_loop_with_id_loop_fwd
+  (T : Type) (i : UInt32) (ls : list_t T) : (result T) :=
+  match ls with
+  | list_t.ListCons x tl =>
+    if i = (UInt32.ofNatCore 0 (by intlit))
+    then result.ret x
+    else
+      do
+        let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+        list_nth_shared_loop_with_id_loop_fwd T i0 tl
+  | list_t.ListNil => result.fail error.panic
+  
+termination_by list_nth_shared_loop_with_id_loop_fwd i ls =>
+                                                            list_nth_shared_loop_with_id_loop_terminates
+                                                            T i ls
+decreasing_by list_nth_shared_loop_with_id_loop_decreases i ls
+
+/- [loops::list_nth_shared_loop_with_id] -/
+def list_nth_shared_loop_with_id_fwd
+  (T : Type) (ls : list_t T) (i : UInt32) : result T :=
+  do
+    let ls0 <- id_shared_fwd T ls
+    list_nth_shared_loop_with_id_loop_fwd T i ls0
+
+/- [loops::list_nth_mut_loop_pair] -/
+def list_nth_mut_loop_pair_loop_fwd
+  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) :
+  (result (T × T))
+  :=
+  match ls0 with
+  | list_t.ListCons x0 tl0 =>
+    match ls1 with
+    | list_t.ListCons x1 tl1 =>
+      if i = (UInt32.ofNatCore 0 (by intlit))
+      then result.ret (x0, x1)
+      else
+        do
+          let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+          list_nth_mut_loop_pair_loop_fwd T tl0 tl1 i0
+    | list_t.ListNil => result.fail error.panic
+    
+  | list_t.ListNil => result.fail error.panic
+  
+termination_by list_nth_mut_loop_pair_loop_fwd ls0 ls1 i =>
+                                                           list_nth_mut_loop_pair_loop_terminates
+                                                           T ls0 ls1 i
+decreasing_by list_nth_mut_loop_pair_loop_decreases ls0 ls1 i
+
+/- [loops::list_nth_mut_loop_pair] -/
+def list_nth_mut_loop_pair_fwd
+  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) :
+  result (T × T)
+  :=
+  list_nth_mut_loop_pair_loop_fwd T ls0 ls1 i
+
+/- [loops::list_nth_mut_loop_pair] -/
+def list_nth_mut_loop_pair_loop_back'a
+  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) (ret0 : T) :
+  (result (list_t T))
+  :=
+  match ls0 with
+  | list_t.ListCons x0 tl0 =>
+    match ls1 with
+    | list_t.ListCons x1 tl1 =>
+      if i = (UInt32.ofNatCore 0 (by intlit))
+      then result.ret (list_t.ListCons ret0 tl0)
+      else
+        do
+          let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+          let tl00 <- list_nth_mut_loop_pair_loop_back'a T tl0 tl1 i0 ret0
+          result.ret (list_t.ListCons x0 tl00)
+    | list_t.ListNil => result.fail error.panic
+    
+  | list_t.ListNil => result.fail error.panic
+  
+termination_by list_nth_mut_loop_pair_loop_back'a ls0 ls1 i ret0 =>
+                                                                   list_nth_mut_loop_pair_loop_terminates
+                                                                   T ls0 ls1 i
+decreasing_by list_nth_mut_loop_pair_loop_decreases ls0 ls1 i
+
+/- [loops::list_nth_mut_loop_pair] -/
+def list_nth_mut_loop_pair_back'a
+  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) (ret0 : T) :
+  result (list_t T)
+  :=
+  list_nth_mut_loop_pair_loop_back'a T ls0 ls1 i ret0
+
+/- [loops::list_nth_mut_loop_pair] -/
+def list_nth_mut_loop_pair_loop_back'b
+  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) (ret0 : T) :
+  (result (list_t T))
+  :=
+  match ls0 with
+  | list_t.ListCons x0 tl0 =>
+    match ls1 with
+    | list_t.ListCons x1 tl1 =>
+      if i = (UInt32.ofNatCore 0 (by intlit))
+      then result.ret (list_t.ListCons ret0 tl1)
+      else
+        do
+          let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+          let tl10 <- list_nth_mut_loop_pair_loop_back'b T tl0 tl1 i0 ret0
+          result.ret (list_t.ListCons x1 tl10)
+    | list_t.ListNil => result.fail error.panic
+    
+  | list_t.ListNil => result.fail error.panic
+  
+termination_by list_nth_mut_loop_pair_loop_back'b ls0 ls1 i ret0 =>
+                                                                   list_nth_mut_loop_pair_loop_terminates
+                                                                   T ls0 ls1 i
+decreasing_by list_nth_mut_loop_pair_loop_decreases ls0 ls1 i
+
+/- [loops::list_nth_mut_loop_pair] -/
+def list_nth_mut_loop_pair_back'b
+  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) (ret0 : T) :
+  result (list_t T)
+  :=
+  list_nth_mut_loop_pair_loop_back'b T ls0 ls1 i ret0
+
+/- [loops::list_nth_shared_loop_pair] -/
+def list_nth_shared_loop_pair_loop_fwd
+  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) :
+  (result (T × T))
+  :=
+  match ls0 with
+  | list_t.ListCons x0 tl0 =>
+    match ls1 with
+    | list_t.ListCons x1 tl1 =>
+      if i = (UInt32.ofNatCore 0 (by intlit))
+      then result.ret (x0, x1)
+      else
+        do
+          let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+          list_nth_shared_loop_pair_loop_fwd T tl0 tl1 i0
+    | list_t.ListNil => result.fail error.panic
+    
+  | list_t.ListNil => result.fail error.panic
+  
+termination_by list_nth_shared_loop_pair_loop_fwd ls0 ls1 i =>
+                                                              list_nth_shared_loop_pair_loop_terminates
+                                                              T ls0 ls1 i
+decreasing_by list_nth_shared_loop_pair_loop_decreases ls0 ls1 i
+
+/- [loops::list_nth_shared_loop_pair] -/
+def list_nth_shared_loop_pair_fwd
+  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) :
+  result (T × T)
+  :=
+  list_nth_shared_loop_pair_loop_fwd T ls0 ls1 i
+
+/- [loops::list_nth_mut_loop_pair_merge] -/
+def list_nth_mut_loop_pair_merge_loop_fwd
+  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) :
+  (result (T × T))
+  :=
+  match ls0 with
+  | list_t.ListCons x0 tl0 =>
+    match ls1 with
+    | list_t.ListCons x1 tl1 =>
+      if i = (UInt32.ofNatCore 0 (by intlit))
+      then result.ret (x0, x1)
+      else
+        do
+          let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+          list_nth_mut_loop_pair_merge_loop_fwd T tl0 tl1 i0
+    | list_t.ListNil => result.fail error.panic
+    
+  | list_t.ListNil => result.fail error.panic
+  
+termination_by list_nth_mut_loop_pair_merge_loop_fwd ls0 ls1 i =>
+                                                                 list_nth_mut_loop_pair_merge_loop_terminates
+                                                                 T ls0 ls1 i
+decreasing_by list_nth_mut_loop_pair_merge_loop_decreases ls0 ls1 i
+
+/- [loops::list_nth_mut_loop_pair_merge] -/
+def list_nth_mut_loop_pair_merge_fwd
+  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) :
+  result (T × T)
+  :=
+  list_nth_mut_loop_pair_merge_loop_fwd T ls0 ls1 i
+
+/- [loops::list_nth_mut_loop_pair_merge] -/
+def list_nth_mut_loop_pair_merge_loop_back
+  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) (ret0 : (T × T)) :
+  (result ((list_t T) × (list_t T)))
+  :=
+  match ls0 with
+  | list_t.ListCons x0 tl0 =>
+    match ls1 with
+    | list_t.ListCons x1 tl1 =>
+      if i = (UInt32.ofNatCore 0 (by intlit))
+      then
+        let (t, t0) := ret0
+        result.ret (list_t.ListCons t tl0, list_t.ListCons t0 tl1)
+      else
+        do
+          let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+          let (tl00, tl10) <-
+            list_nth_mut_loop_pair_merge_loop_back T tl0 tl1 i0 ret0
+          result.ret (list_t.ListCons x0 tl00, list_t.ListCons x1 tl10)
+    | list_t.ListNil => result.fail error.panic
+    
+  | list_t.ListNil => result.fail error.panic
+  
+termination_by list_nth_mut_loop_pair_merge_loop_back ls0 ls1 i ret0 =>
+   list_nth_mut_loop_pair_merge_loop_terminates T ls0 ls1 i
+decreasing_by list_nth_mut_loop_pair_merge_loop_decreases ls0 ls1 i
+
+/- [loops::list_nth_mut_loop_pair_merge] -/
+def list_nth_mut_loop_pair_merge_back
+  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) (ret0 : (T × T)) :
+  result ((list_t T) × (list_t T))
+  :=
+  list_nth_mut_loop_pair_merge_loop_back T ls0 ls1 i ret0
+
+/- [loops::list_nth_shared_loop_pair_merge] -/
+def list_nth_shared_loop_pair_merge_loop_fwd
+  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) :
+  (result (T × T))
+  :=
+  match ls0 with
+  | list_t.ListCons x0 tl0 =>
+    match ls1 with
+    | list_t.ListCons x1 tl1 =>
+      if i = (UInt32.ofNatCore 0 (by intlit))
+      then result.ret (x0, x1)
+      else
+        do
+          let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+          list_nth_shared_loop_pair_merge_loop_fwd T tl0 tl1 i0
+    | list_t.ListNil => result.fail error.panic
+    
+  | list_t.ListNil => result.fail error.panic
+  
+termination_by list_nth_shared_loop_pair_merge_loop_fwd ls0 ls1 i =>
+                                                                    list_nth_shared_loop_pair_merge_loop_terminates
+                                                                    T ls0 ls1 i
+decreasing_by list_nth_shared_loop_pair_merge_loop_decreases ls0 ls1 i
+
+/- [loops::list_nth_shared_loop_pair_merge] -/
+def list_nth_shared_loop_pair_merge_fwd
+  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) :
+  result (T × T)
+  :=
+  list_nth_shared_loop_pair_merge_loop_fwd T ls0 ls1 i
+
+/- [loops::list_nth_mut_shared_loop_pair] -/
+def list_nth_mut_shared_loop_pair_loop_fwd
+  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) :
+  (result (T × T))
+  :=
+  match ls0 with
+  | list_t.ListCons x0 tl0 =>
+    match ls1 with
+    | list_t.ListCons x1 tl1 =>
+      if i = (UInt32.ofNatCore 0 (by intlit))
+      then result.ret (x0, x1)
+      else
+        do
+          let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+          list_nth_mut_shared_loop_pair_loop_fwd T tl0 tl1 i0
+    | list_t.ListNil => result.fail error.panic
+    
+  | list_t.ListNil => result.fail error.panic
+  
+termination_by list_nth_mut_shared_loop_pair_loop_fwd ls0 ls1 i =>
+                                                                  list_nth_mut_shared_loop_pair_loop_terminates
+                                                                  T ls0 ls1 i
+decreasing_by list_nth_mut_shared_loop_pair_loop_decreases ls0 ls1 i
+
+/- [loops::list_nth_mut_shared_loop_pair] -/
+def list_nth_mut_shared_loop_pair_fwd
+  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) :
+  result (T × T)
+  :=
+  list_nth_mut_shared_loop_pair_loop_fwd T ls0 ls1 i
+
+/- [loops::list_nth_mut_shared_loop_pair] -/
+def list_nth_mut_shared_loop_pair_loop_back
+  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) (ret0 : T) :
+  (result (list_t T))
+  :=
+  match ls0 with
+  | list_t.ListCons x0 tl0 =>
+    match ls1 with
+    | list_t.ListCons x1 tl1 =>
+      if i = (UInt32.ofNatCore 0 (by intlit))
+      then result.ret (list_t.ListCons ret0 tl0)
+      else
+        do
+          let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+          let tl00 <- list_nth_mut_shared_loop_pair_loop_back T tl0 tl1 i0 ret0
+          result.ret (list_t.ListCons x0 tl00)
+    | list_t.ListNil => result.fail error.panic
+    
+  | list_t.ListNil => result.fail error.panic
+  
+termination_by list_nth_mut_shared_loop_pair_loop_back ls0 ls1 i ret0 =>
+   list_nth_mut_shared_loop_pair_loop_terminates T ls0 ls1 i
+decreasing_by list_nth_mut_shared_loop_pair_loop_decreases ls0 ls1 i
+
+/- [loops::list_nth_mut_shared_loop_pair] -/
+def list_nth_mut_shared_loop_pair_back
+  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) (ret0 : T) :
+  result (list_t T)
+  :=
+  list_nth_mut_shared_loop_pair_loop_back T ls0 ls1 i ret0
+
+/- [loops::list_nth_mut_shared_loop_pair_merge] -/
+def list_nth_mut_shared_loop_pair_merge_loop_fwd
+  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) :
+  (result (T × T))
+  :=
+  match ls0 with
+  | list_t.ListCons x0 tl0 =>
+    match ls1 with
+    | list_t.ListCons x1 tl1 =>
+      if i = (UInt32.ofNatCore 0 (by intlit))
+      then result.ret (x0, x1)
+      else
+        do
+          let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+          list_nth_mut_shared_loop_pair_merge_loop_fwd T tl0 tl1 i0
+    | list_t.ListNil => result.fail error.panic
+    
+  | list_t.ListNil => result.fail error.panic
+  
+termination_by list_nth_mut_shared_loop_pair_merge_loop_fwd ls0 ls1 i =>
+   list_nth_mut_shared_loop_pair_merge_loop_terminates T ls0 ls1 i
+decreasing_by list_nth_mut_shared_loop_pair_merge_loop_decreases ls0 ls1 i
+
+/- [loops::list_nth_mut_shared_loop_pair_merge] -/
+def list_nth_mut_shared_loop_pair_merge_fwd
+  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) :
+  result (T × T)
+  :=
+  list_nth_mut_shared_loop_pair_merge_loop_fwd T ls0 ls1 i
+
+/- [loops::list_nth_mut_shared_loop_pair_merge] -/
+def list_nth_mut_shared_loop_pair_merge_loop_back
+  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) (ret0 : T) :
+  (result (list_t T))
+  :=
+  match ls0 with
+  | list_t.ListCons x0 tl0 =>
+    match ls1 with
+    | list_t.ListCons x1 tl1 =>
+      if i = (UInt32.ofNatCore 0 (by intlit))
+      then result.ret (list_t.ListCons ret0 tl0)
+      else
+        do
+          let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+          let tl00 <-
+            list_nth_mut_shared_loop_pair_merge_loop_back T tl0 tl1 i0 ret0
+          result.ret (list_t.ListCons x0 tl00)
+    | list_t.ListNil => result.fail error.panic
+    
+  | list_t.ListNil => result.fail error.panic
+  
+termination_by list_nth_mut_shared_loop_pair_merge_loop_back ls0 ls1 i ret0 =>
+   list_nth_mut_shared_loop_pair_merge_loop_terminates T ls0 ls1 i
+decreasing_by list_nth_mut_shared_loop_pair_merge_loop_decreases ls0 ls1 i
+
+/- [loops::list_nth_mut_shared_loop_pair_merge] -/
+def list_nth_mut_shared_loop_pair_merge_back
+  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) (ret0 : T) :
+  result (list_t T)
+  :=
+  list_nth_mut_shared_loop_pair_merge_loop_back T ls0 ls1 i ret0
+
+/- [loops::list_nth_shared_mut_loop_pair] -/
+def list_nth_shared_mut_loop_pair_loop_fwd
+  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) :
+  (result (T × T))
+  :=
+  match ls0 with
+  | list_t.ListCons x0 tl0 =>
+    match ls1 with
+    | list_t.ListCons x1 tl1 =>
+      if i = (UInt32.ofNatCore 0 (by intlit))
+      then result.ret (x0, x1)
+      else
+        do
+          let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+          list_nth_shared_mut_loop_pair_loop_fwd T tl0 tl1 i0
+    | list_t.ListNil => result.fail error.panic
+    
+  | list_t.ListNil => result.fail error.panic
+  
+termination_by list_nth_shared_mut_loop_pair_loop_fwd ls0 ls1 i =>
+                                                                  list_nth_shared_mut_loop_pair_loop_terminates
+                                                                  T ls0 ls1 i
+decreasing_by list_nth_shared_mut_loop_pair_loop_decreases ls0 ls1 i
+
+/- [loops::list_nth_shared_mut_loop_pair] -/
+def list_nth_shared_mut_loop_pair_fwd
+  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) :
+  result (T × T)
+  :=
+  list_nth_shared_mut_loop_pair_loop_fwd T ls0 ls1 i
+
+/- [loops::list_nth_shared_mut_loop_pair] -/
+def list_nth_shared_mut_loop_pair_loop_back
+  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) (ret0 : T) :
+  (result (list_t T))
+  :=
+  match ls0 with
+  | list_t.ListCons x0 tl0 =>
+    match ls1 with
+    | list_t.ListCons x1 tl1 =>
+      if i = (UInt32.ofNatCore 0 (by intlit))
+      then result.ret (list_t.ListCons ret0 tl1)
+      else
+        do
+          let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+          let tl10 <- list_nth_shared_mut_loop_pair_loop_back T tl0 tl1 i0 ret0
+          result.ret (list_t.ListCons x1 tl10)
+    | list_t.ListNil => result.fail error.panic
+    
+  | list_t.ListNil => result.fail error.panic
+  
+termination_by list_nth_shared_mut_loop_pair_loop_back ls0 ls1 i ret0 =>
+   list_nth_shared_mut_loop_pair_loop_terminates T ls0 ls1 i
+decreasing_by list_nth_shared_mut_loop_pair_loop_decreases ls0 ls1 i
+
+/- [loops::list_nth_shared_mut_loop_pair] -/
+def list_nth_shared_mut_loop_pair_back
+  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) (ret0 : T) :
+  result (list_t T)
+  :=
+  list_nth_shared_mut_loop_pair_loop_back T ls0 ls1 i ret0
+
+/- [loops::list_nth_shared_mut_loop_pair_merge] -/
+def list_nth_shared_mut_loop_pair_merge_loop_fwd
+  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) :
+  (result (T × T))
+  :=
+  match ls0 with
+  | list_t.ListCons x0 tl0 =>
+    match ls1 with
+    | list_t.ListCons x1 tl1 =>
+      if i = (UInt32.ofNatCore 0 (by intlit))
+      then result.ret (x0, x1)
+      else
+        do
+          let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+          list_nth_shared_mut_loop_pair_merge_loop_fwd T tl0 tl1 i0
+    | list_t.ListNil => result.fail error.panic
+    
+  | list_t.ListNil => result.fail error.panic
+  
+termination_by list_nth_shared_mut_loop_pair_merge_loop_fwd ls0 ls1 i =>
+   list_nth_shared_mut_loop_pair_merge_loop_terminates T ls0 ls1 i
+decreasing_by list_nth_shared_mut_loop_pair_merge_loop_decreases ls0 ls1 i
+
+/- [loops::list_nth_shared_mut_loop_pair_merge] -/
+def list_nth_shared_mut_loop_pair_merge_fwd
+  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) :
+  result (T × T)
+  :=
+  list_nth_shared_mut_loop_pair_merge_loop_fwd T ls0 ls1 i
+
+/- [loops::list_nth_shared_mut_loop_pair_merge] -/
+def list_nth_shared_mut_loop_pair_merge_loop_back
+  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) (ret0 : T) :
+  (result (list_t T))
+  :=
+  match ls0 with
+  | list_t.ListCons x0 tl0 =>
+    match ls1 with
+    | list_t.ListCons x1 tl1 =>
+      if i = (UInt32.ofNatCore 0 (by intlit))
+      then result.ret (list_t.ListCons ret0 tl1)
+      else
+        do
+          let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+          let tl10 <-
+            list_nth_shared_mut_loop_pair_merge_loop_back T tl0 tl1 i0 ret0
+          result.ret (list_t.ListCons x1 tl10)
+    | list_t.ListNil => result.fail error.panic
+    
+  | list_t.ListNil => result.fail error.panic
+  
+termination_by list_nth_shared_mut_loop_pair_merge_loop_back ls0 ls1 i ret0 =>
+   list_nth_shared_mut_loop_pair_merge_loop_terminates T ls0 ls1 i
+decreasing_by list_nth_shared_mut_loop_pair_merge_loop_decreases ls0 ls1 i
+
+/- [loops::list_nth_shared_mut_loop_pair_merge] -/
+def list_nth_shared_mut_loop_pair_merge_back
+  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) (ret0 : T) :
+  result (list_t T)
+  :=
+  list_nth_shared_mut_loop_pair_merge_loop_back T ls0 ls1 i ret0
+
diff --git a/tests/lean/misc/loops/Loops/Types.lean b/tests/lean/misc/loops/Loops/Types.lean
new file mode 100644
index 00000000..f4b6809e
--- /dev/null
+++ b/tests/lean/misc/loops/Loops/Types.lean
@@ -0,0 +1,9 @@
+-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
+-- [loops]: type definitions
+import Base.Primitives
+
+/- [loops::List] -/
+inductive list_t (T : Type) :=
+| ListCons : T -> list_t T -> list_t T
+| ListNil : list_t T
+
diff --git a/tests/lean/misc/no_nested_borrows/Base/Primitives.lean b/tests/lean/misc/no_nested_borrows/Base/Primitives.lean
new file mode 100644
index 00000000..79958d94
--- /dev/null
+++ b/tests/lean/misc/no_nested_borrows/Base/Primitives.lean
@@ -0,0 +1,373 @@
+import Lean
+import Lean.Meta.Tactic.Simp
+import Init.Data.List.Basic
+import Mathlib.Tactic.RunCmd
+
+-------------
+-- PRELUDE --
+-------------
+
+-- Results & monadic combinators
+
+-- TODO: use syntactic conventions and capitalize error, result, etc.
+
+inductive error where
+   | assertionFailure: error
+   | integerOverflow: error
+   | arrayOutOfBounds: error
+   | maximumSizeExceeded: error
+   | panic: error
+deriving Repr, BEq
+
+open error
+
+inductive result (α : Type u) where
+  | ret (v: α): result α
+  | fail (e: error): result α 
+deriving Repr, BEq
+
+open result
+
+/- HELPERS -/
+
+-- TODO: is there automated syntax for these discriminators?
+def is_ret {α: Type} (r: result α): Bool :=
+  match r with
+  | result.ret _ => true
+  | result.fail _ => false
+
+def massert (b:Bool) : result Unit :=
+  if b then .ret () else fail assertionFailure
+
+def eval_global {α: Type} (x: result α) (_: is_ret x): α :=
+  match x with
+  | result.fail _ => by contradiction
+  | result.ret x => x
+
+/- DO-DSL SUPPORT -/
+
+def bind (x: result α) (f: α -> result β) : result β :=
+  match x with
+  | ret v  => f v 
+  | fail v => fail v
+
+-- Allows using result in do-blocks
+instance : Bind result where
+  bind := bind
+
+-- Allows using return x in do-blocks
+instance : Pure result where
+  pure := fun x => ret x
+
+/- CUSTOM-DSL SUPPORT -/
+
+-- Let-binding the result of a monadic operation is oftentimes not sufficient,
+-- because we may need a hypothesis for equational reasoning in the scope. We
+-- rely on subtype, and a custom let-binding operator, in effect recreating our
+-- own variant of the do-dsl
+
+def result.attach : (o : result α) → result { x : α // o = ret x }
+  | .ret x => .ret ⟨x, rfl⟩
+  | .fail e   => .fail e
+
+macro "let" h:ident " : " e:term " <-- " f:term : doElem =>
+  `(doElem| let ⟨$e, $h⟩ ← result.attach $f)
+
+-- Silly example of the kind of reasoning that this notation enables
+#eval do
+  let h: y <-- .ret (0: Nat)
+  let _: y = 0 := by cases h; decide
+  let r: { x: Nat // x = 0 } := ⟨ y, by assumption ⟩
+  .ret r
+
+----------------------
+-- MACHINE INTEGERS --
+----------------------
+
+-- NOTE: we reuse the USize type from prelude.lean, because at least we know
+-- it's defined in an idiomatic style that is going to make proofs easy (and
+-- indeed, several proofs here are much shortened compared to Aymeric's earlier
+-- attempt.) This is not stricto sensu the *correct* thing to do, because one
+-- can query at run-time the value of USize, which we do *not* want to do (we
+-- don't know what target we'll run on!), but when the day comes, we'll just
+-- define our own USize.
+-- ANOTHER NOTE: there is USize.sub but it has wraparound semantics, which is
+-- not something we want to define (I think), so we use our own monadic sub (but
+-- is it in line with the Rust behavior?)
+
+-- TODO: I am somewhat under the impression that subtraction is defined as a
+-- total function over nats...? the hypothesis in the if condition is not used
+-- in the then-branch which confuses me quite a bit
+
+-- TODO: add a refinement for the result (just like vec_push_back below) that
+-- explains that the toNat of the result (in the case of success) is the sub of
+-- the toNat of the arguments (i.e. intrinsic specification)
+-- ... do we want intrinsic specifications for the builtins? that might require
+-- some careful type annotations in the monadic notation for clients, but may
+-- give us more "for free"
+
+-- Note from Chris Bailey: "If there's more than one salient property of your
+-- definition then the subtyping strategy might get messy, and the property part
+-- of a subtype is less discoverable by the simplifier or tactics like
+-- library_search." Try to settle this with a Lean expert on what is the most
+-- productive way to go about this?
+
+-- One needs to perform a little bit of reasoning in order to successfully
+-- inject constants into USize, so we provide a general-purpose macro
+
+syntax "intlit" : tactic
+
+macro_rules
+  | `(tactic| intlit) => `(tactic|
+    match USize.size, usize_size_eq with
+    | _, Or.inl rfl => decide
+    | _, Or.inr rfl => decide)
+
+-- This is how the macro is expected to be used
+#eval USize.ofNatCore 0 (by intlit)
+
+-- Also works for other integer types (at the expense of a needless disjunction)
+#eval UInt32.ofNatCore 0 (by intlit)
+
+-- Further thoughts: look at what has been done here:
+-- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/Fin/Basic.lean
+-- and
+-- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/UInt.lean
+-- which both contain a fair amount of reasoning already!
+def USize.checked_sub (n: USize) (m: USize): result USize :=
+  -- NOTE: the test USize.toNat n - m >= 0 seems to always succeed?
+  if n >= m then
+    let n' := USize.toNat n
+    let m' := USize.toNat n
+    let r := USize.ofNatCore (n' - m') (by
+      have h: n' - m' <= n' := by
+        apply Nat.sub_le_of_le_add
+        case h => rewrite [ Nat.add_comm ]; apply Nat.le_add_left
+      apply Nat.lt_of_le_of_lt h
+      apply n.val.isLt
+    )
+    return r
+  else
+    fail integerOverflow
+
+def USize.checked_add (n: USize) (m: USize): result USize :=
+  if h: n.val.val + m.val.val <= 4294967295 then
+    .ret ⟨ n.val.val + m.val.val, by
+      have h': 4294967295 < USize.size := by intlit
+      apply Nat.lt_of_le_of_lt h h'
+    ⟩
+  else if h: n.val + m.val < USize.size then
+    .ret ⟨ n.val + m.val, h ⟩
+  else
+    .fail integerOverflow
+
+def USize.checked_rem (n: USize) (m: USize): result USize :=
+  if h: m > 0 then
+    .ret ⟨ n.val % m.val, by
+      have h1: ↑m.val < USize.size := m.val.isLt
+      have h2: n.val.val % m.val.val < m.val.val := @Nat.mod_lt n.val m.val h
+      apply Nat.lt_trans h2 h1
+    ⟩
+  else
+    .fail integerOverflow
+
+def USize.checked_mul (n: USize) (m: USize): result USize :=
+    if h: n.val.val * m.val.val <= 4294967295 then
+    .ret ⟨ n.val.val * m.val.val, by
+      have h': 4294967295 < USize.size := by intlit
+      apply Nat.lt_of_le_of_lt h h'
+    ⟩
+  else if h: n.val * m.val < USize.size then
+    .ret ⟨ n.val * m.val, h ⟩
+  else
+    .fail integerOverflow
+
+def USize.checked_div (n: USize) (m: USize): result USize :=
+  if m > 0 then
+    .ret ⟨ n.val / m.val, by
+      have h1: ↑n.val < USize.size := n.val.isLt
+      have h2: n.val.val / m.val.val <= n.val.val := @Nat.div_le_self n.val m.val
+      apply Nat.lt_of_le_of_lt h2 h1
+    ⟩
+  else
+    .fail integerOverflow
+
+class MachineInteger (t: Type) where
+  size: Nat
+  val: t -> Fin size
+  ofNatCore: (n:Nat) -> LT.lt n size -> t
+
+set_option hygiene false in
+run_cmd
+  for typeName in [`UInt8, `UInt16, `UInt32, `UInt64, `USize].map Lean.mkIdent do
+  Lean.Elab.Command.elabCommand (← `(
+    namespace $typeName
+    instance: MachineInteger $typeName where
+      size := size
+      val := val
+      ofNatCore := ofNatCore
+    end $typeName
+  ))
+
+def scalar_cast { src: Type } (dst: Type) [ MachineInteger src ] [ MachineInteger dst ] (x: src): result dst :=
+  if h: MachineInteger.val x < MachineInteger.size dst then
+    .ret (MachineInteger.ofNatCore (MachineInteger.val x).val h)
+  else
+    .fail integerOverflow
+
+
+-- Test behavior...
+#eval assert! USize.checked_sub 10 20 == fail integerOverflow; 0
+
+#eval USize.checked_sub 20 10
+-- NOTE: compare with concrete behavior here, which I do not think we want
+#eval USize.sub 0 1
+#eval UInt8.add 255 255
+
+-------------
+-- VECTORS --
+-------------
+
+-- Note: unlike F*, Lean seems to use strict upper bounds (e.g. USize.size)
+-- rather than maximum values (usize_max).
+def vec (α : Type u) := { l : List α // List.length l < USize.size }
+
+def vec_new (α : Type u): vec α := ⟨ [], by {
+  match USize.size, usize_size_eq with
+  | _, Or.inl rfl => simp
+  | _, Or.inr rfl => simp
+  } ⟩
+
+#check vec_new
+
+def vec_len (α : Type u) (v : vec α) : USize :=
+  let ⟨ v, l ⟩ := v
+  USize.ofNatCore (List.length v) l
+
+#eval vec_len Nat (vec_new Nat)
+ 
+def vec_push_fwd (α : Type u) (_ : vec α) (_ : α) : Unit := ()
+
+-- NOTE: old version trying to use a subtype notation, but probably better to
+-- leave result elimination to auxiliary lemmas with suitable preconditions
+-- TODO: I originally wrote `List.length v.val < USize.size - 1`; how can one
+-- make the proof work in that case? Probably need to import tactics from
+-- mathlib to deal with inequalities... would love to see an example.
+def vec_push_back_old (α : Type u) (v : vec α) (x : α) : { res: result (vec α) //
+  match res with | fail _ => True | ret v' => List.length v'.val = List.length v.val + 1}
+  :=
+  if h : List.length v.val + 1 < USize.size then
+    ⟨ return ⟨List.concat v.val x,
+      by
+        rw [List.length_concat]
+        assumption
+     ⟩, by simp ⟩
+  else
+    ⟨ fail maximumSizeExceeded, by simp ⟩
+
+#eval do
+  -- NOTE: the // notation is syntactic sugar for Subtype, a refinement with
+  -- fields val and property. However, Lean's elaborator can automatically
+  -- select the `val` field if the context provides a type annotation. We
+  -- annotate `x`, which relieves us of having to write `.val` on the right-hand
+  -- side of the monadic let.
+  let v := vec_new Nat
+  let x: vec Nat ← (vec_push_back_old Nat v 1: result (vec Nat)) -- WHY do we need the type annotation here?
+  -- TODO: strengthen post-condition above and do a demo to show that we can
+  -- safely eliminate the `fail` case
+  return (vec_len Nat x)
+
+def vec_push_back (α : Type u) (v : vec α) (x : α) : result (vec α)
+  :=
+  if h : List.length v.val + 1 <= 4294967295 then
+    return ⟨ List.concat v.val x,
+      by
+        rw [List.length_concat]
+        have h': 4294967295 < USize.size := by intlit
+        apply Nat.lt_of_le_of_lt h h'
+    ⟩
+  else if h: List.length v.val + 1 < USize.size then
+    return ⟨List.concat v.val x,
+      by
+        rw [List.length_concat]
+        assumption
+     ⟩
+  else
+    fail maximumSizeExceeded
+
+def vec_insert_fwd (α : Type u) (v: vec α) (i: USize) (_: α): result Unit :=
+  if i.val < List.length v.val then
+    .ret ()
+  else
+    .fail arrayOutOfBounds
+
+def vec_insert_back (α : Type u) (v: vec α) (i: USize) (x: α): result (vec α) :=
+  if i.val < List.length v.val then
+    .ret ⟨ List.set v.val i.val x, by
+      have h: List.length v.val < USize.size := v.property
+      rewrite [ List.length_set v.val i.val x ]
+      assumption
+    ⟩
+  else
+    .fail arrayOutOfBounds
+
+def vec_index_fwd (α : Type u) (v: vec α) (i: USize): result α :=
+  if h: i.val < List.length v.val then
+    .ret (List.get v.val ⟨i.val, h⟩)
+  else
+    .fail arrayOutOfBounds
+
+def vec_index_back (α : Type u) (v: vec α) (i: USize) (_: α): result Unit :=
+  if i.val < List.length v.val then
+    .ret ()
+  else
+    .fail arrayOutOfBounds
+
+def vec_index_mut_fwd (α : Type u) (v: vec α) (i: USize): result α :=
+  if h: i.val < List.length v.val then
+    .ret (List.get v.val ⟨i.val, h⟩)
+  else
+    .fail arrayOutOfBounds
+
+def vec_index_mut_back (α : Type u) (v: vec α) (i: USize) (x: α): result (vec α) :=
+  if i.val < List.length v.val then
+    .ret ⟨ List.set v.val i.val x, by
+      have h: List.length v.val < USize.size := v.property
+      rewrite [ List.length_set v.val i.val x ]
+      assumption
+    ⟩
+  else
+    .fail arrayOutOfBounds
+
+----------
+-- MISC --
+----------
+
+def mem_replace_fwd (a : Type) (x : a) (_ : a) : a :=
+  x
+
+def mem_replace_back (a : Type) (_ : a) (y : a) : a :=
+  y
+
+--------------------
+-- ASSERT COMMAND --
+--------------------
+
+open Lean Elab Command Term Meta
+
+syntax (name := assert) "#assert" term: command
+
+@[command_elab assert]
+def assertImpl : CommandElab := fun (_stx: Syntax) => do
+  logInfo "Reducing and asserting: "
+  logInfo _stx[1]
+  runTermElabM (fun _ => do
+    let e ← Term.elabTerm _stx[1] none
+    logInfo (Expr.dbgToString e)
+    -- How to evaluate the term and compare the result to true?
+    pure ())
+  -- logInfo (Expr.dbgToString (``true))
+  -- throwError "TODO: assert"
+
+#eval 2 == 2
+#assert (2 == 2)
diff --git a/tests/lean/misc/no_nested_borrows/NoNestedBorrows.lean b/tests/lean/misc/no_nested_borrows/NoNestedBorrows.lean
new file mode 100644
index 00000000..d871392b
--- /dev/null
+++ b/tests/lean/misc/no_nested_borrows/NoNestedBorrows.lean
@@ -0,0 +1,540 @@
+-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
+-- [no_nested_borrows]
+import Base.Primitives
+
+structure OpaqueDefs where
+  
+  /- [no_nested_borrows::Pair] -/
+  structure pair_t (T1 T2 : Type) where  pair_x : T1 pair_y : T2 
+  
+  /- [no_nested_borrows::List] -/
+  inductive list_t (T : Type) :=
+  | ListCons : T -> list_t T -> list_t T
+  | ListNil : list_t T
+  
+  /- [no_nested_borrows::One] -/
+  inductive one_t (T1 : Type) := | OneOne : T1 -> one_t T1
+  
+  /- [no_nested_borrows::EmptyEnum] -/
+  inductive empty_enum_t := | EmptyEnumEmpty : empty_enum_t
+  
+  /- [no_nested_borrows::Enum] -/
+  inductive enum_t := | EnumVariant1 : enum_t | EnumVariant2 : enum_t
+  
+  /- [no_nested_borrows::EmptyStruct] -/
+  structure empty_struct_t where   
+  
+  /- [no_nested_borrows::Sum] -/
+  inductive sum_t (T1 T2 : Type) :=
+  | SumLeft : T1 -> sum_t T1 T2
+  | SumRight : T2 -> sum_t T1 T2
+  
+  /- [no_nested_borrows::neg_test] -/
+  def neg_test_fwd (x : Int32) : result Int32 := Int32.checked_neg x
+  
+  /- [no_nested_borrows::add_test] -/
+  def add_test_fwd (x : UInt32) (y : UInt32) : result UInt32 :=
+    UInt32.checked_add x y
+  
+  /- [no_nested_borrows::subs_test] -/
+  def subs_test_fwd (x : UInt32) (y : UInt32) : result UInt32 :=
+    UInt32.checked_sub x y
+  
+  /- [no_nested_borrows::div_test] -/
+  def div_test_fwd (x : UInt32) (y : UInt32) : result UInt32 :=
+    UInt32.checked_div x y
+  
+  /- [no_nested_borrows::div_test1] -/
+  def div_test1_fwd (x : UInt32) : result UInt32 :=
+    UInt32.checked_div x (UInt32.ofNatCore 2 (by intlit))
+  
+  /- [no_nested_borrows::rem_test] -/
+  def rem_test_fwd (x : UInt32) (y : UInt32) : result UInt32 :=
+    UInt32.checked_rem x y
+  
+  /- [no_nested_borrows::cast_test] -/
+  def cast_test_fwd (x : UInt32) : result Int32 := scalar_cast Int32 x
+  
+  /- [no_nested_borrows::test2] -/
+  def test2_fwd : result Unit :=
+    do
+      let _ <- UInt32.checked_add (UInt32.ofNatCore 23 (by intlit))
+        (UInt32.ofNatCore 44 (by intlit))
+      result.ret ()
+  
+  /- Unit test for [no_nested_borrows::test2] -/
+  #assert (test2_fwd = .ret ())
+  
+  /- [no_nested_borrows::get_max] -/
+  def get_max_fwd (x : UInt32) (y : UInt32) : result UInt32 :=
+    if x >= y then result.ret x else result.ret y
+  
+  /- [no_nested_borrows::test3] -/
+  def test3_fwd : result Unit :=
+    do
+      let x <-
+        get_max_fwd (UInt32.ofNatCore 4 (by intlit))
+          (UInt32.ofNatCore 3 (by intlit))
+      let y <-
+        get_max_fwd (UInt32.ofNatCore 10 (by intlit))
+          (UInt32.ofNatCore 11 (by intlit))
+      let z <- UInt32.checked_add x y
+      if not (z = (UInt32.ofNatCore 15 (by intlit)))
+      then result.fail error.panic
+      else result.ret ()
+  
+  /- Unit test for [no_nested_borrows::test3] -/
+  #assert (test3_fwd = .ret ())
+  
+  /- [no_nested_borrows::test_neg1] -/
+  def test_neg1_fwd : result Unit :=
+    do
+      let y <- Int32.checked_neg (Int32.ofNatCore 3 (by intlit))
+      if not (y = (Int32.ofNatCore -3 (by intlit)))
+      then result.fail error.panic
+      else result.ret ()
+  
+  /- Unit test for [no_nested_borrows::test_neg1] -/
+  #assert (test_neg1_fwd = .ret ())
+  
+  /- [no_nested_borrows::refs_test1] -/
+  def refs_test1_fwd : result Unit :=
+    if not ((Int32.ofNatCore 1 (by intlit)) = (Int32.ofNatCore 1 (by intlit)))
+    then result.fail error.panic
+    else result.ret ()
+  
+  /- Unit test for [no_nested_borrows::refs_test1] -/
+  #assert (refs_test1_fwd = .ret ())
+  
+  /- [no_nested_borrows::refs_test2] -/
+  def refs_test2_fwd : result Unit :=
+    if not ((Int32.ofNatCore 2 (by intlit)) = (Int32.ofNatCore 2 (by intlit)))
+    then result.fail error.panic
+    else
+      if not ((Int32.ofNatCore 0 (by intlit)) =
+        (Int32.ofNatCore 0 (by intlit)))
+      then result.fail error.panic
+      else
+        if not ((Int32.ofNatCore 2 (by intlit)) =
+          (Int32.ofNatCore 2 (by intlit)))
+        then result.fail error.panic
+        else
+          if not ((Int32.ofNatCore 2 (by intlit)) =
+            (Int32.ofNatCore 2 (by intlit)))
+          then result.fail error.panic
+          else result.ret ()
+  
+  /- Unit test for [no_nested_borrows::refs_test2] -/
+  #assert (refs_test2_fwd = .ret ())
+  
+  /- [no_nested_borrows::test_list1] -/
+  def test_list1_fwd : result Unit := result.ret ()
+  
+  /- Unit test for [no_nested_borrows::test_list1] -/
+  #assert (test_list1_fwd = .ret ())
+  
+  /- [no_nested_borrows::test_box1] -/
+  def test_box1_fwd : result Unit :=
+    let b := (Int32.ofNatCore 1 (by intlit))
+    let x := b
+    if not (x = (Int32.ofNatCore 1 (by intlit)))
+    then result.fail error.panic
+    else result.ret ()
+  
+  /- Unit test for [no_nested_borrows::test_box1] -/
+  #assert (test_box1_fwd = .ret ())
+  
+  /- [no_nested_borrows::copy_int] -/
+  def copy_int_fwd (x : Int32) : result Int32 := result.ret x
+  
+  /- [no_nested_borrows::test_unreachable] -/
+  def test_unreachable_fwd (b : Bool) : result Unit :=
+    if b then result.fail error.panic else result.ret ()
+  
+  /- [no_nested_borrows::test_panic] -/
+  def test_panic_fwd (b : Bool) : result Unit :=
+    if b then result.fail error.panic else result.ret ()
+  
+  /- [no_nested_borrows::test_copy_int] -/
+  def test_copy_int_fwd : result Unit :=
+    do
+      let y <- copy_int_fwd (Int32.ofNatCore 0 (by intlit))
+      if not ((Int32.ofNatCore 0 (by intlit)) = y)
+      then result.fail error.panic
+      else result.ret ()
+  
+  /- Unit test for [no_nested_borrows::test_copy_int] -/
+  #assert (test_copy_int_fwd = .ret ())
+  
+  /- [no_nested_borrows::is_cons] -/
+  def is_cons_fwd (T : Type) (l : list_t T) : result Bool :=
+    match l with
+    | list_t.ListCons t l0 => result.ret true
+    | list_t.ListNil => result.ret false
+    
+  
+  /- [no_nested_borrows::test_is_cons] -/
+  def test_is_cons_fwd : result Unit :=
+    do
+      let l := list_t.ListNil
+      let b <-
+        is_cons_fwd Int32 (list_t.ListCons (Int32.ofNatCore 0 (by intlit)) l)
+      if not b then result.fail error.panic else result.ret ()
+  
+  /- Unit test for [no_nested_borrows::test_is_cons] -/
+  #assert (test_is_cons_fwd = .ret ())
+  
+  /- [no_nested_borrows::split_list] -/
+  def split_list_fwd (T : Type) (l : list_t T) : result (T × (list_t T)) :=
+    match l with
+    | list_t.ListCons hd tl => result.ret (hd, tl)
+    | list_t.ListNil => result.fail error.panic
+    
+  
+  /- [no_nested_borrows::test_split_list] -/
+  def test_split_list_fwd : result Unit :=
+    do
+      let l := list_t.ListNil
+      let p <-
+        split_list_fwd Int32 (list_t.ListCons (Int32.ofNatCore 0 (by intlit))
+          l)
+      let (hd, _) := p
+      if not (hd = (Int32.ofNatCore 0 (by intlit)))
+      then result.fail error.panic
+      else result.ret ()
+  
+  /- Unit test for [no_nested_borrows::test_split_list] -/
+  #assert (test_split_list_fwd = .ret ())
+  
+  /- [no_nested_borrows::choose] -/
+  def choose_fwd (T : Type) (b : Bool) (x : T) (y : T) : result T :=
+    if b then result.ret x else result.ret y
+  
+  /- [no_nested_borrows::choose] -/
+  def choose_back
+    (T : Type) (b : Bool) (x : T) (y : T) (ret0 : T) : result (T × T) :=
+    if b then result.ret (ret0, y) else result.ret (x, ret0)
+  
+  /- [no_nested_borrows::choose_test] -/
+  def choose_test_fwd : result Unit :=
+    do
+      let z <-
+        choose_fwd Int32 true (Int32.ofNatCore 0 (by intlit))
+          (Int32.ofNatCore 0 (by intlit))
+      let z0 <- Int32.checked_add z (Int32.ofNatCore 1 (by intlit))
+      if not (z0 = (Int32.ofNatCore 1 (by intlit)))
+      then result.fail error.panic
+      else
+        do
+          let (x, y) <-
+            choose_back Int32 true (Int32.ofNatCore 0 (by intlit))
+              (Int32.ofNatCore 0 (by intlit)) z0
+          if not (x = (Int32.ofNatCore 1 (by intlit)))
+          then result.fail error.panic
+          else
+            if not (y = (Int32.ofNatCore 0 (by intlit)))
+            then result.fail error.panic
+            else result.ret ()
+  
+  /- Unit test for [no_nested_borrows::choose_test] -/
+  #assert (choose_test_fwd = .ret ())
+  
+  /- [no_nested_borrows::test_char] -/
+  def test_char_fwd : result Char := result.ret 'a'
+  
+  /- [no_nested_borrows::NodeElem] -/
+  mutual inductive node_elem_t (T : Type) :=
+  | NodeElemCons : tree_t T -> node_elem_t T -> node_elem_t T
+  | NodeElemNil : node_elem_t T
+  
+  /- [no_nested_borrows::Tree] -/
+  inductive tree_t (T : Type) :=
+  | TreeLeaf : T -> tree_t T
+  | TreeNode : T -> node_elem_t T -> tree_t T -> tree_t T
+  
+  /- [no_nested_borrows::list_length] -/
+  def list_length_fwd (T : Type) (l : list_t T) : result UInt32 :=
+    match l with
+    | list_t.ListCons t l1 =>
+      do
+        let i <- list_length_fwd T l1
+        UInt32.checked_add (UInt32.ofNatCore 1 (by intlit)) i
+    | list_t.ListNil => result.ret (UInt32.ofNatCore 0 (by intlit))
+    
+  
+  /- [no_nested_borrows::list_nth_shared] -/
+  def list_nth_shared_fwd (T : Type) (l : list_t T) (i : UInt32) : result T :=
+    match l with
+    | list_t.ListCons x tl =>
+      if i = (UInt32.ofNatCore 0 (by intlit))
+      then result.ret x
+      else
+        do
+          let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+          list_nth_shared_fwd T tl i0
+    | list_t.ListNil => result.fail error.panic
+    
+  
+  /- [no_nested_borrows::list_nth_mut] -/
+  def list_nth_mut_fwd (T : Type) (l : list_t T) (i : UInt32) : result T :=
+    match l with
+    | list_t.ListCons x tl =>
+      if i = (UInt32.ofNatCore 0 (by intlit))
+      then result.ret x
+      else
+        do
+          let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+          list_nth_mut_fwd T tl i0
+    | list_t.ListNil => result.fail error.panic
+    
+  
+  /- [no_nested_borrows::list_nth_mut] -/
+  def list_nth_mut_back
+    (T : Type) (l : list_t T) (i : UInt32) (ret0 : T) : result (list_t T) :=
+    match l with
+    | list_t.ListCons x tl =>
+      if i = (UInt32.ofNatCore 0 (by intlit))
+      then result.ret (list_t.ListCons ret0 tl)
+      else
+        do
+          let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+          let tl0 <- list_nth_mut_back T tl i0 ret0
+          result.ret (list_t.ListCons x tl0)
+    | list_t.ListNil => result.fail error.panic
+    
+  
+  /- [no_nested_borrows::list_rev_aux] -/
+  def list_rev_aux_fwd
+    (T : Type) (li : list_t T) (lo : list_t T) : result (list_t T) :=
+    match li with
+    | list_t.ListCons hd tl => list_rev_aux_fwd T tl (list_t.ListCons hd lo)
+    | list_t.ListNil => result.ret lo
+    
+  
+  /- [no_nested_borrows::list_rev] -/
+  def list_rev_fwd_back (T : Type) (l : list_t T) : result (list_t T) :=
+    let li := mem_replace_fwd (list_t T) l list_t.ListNil
+    list_rev_aux_fwd T li list_t.ListNil
+  
+  /- [no_nested_borrows::test_list_functions] -/
+  def test_list_functions_fwd : result Unit :=
+    do
+      let l := list_t.ListNil
+      let l0 := list_t.ListCons (Int32.ofNatCore 2 (by intlit)) l
+      let l1 := list_t.ListCons (Int32.ofNatCore 1 (by intlit)) l0
+      let i <-
+        list_length_fwd Int32 (list_t.ListCons (Int32.ofNatCore 0 (by intlit))
+          l1)
+      if not (i = (UInt32.ofNatCore 3 (by intlit)))
+      then result.fail error.panic
+      else
+        do
+          let i0 <-
+            list_nth_shared_fwd Int32 (list_t.ListCons
+              (Int32.ofNatCore 0 (by intlit)) l1)
+              (UInt32.ofNatCore 0 (by intlit))
+          if not (i0 = (Int32.ofNatCore 0 (by intlit)))
+          then result.fail error.panic
+          else
+            do
+              let i1 <-
+                list_nth_shared_fwd Int32 (list_t.ListCons
+                  (Int32.ofNatCore 0 (by intlit)) l1)
+                  (UInt32.ofNatCore 1 (by intlit))
+              if not (i1 = (Int32.ofNatCore 1 (by intlit)))
+              then result.fail error.panic
+              else
+                do
+                  let i2 <-
+                    list_nth_shared_fwd Int32 (list_t.ListCons
+                      (Int32.ofNatCore 0 (by intlit)) l1)
+                      (UInt32.ofNatCore 2 (by intlit))
+                  if not (i2 = (Int32.ofNatCore 2 (by intlit)))
+                  then result.fail error.panic
+                  else
+                    do
+                      let ls <-
+                        list_nth_mut_back Int32 (list_t.ListCons
+                          (Int32.ofNatCore 0 (by intlit)) l1)
+                          (UInt32.ofNatCore 1 (by intlit))
+                          (Int32.ofNatCore 3 (by intlit))
+                      let i3 <-
+                        list_nth_shared_fwd Int32 ls
+                          (UInt32.ofNatCore 0 (by intlit))
+                      if not (i3 = (Int32.ofNatCore 0 (by intlit)))
+                      then result.fail error.panic
+                      else
+                        do
+                          let i4 <-
+                            list_nth_shared_fwd Int32 ls
+                              (UInt32.ofNatCore 1 (by intlit))
+                          if not (i4 = (Int32.ofNatCore 3 (by intlit)))
+                          then result.fail error.panic
+                          else
+                            do
+                              let i5 <-
+                                list_nth_shared_fwd Int32 ls
+                                  (UInt32.ofNatCore 2 (by intlit))
+                              if not (i5 = (Int32.ofNatCore 2 (by intlit)))
+                              then result.fail error.panic
+                              else result.ret ()
+  
+  /- Unit test for [no_nested_borrows::test_list_functions] -/
+  #assert (test_list_functions_fwd = .ret ())
+  
+  /- [no_nested_borrows::id_mut_pair1] -/
+  def id_mut_pair1_fwd (T1 T2 : Type) (x : T1) (y : T2) : result (T1 × T2) :=
+    result.ret (x, y)
+  
+  /- [no_nested_borrows::id_mut_pair1] -/
+  def id_mut_pair1_back
+    (T1 T2 : Type) (x : T1) (y : T2) (ret0 : (T1 × T2)) : result (T1 × T2) :=
+    let (t, t0) := ret0 result.ret (t, t0)
+  
+  /- [no_nested_borrows::id_mut_pair2] -/
+  def id_mut_pair2_fwd (T1 T2 : Type) (p : (T1 × T2)) : result (T1 × T2) :=
+    let (t, t0) := p result.ret (t, t0)
+  
+  /- [no_nested_borrows::id_mut_pair2] -/
+  def id_mut_pair2_back
+    (T1 T2 : Type) (p : (T1 × T2)) (ret0 : (T1 × T2)) : result (T1 × T2) :=
+    let (t, t0) := ret0 result.ret (t, t0)
+  
+  /- [no_nested_borrows::id_mut_pair3] -/
+  def id_mut_pair3_fwd (T1 T2 : Type) (x : T1) (y : T2) : result (T1 × T2) :=
+    result.ret (x, y)
+  
+  /- [no_nested_borrows::id_mut_pair3] -/
+  def id_mut_pair3_back'a
+    (T1 T2 : Type) (x : T1) (y : T2) (ret0 : T1) : result T1 :=
+    result.ret ret0
+  
+  /- [no_nested_borrows::id_mut_pair3] -/
+  def id_mut_pair3_back'b
+    (T1 T2 : Type) (x : T1) (y : T2) (ret0 : T2) : result T2 :=
+    result.ret ret0
+  
+  /- [no_nested_borrows::id_mut_pair4] -/
+  def id_mut_pair4_fwd (T1 T2 : Type) (p : (T1 × T2)) : result (T1 × T2) :=
+    let (t, t0) := p result.ret (t, t0)
+  
+  /- [no_nested_borrows::id_mut_pair4] -/
+  def id_mut_pair4_back'a
+    (T1 T2 : Type) (p : (T1 × T2)) (ret0 : T1) : result T1 :=
+    result.ret ret0
+  
+  /- [no_nested_borrows::id_mut_pair4] -/
+  def id_mut_pair4_back'b
+    (T1 T2 : Type) (p : (T1 × T2)) (ret0 : T2) : result T2 :=
+    result.ret ret0
+  
+  /- [no_nested_borrows::StructWithTuple] -/
+  structure struct_with_tuple_t (T1 T2 : Type) where
+  
+    struct_with_tuple_p : (T1 × T2)
+  
+  
+  /- [no_nested_borrows::new_tuple1] -/
+  def new_tuple1_fwd : result (struct_with_tuple_t UInt32 UInt32) :=
+    result.ret
+    {
+      struct_with_tuple_p := ((UInt32.ofNatCore 1 (by intlit)),
+                               (UInt32.ofNatCore 2 (by intlit)))
+    }
+  
+  /- [no_nested_borrows::new_tuple2] -/
+  def new_tuple2_fwd : result (struct_with_tuple_t Int16 Int16) :=
+    result.ret
+    {
+      struct_with_tuple_p := ((Int16.ofNatCore 1 (by intlit)),
+                               (Int16.ofNatCore 2 (by intlit)))
+    }
+  
+  /- [no_nested_borrows::new_tuple3] -/
+  def new_tuple3_fwd : result (struct_with_tuple_t UInt64 Int64) :=
+    result.ret
+    {
+      struct_with_tuple_p := ((UInt64.ofNatCore 1 (by intlit)),
+                               (Int64.ofNatCore 2 (by intlit)))
+    }
+  
+  /- [no_nested_borrows::StructWithPair] -/
+  structure struct_with_pair_t (T1 T2 : Type) where
+  
+    struct_with_pair_p : pair_t T1 T2
+  
+  
+  /- [no_nested_borrows::new_pair1] -/
+  def new_pair1_fwd : result (struct_with_pair_t UInt32 UInt32) :=
+    result.ret
+    {
+      struct_with_pair_p := {
+                              pair_x := (UInt32.ofNatCore 1 (by intlit)),
+                              pair_y := (UInt32.ofNatCore 2 (by intlit))
+                            }
+    }
+  
+  /- [no_nested_borrows::test_constants] -/
+  def test_constants_fwd : result Unit :=
+    do
+      let swt <- new_tuple1_fwd
+      let (i, _) := swt.struct_with_tuple_p
+      if not (i = (UInt32.ofNatCore 1 (by intlit)))
+      then result.fail error.panic
+      else
+        do
+          let swt0 <- new_tuple2_fwd
+          let (i0, _) := swt0.struct_with_tuple_p
+          if not (i0 = (Int16.ofNatCore 1 (by intlit)))
+          then result.fail error.panic
+          else
+            do
+              let swt1 <- new_tuple3_fwd
+              let (i1, _) := swt1.struct_with_tuple_p
+              if not (i1 = (UInt64.ofNatCore 1 (by intlit)))
+              then result.fail error.panic
+              else
+                do
+                  let swp <- new_pair1_fwd
+                  if not (swp.struct_with_pair_p.pair_x =
+                    (UInt32.ofNatCore 1 (by intlit)))
+                  then result.fail error.panic
+                  else result.ret ()
+  
+  /- Unit test for [no_nested_borrows::test_constants] -/
+  #assert (test_constants_fwd = .ret ())
+  
+  /- [no_nested_borrows::test_weird_borrows1] -/
+  def test_weird_borrows1_fwd : result Unit := result.ret ()
+  
+  /- Unit test for [no_nested_borrows::test_weird_borrows1] -/
+  #assert (test_weird_borrows1_fwd = .ret ())
+  
+  /- [no_nested_borrows::test_mem_replace] -/
+  def test_mem_replace_fwd_back (px : UInt32) : result UInt32 :=
+    let y := mem_replace_fwd UInt32 px (UInt32.ofNatCore 1 (by intlit))
+    if not (y = (UInt32.ofNatCore 0 (by intlit)))
+    then result.fail error.panic
+    else result.ret (UInt32.ofNatCore 2 (by intlit))
+  
+  /- [no_nested_borrows::test_shared_borrow_bool1] -/
+  def test_shared_borrow_bool1_fwd (b : Bool) : result UInt32 :=
+    if b
+    then result.ret (UInt32.ofNatCore 0 (by intlit))
+    else result.ret (UInt32.ofNatCore 1 (by intlit))
+  
+  /- [no_nested_borrows::test_shared_borrow_bool2] -/
+  def test_shared_borrow_bool2_fwd : result UInt32 :=
+    result.ret (UInt32.ofNatCore 0 (by intlit))
+  
+  /- [no_nested_borrows::test_shared_borrow_enum1] -/
+  def test_shared_borrow_enum1_fwd (l : list_t UInt32) : result UInt32 :=
+    match l with
+    | list_t.ListCons i l0 => result.ret (UInt32.ofNatCore 1 (by intlit))
+    | list_t.ListNil => result.ret (UInt32.ofNatCore 0 (by intlit))
+    
+  
+  /- [no_nested_borrows::test_shared_borrow_enum2] -/
+  def test_shared_borrow_enum2_fwd : result UInt32 :=
+    result.ret (UInt32.ofNatCore 0 (by intlit))
+  
diff --git a/tests/lean/misc/paper/Base/Primitives.lean b/tests/lean/misc/paper/Base/Primitives.lean
new file mode 100644
index 00000000..79958d94
--- /dev/null
+++ b/tests/lean/misc/paper/Base/Primitives.lean
@@ -0,0 +1,373 @@
+import Lean
+import Lean.Meta.Tactic.Simp
+import Init.Data.List.Basic
+import Mathlib.Tactic.RunCmd
+
+-------------
+-- PRELUDE --
+-------------
+
+-- Results & monadic combinators
+
+-- TODO: use syntactic conventions and capitalize error, result, etc.
+
+inductive error where
+   | assertionFailure: error
+   | integerOverflow: error
+   | arrayOutOfBounds: error
+   | maximumSizeExceeded: error
+   | panic: error
+deriving Repr, BEq
+
+open error
+
+inductive result (α : Type u) where
+  | ret (v: α): result α
+  | fail (e: error): result α 
+deriving Repr, BEq
+
+open result
+
+/- HELPERS -/
+
+-- TODO: is there automated syntax for these discriminators?
+def is_ret {α: Type} (r: result α): Bool :=
+  match r with
+  | result.ret _ => true
+  | result.fail _ => false
+
+def massert (b:Bool) : result Unit :=
+  if b then .ret () else fail assertionFailure
+
+def eval_global {α: Type} (x: result α) (_: is_ret x): α :=
+  match x with
+  | result.fail _ => by contradiction
+  | result.ret x => x
+
+/- DO-DSL SUPPORT -/
+
+def bind (x: result α) (f: α -> result β) : result β :=
+  match x with
+  | ret v  => f v 
+  | fail v => fail v
+
+-- Allows using result in do-blocks
+instance : Bind result where
+  bind := bind
+
+-- Allows using return x in do-blocks
+instance : Pure result where
+  pure := fun x => ret x
+
+/- CUSTOM-DSL SUPPORT -/
+
+-- Let-binding the result of a monadic operation is oftentimes not sufficient,
+-- because we may need a hypothesis for equational reasoning in the scope. We
+-- rely on subtype, and a custom let-binding operator, in effect recreating our
+-- own variant of the do-dsl
+
+def result.attach : (o : result α) → result { x : α // o = ret x }
+  | .ret x => .ret ⟨x, rfl⟩
+  | .fail e   => .fail e
+
+macro "let" h:ident " : " e:term " <-- " f:term : doElem =>
+  `(doElem| let ⟨$e, $h⟩ ← result.attach $f)
+
+-- Silly example of the kind of reasoning that this notation enables
+#eval do
+  let h: y <-- .ret (0: Nat)
+  let _: y = 0 := by cases h; decide
+  let r: { x: Nat // x = 0 } := ⟨ y, by assumption ⟩
+  .ret r
+
+----------------------
+-- MACHINE INTEGERS --
+----------------------
+
+-- NOTE: we reuse the USize type from prelude.lean, because at least we know
+-- it's defined in an idiomatic style that is going to make proofs easy (and
+-- indeed, several proofs here are much shortened compared to Aymeric's earlier
+-- attempt.) This is not stricto sensu the *correct* thing to do, because one
+-- can query at run-time the value of USize, which we do *not* want to do (we
+-- don't know what target we'll run on!), but when the day comes, we'll just
+-- define our own USize.
+-- ANOTHER NOTE: there is USize.sub but it has wraparound semantics, which is
+-- not something we want to define (I think), so we use our own monadic sub (but
+-- is it in line with the Rust behavior?)
+
+-- TODO: I am somewhat under the impression that subtraction is defined as a
+-- total function over nats...? the hypothesis in the if condition is not used
+-- in the then-branch which confuses me quite a bit
+
+-- TODO: add a refinement for the result (just like vec_push_back below) that
+-- explains that the toNat of the result (in the case of success) is the sub of
+-- the toNat of the arguments (i.e. intrinsic specification)
+-- ... do we want intrinsic specifications for the builtins? that might require
+-- some careful type annotations in the monadic notation for clients, but may
+-- give us more "for free"
+
+-- Note from Chris Bailey: "If there's more than one salient property of your
+-- definition then the subtyping strategy might get messy, and the property part
+-- of a subtype is less discoverable by the simplifier or tactics like
+-- library_search." Try to settle this with a Lean expert on what is the most
+-- productive way to go about this?
+
+-- One needs to perform a little bit of reasoning in order to successfully
+-- inject constants into USize, so we provide a general-purpose macro
+
+syntax "intlit" : tactic
+
+macro_rules
+  | `(tactic| intlit) => `(tactic|
+    match USize.size, usize_size_eq with
+    | _, Or.inl rfl => decide
+    | _, Or.inr rfl => decide)
+
+-- This is how the macro is expected to be used
+#eval USize.ofNatCore 0 (by intlit)
+
+-- Also works for other integer types (at the expense of a needless disjunction)
+#eval UInt32.ofNatCore 0 (by intlit)
+
+-- Further thoughts: look at what has been done here:
+-- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/Fin/Basic.lean
+-- and
+-- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/UInt.lean
+-- which both contain a fair amount of reasoning already!
+def USize.checked_sub (n: USize) (m: USize): result USize :=
+  -- NOTE: the test USize.toNat n - m >= 0 seems to always succeed?
+  if n >= m then
+    let n' := USize.toNat n
+    let m' := USize.toNat n
+    let r := USize.ofNatCore (n' - m') (by
+      have h: n' - m' <= n' := by
+        apply Nat.sub_le_of_le_add
+        case h => rewrite [ Nat.add_comm ]; apply Nat.le_add_left
+      apply Nat.lt_of_le_of_lt h
+      apply n.val.isLt
+    )
+    return r
+  else
+    fail integerOverflow
+
+def USize.checked_add (n: USize) (m: USize): result USize :=
+  if h: n.val.val + m.val.val <= 4294967295 then
+    .ret ⟨ n.val.val + m.val.val, by
+      have h': 4294967295 < USize.size := by intlit
+      apply Nat.lt_of_le_of_lt h h'
+    ⟩
+  else if h: n.val + m.val < USize.size then
+    .ret ⟨ n.val + m.val, h ⟩
+  else
+    .fail integerOverflow
+
+def USize.checked_rem (n: USize) (m: USize): result USize :=
+  if h: m > 0 then
+    .ret ⟨ n.val % m.val, by
+      have h1: ↑m.val < USize.size := m.val.isLt
+      have h2: n.val.val % m.val.val < m.val.val := @Nat.mod_lt n.val m.val h
+      apply Nat.lt_trans h2 h1
+    ⟩
+  else
+    .fail integerOverflow
+
+def USize.checked_mul (n: USize) (m: USize): result USize :=
+    if h: n.val.val * m.val.val <= 4294967295 then
+    .ret ⟨ n.val.val * m.val.val, by
+      have h': 4294967295 < USize.size := by intlit
+      apply Nat.lt_of_le_of_lt h h'
+    ⟩
+  else if h: n.val * m.val < USize.size then
+    .ret ⟨ n.val * m.val, h ⟩
+  else
+    .fail integerOverflow
+
+def USize.checked_div (n: USize) (m: USize): result USize :=
+  if m > 0 then
+    .ret ⟨ n.val / m.val, by
+      have h1: ↑n.val < USize.size := n.val.isLt
+      have h2: n.val.val / m.val.val <= n.val.val := @Nat.div_le_self n.val m.val
+      apply Nat.lt_of_le_of_lt h2 h1
+    ⟩
+  else
+    .fail integerOverflow
+
+class MachineInteger (t: Type) where
+  size: Nat
+  val: t -> Fin size
+  ofNatCore: (n:Nat) -> LT.lt n size -> t
+
+set_option hygiene false in
+run_cmd
+  for typeName in [`UInt8, `UInt16, `UInt32, `UInt64, `USize].map Lean.mkIdent do
+  Lean.Elab.Command.elabCommand (← `(
+    namespace $typeName
+    instance: MachineInteger $typeName where
+      size := size
+      val := val
+      ofNatCore := ofNatCore
+    end $typeName
+  ))
+
+def scalar_cast { src: Type } (dst: Type) [ MachineInteger src ] [ MachineInteger dst ] (x: src): result dst :=
+  if h: MachineInteger.val x < MachineInteger.size dst then
+    .ret (MachineInteger.ofNatCore (MachineInteger.val x).val h)
+  else
+    .fail integerOverflow
+
+
+-- Test behavior...
+#eval assert! USize.checked_sub 10 20 == fail integerOverflow; 0
+
+#eval USize.checked_sub 20 10
+-- NOTE: compare with concrete behavior here, which I do not think we want
+#eval USize.sub 0 1
+#eval UInt8.add 255 255
+
+-------------
+-- VECTORS --
+-------------
+
+-- Note: unlike F*, Lean seems to use strict upper bounds (e.g. USize.size)
+-- rather than maximum values (usize_max).
+def vec (α : Type u) := { l : List α // List.length l < USize.size }
+
+def vec_new (α : Type u): vec α := ⟨ [], by {
+  match USize.size, usize_size_eq with
+  | _, Or.inl rfl => simp
+  | _, Or.inr rfl => simp
+  } ⟩
+
+#check vec_new
+
+def vec_len (α : Type u) (v : vec α) : USize :=
+  let ⟨ v, l ⟩ := v
+  USize.ofNatCore (List.length v) l
+
+#eval vec_len Nat (vec_new Nat)
+ 
+def vec_push_fwd (α : Type u) (_ : vec α) (_ : α) : Unit := ()
+
+-- NOTE: old version trying to use a subtype notation, but probably better to
+-- leave result elimination to auxiliary lemmas with suitable preconditions
+-- TODO: I originally wrote `List.length v.val < USize.size - 1`; how can one
+-- make the proof work in that case? Probably need to import tactics from
+-- mathlib to deal with inequalities... would love to see an example.
+def vec_push_back_old (α : Type u) (v : vec α) (x : α) : { res: result (vec α) //
+  match res with | fail _ => True | ret v' => List.length v'.val = List.length v.val + 1}
+  :=
+  if h : List.length v.val + 1 < USize.size then
+    ⟨ return ⟨List.concat v.val x,
+      by
+        rw [List.length_concat]
+        assumption
+     ⟩, by simp ⟩
+  else
+    ⟨ fail maximumSizeExceeded, by simp ⟩
+
+#eval do
+  -- NOTE: the // notation is syntactic sugar for Subtype, a refinement with
+  -- fields val and property. However, Lean's elaborator can automatically
+  -- select the `val` field if the context provides a type annotation. We
+  -- annotate `x`, which relieves us of having to write `.val` on the right-hand
+  -- side of the monadic let.
+  let v := vec_new Nat
+  let x: vec Nat ← (vec_push_back_old Nat v 1: result (vec Nat)) -- WHY do we need the type annotation here?
+  -- TODO: strengthen post-condition above and do a demo to show that we can
+  -- safely eliminate the `fail` case
+  return (vec_len Nat x)
+
+def vec_push_back (α : Type u) (v : vec α) (x : α) : result (vec α)
+  :=
+  if h : List.length v.val + 1 <= 4294967295 then
+    return ⟨ List.concat v.val x,
+      by
+        rw [List.length_concat]
+        have h': 4294967295 < USize.size := by intlit
+        apply Nat.lt_of_le_of_lt h h'
+    ⟩
+  else if h: List.length v.val + 1 < USize.size then
+    return ⟨List.concat v.val x,
+      by
+        rw [List.length_concat]
+        assumption
+     ⟩
+  else
+    fail maximumSizeExceeded
+
+def vec_insert_fwd (α : Type u) (v: vec α) (i: USize) (_: α): result Unit :=
+  if i.val < List.length v.val then
+    .ret ()
+  else
+    .fail arrayOutOfBounds
+
+def vec_insert_back (α : Type u) (v: vec α) (i: USize) (x: α): result (vec α) :=
+  if i.val < List.length v.val then
+    .ret ⟨ List.set v.val i.val x, by
+      have h: List.length v.val < USize.size := v.property
+      rewrite [ List.length_set v.val i.val x ]
+      assumption
+    ⟩
+  else
+    .fail arrayOutOfBounds
+
+def vec_index_fwd (α : Type u) (v: vec α) (i: USize): result α :=
+  if h: i.val < List.length v.val then
+    .ret (List.get v.val ⟨i.val, h⟩)
+  else
+    .fail arrayOutOfBounds
+
+def vec_index_back (α : Type u) (v: vec α) (i: USize) (_: α): result Unit :=
+  if i.val < List.length v.val then
+    .ret ()
+  else
+    .fail arrayOutOfBounds
+
+def vec_index_mut_fwd (α : Type u) (v: vec α) (i: USize): result α :=
+  if h: i.val < List.length v.val then
+    .ret (List.get v.val ⟨i.val, h⟩)
+  else
+    .fail arrayOutOfBounds
+
+def vec_index_mut_back (α : Type u) (v: vec α) (i: USize) (x: α): result (vec α) :=
+  if i.val < List.length v.val then
+    .ret ⟨ List.set v.val i.val x, by
+      have h: List.length v.val < USize.size := v.property
+      rewrite [ List.length_set v.val i.val x ]
+      assumption
+    ⟩
+  else
+    .fail arrayOutOfBounds
+
+----------
+-- MISC --
+----------
+
+def mem_replace_fwd (a : Type) (x : a) (_ : a) : a :=
+  x
+
+def mem_replace_back (a : Type) (_ : a) (y : a) : a :=
+  y
+
+--------------------
+-- ASSERT COMMAND --
+--------------------
+
+open Lean Elab Command Term Meta
+
+syntax (name := assert) "#assert" term: command
+
+@[command_elab assert]
+def assertImpl : CommandElab := fun (_stx: Syntax) => do
+  logInfo "Reducing and asserting: "
+  logInfo _stx[1]
+  runTermElabM (fun _ => do
+    let e ← Term.elabTerm _stx[1] none
+    logInfo (Expr.dbgToString e)
+    -- How to evaluate the term and compare the result to true?
+    pure ())
+  -- logInfo (Expr.dbgToString (``true))
+  -- throwError "TODO: assert"
+
+#eval 2 == 2
+#assert (2 == 2)
diff --git a/tests/lean/misc/paper/Paper.lean b/tests/lean/misc/paper/Paper.lean
new file mode 100644
index 00000000..2d23f394
--- /dev/null
+++ b/tests/lean/misc/paper/Paper.lean
@@ -0,0 +1,127 @@
+-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
+-- [paper]
+import Base.Primitives
+
+structure OpaqueDefs where
+  
+  /- [paper::ref_incr] -/
+  def ref_incr_fwd_back (x : Int32) : result Int32 :=
+    Int32.checked_add x (Int32.ofNatCore 1 (by intlit))
+  
+  /- [paper::test_incr] -/
+  def test_incr_fwd : result Unit :=
+    do
+      let x <- ref_incr_fwd_back (Int32.ofNatCore 0 (by intlit))
+      if not (x = (Int32.ofNatCore 1 (by intlit)))
+      then result.fail error.panic
+      else result.ret ()
+  
+  /- Unit test for [paper::test_incr] -/
+  #assert (test_incr_fwd = .ret ())
+  
+  /- [paper::choose] -/
+  def choose_fwd (T : Type) (b : Bool) (x : T) (y : T) : result T :=
+    if b then result.ret x else result.ret y
+  
+  /- [paper::choose] -/
+  def choose_back
+    (T : Type) (b : Bool) (x : T) (y : T) (ret0 : T) : result (T × T) :=
+    if b then result.ret (ret0, y) else result.ret (x, ret0)
+  
+  /- [paper::test_choose] -/
+  def test_choose_fwd : result Unit :=
+    do
+      let z <-
+        choose_fwd Int32 true (Int32.ofNatCore 0 (by intlit))
+          (Int32.ofNatCore 0 (by intlit))
+      let z0 <- Int32.checked_add z (Int32.ofNatCore 1 (by intlit))
+      if not (z0 = (Int32.ofNatCore 1 (by intlit)))
+      then result.fail error.panic
+      else
+        do
+          let (x, y) <-
+            choose_back Int32 true (Int32.ofNatCore 0 (by intlit))
+              (Int32.ofNatCore 0 (by intlit)) z0
+          if not (x = (Int32.ofNatCore 1 (by intlit)))
+          then result.fail error.panic
+          else
+            if not (y = (Int32.ofNatCore 0 (by intlit)))
+            then result.fail error.panic
+            else result.ret ()
+  
+  /- Unit test for [paper::test_choose] -/
+  #assert (test_choose_fwd = .ret ())
+  
+  /- [paper::List] -/
+  inductive list_t (T : Type) :=
+  | ListCons : T -> list_t T -> list_t T
+  | ListNil : list_t T
+  
+  /- [paper::list_nth_mut] -/
+  def list_nth_mut_fwd (T : Type) (l : list_t T) (i : UInt32) : result T :=
+    match l with
+    | list_t.ListCons x tl =>
+      if i = (UInt32.ofNatCore 0 (by intlit))
+      then result.ret x
+      else
+        do
+          let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+          list_nth_mut_fwd T tl i0
+    | list_t.ListNil => result.fail error.panic
+    
+  
+  /- [paper::list_nth_mut] -/
+  def list_nth_mut_back
+    (T : Type) (l : list_t T) (i : UInt32) (ret0 : T) : result (list_t T) :=
+    match l with
+    | list_t.ListCons x tl =>
+      if i = (UInt32.ofNatCore 0 (by intlit))
+      then result.ret (list_t.ListCons ret0 tl)
+      else
+        do
+          let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+          let tl0 <- list_nth_mut_back T tl i0 ret0
+          result.ret (list_t.ListCons x tl0)
+    | list_t.ListNil => result.fail error.panic
+    
+  
+  /- [paper::sum] -/
+  def sum_fwd (l : list_t Int32) : result Int32 :=
+    match l with
+    | list_t.ListCons x tl => do
+                                let i <- sum_fwd tl
+                                Int32.checked_add x i
+    | list_t.ListNil => result.ret (Int32.ofNatCore 0 (by intlit))
+    
+  
+  /- [paper::test_nth] -/
+  def test_nth_fwd : result Unit :=
+    do
+      let l := list_t.ListNil
+      let l0 := list_t.ListCons (Int32.ofNatCore 3 (by intlit)) l
+      let l1 := list_t.ListCons (Int32.ofNatCore 2 (by intlit)) l0
+      let x <-
+        list_nth_mut_fwd Int32 (list_t.ListCons (Int32.ofNatCore 1 (by intlit))
+          l1) (UInt32.ofNatCore 2 (by intlit))
+      let x0 <- Int32.checked_add x (Int32.ofNatCore 1 (by intlit))
+      let l2 <-
+        list_nth_mut_back Int32 (list_t.ListCons
+          (Int32.ofNatCore 1 (by intlit)) l1) (UInt32.ofNatCore 2 (by intlit))
+          x0
+      let i <- sum_fwd l2
+      if not (i = (Int32.ofNatCore 7 (by intlit)))
+      then result.fail error.panic
+      else result.ret ()
+  
+  /- Unit test for [paper::test_nth] -/
+  #assert (test_nth_fwd = .ret ())
+  
+  /- [paper::call_choose] -/
+  def call_choose_fwd (p : (UInt32 × UInt32)) : result UInt32 :=
+    do
+      let (px, py) := p
+      let pz <- choose_fwd UInt32 true px py
+      let pz0 <- UInt32.checked_add pz (UInt32.ofNatCore 1 (by intlit))
+      let (px0, _) <- choose_back UInt32 true px py pz0
+      result.ret px0
+