From 00705bba68fed61d3b0bcde2c5fe0ecc83880870 Mon Sep 17 00:00:00 2001
From: Son Ho
Date: Thu, 9 Nov 2023 18:37:07 +0100
Subject: Update the failing proofs

---
 tests/fstar/misc/Loops.fst | 784 ---------------------------------------------
 1 file changed, 784 deletions(-)
 delete mode 100644 tests/fstar/misc/Loops.fst

(limited to 'tests/fstar/misc/Loops.fst')

diff --git a/tests/fstar/misc/Loops.fst b/tests/fstar/misc/Loops.fst
deleted file mode 100644
index 823acdd4..00000000
--- a/tests/fstar/misc/Loops.fst
+++ /dev/null
@@ -1,784 +0,0 @@
-(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
-(** [loops] *)
-module Loops
-open Primitives
-
-#set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
-
-(** [loops::sum]: decreases clause *)
-unfold let sum_loop_decreases (max : u32) (i : u32) (s : u32) : nat = admit ()
-
-(** [loops::sum]: loop 0: forward function *)
-let rec sum_loop
-  (max : u32) (i : u32) (s : u32) :
-  Tot (result u32) (decreases (sum_loop_decreases max i s))
-  =
-  if i < max
-  then let* s0 = u32_add s i in let* i0 = u32_add i 1 in sum_loop max i0 s0
-  else u32_mul s 2
-
-(** [loops::sum]: forward function *)
-let sum (max : u32) : result u32 =
-  sum_loop max 0 0
-
-(** [loops::sum_with_mut_borrows]: decreases clause *)
-unfold
-let sum_with_mut_borrows_loop_decreases (max : u32) (mi : u32) (ms : u32) : nat
-  =
-  admit ()
-
-(** [loops::sum_with_mut_borrows]: loop 0: forward function *)
-let rec sum_with_mut_borrows_loop
-  (max : u32) (mi : u32) (ms : u32) :
-  Tot (result u32) (decreases (sum_with_mut_borrows_loop_decreases max mi ms))
-  =
-  if mi < max
-  then
-    let* ms0 = u32_add ms mi in
-    let* mi0 = u32_add mi 1 in
-    sum_with_mut_borrows_loop max mi0 ms0
-  else u32_mul ms 2
-
-(** [loops::sum_with_mut_borrows]: forward function *)
-let sum_with_mut_borrows (max : u32) : result u32 =
-  sum_with_mut_borrows_loop max 0 0
-
-(** [loops::sum_with_shared_borrows]: decreases clause *)
-unfold
-let sum_with_shared_borrows_loop_decreases (max : u32) (i : u32) (s : u32) :
-  nat =
-  admit ()
-
-(** [loops::sum_with_shared_borrows]: loop 0: forward function *)
-let rec sum_with_shared_borrows_loop
-  (max : u32) (i : u32) (s : u32) :
-  Tot (result u32) (decreases (sum_with_shared_borrows_loop_decreases max i s))
-  =
-  if i < max
-  then
-    let* i0 = u32_add i 1 in
-    let* s0 = u32_add s i0 in
-    sum_with_shared_borrows_loop max i0 s0
-  else u32_mul s 2
-
-(** [loops::sum_with_shared_borrows]: forward function *)
-let sum_with_shared_borrows (max : u32) : result u32 =
-  sum_with_shared_borrows_loop max 0 0
-
-(** [loops::clear]: decreases clause *)
-unfold
-let clear_loop_decreases (v : alloc_vec_Vec u32) (i : usize) : nat = admit ()
-
-(** [loops::clear]: loop 0: merged forward/backward function
-    (there is a single backward function, and the forward function returns ()) *)
-let rec clear_loop
-  (v : alloc_vec_Vec u32) (i : usize) :
-  Tot (result (alloc_vec_Vec u32)) (decreases (clear_loop_decreases v i))
-  =
-  let i0 = alloc_vec_Vec_len u32 v in
-  if i < i0
-  then
-    let* i1 = usize_add i 1 in
-    let* v0 =
-      alloc_vec_Vec_index_mut_back u32 usize
-        (core_slice_index_usize_coresliceindexSliceIndexInst u32) v i 0 in
-    clear_loop v0 i1
-  else Return v
-
-(** [loops::clear]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ()) *)
-let clear (v : alloc_vec_Vec u32) : result (alloc_vec_Vec u32) =
-  clear_loop v 0
-
-(** [loops::List] *)
-type list_t (t : Type0) =
-| List_Cons : t -> list_t t -> list_t t
-| List_Nil : list_t t
-
-(** [loops::list_mem]: decreases clause *)
-unfold let list_mem_loop_decreases (x : u32) (ls : list_t u32) : nat = admit ()
-
-(** [loops::list_mem]: loop 0: forward function *)
-let rec list_mem_loop
-  (x : u32) (ls : list_t u32) :
-  Tot (result bool) (decreases (list_mem_loop_decreases x ls))
-  =
-  begin match ls with
-  | List_Cons y tl -> if y = x then Return true else list_mem_loop x tl
-  | List_Nil -> Return false
-  end
-
-(** [loops::list_mem]: forward function *)
-let list_mem (x : u32) (ls : list_t u32) : result bool =
-  list_mem_loop x ls
-
-(** [loops::list_nth_mut_loop]: decreases clause *)
-unfold
-let list_nth_mut_loop_loop_decreases (t : Type0) (ls : list_t t) (i : u32) :
-  nat =
-  admit ()
-
-(** [loops::list_nth_mut_loop]: loop 0: forward function *)
-let rec list_nth_mut_loop_loop
-  (t : Type0) (ls : list_t t) (i : u32) :
-  Tot (result t) (decreases (list_nth_mut_loop_loop_decreases t ls i))
-  =
-  begin match ls with
-  | List_Cons x tl ->
-    if i = 0
-    then Return x
-    else let* i0 = u32_sub i 1 in list_nth_mut_loop_loop t tl i0
-  | List_Nil -> Fail Failure
-  end
-
-(** [loops::list_nth_mut_loop]: forward function *)
-let list_nth_mut_loop (t : Type0) (ls : list_t t) (i : u32) : result t =
-  list_nth_mut_loop_loop t ls i
-
-(** [loops::list_nth_mut_loop]: loop 0: backward function 0 *)
-let rec list_nth_mut_loop_loop_back
-  (t : Type0) (ls : list_t t) (i : u32) (ret : t) :
-  Tot (result (list_t t)) (decreases (list_nth_mut_loop_loop_decreases t ls i))
-  =
-  begin match ls with
-  | List_Cons x tl ->
-    if i = 0
-    then Return (List_Cons ret tl)
-    else
-      let* i0 = u32_sub i 1 in
-      let* tl0 = list_nth_mut_loop_loop_back t tl i0 ret in
-      Return (List_Cons x tl0)
-  | List_Nil -> Fail Failure
-  end
-
-(** [loops::list_nth_mut_loop]: backward function 0 *)
-let list_nth_mut_loop_back
-  (t : Type0) (ls : list_t t) (i : u32) (ret : t) : result (list_t t) =
-  list_nth_mut_loop_loop_back t ls i ret
-
-(** [loops::list_nth_shared_loop]: decreases clause *)
-unfold
-let list_nth_shared_loop_loop_decreases (t : Type0) (ls : list_t t) (i : u32) :
-  nat =
-  admit ()
-
-(** [loops::list_nth_shared_loop]: loop 0: forward function *)
-let rec list_nth_shared_loop_loop
-  (t : Type0) (ls : list_t t) (i : u32) :
-  Tot (result t) (decreases (list_nth_shared_loop_loop_decreases t ls i))
-  =
-  begin match ls with
-  | List_Cons x tl ->
-    if i = 0
-    then Return x
-    else let* i0 = u32_sub i 1 in list_nth_shared_loop_loop t tl i0
-  | List_Nil -> Fail Failure
-  end
-
-(** [loops::list_nth_shared_loop]: forward function *)
-let list_nth_shared_loop (t : Type0) (ls : list_t t) (i : u32) : result t =
-  list_nth_shared_loop_loop t ls i
-
-(** [loops::get_elem_mut]: decreases clause *)
-unfold
-let get_elem_mut_loop_decreases (x : usize) (ls : list_t usize) : nat =
-  admit ()
-
-(** [loops::get_elem_mut]: loop 0: forward function *)
-let rec get_elem_mut_loop
-  (x : usize) (ls : list_t usize) :
-  Tot (result usize) (decreases (get_elem_mut_loop_decreases x ls))
-  =
-  begin match ls with
-  | List_Cons y tl -> if y = x then Return y else get_elem_mut_loop x tl
-  | List_Nil -> Fail Failure
-  end
-
-(** [loops::get_elem_mut]: forward function *)
-let get_elem_mut
-  (slots : alloc_vec_Vec (list_t usize)) (x : usize) : result usize =
-  let* l =
-    alloc_vec_Vec_index_mut (list_t usize) usize
-      (core_slice_index_usize_coresliceindexSliceIndexInst (list_t usize))
-      slots 0 in
-  get_elem_mut_loop x l
-
-(** [loops::get_elem_mut]: loop 0: backward function 0 *)
-let rec get_elem_mut_loop_back
-  (x : usize) (ls : list_t usize) (ret : usize) :
-  Tot (result (list_t usize)) (decreases (get_elem_mut_loop_decreases x ls))
-  =
-  begin match ls with
-  | List_Cons y tl ->
-    if y = x
-    then Return (List_Cons ret tl)
-    else let* tl0 = get_elem_mut_loop_back x tl ret in Return (List_Cons y tl0)
-  | List_Nil -> Fail Failure
-  end
-
-(** [loops::get_elem_mut]: backward function 0 *)
-let get_elem_mut_back
-  (slots : alloc_vec_Vec (list_t usize)) (x : usize) (ret : usize) :
-  result (alloc_vec_Vec (list_t usize))
-  =
-  let* l =
-    alloc_vec_Vec_index_mut (list_t usize) usize
-      (core_slice_index_usize_coresliceindexSliceIndexInst (list_t usize))
-      slots 0 in
-  let* l0 = get_elem_mut_loop_back x l ret in
-  alloc_vec_Vec_index_mut_back (list_t usize) usize
-    (core_slice_index_usize_coresliceindexSliceIndexInst (list_t usize)) slots
-    0 l0
-
-(** [loops::get_elem_shared]: decreases clause *)
-unfold
-let get_elem_shared_loop_decreases (x : usize) (ls : list_t usize) : nat =
-  admit ()
-
-(** [loops::get_elem_shared]: loop 0: forward function *)
-let rec get_elem_shared_loop
-  (x : usize) (ls : list_t usize) :
-  Tot (result usize) (decreases (get_elem_shared_loop_decreases x ls))
-  =
-  begin match ls with
-  | List_Cons y tl -> if y = x then Return y else get_elem_shared_loop x tl
-  | List_Nil -> Fail Failure
-  end
-
-(** [loops::get_elem_shared]: forward function *)
-let get_elem_shared
-  (slots : alloc_vec_Vec (list_t usize)) (x : usize) : result usize =
-  let* l =
-    alloc_vec_Vec_index (list_t usize) usize
-      (core_slice_index_usize_coresliceindexSliceIndexInst (list_t usize))
-      slots 0 in
-  get_elem_shared_loop x l
-
-(** [loops::id_mut]: forward function *)
-let id_mut (t : Type0) (ls : list_t t) : result (list_t t) =
-  Return ls
-
-(** [loops::id_mut]: backward function 0 *)
-let id_mut_back
-  (t : Type0) (ls : list_t t) (ret : list_t t) : result (list_t t) =
-  Return ret
-
-(** [loops::id_shared]: forward function *)
-let id_shared (t : Type0) (ls : list_t t) : result (list_t t) =
-  Return ls
-
-(** [loops::list_nth_mut_loop_with_id]: decreases clause *)
-unfold
-let list_nth_mut_loop_with_id_loop_decreases (t : Type0) (i : u32)
-  (ls : list_t t) : nat =
-  admit ()
-
-(** [loops::list_nth_mut_loop_with_id]: loop 0: forward function *)
-let rec list_nth_mut_loop_with_id_loop
-  (t : Type0) (i : u32) (ls : list_t t) :
-  Tot (result t) (decreases (list_nth_mut_loop_with_id_loop_decreases t i ls))
-  =
-  begin match ls with
-  | List_Cons x tl ->
-    if i = 0
-    then Return x
-    else let* i0 = u32_sub i 1 in list_nth_mut_loop_with_id_loop t i0 tl
-  | List_Nil -> Fail Failure
-  end
-
-(** [loops::list_nth_mut_loop_with_id]: forward function *)
-let list_nth_mut_loop_with_id
-  (t : Type0) (ls : list_t t) (i : u32) : result t =
-  let* ls0 = id_mut t ls in list_nth_mut_loop_with_id_loop t i ls0
-
-(** [loops::list_nth_mut_loop_with_id]: loop 0: backward function 0 *)
-let rec list_nth_mut_loop_with_id_loop_back
-  (t : Type0) (i : u32) (ls : list_t t) (ret : t) :
-  Tot (result (list_t t))
-  (decreases (list_nth_mut_loop_with_id_loop_decreases t i ls))
-  =
-  begin match ls with
-  | List_Cons x tl ->
-    if i = 0
-    then Return (List_Cons ret tl)
-    else
-      let* i0 = u32_sub i 1 in
-      let* tl0 = list_nth_mut_loop_with_id_loop_back t i0 tl ret in
-      Return (List_Cons x tl0)
-  | List_Nil -> Fail Failure
-  end
-
-(** [loops::list_nth_mut_loop_with_id]: backward function 0 *)
-let list_nth_mut_loop_with_id_back
-  (t : Type0) (ls : list_t t) (i : u32) (ret : t) : result (list_t t) =
-  let* ls0 = id_mut t ls in
-  let* l = list_nth_mut_loop_with_id_loop_back t i ls0 ret in
-  id_mut_back t ls l
-
-(** [loops::list_nth_shared_loop_with_id]: decreases clause *)
-unfold
-let list_nth_shared_loop_with_id_loop_decreases (t : Type0) (i : u32)
-  (ls : list_t t) : nat =
-  admit ()
-
-(** [loops::list_nth_shared_loop_with_id]: loop 0: forward function *)
-let rec list_nth_shared_loop_with_id_loop
-  (t : Type0) (i : u32) (ls : list_t t) :
-  Tot (result t)
-  (decreases (list_nth_shared_loop_with_id_loop_decreases t i ls))
-  =
-  begin match ls with
-  | List_Cons x tl ->
-    if i = 0
-    then Return x
-    else let* i0 = u32_sub i 1 in list_nth_shared_loop_with_id_loop t i0 tl
-  | List_Nil -> Fail Failure
-  end
-
-(** [loops::list_nth_shared_loop_with_id]: forward function *)
-let list_nth_shared_loop_with_id
-  (t : Type0) (ls : list_t t) (i : u32) : result t =
-  let* ls0 = id_shared t ls in list_nth_shared_loop_with_id_loop t i ls0
-
-(** [loops::list_nth_mut_loop_pair]: decreases clause *)
-unfold
-let list_nth_mut_loop_pair_loop_decreases (t : Type0) (ls0 : list_t t)
-  (ls1 : list_t t) (i : u32) : nat =
-  admit ()
-
-(** [loops::list_nth_mut_loop_pair]: loop 0: forward function *)
-let rec list_nth_mut_loop_pair_loop
-  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) :
-  Tot (result (t & t))
-  (decreases (list_nth_mut_loop_pair_loop_decreases t ls0 ls1 i))
-  =
-  begin match ls0 with
-  | List_Cons x0 tl0 ->
-    begin match ls1 with
-    | List_Cons x1 tl1 ->
-      if i = 0
-      then Return (x0, x1)
-      else let* i0 = u32_sub i 1 in list_nth_mut_loop_pair_loop t tl0 tl1 i0
-    | List_Nil -> Fail Failure
-    end
-  | List_Nil -> Fail Failure
-  end
-
-(** [loops::list_nth_mut_loop_pair]: forward function *)
-let list_nth_mut_loop_pair
-  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) : result (t & t) =
-  list_nth_mut_loop_pair_loop t ls0 ls1 i
-
-(** [loops::list_nth_mut_loop_pair]: loop 0: backward function 0 *)
-let rec list_nth_mut_loop_pair_loop_back'a
-  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) :
-  Tot (result (list_t t))
-  (decreases (list_nth_mut_loop_pair_loop_decreases t ls0 ls1 i))
-  =
-  begin match ls0 with
-  | List_Cons x0 tl0 ->
-    begin match ls1 with
-    | List_Cons x1 tl1 ->
-      if i = 0
-      then Return (List_Cons ret tl0)
-      else
-        let* i0 = u32_sub i 1 in
-        let* tl00 = list_nth_mut_loop_pair_loop_back'a t tl0 tl1 i0 ret in
-        Return (List_Cons x0 tl00)
-    | List_Nil -> Fail Failure
-    end
-  | List_Nil -> Fail Failure
-  end
-
-(** [loops::list_nth_mut_loop_pair]: backward function 0 *)
-let list_nth_mut_loop_pair_back'a
-  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) :
-  result (list_t t)
-  =
-  list_nth_mut_loop_pair_loop_back'a t ls0 ls1 i ret
-
-(** [loops::list_nth_mut_loop_pair]: loop 0: backward function 1 *)
-let rec list_nth_mut_loop_pair_loop_back'b
-  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) :
-  Tot (result (list_t t))
-  (decreases (list_nth_mut_loop_pair_loop_decreases t ls0 ls1 i))
-  =
-  begin match ls0 with
-  | List_Cons x0 tl0 ->
-    begin match ls1 with
-    | List_Cons x1 tl1 ->
-      if i = 0
-      then Return (List_Cons ret tl1)
-      else
-        let* i0 = u32_sub i 1 in
-        let* tl10 = list_nth_mut_loop_pair_loop_back'b t tl0 tl1 i0 ret in
-        Return (List_Cons x1 tl10)
-    | List_Nil -> Fail Failure
-    end
-  | List_Nil -> Fail Failure
-  end
-
-(** [loops::list_nth_mut_loop_pair]: backward function 1 *)
-let list_nth_mut_loop_pair_back'b
-  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) :
-  result (list_t t)
-  =
-  list_nth_mut_loop_pair_loop_back'b t ls0 ls1 i ret
-
-(** [loops::list_nth_shared_loop_pair]: decreases clause *)
-unfold
-let list_nth_shared_loop_pair_loop_decreases (t : Type0) (ls0 : list_t t)
-  (ls1 : list_t t) (i : u32) : nat =
-  admit ()
-
-(** [loops::list_nth_shared_loop_pair]: loop 0: forward function *)
-let rec list_nth_shared_loop_pair_loop
-  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) :
-  Tot (result (t & t))
-  (decreases (list_nth_shared_loop_pair_loop_decreases t ls0 ls1 i))
-  =
-  begin match ls0 with
-  | List_Cons x0 tl0 ->
-    begin match ls1 with
-    | List_Cons x1 tl1 ->
-      if i = 0
-      then Return (x0, x1)
-      else let* i0 = u32_sub i 1 in list_nth_shared_loop_pair_loop t tl0 tl1 i0
-    | List_Nil -> Fail Failure
-    end
-  | List_Nil -> Fail Failure
-  end
-
-(** [loops::list_nth_shared_loop_pair]: forward function *)
-let list_nth_shared_loop_pair
-  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) : result (t & t) =
-  list_nth_shared_loop_pair_loop t ls0 ls1 i
-
-(** [loops::list_nth_mut_loop_pair_merge]: decreases clause *)
-unfold
-let list_nth_mut_loop_pair_merge_loop_decreases (t : Type0) (ls0 : list_t t)
-  (ls1 : list_t t) (i : u32) : nat =
-  admit ()
-
-(** [loops::list_nth_mut_loop_pair_merge]: loop 0: forward function *)
-let rec list_nth_mut_loop_pair_merge_loop
-  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) :
-  Tot (result (t & t))
-  (decreases (list_nth_mut_loop_pair_merge_loop_decreases t ls0 ls1 i))
-  =
-  begin match ls0 with
-  | List_Cons x0 tl0 ->
-    begin match ls1 with
-    | List_Cons x1 tl1 ->
-      if i = 0
-      then Return (x0, x1)
-      else
-        let* i0 = u32_sub i 1 in list_nth_mut_loop_pair_merge_loop t tl0 tl1 i0
-    | List_Nil -> Fail Failure
-    end
-  | List_Nil -> Fail Failure
-  end
-
-(** [loops::list_nth_mut_loop_pair_merge]: forward function *)
-let list_nth_mut_loop_pair_merge
-  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) : result (t & t) =
-  list_nth_mut_loop_pair_merge_loop t ls0 ls1 i
-
-(** [loops::list_nth_mut_loop_pair_merge]: loop 0: backward function 0 *)
-let rec list_nth_mut_loop_pair_merge_loop_back
-  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : (t & t)) :
-  Tot (result ((list_t t) & (list_t t)))
-  (decreases (list_nth_mut_loop_pair_merge_loop_decreases t ls0 ls1 i))
-  =
-  begin match ls0 with
-  | List_Cons x0 tl0 ->
-    begin match ls1 with
-    | List_Cons x1 tl1 ->
-      if i = 0
-      then let (x, x2) = ret in Return (List_Cons x tl0, List_Cons x2 tl1)
-      else
-        let* i0 = u32_sub i 1 in
-        let* (tl00, tl10) =
-          list_nth_mut_loop_pair_merge_loop_back t tl0 tl1 i0 ret in
-        Return (List_Cons x0 tl00, List_Cons x1 tl10)
-    | List_Nil -> Fail Failure
-    end
-  | List_Nil -> Fail Failure
-  end
-
-(** [loops::list_nth_mut_loop_pair_merge]: backward function 0 *)
-let list_nth_mut_loop_pair_merge_back
-  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : (t & t)) :
-  result ((list_t t) & (list_t t))
-  =
-  list_nth_mut_loop_pair_merge_loop_back t ls0 ls1 i ret
-
-(** [loops::list_nth_shared_loop_pair_merge]: decreases clause *)
-unfold
-let list_nth_shared_loop_pair_merge_loop_decreases (t : Type0) (ls0 : list_t t)
-  (ls1 : list_t t) (i : u32) : nat =
-  admit ()
-
-(** [loops::list_nth_shared_loop_pair_merge]: loop 0: forward function *)
-let rec list_nth_shared_loop_pair_merge_loop
-  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) :
-  Tot (result (t & t))
-  (decreases (list_nth_shared_loop_pair_merge_loop_decreases t ls0 ls1 i))
-  =
-  begin match ls0 with
-  | List_Cons x0 tl0 ->
-    begin match ls1 with
-    | List_Cons x1 tl1 ->
-      if i = 0
-      then Return (x0, x1)
-      else
-        let* i0 = u32_sub i 1 in
-        list_nth_shared_loop_pair_merge_loop t tl0 tl1 i0
-    | List_Nil -> Fail Failure
-    end
-  | List_Nil -> Fail Failure
-  end
-
-(** [loops::list_nth_shared_loop_pair_merge]: forward function *)
-let list_nth_shared_loop_pair_merge
-  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) : result (t & t) =
-  list_nth_shared_loop_pair_merge_loop t ls0 ls1 i
-
-(** [loops::list_nth_mut_shared_loop_pair]: decreases clause *)
-unfold
-let list_nth_mut_shared_loop_pair_loop_decreases (t : Type0) (ls0 : list_t t)
-  (ls1 : list_t t) (i : u32) : nat =
-  admit ()
-
-(** [loops::list_nth_mut_shared_loop_pair]: loop 0: forward function *)
-let rec list_nth_mut_shared_loop_pair_loop
-  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) :
-  Tot (result (t & t))
-  (decreases (list_nth_mut_shared_loop_pair_loop_decreases t ls0 ls1 i))
-  =
-  begin match ls0 with
-  | List_Cons x0 tl0 ->
-    begin match ls1 with
-    | List_Cons x1 tl1 ->
-      if i = 0
-      then Return (x0, x1)
-      else
-        let* i0 = u32_sub i 1 in
-        list_nth_mut_shared_loop_pair_loop t tl0 tl1 i0
-    | List_Nil -> Fail Failure
-    end
-  | List_Nil -> Fail Failure
-  end
-
-(** [loops::list_nth_mut_shared_loop_pair]: forward function *)
-let list_nth_mut_shared_loop_pair
-  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) : result (t & t) =
-  list_nth_mut_shared_loop_pair_loop t ls0 ls1 i
-
-(** [loops::list_nth_mut_shared_loop_pair]: loop 0: backward function 0 *)
-let rec list_nth_mut_shared_loop_pair_loop_back
-  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) :
-  Tot (result (list_t t))
-  (decreases (list_nth_mut_shared_loop_pair_loop_decreases t ls0 ls1 i))
-  =
-  begin match ls0 with
-  | List_Cons x0 tl0 ->
-    begin match ls1 with
-    | List_Cons x1 tl1 ->
-      if i = 0
-      then Return (List_Cons ret tl0)
-      else
-        let* i0 = u32_sub i 1 in
-        let* tl00 = list_nth_mut_shared_loop_pair_loop_back t tl0 tl1 i0 ret in
-        Return (List_Cons x0 tl00)
-    | List_Nil -> Fail Failure
-    end
-  | List_Nil -> Fail Failure
-  end
-
-(** [loops::list_nth_mut_shared_loop_pair]: backward function 0 *)
-let list_nth_mut_shared_loop_pair_back
-  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) :
-  result (list_t t)
-  =
-  list_nth_mut_shared_loop_pair_loop_back t ls0 ls1 i ret
-
-(** [loops::list_nth_mut_shared_loop_pair_merge]: decreases clause *)
-unfold
-let list_nth_mut_shared_loop_pair_merge_loop_decreases (t : Type0)
-  (ls0 : list_t t) (ls1 : list_t t) (i : u32) : nat =
-  admit ()
-
-(** [loops::list_nth_mut_shared_loop_pair_merge]: loop 0: forward function *)
-let rec list_nth_mut_shared_loop_pair_merge_loop
-  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) :
-  Tot (result (t & t))
-  (decreases (list_nth_mut_shared_loop_pair_merge_loop_decreases t ls0 ls1 i))
-  =
-  begin match ls0 with
-  | List_Cons x0 tl0 ->
-    begin match ls1 with
-    | List_Cons x1 tl1 ->
-      if i = 0
-      then Return (x0, x1)
-      else
-        let* i0 = u32_sub i 1 in
-        list_nth_mut_shared_loop_pair_merge_loop t tl0 tl1 i0
-    | List_Nil -> Fail Failure
-    end
-  | List_Nil -> Fail Failure
-  end
-
-(** [loops::list_nth_mut_shared_loop_pair_merge]: forward function *)
-let list_nth_mut_shared_loop_pair_merge
-  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) : result (t & t) =
-  list_nth_mut_shared_loop_pair_merge_loop t ls0 ls1 i
-
-(** [loops::list_nth_mut_shared_loop_pair_merge]: loop 0: backward function 0 *)
-let rec list_nth_mut_shared_loop_pair_merge_loop_back
-  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) :
-  Tot (result (list_t t))
-  (decreases (list_nth_mut_shared_loop_pair_merge_loop_decreases t ls0 ls1 i))
-  =
-  begin match ls0 with
-  | List_Cons x0 tl0 ->
-    begin match ls1 with
-    | List_Cons x1 tl1 ->
-      if i = 0
-      then Return (List_Cons ret tl0)
-      else
-        let* i0 = u32_sub i 1 in
-        let* tl00 =
-          list_nth_mut_shared_loop_pair_merge_loop_back t tl0 tl1 i0 ret in
-        Return (List_Cons x0 tl00)
-    | List_Nil -> Fail Failure
-    end
-  | List_Nil -> Fail Failure
-  end
-
-(** [loops::list_nth_mut_shared_loop_pair_merge]: backward function 0 *)
-let list_nth_mut_shared_loop_pair_merge_back
-  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) :
-  result (list_t t)
-  =
-  list_nth_mut_shared_loop_pair_merge_loop_back t ls0 ls1 i ret
-
-(** [loops::list_nth_shared_mut_loop_pair]: decreases clause *)
-unfold
-let list_nth_shared_mut_loop_pair_loop_decreases (t : Type0) (ls0 : list_t t)
-  (ls1 : list_t t) (i : u32) : nat =
-  admit ()
-
-(** [loops::list_nth_shared_mut_loop_pair]: loop 0: forward function *)
-let rec list_nth_shared_mut_loop_pair_loop
-  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) :
-  Tot (result (t & t))
-  (decreases (list_nth_shared_mut_loop_pair_loop_decreases t ls0 ls1 i))
-  =
-  begin match ls0 with
-  | List_Cons x0 tl0 ->
-    begin match ls1 with
-    | List_Cons x1 tl1 ->
-      if i = 0
-      then Return (x0, x1)
-      else
-        let* i0 = u32_sub i 1 in
-        list_nth_shared_mut_loop_pair_loop t tl0 tl1 i0
-    | List_Nil -> Fail Failure
-    end
-  | List_Nil -> Fail Failure
-  end
-
-(** [loops::list_nth_shared_mut_loop_pair]: forward function *)
-let list_nth_shared_mut_loop_pair
-  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) : result (t & t) =
-  list_nth_shared_mut_loop_pair_loop t ls0 ls1 i
-
-(** [loops::list_nth_shared_mut_loop_pair]: loop 0: backward function 1 *)
-let rec list_nth_shared_mut_loop_pair_loop_back
-  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) :
-  Tot (result (list_t t))
-  (decreases (list_nth_shared_mut_loop_pair_loop_decreases t ls0 ls1 i))
-  =
-  begin match ls0 with
-  | List_Cons x0 tl0 ->
-    begin match ls1 with
-    | List_Cons x1 tl1 ->
-      if i = 0
-      then Return (List_Cons ret tl1)
-      else
-        let* i0 = u32_sub i 1 in
-        let* tl10 = list_nth_shared_mut_loop_pair_loop_back t tl0 tl1 i0 ret in
-        Return (List_Cons x1 tl10)
-    | List_Nil -> Fail Failure
-    end
-  | List_Nil -> Fail Failure
-  end
-
-(** [loops::list_nth_shared_mut_loop_pair]: backward function 1 *)
-let list_nth_shared_mut_loop_pair_back
-  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) :
-  result (list_t t)
-  =
-  list_nth_shared_mut_loop_pair_loop_back t ls0 ls1 i ret
-
-(** [loops::list_nth_shared_mut_loop_pair_merge]: decreases clause *)
-unfold
-let list_nth_shared_mut_loop_pair_merge_loop_decreases (t : Type0)
-  (ls0 : list_t t) (ls1 : list_t t) (i : u32) : nat =
-  admit ()
-
-(** [loops::list_nth_shared_mut_loop_pair_merge]: loop 0: forward function *)
-let rec list_nth_shared_mut_loop_pair_merge_loop
-  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) :
-  Tot (result (t & t))
-  (decreases (list_nth_shared_mut_loop_pair_merge_loop_decreases t ls0 ls1 i))
-  =
-  begin match ls0 with
-  | List_Cons x0 tl0 ->
-    begin match ls1 with
-    | List_Cons x1 tl1 ->
-      if i = 0
-      then Return (x0, x1)
-      else
-        let* i0 = u32_sub i 1 in
-        list_nth_shared_mut_loop_pair_merge_loop t tl0 tl1 i0
-    | List_Nil -> Fail Failure
-    end
-  | List_Nil -> Fail Failure
-  end
-
-(** [loops::list_nth_shared_mut_loop_pair_merge]: forward function *)
-let list_nth_shared_mut_loop_pair_merge
-  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) : result (t & t) =
-  list_nth_shared_mut_loop_pair_merge_loop t ls0 ls1 i
-
-(** [loops::list_nth_shared_mut_loop_pair_merge]: loop 0: backward function 0 *)
-let rec list_nth_shared_mut_loop_pair_merge_loop_back
-  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) :
-  Tot (result (list_t t))
-  (decreases (list_nth_shared_mut_loop_pair_merge_loop_decreases t ls0 ls1 i))
-  =
-  begin match ls0 with
-  | List_Cons x0 tl0 ->
-    begin match ls1 with
-    | List_Cons x1 tl1 ->
-      if i = 0
-      then Return (List_Cons ret tl1)
-      else
-        let* i0 = u32_sub i 1 in
-        let* tl10 =
-          list_nth_shared_mut_loop_pair_merge_loop_back t tl0 tl1 i0 ret in
-        Return (List_Cons x1 tl10)
-    | List_Nil -> Fail Failure
-    end
-  | List_Nil -> Fail Failure
-  end
-
-(** [loops::list_nth_shared_mut_loop_pair_merge]: backward function 0 *)
-let list_nth_shared_mut_loop_pair_merge_back
-  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) :
-  result (list_t t)
-  =
-  list_nth_shared_mut_loop_pair_merge_loop_back t ls0 ls1 i ret
-
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