(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
(** [loops]: function definitions *)
module Loops.Funs
open Primitives
include Loops.Types
include Loops.Clauses

#set-options "--z3rlimit 50 --fuel 1 --ifuel 1"

(** [loops::sum]: loop 0: forward function
    Source: 'src/loops.rs', lines 4:0-14:1 *)
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
    Source: 'src/loops.rs', lines 4:0-4:27 *)
let sum (max : u32) : result u32 =
  sum_loop max 0 0

(** [loops::sum_with_mut_borrows]: loop 0: forward function
    Source: 'src/loops.rs', lines 19:0-31:1 *)
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
    Source: 'src/loops.rs', lines 19:0-19:44 *)
let sum_with_mut_borrows (max : u32) : result u32 =
  sum_with_mut_borrows_loop max 0 0

(** [loops::sum_with_shared_borrows]: loop 0: forward function
    Source: 'src/loops.rs', lines 34:0-48:1 *)
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
    Source: 'src/loops.rs', lines 34:0-34:47 *)
let sum_with_shared_borrows (max : u32) : result u32 =
  sum_with_shared_borrows_loop max 0 0

(** [loops::clear]: loop 0: merged forward/backward function
    (there is a single backward function, and the forward function returns ())
    Source: 'src/loops.rs', lines 52:0-58:1 *)
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_SliceIndexUsizeSliceTInst 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 ())
    Source: 'src/loops.rs', lines 52:0-52:30 *)
let clear (v : alloc_vec_Vec u32) : result (alloc_vec_Vec u32) =
  clear_loop v 0

(** [loops::list_mem]: loop 0: forward function
    Source: 'src/loops.rs', lines 66:0-75:1 *)
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
    Source: 'src/loops.rs', lines 66:0-66:52 *)
let list_mem (x : u32) (ls : list_t u32) : result bool =
  list_mem_loop x ls

(** [loops::list_nth_mut_loop]: loop 0: forward function
    Source: 'src/loops.rs', lines 78:0-88:1 *)
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
    Source: 'src/loops.rs', lines 78:0-78:71 *)
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
    Source: 'src/loops.rs', lines 78:0-88:1 *)
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
    Source: 'src/loops.rs', lines 78:0-78:71 *)
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]: loop 0: forward function
    Source: 'src/loops.rs', lines 91:0-101:1 *)
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
    Source: 'src/loops.rs', lines 91:0-91:66 *)
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]: loop 0: forward function
    Source: 'src/loops.rs', lines 103:0-117:1 *)
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
    Source: 'src/loops.rs', lines 103:0-103:73 *)
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_SliceIndexUsizeSliceTInst (list_t usize)) slots 0 in
  get_elem_mut_loop x l

(** [loops::get_elem_mut]: loop 0: backward function 0
    Source: 'src/loops.rs', lines 103:0-117:1 *)
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
    Source: 'src/loops.rs', lines 103:0-103:73 *)
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_SliceIndexUsizeSliceTInst (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_SliceIndexUsizeSliceTInst (list_t usize)) slots 0 l0

(** [loops::get_elem_shared]: loop 0: forward function
    Source: 'src/loops.rs', lines 119:0-133:1 *)
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
    Source: 'src/loops.rs', lines 119:0-119:68 *)
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_SliceIndexUsizeSliceTInst (list_t usize)) slots 0 in
  get_elem_shared_loop x l

(** [loops::id_mut]: forward function
    Source: 'src/loops.rs', lines 135:0-135:50 *)
let id_mut (t : Type0) (ls : list_t t) : result (list_t t) =
  Return ls

(** [loops::id_mut]: backward function 0
    Source: 'src/loops.rs', lines 135:0-135:50 *)
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
    Source: 'src/loops.rs', lines 139:0-139:45 *)
let id_shared (t : Type0) (ls : list_t t) : result (list_t t) =
  Return ls

(** [loops::list_nth_mut_loop_with_id]: loop 0: forward function
    Source: 'src/loops.rs', lines 144:0-155:1 *)
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
    Source: 'src/loops.rs', lines 144:0-144:75 *)
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
    Source: 'src/loops.rs', lines 144:0-155:1 *)
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
    Source: 'src/loops.rs', lines 144:0-144:75 *)
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]: loop 0: forward function
    Source: 'src/loops.rs', lines 158:0-169:1 *)
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
    Source: 'src/loops.rs', lines 158:0-158:70 *)
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]: loop 0: forward function
    Source: 'src/loops.rs', lines 174:0-195:1 *)
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
    Source: 'src/loops.rs', lines 174:0-178:27 *)
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
    Source: 'src/loops.rs', lines 174:0-195:1 *)
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
    Source: 'src/loops.rs', lines 174:0-178:27 *)
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
    Source: 'src/loops.rs', lines 174:0-195:1 *)
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
    Source: 'src/loops.rs', lines 174:0-178:27 *)
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]: loop 0: forward function
    Source: 'src/loops.rs', lines 198:0-219:1 *)
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
    Source: 'src/loops.rs', lines 198:0-202:19 *)
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]: loop 0: forward function
    Source: 'src/loops.rs', lines 223:0-238:1 *)
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
    Source: 'src/loops.rs', lines 223:0-227:27 *)
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
    Source: 'src/loops.rs', lines 223:0-238:1 *)
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
    Source: 'src/loops.rs', lines 223:0-227:27 *)
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]: loop 0: forward function
    Source: 'src/loops.rs', lines 241:0-256:1 *)
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
    Source: 'src/loops.rs', lines 241:0-245:19 *)
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]: loop 0: forward function
    Source: 'src/loops.rs', lines 259:0-274:1 *)
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
    Source: 'src/loops.rs', lines 259:0-263:23 *)
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
    Source: 'src/loops.rs', lines 259:0-274:1 *)
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
    Source: 'src/loops.rs', lines 259:0-263:23 *)
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]: loop 0: forward function
    Source: 'src/loops.rs', lines 278:0-293:1 *)
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
    Source: 'src/loops.rs', lines 278:0-282:23 *)
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
    Source: 'src/loops.rs', lines 278:0-293:1 *)
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
    Source: 'src/loops.rs', lines 278:0-282:23 *)
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]: loop 0: forward function
    Source: 'src/loops.rs', lines 297:0-312:1 *)
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
    Source: 'src/loops.rs', lines 297:0-301:23 *)
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
    Source: 'src/loops.rs', lines 297:0-312:1 *)
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
    Source: 'src/loops.rs', lines 297:0-301:23 *)
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]: loop 0: forward function
    Source: 'src/loops.rs', lines 316:0-331:1 *)
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
    Source: 'src/loops.rs', lines 316:0-320:23 *)
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
    Source: 'src/loops.rs', lines 316:0-331:1 *)
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
    Source: 'src/loops.rs', lines 316:0-320:23 *)
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