(** 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] *)
let rec sum_loop_fwd
  (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_fwd max i0 s0
  else u32_mul s 2

(** [loops::sum] *)
let sum_fwd (max : u32) : result u32 =
  sum_loop_fwd max 0 0

(** [loops::sum_with_mut_borrows] *)
let rec sum_with_mut_borrows_loop_fwd
  (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_fwd max mi0 ms0
  else u32_mul ms 2

(** [loops::sum_with_mut_borrows] *)
let sum_with_mut_borrows_fwd (max : u32) : result u32 =
  sum_with_mut_borrows_loop_fwd max 0 0

(** [loops::sum_with_shared_borrows] *)
let rec sum_with_shared_borrows_loop_fwd
  (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_fwd max i0 s0
  else u32_mul s 2

(** [loops::sum_with_shared_borrows] *)
let sum_with_shared_borrows_fwd (max : u32) : result u32 =
  sum_with_shared_borrows_loop_fwd max 0 0

(** [loops::clear] *)
let rec clear_loop_fwd_back
  (v : vec u32) (i : usize) :
  Tot (result (vec u32)) (decreases (clear_loop_decreases v i))
  =
  let i0 = vec_len u32 v in
  if i < i0
  then
    let* i1 = usize_add i 1 in
    let* v0 = vec_index_mut_back u32 v i 0 in
    clear_loop_fwd_back v0 i1
  else Return v

(** [loops::clear] *)
let clear_fwd_back (v : vec u32) : result (vec u32) =
  clear_loop_fwd_back v 0

(** [loops::list_mem] *)
let rec list_mem_loop_fwd
  (x : u32) (ls : list_t u32) :
  Tot (result bool) (decreases (list_mem_loop_decreases x ls))
  =
  begin match ls with
  | ListCons y tl -> if y = x then Return true else list_mem_loop_fwd x tl
  | ListNil -> Return false
  end

(** [loops::list_mem] *)
let list_mem_fwd (x : u32) (ls : list_t u32) : result bool =
  list_mem_loop_fwd x ls

(** [loops::list_nth_mut_loop] *)
let rec list_nth_mut_loop_loop_fwd
  (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
  | ListCons x tl ->
    if i = 0
    then Return x
    else let* i0 = u32_sub i 1 in list_nth_mut_loop_loop_fwd t tl i0
  | ListNil -> Fail Failure
  end

(** [loops::list_nth_mut_loop] *)
let list_nth_mut_loop_fwd (t : Type0) (ls : list_t t) (i : u32) : result t =
  list_nth_mut_loop_loop_fwd t ls i

(** [loops::list_nth_mut_loop] *)
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
  | ListCons x tl ->
    if i = 0
    then Return (ListCons ret tl)
    else
      let* i0 = u32_sub i 1 in
      let* tl0 = list_nth_mut_loop_loop_back t tl i0 ret in
      Return (ListCons x tl0)
  | ListNil -> Fail Failure
  end

(** [loops::list_nth_mut_loop] *)
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] *)
let rec list_nth_shared_loop_loop_fwd
  (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
  | ListCons x tl ->
    if i = 0
    then Return x
    else let* i0 = u32_sub i 1 in list_nth_shared_loop_loop_fwd t tl i0
  | ListNil -> Fail Failure
  end

(** [loops::list_nth_shared_loop] *)
let list_nth_shared_loop_fwd (t : Type0) (ls : list_t t) (i : u32) : result t =
  list_nth_shared_loop_loop_fwd t ls i

(** [loops::get_elem_mut] *)
let rec get_elem_mut_loop_fwd
  (x : usize) (ls : list_t usize) :
  Tot (result usize) (decreases (get_elem_mut_loop_decreases x ls))
  =
  begin match ls with
  | ListCons y tl -> if y = x then Return y else get_elem_mut_loop_fwd x tl
  | ListNil -> Fail Failure
  end

(** [loops::get_elem_mut] *)
let get_elem_mut_fwd (slots : vec (list_t usize)) (x : usize) : result usize =
  let* l = vec_index_mut_fwd (list_t usize) slots 0 in
  get_elem_mut_loop_fwd x l

(** [loops::get_elem_mut] *)
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
  | ListCons y tl ->
    if y = x
    then Return (ListCons ret tl)
    else let* tl0 = get_elem_mut_loop_back x tl ret in Return (ListCons y tl0)
  | ListNil -> Fail Failure
  end

(** [loops::get_elem_mut] *)
let get_elem_mut_back
  (slots : vec (list_t usize)) (x : usize) (ret : usize) :
  result (vec (list_t usize))
  =
  let* l = vec_index_mut_fwd (list_t usize) slots 0 in
  let* l0 = get_elem_mut_loop_back x l ret in
  vec_index_mut_back (list_t usize) slots 0 l0

(** [loops::get_elem_shared] *)
let rec get_elem_shared_loop_fwd
  (x : usize) (ls : list_t usize) :
  Tot (result usize) (decreases (get_elem_shared_loop_decreases x ls))
  =
  begin match ls with
  | ListCons y tl -> if y = x then Return y else get_elem_shared_loop_fwd x tl
  | ListNil -> Fail Failure
  end

(** [loops::get_elem_shared] *)
let get_elem_shared_fwd
  (slots : vec (list_t usize)) (x : usize) : result usize =
  let* l = vec_index_fwd (list_t usize) slots 0 in get_elem_shared_loop_fwd x l

(** [loops::id_mut] *)
let id_mut_fwd (t : Type0) (ls : list_t t) : result (list_t t) =
  Return ls

(** [loops::id_mut] *)
let id_mut_back
  (t : Type0) (ls : list_t t) (ret : list_t t) : result (list_t t) =
  Return ret

(** [loops::id_shared] *)
let id_shared_fwd (t : Type0) (ls : list_t t) : result (list_t t) =
  Return ls

(** [loops::list_nth_mut_loop_with_id] *)
let rec list_nth_mut_loop_with_id_loop_fwd
  (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
  | ListCons x tl ->
    if i = 0
    then Return x
    else let* i0 = u32_sub i 1 in list_nth_mut_loop_with_id_loop_fwd t i0 tl
  | ListNil -> Fail Failure
  end

(** [loops::list_nth_mut_loop_with_id] *)
let list_nth_mut_loop_with_id_fwd
  (t : Type0) (ls : list_t t) (i : u32) : result t =
  let* ls0 = id_mut_fwd t ls in list_nth_mut_loop_with_id_loop_fwd t i ls0

(** [loops::list_nth_mut_loop_with_id] *)
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
  | ListCons x tl ->
    if i = 0
    then Return (ListCons 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 (ListCons x tl0)
  | ListNil -> Fail Failure
  end

(** [loops::list_nth_mut_loop_with_id] *)
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_fwd 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] *)
let rec list_nth_shared_loop_with_id_loop_fwd
  (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
  | ListCons x tl ->
    if i = 0
    then Return x
    else let* i0 = u32_sub i 1 in list_nth_shared_loop_with_id_loop_fwd t i0 tl
  | ListNil -> Fail Failure
  end

(** [loops::list_nth_shared_loop_with_id] *)
let list_nth_shared_loop_with_id_fwd
  (t : Type0) (ls : list_t t) (i : u32) : result t =
  let* ls0 = id_shared_fwd t ls in
  list_nth_shared_loop_with_id_loop_fwd t i ls0

(** [loops::list_nth_mut_loop_pair] *)
let rec list_nth_mut_loop_pair_loop_fwd
  (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
  | ListCons x0 tl0 ->
    begin match ls1 with
    | ListCons x1 tl1 ->
      if i = 0
      then Return (x0, x1)
      else
        let* i0 = u32_sub i 1 in list_nth_mut_loop_pair_loop_fwd t tl0 tl1 i0
    | ListNil -> Fail Failure
    end
  | ListNil -> Fail Failure
  end

(** [loops::list_nth_mut_loop_pair] *)
let list_nth_mut_loop_pair_fwd
  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) : result (t & t) =
  list_nth_mut_loop_pair_loop_fwd t ls0 ls1 i

(** [loops::list_nth_mut_loop_pair] *)
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
  | ListCons x0 tl0 ->
    begin match ls1 with
    | ListCons x1 tl1 ->
      if i = 0
      then Return (ListCons 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 (ListCons x0 tl00)
    | ListNil -> Fail Failure
    end
  | ListNil -> Fail Failure
  end

(** [loops::list_nth_mut_loop_pair] *)
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] *)
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
  | ListCons x0 tl0 ->
    begin match ls1 with
    | ListCons x1 tl1 ->
      if i = 0
      then Return (ListCons 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 (ListCons x1 tl10)
    | ListNil -> Fail Failure
    end
  | ListNil -> Fail Failure
  end

(** [loops::list_nth_mut_loop_pair] *)
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] *)
let rec list_nth_shared_loop_pair_loop_fwd
  (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
  | ListCons x0 tl0 ->
    begin match ls1 with
    | ListCons x1 tl1 ->
      if i = 0
      then Return (x0, x1)
      else
        let* i0 = u32_sub i 1 in
        list_nth_shared_loop_pair_loop_fwd t tl0 tl1 i0
    | ListNil -> Fail Failure
    end
  | ListNil -> Fail Failure
  end

(** [loops::list_nth_shared_loop_pair] *)
let list_nth_shared_loop_pair_fwd
  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) : result (t & t) =
  list_nth_shared_loop_pair_loop_fwd t ls0 ls1 i

(** [loops::list_nth_mut_loop_pair_merge] *)
let rec list_nth_mut_loop_pair_merge_loop_fwd
  (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
  | ListCons x0 tl0 ->
    begin match ls1 with
    | ListCons x1 tl1 ->
      if i = 0
      then Return (x0, x1)
      else
        let* i0 = u32_sub i 1 in
        list_nth_mut_loop_pair_merge_loop_fwd t tl0 tl1 i0
    | ListNil -> Fail Failure
    end
  | ListNil -> Fail Failure
  end

(** [loops::list_nth_mut_loop_pair_merge] *)
let list_nth_mut_loop_pair_merge_fwd
  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) : result (t & t) =
  list_nth_mut_loop_pair_merge_loop_fwd t ls0 ls1 i

(** [loops::list_nth_mut_loop_pair_merge] *)
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
  | ListCons x0 tl0 ->
    begin match ls1 with
    | ListCons x1 tl1 ->
      if i = 0
      then let (x, x2) = ret in Return (ListCons x tl0, ListCons 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 (ListCons x0 tl00, ListCons x1 tl10)
    | ListNil -> Fail Failure
    end
  | ListNil -> Fail Failure
  end

(** [loops::list_nth_mut_loop_pair_merge] *)
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] *)
let rec list_nth_shared_loop_pair_merge_loop_fwd
  (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
  | ListCons x0 tl0 ->
    begin match ls1 with
    | ListCons x1 tl1 ->
      if i = 0
      then Return (x0, x1)
      else
        let* i0 = u32_sub i 1 in
        list_nth_shared_loop_pair_merge_loop_fwd t tl0 tl1 i0
    | ListNil -> Fail Failure
    end
  | ListNil -> Fail Failure
  end

(** [loops::list_nth_shared_loop_pair_merge] *)
let list_nth_shared_loop_pair_merge_fwd
  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) : result (t & t) =
  list_nth_shared_loop_pair_merge_loop_fwd t ls0 ls1 i

(** [loops::list_nth_mut_shared_loop_pair] *)
let rec list_nth_mut_shared_loop_pair_loop_fwd
  (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
  | ListCons x0 tl0 ->
    begin match ls1 with
    | ListCons x1 tl1 ->
      if i = 0
      then Return (x0, x1)
      else
        let* i0 = u32_sub i 1 in
        list_nth_mut_shared_loop_pair_loop_fwd t tl0 tl1 i0
    | ListNil -> Fail Failure
    end
  | ListNil -> Fail Failure
  end

(** [loops::list_nth_mut_shared_loop_pair] *)
let list_nth_mut_shared_loop_pair_fwd
  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) : result (t & t) =
  list_nth_mut_shared_loop_pair_loop_fwd t ls0 ls1 i

(** [loops::list_nth_mut_shared_loop_pair] *)
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
  | ListCons x0 tl0 ->
    begin match ls1 with
    | ListCons x1 tl1 ->
      if i = 0
      then Return (ListCons 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 (ListCons x0 tl00)
    | ListNil -> Fail Failure
    end
  | ListNil -> Fail Failure
  end

(** [loops::list_nth_mut_shared_loop_pair] *)
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] *)
let rec list_nth_mut_shared_loop_pair_merge_loop_fwd
  (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
  | ListCons x0 tl0 ->
    begin match ls1 with
    | ListCons 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_fwd t tl0 tl1 i0
    | ListNil -> Fail Failure
    end
  | ListNil -> Fail Failure
  end

(** [loops::list_nth_mut_shared_loop_pair_merge] *)
let list_nth_mut_shared_loop_pair_merge_fwd
  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) : result (t & t) =
  list_nth_mut_shared_loop_pair_merge_loop_fwd t ls0 ls1 i

(** [loops::list_nth_mut_shared_loop_pair_merge] *)
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
  | ListCons x0 tl0 ->
    begin match ls1 with
    | ListCons x1 tl1 ->
      if i = 0
      then Return (ListCons 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 (ListCons x0 tl00)
    | ListNil -> Fail Failure
    end
  | ListNil -> Fail Failure
  end

(** [loops::list_nth_mut_shared_loop_pair_merge] *)
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] *)
let rec list_nth_shared_mut_loop_pair_loop_fwd
  (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
  | ListCons x0 tl0 ->
    begin match ls1 with
    | ListCons x1 tl1 ->
      if i = 0
      then Return (x0, x1)
      else
        let* i0 = u32_sub i 1 in
        list_nth_shared_mut_loop_pair_loop_fwd t tl0 tl1 i0
    | ListNil -> Fail Failure
    end
  | ListNil -> Fail Failure
  end

(** [loops::list_nth_shared_mut_loop_pair] *)
let list_nth_shared_mut_loop_pair_fwd
  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) : result (t & t) =
  list_nth_shared_mut_loop_pair_loop_fwd t ls0 ls1 i

(** [loops::list_nth_shared_mut_loop_pair] *)
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
  | ListCons x0 tl0 ->
    begin match ls1 with
    | ListCons x1 tl1 ->
      if i = 0
      then Return (ListCons 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 (ListCons x1 tl10)
    | ListNil -> Fail Failure
    end
  | ListNil -> Fail Failure
  end

(** [loops::list_nth_shared_mut_loop_pair] *)
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] *)
let rec list_nth_shared_mut_loop_pair_merge_loop_fwd
  (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
  | ListCons x0 tl0 ->
    begin match ls1 with
    | ListCons 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_fwd t tl0 tl1 i0
    | ListNil -> Fail Failure
    end
  | ListNil -> Fail Failure
  end

(** [loops::list_nth_shared_mut_loop_pair_merge] *)
let list_nth_shared_mut_loop_pair_merge_fwd
  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) : result (t & t) =
  list_nth_shared_mut_loop_pair_merge_loop_fwd t ls0 ls1 i

(** [loops::list_nth_shared_mut_loop_pair_merge] *)
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
  | ListCons x0 tl0 ->
    begin match ls1 with
    | ListCons x1 tl1 ->
      if i = 0
      then Return (ListCons 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 (ListCons x1 tl10)
    | ListNil -> Fail Failure
    end
  | ListNil -> Fail Failure
  end

(** [loops::list_nth_shared_mut_loop_pair_merge] *)
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