(** 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_decreases max i s))
  =
  if i < max
  then
    begin match u32_add s i with
    | Fail e -> Fail e
    | Return s0 ->
      begin match u32_add i 1 with
      | Fail e -> Fail e
      | Return i0 -> sum_loop_fwd max i0 s0
      end
    end
  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_decreases max mi ms))
  =
  if mi < max
  then
    begin match u32_add ms mi with
    | Fail e -> Fail e
    | Return ms0 ->
      begin match u32_add mi 1 with
      | Fail e -> Fail e
      | Return mi0 -> sum_with_mut_borrows_loop_fwd max mi0 ms0
      end
    end
  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_decreases max i s))
  =
  if i < max
  then
    begin match u32_add i 1 with
    | Fail e -> Fail e
    | Return i0 ->
      begin match u32_add s i0 with
      | Fail e -> Fail e
      | Return s0 -> sum_with_shared_borrows_loop_fwd max i0 s0
      end
    end
  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::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_decreases t ls i))
  =
  begin match ls with
  | ListCons x tl ->
    if i = 0
    then Return x
    else
      begin match u32_sub i 1 with
      | Fail e -> Fail e
      | Return i0 -> list_nth_mut_loop_loop_fwd t tl i0
      end
  | 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_decreases t ls i))
  =
  begin match ls with
  | ListCons x tl ->
    if i = 0
    then Return (ListCons ret tl)
    else
      begin match u32_sub i 1 with
      | Fail e -> Fail e
      | Return i0 ->
        begin match list_nth_mut_loop_loop_back t tl i0 ret with
        | Fail e -> Fail e
        | Return l -> Return (ListCons x l)
        end
      end
  | 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_decreases t ls i))
  =
  begin match ls with
  | ListCons x tl ->
    if i = 0
    then Return x
    else
      begin match u32_sub i 1 with
      | Fail e -> Fail e
      | Return i0 -> list_nth_shared_loop_loop_fwd t tl i0
      end
  | 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::list_nth_mut_loop_pair] *)
let rec list_nth_mut_loop_pair_loop_fwd
  (t : Type0) (l : list_t t) (l0 : list_t t) (i : u32) :
  Tot (result (t & t)) (decreases (list_nth_mut_loop_pair_decreases t l l0 i))
  =
  begin match l with
  | ListCons x0 tl0 ->
    begin match l0 with
    | ListCons x1 tl1 ->
      if i = 0
      then Return (x0, x1)
      else
        begin match u32_sub i 1 with
        | Fail e -> Fail e
        | Return i0 -> list_nth_mut_loop_pair_loop_fwd t tl0 tl1 i0
        end
    | 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) (l : list_t t) (l0 : list_t t) (i : u32) (ret : t) :
  Tot (result (list_t t))
  (decreases (list_nth_mut_loop_pair_decreases t l l0 i))
  =
  begin match l with
  | ListCons x0 tl0 ->
    begin match l0 with
    | ListCons x1 tl1 ->
      if i = 0
      then Return (ListCons ret tl0)
      else
        begin match u32_sub i 1 with
        | Fail e -> Fail e
        | Return i0 ->
          begin match list_nth_mut_loop_pair_loop_back'a t tl0 tl1 i0 ret with
          | Fail e -> Fail e
          | Return l1 -> Return (ListCons x0 l1)
          end
        end
    | 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) (l : list_t t) (l0 : list_t t) (i : u32) (ret : t) :
  Tot (result (list_t t))
  (decreases (list_nth_mut_loop_pair_decreases t l l0 i))
  =
  begin match l with
  | ListCons x0 tl0 ->
    begin match l0 with
    | ListCons x1 tl1 ->
      if i = 0
      then Return (ListCons ret tl1)
      else
        begin match u32_sub i 1 with
        | Fail e -> Fail e
        | Return i0 ->
          begin match list_nth_mut_loop_pair_loop_back'b t tl0 tl1 i0 ret with
          | Fail e -> Fail e
          | Return l1 -> Return (ListCons x1 l1)
          end
        end
    | 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) (l : list_t t) (l0 : list_t t) (i : u32) :
  Tot (result (t & t))
  (decreases (list_nth_shared_loop_pair_decreases t l l0 i))
  =
  begin match l with
  | ListCons x0 tl0 ->
    begin match l0 with
    | ListCons x1 tl1 ->
      if i = 0
      then Return (x0, x1)
      else
        begin match u32_sub i 1 with
        | Fail e -> Fail e
        | Return i0 -> list_nth_shared_loop_pair_loop_fwd t tl0 tl1 i0
        end
    | 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) (l : list_t t) (l0 : list_t t) (i : u32) :
  Tot (result (t & t))
  (decreases (list_nth_mut_loop_pair_merge_decreases t l l0 i))
  =
  begin match l with
  | ListCons x0 tl0 ->
    begin match l0 with
    | ListCons x1 tl1 ->
      if i = 0
      then Return (x0, x1)
      else
        begin match u32_sub i 1 with
        | Fail e -> Fail e
        | Return i0 -> list_nth_mut_loop_pair_merge_loop_fwd t tl0 tl1 i0
        end
    | 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) (l : list_t t) (l0 : list_t t) (i : u32) (ret : (t & t)) :
  Tot (result ((list_t t) & (list_t t)))
  (decreases (list_nth_mut_loop_pair_merge_decreases t l l0 i))
  =
  begin match l with
  | ListCons x0 tl0 ->
    begin match l0 with
    | ListCons x1 tl1 ->
      if i = 0
      then let (x, x2) = ret in Return (ListCons x tl0, ListCons x2 tl1)
      else
        begin match u32_sub i 1 with
        | Fail e -> Fail e
        | Return i0 ->
          begin match list_nth_mut_loop_pair_merge_loop_back t tl0 tl1 i0 ret
            with
          | Fail e -> Fail e
          | Return (l1, l2) -> Return (ListCons x0 l1, ListCons x1 l2)
          end
        end
    | 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) (l : list_t t) (l0 : list_t t) (i : u32) :
  Tot (result (t & t))
  (decreases (list_nth_shared_loop_pair_merge_decreases t l l0 i))
  =
  begin match l with
  | ListCons x0 tl0 ->
    begin match l0 with
    | ListCons x1 tl1 ->
      if i = 0
      then Return (x0, x1)
      else
        begin match u32_sub i 1 with
        | Fail e -> Fail e
        | Return i0 -> list_nth_shared_loop_pair_merge_loop_fwd t tl0 tl1 i0
        end
    | 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) (l : list_t t) (l0 : list_t t) (i : u32) :
  Tot (result (t & t))
  (decreases (list_nth_mut_shared_loop_pair_decreases t l l0 i))
  =
  begin match l with
  | ListCons x0 tl0 ->
    begin match l0 with
    | ListCons x1 tl1 ->
      if i = 0
      then Return (x0, x1)
      else
        begin match u32_sub i 1 with
        | Fail e -> Fail e
        | Return i0 -> list_nth_mut_shared_loop_pair_loop_fwd t tl0 tl1 i0
        end
    | 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) (l : list_t t) (l0 : list_t t) (i : u32) (ret : t) :
  Tot (result (list_t t))
  (decreases (list_nth_mut_shared_loop_pair_decreases t l l0 i))
  =
  begin match l with
  | ListCons x0 tl0 ->
    begin match l0 with
    | ListCons x1 tl1 ->
      if i = 0
      then Return (ListCons ret tl0)
      else
        begin match u32_sub i 1 with
        | Fail e -> Fail e
        | Return i0 ->
          begin match list_nth_mut_shared_loop_pair_loop_back t tl0 tl1 i0 ret
            with
          | Fail e -> Fail e
          | Return l1 -> Return (ListCons x0 l1)
          end
        end
    | 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) (l : list_t t) (l0 : list_t t) (i : u32) :
  Tot (result (t & t))
  (decreases (list_nth_mut_shared_loop_pair_merge_decreases t l l0 i))
  =
  begin match l with
  | ListCons x0 tl0 ->
    begin match l0 with
    | ListCons x1 tl1 ->
      if i = 0
      then Return (x0, x1)
      else
        begin match u32_sub i 1 with
        | Fail e -> Fail e
        | Return i0 ->
          list_nth_mut_shared_loop_pair_merge_loop_fwd t tl0 tl1 i0
        end
    | 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) (l : list_t t) (l0 : list_t t) (i : u32) (ret : t) :
  Tot (result (list_t t))
  (decreases (list_nth_mut_shared_loop_pair_merge_decreases t l l0 i))
  =
  begin match l with
  | ListCons x0 tl0 ->
    begin match l0 with
    | ListCons x1 tl1 ->
      if i = 0
      then Return (ListCons ret tl0)
      else
        begin match u32_sub i 1 with
        | Fail e -> Fail e
        | Return i0 ->
          begin match
            list_nth_mut_shared_loop_pair_merge_loop_back t tl0 tl1 i0 ret with
          | Fail e -> Fail e
          | Return l1 -> Return (ListCons x0 l1)
          end
        end
    | 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) (l : list_t t) (l0 : list_t t) (i : u32) :
  Tot (result (t & t))
  (decreases (list_nth_shared_mut_loop_pair_decreases t l l0 i))
  =
  begin match l with
  | ListCons x0 tl0 ->
    begin match l0 with
    | ListCons x1 tl1 ->
      if i = 0
      then Return (x0, x1)
      else
        begin match u32_sub i 1 with
        | Fail e -> Fail e
        | Return i0 -> list_nth_shared_mut_loop_pair_loop_fwd t tl0 tl1 i0
        end
    | 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) (l : list_t t) (l0 : list_t t) (i : u32) (ret : t) :
  Tot (result (list_t t))
  (decreases (list_nth_shared_mut_loop_pair_decreases t l l0 i))
  =
  begin match l with
  | ListCons x0 tl0 ->
    begin match l0 with
    | ListCons x1 tl1 ->
      if i = 0
      then Return (ListCons ret tl1)
      else
        begin match u32_sub i 1 with
        | Fail e -> Fail e
        | Return i0 ->
          begin match list_nth_shared_mut_loop_pair_loop_back t tl0 tl1 i0 ret
            with
          | Fail e -> Fail e
          | Return l1 -> Return (ListCons x1 l1)
          end
        end
    | 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) (l : list_t t) (l0 : list_t t) (i : u32) :
  Tot (result (t & t))
  (decreases (list_nth_shared_mut_loop_pair_merge_decreases t l l0 i))
  =
  begin match l with
  | ListCons x0 tl0 ->
    begin match l0 with
    | ListCons x1 tl1 ->
      if i = 0
      then Return (x0, x1)
      else
        begin match u32_sub i 1 with
        | Fail e -> Fail e
        | Return i0 ->
          list_nth_shared_mut_loop_pair_merge_loop_fwd t tl0 tl1 i0
        end
    | 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) (l : list_t t) (l0 : list_t t) (i : u32) (ret : t) :
  Tot (result (list_t t))
  (decreases (list_nth_shared_mut_loop_pair_merge_decreases t l l0 i))
  =
  begin match l with
  | ListCons x0 tl0 ->
    begin match l0 with
    | ListCons x1 tl1 ->
      if i = 0
      then Return (ListCons ret tl1)
      else
        begin match u32_sub i 1 with
        | Fail e -> Fail e
        | Return i0 ->
          begin match
            list_nth_shared_mut_loop_pair_merge_loop_back t tl0 tl1 i0 ret with
          | Fail e -> Fail e
          | Return l1 -> Return (ListCons x1 l1)
          end
        end
    | 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