(************************************************************************)
(*         *   The Coq Proof Assistant / The Coq Development Team       *)
(*  v      *   INRIA, CNRS and contributors - Copyright 1999-2018       *)
(* <O___,, *       (see CREDITS file for the list of authors)           *)
(*   \VV/  **************************************************************)
(*    //   *    This file is distributed under the terms of the         *)
(*         *     GNU Lesser General Public License Version 2.1          *)
(*         *     (see LICENSE file for the text of the license)         *)
(************************************************************************)
(************************************************************************)
(** Contributed by Laurent Théry (INRIA); Adapted to Coq V8 by the Coq Development Team *)
(** * Definition of ascii characters *)
(** Definition of ascii character as a 8 bits constructor *)
Inductive ascii : Set := Ascii (_ _ _ _ _ _ _ _ : bool).
Declare Scope char_scope.
Delimit Scope char_scope with char.
Bind Scope char_scope with ascii.
Definition zero := Ascii false false false false false false false false.
Definition one := Ascii true false false false false false false false.
Definition shift (c : bool) (a : ascii) :=
match a with
| Ascii a1 a2 a3 a4 a5 a6 a7 a8 => Ascii c a1 a2 a3 a4 a5 a6 a7
end.
(** Definition of a decidable function that is effective *)
Definition ascii_dec : forall a b : ascii, {a = b} + {a <> b}.
Local Ltac t_eqb :=
repeat first [ congruence
| progress subst
| apply conj
| match goal with
| [ |- context[eqb ?x ?y] ] => destruct (eqb_spec x y)
end
| intro ].

Theorem N_ascii_embedding :
forall n:N, (n < 256)%N -> N_of_ascii (ascii_of_N n) = n.