need.v

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(* 02110-1301 USA                                                     *)


(* Contribution to the Coq Library   V6.3 (July 1999)                    *)

(****************************************************************************)
(*                 The Calculus of Inductive Constructions                  *)
(*                                                                          *)
(*                                Projet Coq                                *)
(*                                                                          *)
(*                     INRIA                        ENS-CNRS                *)
(*              Rocquencourt                        Lyon                    *)
(*                                                                          *)
(*                                Coq V5.10                                 *)
(*                              Nov 25th 1994                               *)
(*                                                                          *)
(****************************************************************************)
(*                                  need.v                                  *)
(****************************************************************************)
(*              Formal Language Theory                                      *)
(*                                                                          *)
(*              Judicael Courant - Jean-Christophe Filliatre                *)
(*                                                                          *)
(*              Developped in V5.8  June-July 1993                          *)
(*              Ported     to V5.10 October 1994                            *)
(****************************************************************************)

Require Import Ensf.
Require Import Words.
Require Import more_words.

Axiom Dans_spec : forall (a : Elt) (E : Ensf), {dans a E} + {~ dans a E}.

Definition Dans (a : Elt) (E : Ensf) :=
  match Dans_spec a E return bool with
  | left a => true
  | right a => false
  end.


Axiom
  Append_Append :
    forall a a' b b' : Word,
    Append a b = Append a' b' ->
    exists w : Word,
      a = Append a' w /\ b' = Append w b \/
      a' = Append a w /\ b = Append w b'.


Axiom
  inmonoid_Append_inv2 :
    forall (X : Ensf) (a b : Word), inmonoid X (Append a b) -> inmonoid X b.


Hint Resolve dans_add.