(* This program is free software; you can redistribute it and/or      *)
(* modify it under the terms of the GNU Lesser General Public License *)
(* as published by the Free Software Foundation; either version 2.1   *)
(* of the License, or (at your option) any later version.             *)
(*                                                                    *)
(* This program is distributed in the hope that it will be useful,    *)
(* but WITHOUT ANY WARRANTY; without even the implied warranty of     *)
(* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the      *)
(* GNU General Public License for more details.                       *)
(*                                                                    *)
(* You should have received a copy of the GNU Lesser General Public   *)
(* License along with this program; if not, write to the Free         *)
(* Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA *)
(* 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                               *)
(*                                                                          *)
(****************************************************************************)
(*                                 gram5.v                                  *)
(****************************************************************************)
(*              Formal Language Theory                                      *)
(*                                                                          *)
(*              Judicael Courant - Jean-Christophe Filliatre                *)
(*                                                                          *)
(*              Developped in V5.8  June-July 1993                          *)
(*              Ported     to V5.10 October 1994                            *)
(****************************************************************************)
Section gram5.
Variable X : Ensf.
Variable V1 R1 : Ensf.
Variable S1 : Elt.
Variable V2 R2 : Ensf.
Variable S2 : Elt.
Let S' := zero.
Let G1 := imageGram (injproducg V1) X V1 R1 S1.
Let G2 := imageGram (injproducd V2) X V2 R2 S2.
Let X1' := fst G1.
Let GG1 := snd G1.
Let V1' := fst GG1.
Let GGG1 := snd GG1.
Let R1' := fst GGG1.
Let S1' := snd GGG1.
Let X2' := fst G2.
Let GG2 := snd G2.
Let V2' := fst GG2.
Let GGG2 := snd GG2.
Let R2' := fst GGG2.
Let S2' := snd GGG2.
Let Gim := Gunion_disj_p V1' R1' S1' V2' R2' S2' S'.
Let Vu := fst Gim.
Let C' := snd Gim.
Let Ru := fst C'.
Let Su := snd C'.
Hypothesis Grammaire1 : isGram X V1 R1 S1.
Hypothesis Grammaire2 : isGram X V2 R2 S2.
Hint Resolve Grammaire1.
Hint Resolve Grammaire2.

Lemma Mots_X : Mots X.
apply isGram1 with V1 R1 S1.