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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                               *)
(*                                                                          *)
(****************************************************************************)
(*                                 gram4.v                                  *)
(****************************************************************************)
(*              Formal Language Theory                                      *)
(*                                                                          *)
(*              Judicael Courant - Jean-Christophe Filliatre                *)
(*                                                                          *)
(*              Developped in V5.8  June-July 1993                          *)
(*              Ported     to V5.10 October 1994                            *)
(****************************************************************************)
Section gram4.
Variable X V1 R1 : Ensf.
Variable S1 : Elt.
Variable V2 R2 : Ensf.
Variable S2 : Elt.
Variable S : Elt.
Let C := Gunion_disj_p V1 R1 S1 V2 R2 S2 S.
Let Vu := fst C.
Let C' := snd C.
Let Ru := fst C'.
Let Su := snd C'.

Lemma inter_X_V1_u_V2 :
isGram X V1 R1 S1 -> isGram X V2 R2 S2 -> inter X (union V1 V2) empty.