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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                               *)
(*                                                                          *)
(****************************************************************************)
(*                                 gram3.v                                  *)
(****************************************************************************)
(*              Formal Language Theory                                      *)
(*                                                                          *)
(*              Judicael Courant - Jean-Christophe Filliatre                *)
(*                                                                          *)
(*              Developped in V5.8  June-July 1993                          *)
(*              Ported     to V5.10 October 1994                            *)
(****************************************************************************)
Section resultats_iso_image.
Variable X V R : Ensf.
Variable S : Elt.
Variable f : Elt -> Elt.
Let Gim := imageGram f X V R S.
Let Xim := fst Gim.
Let Gim2 := snd Gim.
Let Vim := fst Gim2.
Let Gim3 := snd Gim2.
Let Rim := fst Gim3.
Let Sim := snd Gim3.
Let invf := inv (union X V) (union Xim Vim) f.
Let Gim' := imageGram invf Xim Vim Rim Sim.
Let Xim' := fst Gim'.
Let Gim2' := snd Gim'.
Let Vim' := fst Gim2'.
Let Gim3' := snd Gim2'.
Let Rim' := fst Gim3'.
Let Sim' := snd Gim3'.
Hypothesis Gram : isGram X V R S.

(* Specifications: *)
Lemma Regles_X_V_R : Regles X V R.
Proof isGram4 X V R S Gram.