prolog [ isGram5 isGram1 inter_X_Vu Gunion_Regles ] 7.
(*Intros. Apply isGram5.  Apply isGram1 with V1 R1 S1 ; Assumption.  Apply inter_X_Vu ; Assumption.  Assumption.  Apply Gunion_Regles; Assumption.*)
Qed.
Variable f : Elt -> Elt.
Let wef := Word_ext f.
Let fet (w : Elt) := word (wef (word_inv w)).
Let fonc (P : Elt) := couple (f (first P)) (fet (second P)).
Let Gim := imageGram f X V1 R1 S1.
Let Xim := fst Gim.
Let Gim2 := snd Gim.
Let Vim := fst Gim2.
Let Gim3 := snd Gim2.
Let Rim := fst Gim3.
Let Sim := snd Gim3.

(* Specifications: *)
Lemma dans_Rim :
forall (A : Elt) (u : Word),
dans (couple A (word u)) R1 -> dans (couple (f A) (word (wef u))) Rim.