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'.
prolog [ isGram2 union_inter ] 5.
(*Intro G1. Intro G2. Apply union_inter. Apply isGram2 with R1 S1; Assumption. Apply isGram2 with R2 S2; Assumption.*)
Qed.

Lemma inter_X_Vu_d :
isGram X V1 R1 S1 -> isGram X V2 R2 S2 -> ~ dans S X -> inter X Vu empty.