replace X with X2'.
unfold X2', V2', R2', S2', GGG2, GG2, G2 in |- *.
apply egal_LG.
auto.
auto.
red in |- *; auto.
unfold X2' in |- *; simpl in |- *.
apply map_Id.
red in |- *.
auto.
Qed.
Hint Resolve egal_LG_2_2'.

Lemma egal_X_X1' : X1' = X :>Ensf.
unfold X1' in |- *. simpl in |- *.