replace X with X1'.
unfold X1', V1', R1', S1', GGG1, GG1, G1 in |- *.
apply egal_LG.
auto.
auto.
red in |- *; auto.
unfold X1' in |- *; simpl in |- *.
apply map_Id.
red in |- *.
auto.
Qed.
Hint Resolve egal_LG_1_1'.

Lemma egal_LG_2_2' : l_egal (LG X V2 R2 S2) (LG X V2' R2' S2').
pattern X at 2 in |- *.