lemma gget_inv_gt: ∀G1,G2,e. ⇩[e] G1 ≡ G2 → |G1| ≤ e → G2 = ⋆.
#G1 #G2 #e * -G1 -G2 //
-[ #G #H >H -H >commutative_plus #H
+[ #G #H >H -H >commutative_plus #H (**) (* lemma needed here *)
lapply (le_plus_to_le_r … 0 H) -H #H
lapply (le_n_O_to_eq … H) -H #H destruct
| #I #G1 #G2 #V #H1 #_ #H2
lemma gget_inv_eq: ∀G1,G2,e. ⇩[e] G1 ≡ G2 → |G1| = e + 1 → G1 = G2.
#G1 #G2 #e * -G1 -G2 //
-[ #G #H1 #H2 >H2 in H1; -H2 >commutative_plus #H
+[ #G #H1 #H2 >H2 in H1; -H2 >commutative_plus #H (**) (* lemma needed here *)
lapply (le_plus_to_le_r … 0 H) -H #H
lapply (le_n_O_to_eq … H) -H #H destruct
| #I #G1 #G2 #V #H1 #_ normalize #H2