proposition: Lemma sub_vnum e1 e2 : subenv e1 e2 -> forall x, num e1 x < sn e1 -> num e2 x = num e1 x.
proof: Proof. move=> sube12 x /ltnW num_lt; rewrite (sub_snum sube12)//. by rewrite (leq_trans num_lt)// max_card. Qed.
imports: mathcomp(all_ssreflect) extra_nocolors