proposition: Lemma posbig_size_cons l s : posbig (l :: s) < size (l :: s).
proof: Proof. Proof using. elim H : s l => [//= | s0 s' IHs] l; rewrite -H /=. by case (allLtn s l); rewrite // H ltnS; apply: IHs. Qed.
imports: HB(structures) mathcomp(all_ssreflect) mathcomp(order) tools