proposition: Lemma lt_inv_head : forall a n b a' n' b', lt (cons a n b) (cons a' n' b') -> leq lt a a'.
proof: Proof. intros * H. apply lt_inv_strong in H as [Hlt | Heqa Hlt | Heqa Heqn Hlt]; intuition. - now left. - subst; now right. - subst; now right. Qed.
imports: Coq(Arith Max Bool Lia Compare_dec Relations Ensembles Wellfounded Bool RelationClasses Operators_Properties ArithRing Logic.Eqdep_dec) hydras(More_Arith Restriction DecPreOrder) hydras(OrdNotations)