proposition: Lemma lt_inv_tail : forall a n b b', lt (cons a n b) (cons a n b') -> lt b b'.
proof: Proof. intros * H. apply lt_inv_coeff_dec in H as [Hlt | (Heqn, Hlt)]. - lia. - assumption. 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)