proposition: Lemma lt_inv_coeff_dec : forall a n n' b b', lt (cons a n b) (cons a n' b') -> {(n < n')%nat} + { n = n' /\ lt b b'}.
proof: Proof. intros * H. apply lt_inv_strong in H as [Hlt | Heqa Hlt | Heqa Heqn Hlt]. 1: now apply lt_irrefl in Hlt. all: tauto. 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)