proposition: Theorem lt_inv : forall a n b a' n' b', lt (cons a n b) (cons a' n' b') -> lt a a' \/ a = a' /\ (n < n')%nat \/ a = a' /\ n = n' /\ lt b b'.
proof: Proof. intros; destruct (lt_inv_strong H). - now left. - right; left; auto. - right; right; auto. 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)