proposition: Lemma LT_inv_strong : forall a b n a' b' n', cons a n b t1< cons a' n' b' -> LT_cases a b n a' b' n'.
proof: Proof. intros a b n a' b' n' H. case H. - clear H;intros H (H0,H1); case (lt_inv_strong H0). + constructor 1. split. * eapply nf_inv1; eauto. * split;auto; eapply nf_inv1; eauto. + intros; subst. constructor 2; auto. + constructor 3 ; auto. split; eauto with T1. Defined.
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)