proposition: Lemma LT_succ_LE : forall alpha beta , alpha t1< beta -> succ alpha t1<= beta.
proof: Proof. intros. destruct H as [H1 [H2 H3]]; repeat split; auto. apply succ_nf;auto. apply lt_succ_le; 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)