proposition: Lemma LT_succ_LE_R : forall alpha beta, nf alpha -> succ alpha t1<= beta -> alpha t1< beta.
proof: Proof. intros * H H0; destruct H0 as [H1 [H2 H3]]. repeat split; auto. apply lt_succ_le_R; 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)