proposition: Lemma succ_strict_mono_LT : forall alpha beta, alpha t1< beta -> succ alpha t1< succ beta.
proof: Proof. intros alpha beta H; destruct H as [H [H0 H1]]; repeat split;auto. - now apply succ_nf. - now apply succ_strict_mono. - now apply succ_nf. 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)