proposition: Lemma succ_lt_limit alpha (Halpha : nf alpha)(H : T1limit alpha ): forall beta, beta t1< alpha -> succ beta t1< alpha.
proof: Proof. intros beta H0; assert (H1 :succ beta t1<= alpha) by (apply LT_succ_LE; auto). destruct (LE_LT_eq_dec H1); auto. subst alpha; destruct (@T1limit_succ beta ); eauto with T1. 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)