proposition: Lemma LT_eq_LT_dec : forall alpha beta, nf alpha -> nf beta -> {alpha t1< beta} + {alpha = beta} + {beta t1< alpha}.
proof: Proof. intros; destruct (lt_eq_lt_dec alpha beta) as [[H1 | H1] | H1]. - left; left; split; eauto with T1. - left; now right. - right; split; auto 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)