proposition: Lemma LT_LE_trans (alpha beta gamma : T1) : alpha t1< beta -> beta t1<= gamma -> alpha t1< gamma.
proof: Proof. intros [H [H0 H1]] [H' [H'0 H'1]]; repeat split; auto with T1. apply lt_le_trans with beta;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)