proposition: Lemma LE_LT_trans : forall alpha beta gamma, alpha t1<= beta -> beta t1< gamma -> alpha t1< gamma.
proof: Proof. intros alpha beta gamma [H1 [H2 H3]] [H4 [H5 H6]]; repeat split; auto. apply le_lt_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)