proposition: Theorem lt_irrefl (alpha: T1): ~ lt alpha alpha.
proof: Proof. induction alpha. - apply not_lt_zero. - intro H. apply lt_inv_strong in H as [Hlt_a | aHeq_a Hlt_n | Heq_a Heq_n Hlt_b]. 1,3: contradiction. lia. 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)