proposition: Lemma lt_one (alpha:T1) : lt alpha one -> alpha = zero.
proof: Proof. destruct alpha. - auto. - intro H; destruct (lt_inv H) as [H0 | H0]. + destruct (not_lt_zero H0). + destruct H0 as [[_ H1] | [_ [_ H1]]]. * abstract lia. * destruct (not_lt_zero H1). 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)