proposition: Theorem le_zero_inv : forall a, leq lt a zero -> a = zero.
proof: Proof. intros a H; rewrite le_lt_eq in H; destruct H. - now apply not_lt_zero in H. - assumption. 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)