proposition: Lemma succ_mono : forall a b, nf a -> nf b -> leq lt a b -> leq lt (succ a) (succ b).
proof: Proof. intros a b Ha Hb Hle. rewrite le_lt_eq in *. destruct Hle as [Hlt | Heq]. - left; now apply succ_strict_mono_LT. - subst; now right. 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)