proposition: Lemma compare_lt_impl a b : compare a b = Lt -> lt a b.
proof: Proof. intros * H. pose proof (compare_reflect a b). now rewrite H in *; simpl. 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)