proposition: Lemma respectful_compond_relation: forall {A B} (f: A -> B) R1 R2, inclusion _ (compond_relation (respectful_relation f R1) (respectful_relation f R2)) (respectful_relation f (compond_relation R1 R2)).
proof: Proof. intros. intros a1 a2 ?. inversion H; subst. apply compond_intro with (f y); auto. Qed.
imports: Coq.Relations.Relation_Definitions Coq.Classes.Morphisms Coq.Classes.Equivalence