proposition: Lemma precategory_RelMonad_axioms {C : precategory_data} {D : precategory} (hs : has_homsets D) (J : functor_data C D) : is_precategory (precategory_RelMonad_data J).
proof: Proof. repeat split; simpl; intros. - apply (invmap (RelMonadMor_equiv hs _ _ )). apply funextsec. intros x. apply id_left. - apply (invmap (RelMonadMor_equiv hs _ _ )). apply funextsec. intros x. apply id_right. - apply (invmap (RelMonadMor_equiv hs _ _ )). apply funextsec. intros x. apply assoc. - apply (invmap (RelMonadMor_equiv hs _ _ )). apply funextsec. intros x. apply assoc'. Defined.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.MoreFoundations.Tactics UniMath.MoreFoundations.PartA UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Adjunctions.Core