proposition: Lemma Kleisli_precat_is_precat (R : RelMonad J) : is_precategory (Kleisli_precat_data R).
proof: Proof. apply is_precategory_one_assoc_to_two. do 2 try apply tpair; try unfold compose; simpl. - intros a b f. apply (r_eta_r_bind R). - intros a b f. now rewrite (r_bind_r_eta R), id_right. - intros a b c d f g h. now rewrite <- assoc, (r_bind_r_bind R). Qed.
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