proposition: Lemma precategory_Kleisli_axioms (C : category) : is_precategory (precategory_Kleisli_Data C).
proof: Proof. repeat split; simpl; intros. - apply (invmap (Kleisli_Mor_equiv _ _ )). apply funextsec. intros x. apply id_left. - apply (invmap (Kleisli_Mor_equiv _ _ )). apply funextsec. intros x. apply id_right. - apply (invmap (Kleisli_Mor_equiv _ _ )). apply funextsec. intros x. apply assoc. - apply (invmap (Kleisli_Mor_equiv _ _ )). apply funextsec. intros x. apply assoc'. Defined.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.MoreFoundations.Tactics UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.Monads.Monads UniMath.CategoryTheory.Monads.RelativeMonads