proposition: Lemma functor_of_kleisli_comm_nat_z_iso {x y : univalent_category} {f : x ⟶ y} {kx : kleisli_triple x} {ky : kleisli_triple y} (kf : kleisli_triple_on_functor kx ky f) : is_nat_z_iso (functor_of_kleisli_comm kf).
proof: Proof. intro a. apply is_z_iso_inv_from_z_iso. Defined.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Prelude UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.opp_precat UniMath.CategoryTheory.DisplayedCats.Core UniMath.Bicategories.Core.Examples.BicatOfUnivCats UniMath.Bicategories.Core.Bicat UniMath.Bicategories.Morphisms.Adjunctions UniMath.Bicategories.Core.AdjointUnique UniMath.Bicategories.Core.Invertible_2cells UniMath.Bicategories.Core.Univalence UniMath.Bicategories.PseudoFunctors.Display.PseudoFunctorBicat UniMath.Bicategories.PseudoFunctors.PseudoFunctor UniMath.Bicategories.DisplayedBicats.DispBicat UniMath.Bicategories.DisplayedBicats.DispAdjunctions UniMath.Bicategories.DisplayedBicats.DispInvertibles UniMath.Bicategories.DisplayedBicats.DispUnivalence UniMath.Bicategories.PseudoFunctors.Examples.Identity UniMath.Bicategories.PseudoFunctors.Examples.Composition UniMath.Bicategories.PseudoFunctors.Examples.Projection UniMath.Bicategories.Transformations.PseudoTransformation UniMath.Bicategories.Transformations.Examples.AlgebraMap UniMath.Bicategories.Modifications.Modification UniMath.Bicategories.PseudoFunctors.Biequivalence UniMath.Bicategories.Core.Unitors UniMath.Bicategories.DisplayedBicats.DispPseudofunctor UniMath.Bicategories.DisplayedBicats.Examples.Algebras UniMath.Bicategories.DisplayedBicats.Examples.Add2Cell UniMath.Bicategories.DisplayedBicats.Examples.Prod UniMath.Bicategories.DisplayedBicats.Examples.FullSub UniMath.Bicategories.DisplayedBicats.Examples.Monads UniMath.Bicategories.DisplayedBicats.Examples.KleisliTriple UniMath.Bicategories.DisplayedBicats.DispBuilders UniMath.Bicategories.DisplayedBicats.DispTransformation UniMath.Bicategories.DisplayedBicats.DispModification UniMath.Bicategories.DisplayedBicats.DispBiequivalence UniMath.Bicategories.Transformations.Examples.Unitality UniMath.Bicategories.DisplayedBicats.Examples.KleisliTriple UniMath.CategoryTheory.Equivalences.CompositesAndInverses