proposition: Lemma bind_kt_monad_to_kleisli {x : univalent_category} (k : kleisli_triple x) {a b : x} (f : x ⟦ a, k b ⟧) : bind_kt (Monad_to_Ktriple_data (unit_mu_kleisli k)) f = bind_kt k f.
proof: Proof. unfold bind_kt at 1; simpl. unfold monad_bind; simpl. rewrite (bind_bind k). apply maponpaths. etrans; [ idtac | apply id_right ]. rewrite assoc'. apply maponpaths. apply (unit_bind k). Qed.
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