proposition: Lemma unkleislify_data_eq (T : KleisliMonad C) : Monad_Kleisli_data (unkleislify T) = T.
proof: Proof. apply (maponpaths (λ p, tpair _ _ p )). apply pair_path_in2. simpl. apply funextsec. intro a. apply funextsec. intro b. apply funextfun. intro f. unfold Monads.bind. abstract (simpl; unfold μ; rewrite (bind_map T); rewrite id_right; apply idpath). Defined.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.MoreFoundations.Tactics UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.Monads.Monads UniMath.CategoryTheory.Monads.KTriples UniMath.CategoryTheory.catiso UniMath.CategoryTheory.Adjunctions.Core UniMath.CategoryTheory.Equivalences.Core UniMath.CategoryTheory.Equivalences.FullyFaithful