proposition: Lemma unkleislify_mor_laws {C : category} {T T' : KleisliMonad C} (α : Kleisli_Mor T T') : Monad_Mor_laws (T := unkleislify T) (T' := unkleislify T') (nat_trans_kleisli_mor α).
proof: Proof. split; simpl; intros; unfold μ. + rewrite <- assoc. rewrite (bind_map T'). rewrite id_right. rewrite <- (Kleisli_Mor_bind α). now rewrite id_left. + apply Kleisli_Mor_η. 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