proposition: Lemma bind_bind {a b c : C} (f : C⟦a,T b⟧) (g : C⟦b,T c⟧) : bind f · bind g = bind (f · bind g).
proof: Proof. unfold bind; rewrite <- assoc. eapply pathscomp0; [apply maponpaths; rewrite assoc; apply cancel_postcomposition, (!nat_trans_ax (μ T) _ _ g)|]. rewrite !functor_comp, <- !assoc. now apply maponpaths, maponpaths, (!Monad_law3 c). Qed.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.MoreFoundations.Tactics UniMath.MoreFoundations.Notations UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.Adjunctions.Core UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Total UniMath.CategoryTheory.DisplayedCats.Constructions UniMath.CategoryTheory.DisplayedCats.Isos UniMath.CategoryTheory.DisplayedCats.SIP UniMath.CategoryTheory.DisplayedCats.Univalence UniMath.CategoryTheory.Core.Univalence