proposition: Lemma μ_2_is_ptd_mor : ∏ c : C, (ptd_pt C T_squared) c · μ_2 c = pr1 (η T) c.
proof: Proof. intro c. unfold μ_2. unfold T_squared. unfold ptd_compose. rewrite functorial_composition_pre_post. simpl. assert (H' := Monad_law_2_from_hss c). simpl in H'. intermediate_path (pr1 (η T) c · identity _ ). - unfold eta_from_alg; simpl. repeat rewrite <- assoc. apply maponpaths. apply maponpaths. exact H'. - apply id_right. Qed.
imports: UniMath.Foundations.PartD UniMath.MoreFoundations.Tactics UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.Monads.Monads UniMath.CategoryTheory.FunctorAlgebras UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.PointedFunctors UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.HorizontalComposition UniMath.CategoryTheory.PointedFunctorsComposition UniMath.CategoryTheory.BicatOfCatsElementary UniMath.SubstitutionSystems.Signatures UniMath.SubstitutionSystems.SimplifiedHSS.SubstitutionSystems UniMath.SubstitutionSystems.Notation