proposition: Lemma disp_Monad_laws_from_hss : disp_Monad_laws disp_Monad_data_from_hss.
proof: Proof. split. - unfold disp_Monad_data_from_hss; simpl; split. + apply Monad_law_1_from_hss. + apply Monad_law_2_from_hss. - unfold disp_Monad_data_from_hss; simpl. intro c. intermediate_path (pr1 μ_3 c). + set (H1 := μ_3_T_μ_2_μ_2). set (H2 := nat_trans_eq_weq (homset_property C) _ _ H1). apply pathsinv0, H2. + set (H1 := μ_3_μ_2_T_μ_2). set (H2 := nat_trans_eq_weq (homset_property C) _ _ H1). apply pathsinv0, H2. 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