proposition: Lemma Monad_law_1_from_hss : ∏ c : C, μ_0 (pr1 (`T) c) · μ_2 c = identity ((pr1 (`T)) c).
proof: Proof. intro c. unfold μ_0. set (H' := prejoin_from_hetsubst_η T). set (H2:= nat_trans_eq_weq (homset_property C) _ _ H'). apply pathsinv0. apply 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