proposition: Lemma δ_law2_nicer_implies_δ_law2: δ_law2_nicer -> δ_law2.
proof: Proof. intros Hyp Ze Ze'. assert (Hypinst := Hyp Ze Ze'). etrans. { exact Hypinst. } unfold D'. apply nat_trans_eq_alt. intro c. cbn. do 2 rewrite id_left. rewrite id_right. apply idpath. 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.Limits.BinCoproducts UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.FunctorAlgebras UniMath.CategoryTheory.PointedFunctors UniMath.SubstitutionSystems.Signatures UniMath.CategoryTheory.BicatOfCatsElementary UniMath.SubstitutionSystems.Notation UniMath.CategoryTheory.PointedFunctorsComposition