proposition: Lemma SumStrength2 : θ_Strength2 θ.
proof: Proof. intros X Z Z' Y α. apply nat_trans_eq_alt; intro x. etrans; [ apply BinCoproductOfArrows_comp |]. apply pathsinv0. etrans. { apply cancel_postcomposition. simpl. apply BinCoproductOfArrows_comp. } etrans; [apply BinCoproductOfArrows_comp |]. apply pathsinv0. apply maponpaths_12. - assert (Ha:=S12 X Z Z' Y α). simpl in Ha. assert (Ha_x := nat_trans_eq_pointwise Ha x). apply Ha_x. - assert (Ha:=S22 X Z Z' Y α). simpl in Ha. assert (Ha_x := nat_trans_eq_pointwise Ha x). apply Ha_x. Qed.
imports: UniMath.Foundations.PartD UniMath.MoreFoundations.PartA UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.PointedFunctors UniMath.CategoryTheory.PointedFunctorsComposition UniMath.SubstitutionSystems.Signatures UniMath.SubstitutionSystems.Notation UniMath.CategoryTheory.Chains.Chains UniMath.CategoryTheory.Chains.OmegaCocontFunctors UniMath.CategoryTheory.Limits.BinProducts