proposition: Lemma SumStrength1' : θ_Strength1_int θ.
proof: Proof. clear S11 S12 S21 S22 S12' S22'; intro X. apply nat_trans_eq_alt; intro x. etrans; [ apply BinCoproductOfArrows_comp |]. apply pathsinv0, BinCoproduct_endo_is_identity. + rewrite BinCoproductOfArrowsIn1. assert (Ha := nat_trans_eq_pointwise (S11' X) x). simpl in Ha. etrans; [ | apply id_left]. apply cancel_postcomposition. apply Ha. + rewrite BinCoproductOfArrowsIn2. assert (Ha := nat_trans_eq_pointwise (S21' X) x). simpl in Ha. etrans; [ | apply id_left]. apply cancel_postcomposition. apply Ha. 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