proposition: Lemma SumStrength1 : θ_Strength1 θ.
proof: Proof. intro X. apply nat_trans_eq_alt. intro x; simpl. etrans; [ apply BinCoproductOfArrows_comp |]. apply pathsinv0, BinCoproduct_endo_is_identity. + rewrite BinCoproductOfArrowsIn1. unfold θ_Strength1 in S11. assert (Ha := nat_trans_eq_pointwise (S11 X) x). eapply pathscomp0; [ | apply id_left]. apply cancel_postcomposition. apply Ha. + rewrite BinCoproductOfArrowsIn2. unfold θ_Strength1 in S21. assert (Ha := nat_trans_eq_pointwise (S21 X) x). eapply pathscomp0; [ | 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