proposition: Lemma ProductStrength2' : θ_Strength2_int θ.
proof: Proof. clear S11 S12 S21 S22 S11' S21'; intros X Z Z'. apply nat_trans_eq_alt; intro x; simpl. rewrite id_left. eapply pathscomp0; [apply BinProductOfArrows_comp|]. apply pathsinv0. eapply pathscomp0; [apply BinProductOfArrows_comp|]. apply pathsinv0, maponpaths_12. - assert (Ha_x := nat_trans_eq_pointwise (S12' X Z Z') x). simpl in Ha_x; rewrite id_left in Ha_x. exact Ha_x. - assert (Ha_x := nat_trans_eq_pointwise (S22' X Z Z') x). simpl in Ha_x; rewrite id_left in Ha_x. exact 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.BinProducts 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.exponentials