proposition: Lemma ProductStrength2 : θ_Strength2 θ.
proof: Proof. intros X Z Z' Y α. apply nat_trans_eq_alt; intro x. eapply pathscomp0; [ apply BinProductOfArrows_comp |]. apply pathsinv0. eapply pathscomp0; [ apply cancel_postcomposition; simpl; apply BinProductOfArrows_comp|]. eapply pathscomp0; [ apply BinProductOfArrows_comp|]. apply pathsinv0, maponpaths_12. - assert (Ha := S12 X Z Z' Y α); simpl in Ha. apply (nat_trans_eq_pointwise Ha x). - assert (Ha := S22 X Z Z' Y α); simpl in Ha. apply (nat_trans_eq_pointwise 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