proposition: Lemma ProductStrength1' : θ_Strength1_int θ.
proof: Proof. clear S11 S12 S21 S22 S12' S22'; intro X. apply nat_trans_eq_alt; intro x. eapply pathscomp0; [ apply BinProductOfArrows_comp |]. apply pathsinv0, BinProduct_endo_is_identity. + rewrite BinProductOfArrowsPr1. eapply pathscomp0; [ | apply id_right]; apply maponpaths. exact (nat_trans_eq_pointwise (S11' X) x). + rewrite BinProductOfArrowsPr2. eapply pathscomp0; [ | apply id_right]; apply maponpaths. exact (nat_trans_eq_pointwise (S21' X) 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