proposition: Lemma App_θ_strength2_int: θ_Strength2_int App_θ.
proof: Proof. red. intros. unfold App_θ, App_H. simpl. unfold App_θ_data. apply nat_trans_eq; [apply homset_property |]. intro c. simpl. do 3 rewrite id_left. unfold binproduct_nat_trans_data. apply pathsinv0. apply BinProductArrowUnique. + rewrite id_left. simpl. rewrite id_right. apply idpath. + rewrite id_left. simpl. rewrite id_right. apply idpath. Qed.
imports: UniMath.Foundations.PartD UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.PointedFunctors UniMath.CategoryTheory.HorizontalComposition UniMath.CategoryTheory.PointedFunctorsComposition UniMath.CategoryTheory.PrecategoryBinProduct UniMath.SubstitutionSystems.Signatures UniMath.CategoryTheory.BicatOfCatsElementary UniMath.SubstitutionSystems.BinSumOfSignatures UniMath.SubstitutionSystems.Notation UniMath.CategoryTheory.Chains.Chains UniMath.CategoryTheory.Chains.OmegaCocontFunctors UniMath.CategoryTheory.exponentials UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.Limits.Graphs.Colimits