proposition: Lemma signature_from_ab_strength_law2 : θ_Strength2_int θ_for_signature.
proof: Proof. intros X Z Z'. apply nat_trans_eq_alt. intro c. etrans. 2: { apply assoc. } etrans. 2: { apply maponpaths. exact (test' X Z Z' c). } simpl. etrans. 2: { apply pathsinv0. apply id_left. } etrans. 2: { apply cancel_postcomposition. apply pathsinv0. apply remove_id_left. - etrans. { apply id_left. } apply functor_id. - apply idpath. } simpl. apply maponpaths_12. - apply idpath. - apply nat_trans_eq_pointwise. clear c. apply maponpaths. apply nat_trans_eq_alt. intro c. etrans. 2: { apply pathsinv0. apply id_right. } apply pathsinv0. simpl. apply functor_id. Qed.
imports: UniMath.Foundations.PartD UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.PointedFunctors UniMath.CategoryTheory.HorizontalComposition UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.Monoidal.AlternativeDefinitions.MonoidalCategoriesTensored UniMath.CategoryTheory.Monoidal.AlternativeDefinitions.MonoidalFunctorsTensored UniMath.CategoryTheory.Adjunctions.Core UniMath.CategoryTheory.Equivalences.Core UniMath.Bicategories.MonoidalCategories.PointedFunctorsMonoidal UniMath.Bicategories.MonoidalCategories.Actions UniMath.Bicategories.MonoidalCategories.ConstructionOfActions UniMath.Bicategories.MonoidalCategories.ActionOfEndomorphismsInBicat UniMath.Bicategories.MonoidalCategories.ActionBasedStrength UniMath.Bicategories.MonoidalCategories.MonoidalFromBicategory UniMath.Bicategories.MonoidalCategories.ActionBasedStrongFunctorCategory UniMath.Bicategories.Core.Bicat UniMath.Bicategories.Core.Examples.BicatOfCats UniMath.SubstitutionSystems.Signatures UniMath.SubstitutionSystems.SignatureCategory UniMath.CategoryTheory.Core.Univalence