proposition: Lemma triangle_eq_from_alt : actionbased_strength_triangle_eq actionA actionA' F strength_nat_from_alt.
proof: Proof. red. intro a. apply param_distr_triangle_eq_variant_follows in δ_triangle_eq. red in δ_triangle_eq. apply (maponpaths pr1) in δ_triangle_eq. apply toforallpaths in δ_triangle_eq. assert (δ_triangle_eq_inst := δ_triangle_eq a). clear δ_triangle_eq δ_pentagon_eq. cbn in δ_triangle_eq_inst. unfold strength_nat_from_alt, actionA, actionA'. cbn. do 3 rewrite id_left. rewrite id_right. exact δ_triangle_eq_inst. Qed.
imports: UniMath.Foundations.PartD UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.HorizontalComposition UniMath.CategoryTheory.Monoidal.Categories UniMath.CategoryTheory.Monoidal.Functors UniMath.Bicategories.MonoidalCategories.EndofunctorsMonoidal UniMath.Bicategories.MonoidalCategories.Actions UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors UniMath.CategoryTheory.Monoidal.AlternativeDefinitions.MonoidalCategoriesTensored UniMath.CategoryTheory.Monoidal.AlternativeDefinitions.MonoidalFunctorsTensored UniMath.Bicategories.MonoidalCategories.EndofunctorsWhiskeredMonoidal UniMath.Bicategories.Core.Bicat UniMath.Bicategories.Core.Examples.BicatOfCats