Lemma triangle_eq_from_alt : actionbased_strength_triangle_eq actionA actionA' F strength_nat_from_alt. 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.
Require Import UniMath.Foundations.PartD. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.HorizontalComposition. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monoidal.Functors. Require Import UniMath.Bicategories.MonoidalCategories.EndofunctorsMonoidal. Require Import UniMath.Bicategories.MonoidalCategories.Actions. Require Import UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors. Require Import UniMath.CategoryTheory.Monoidal.AlternativeDefinitions.MonoidalCategoriesTensored. Require Import UniMath.CategoryTheory.Monoidal.AlternativeDefinitions.MonoidalFunctorsTensored. Require Import UniMath.Bicategories.MonoidalCategories.EndofunctorsWhiskeredMonoidal. Require Import UniMath.Bicategories.Core.Bicat. Require Import UniMath.Bicategories.Core.Examples.BicatOfCats. Import MonoidalNotations. Import BifunctorNotations. Import MonoidalNotations.