proposition: Lemma actionbased_strength_pentagon_eq_fromvariant1 (ϛ : actionbased_strength_nat): actionbased_strength_pentagon_eq_variant1 ϛ -> actionbased_strength_pentagon_eq ϛ.
proof: Proof. intros Heq a v w. red in Heq. unfold nat_z_iso_to_trans_inv in Heq; cbn in Heq. unfold is_z_isomorphism_mor in Heq. apply pathsinv0. apply (z_iso_inv_to_left _ _ _ (make_z_iso _ _ (pr2 χ' ((F a, v), w)))). cbn. apply pathsinv0. do 2 rewrite assoc. apply Heq. 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