proposition: Lemma actionbased_strength_eq {F : A ⟶ A'} (sη sη': actionbased_strength F) : pr1 sη = pr1 sη' -> sη = sη'.
proof: Proof. intro Heq. apply subtypePath; trivial. intro ϛ. apply isapropdirprod. + apply isaprop_actionbased_strength_triangle_eq. + apply isaprop_actionbased_strength_pentagon_eq. 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