proposition: Lemma param_distr_bicat_pentagon_eq_body_variant_implies (δ : parameterized_distributivity_bicat_nat) (v w : V): param_distr_bicat_pentagon_eq_body_variant δ v w -> param_distr_bicat_pentagon_eq_body δ v w.
proof: Proof. intro Hyp. red in Hyp. unfold param_distr_bicat_pentagon_eq_body_variant_RHS in Hyp. apply pathsinv0, (rhs_left_inv_cell _ _ _ (lwhisker_with_μ_inv_inv2cell v w)) in Hyp. apply (rhs_left_inv_cell _ _ _ (is_invertible_2cell_lassociator _ _ _)), pathsinv0 in Hyp. etrans. 2: { exact Hyp. } apply vassocl. 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.FunctorCategory UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.Categories.Dialgebras UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Total UniMath.CategoryTheory.DisplayedCats.Constructions UniMath.CategoryTheory.Monoidal.Categories UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors UniMath.CategoryTheory.Monoidal.Functors UniMath.CategoryTheory.Monoidal.Displayed.WhiskeredDisplayedBifunctors UniMath.CategoryTheory.Monoidal.Displayed.Monoidal UniMath.CategoryTheory.Monoidal.Displayed.TotalMonoidal UniMath.CategoryTheory.Monoidal.Displayed.MonoidalSections UniMath.Bicategories.MonoidalCategories.EndofunctorsWhiskeredMonoidal UniMath.Bicategories.MonoidalCategories.Actions UniMath.Bicategories.MonoidalCategories.ActionBasedStrength UniMath.Bicategories.MonoidalCategories.WhiskeredMonoidalFromBicategory UniMath.Bicategories.Core.Bicat UniMath.Bicategories.Core.BicategoryLaws UniMath.Bicategories.Core.Unitors UniMath.Bicategories.Core.Invertible_2cells UniMath.Bicategories.Core.Examples.BicatOfCats