proposition: Lemma disp_actionbicat_disp_id_triangle {a : B} {FA : V ⟶ category_from_bicat_and_ob a} (FAm : fmonoidal Mon_V (monoidal_from_bicat_and_ob a) FA): param_distr_bicat_triangle_eq Mon_V FAm FAm (id₁ a) (disp_actionbicat_disp_id_nat_trans FAm).
proof: Proof. red; cbn. rewrite vassocr. rewrite vcomp_lunitor. do 2 rewrite vassocl. rewrite lunitor_id_is_left_unit_id. apply maponpaths. apply pathsinv0, (rhs_right_inv_cell _ _ _ (is_invertible_2cell_runitor _)). rewrite vassocl. apply pathsinv0, (rhs_left_inv_cell _ _ _ (is_invertible_2cell_lunitor _)). rewrite vcomp_runitor. rewrite lunitor_id_is_left_unit_id. apply idpath. 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.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.Bicategories.MonoidalCategories.EndofunctorsWhiskeredMonoidal UniMath.Bicategories.MonoidalCategories.WhiskeredMonoidalFromBicategory UniMath.Bicategories.MonoidalCategories.ActionBasedStrongFunctorsWhiskeredMonoidal UniMath.Bicategories.Core.Bicat UniMath.Bicategories.Core.BicategoryLaws UniMath.Bicategories.Core.Unitors UniMath.Bicategories.DisplayedBicats.DispBicat UniMath.Bicategories.Core.Invertible_2cells