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. 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.
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.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Total. Require Import UniMath.CategoryTheory.DisplayedCats.Constructions. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Functors. Require Import UniMath.CategoryTheory.Monoidal.Displayed.WhiskeredDisplayedBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Displayed.Monoidal. Require Import UniMath.CategoryTheory.Monoidal.Displayed.TotalMonoidal. Require Import UniMath.Bicategories.MonoidalCategories.EndofunctorsWhiskeredMonoidal. Require Import UniMath.Bicategories.MonoidalCategories.WhiskeredMonoidalFromBicategory. Require Import UniMath.Bicategories.MonoidalCategories.ActionBasedStrongFunctorsWhiskeredMonoidal. Require Import UniMath.Bicategories.Core.Bicat. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Require Import UniMath.Bicategories.Core.Invertible_2cells. Import Bicat.Notations. Import BifunctorNotations. Import DisplayedBifunctorNotations.