Definition disp_actionbicat_disp_id_comp : disp_cat_id_comp B disp_actionbicat_disp_ob_mor. Proof. split. - intros a [FA FAm]. use tpair. + exact (disp_actionbicat_disp_id_nat_trans FAm). + split; [apply disp_actionbicat_disp_id_triangle | apply disp_actionbicat_disp_id_pentagon]; assumption. - intros a0 a1 a2 g1 g2 [FA FAm] [FA' FA'm] [FA'' FA''m] Hyp1 Hyp2. cbn in Hyp1, Hyp2. exists (disp_actionbicat_disp_comp_nat_trans Hyp1 Hyp2). + split; [apply disp_actionbicat_disp_comp_triangle | apply disp_actionbicat_disp_comp_pentagon]; assumption. Defined.
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.