Definition vcomp_is_cartesian_2cell {B : bicat} {D : disp_bicat B} {x y : B} {f g h : x --> y} {α : f ==> g} {β : g ==> h} {xx : D x} {yy : D y} {ff : xx -->[ f ] yy} {gg : xx -->[ g ] yy} {hh : xx -->[ h ] yy} {αα : ff ==>[ α ] gg} {ββ : gg ==>[ β ] hh} (Hαα : is_cartesian_2cell D αα) (Hββ : is_cartesian_2cell D ββ) : is_cartesian_2cell D (αα •• ββ). Proof. apply cartesian_to_cartesian_2cell. exact (@is_cartesian_comp_disp _ (disp_hom xx yy) f ff g gg h hh α β αα ββ (cartesian_2cell_to_cartesian _ Hαα) (cartesian_2cell_to_cartesian _ Hββ)). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Fibrations. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Core.TransportLaws. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Import DispBicat.Notations. Require Import UniMath.Bicategories.DisplayedBicats.DispInvertibles.