Definition disp_hcomp_is_cartesian_2cell {B : bicat} {D : disp_bicat B} (CD : cleaving_of_bicats D) {b₁ b₂ b₃ : B} {f₁ f₂ : b₁ --> b₂} {g₁ g₂ : b₂ --> b₃} {α : f₁ ==> f₂} {β : g₁ ==> g₂} {bb₁ : D b₁} {bb₂ : D b₂} {bb₃ : D b₃} {ff₁ : bb₁ -->[ f₁ ] bb₂} {ff₂ : bb₁ -->[ f₂ ] bb₂} {gg₁ : bb₂ -->[ g₁ ] bb₃} {gg₂ : bb₂ -->[ g₂ ] bb₃} {αα : ff₁ ==>[ α ] ff₂} {ββ : gg₁ ==>[ β ] gg₂} (Hαα : is_cartesian_2cell D αα) (Hββ : is_cartesian_2cell D ββ) : is_cartesian_2cell D (disp_hcomp αα ββ). Proof. use vcomp_is_cartesian_2cell. - apply CD. exact Hαα. - apply CD. exact 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.