Definition vcomp_disp_invertible {B : bicat} {D : disp_bicat B} {a b : B} {aa : D a} {bb : D b} {f g h : a --> b} {ff : aa -->[ f ] bb} {gg : aa -->[ g ] bb} {hh : aa -->[ h ] bb} {α : invertible_2cell f g} {β : invertible_2cell g h} (αα : disp_invertible_2cell α ff gg) (ββ : disp_invertible_2cell β gg hh) : disp_invertible_2cell (comp_of_invertible_2cell α β) ff hh. Proof. use tpair. { repeat use tpair. exact (αα •• ββ). } apply vcomp_disp_is_invertible. Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Isos. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Import DispBicat.Notations. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Core.Invertible_2cells.