Lemma disp_lhs_right_invert_cell {a b : C} {f g h : a --> b} {x : f ==> g} {y : g ==> h} {z : f ==> h} (inv_y : is_invertible_2cell y) {aa : D a} {bb : D b} {ff : aa -->[f] bb} {gg : aa -->[g] bb} {hh : aa -->[h] bb} (xx : ff ==>[x] gg) (yy : gg ==>[y] hh) (zz : ff ==>[z] hh) (H : is_disp_invertible_2cell inv_y yy) (q : x • y = z) (p := rhs_right_inv_cell _ _ _ inv_y q : x = z • inv_y^-1) (pp : xx = transportb (λ x, _ ==>[x] _) p (zz •• disp_inv_cell ((yy,,H):disp_invertible_2cell (y,,inv_y) gg hh))) : xx •• yy = transportb (λ x, _ ==>[x] _) q zz. Proof. etrans. { use (disp_lhs_right_invert_cell' _ _ _ _ pp). } apply maponpaths_2. apply cellset_property. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Total. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.Core.Univalence.