Lemma inv_cell_eq {C : bicat} {a b : C} {f g : C ⟦a, b⟧} (x y : f ==> g) (inv_x : is_invertible_2cell x) (inv_y : is_invertible_2cell y) (p : inv_x^-1 = inv_y^-1) : x = y. Proof. apply (vcomp_rcancel _ (is_invertible_2cell_inv inv_x)). rewrite vcomp_rinv, p. apply (!vcomp_rinv _). Qed.
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.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.PrecategoryBinProduct.