Lemma 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) : x = z • inv_y^-1 -> x • y = z. Proof. intro H1. etrans. { apply maponpaths_2. apply H1. } etrans. { apply vassocl. } etrans. { apply maponpaths. apply (vcomp_linv inv_y). } apply id2_right. 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.