Lemma rhs_left_inv_cell {a b : C} {f g h : a --> b} (x : g ==> h) (y : f ==> g) (z : f ==> h) (inv_y : is_invertible_2cell y) : y • x = z -> x = inv_y^-1 • z. Proof. intro H1. apply (vcomp_lcancel _ inv_y). etrans. { apply H1. } etrans. 2: apply vassocl. apply pathsinv0. etrans. { apply maponpaths_2. apply (vcomp_rinv inv_y). } apply id2_left. 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.