Lemma lhs_left_invert_cell {a b : C} {f g h : a --> b} (x : f ==> g) (y : g ==> h) (z : f ==> h) (inv_x : is_invertible_2cell x) : y = inv_x^-1 • z -> x • y = z. Proof. intro H1. etrans. { apply maponpaths. apply H1. } etrans. { apply vassocr. } etrans. { apply maponpaths_2. apply (vcomp_rinv inv_x). } 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.