Lemma rhs_right_inv_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 • y = z -> x = z • inv_y^-1. Proof. intro H1. apply (vcomp_rcancel _ inv_y). etrans. { apply H1. } etrans. 2: apply vassocr. apply pathsinv0. etrans. { apply maponpaths. apply vcomp_linv. } 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.