Lemma id_2mor_right {C : prebicategory} {a b : C} {f f' : a -1-> b} (alpha : f -2-> f') : alpha ;h; identity (identity1 b) = right_unitor f ;v; alpha ;v; inv_from_z_iso (right_unitor f'). Proof. apply z_iso_inv_on_left. apply pathsinv0. apply (nat_trans_ax (right_unitor_trans a b)). Defined.
Require Import UniMath.Foundations.PartD. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.Categories.StandardCategories. Require Import UniMath.CategoryTheory.HorizontalComposition. Require Import UniMath.CategoryTheory.Equivalences.Core.