Lemma triangle_identity' {C : prebicategory} {a b c : C} (f : a -1-> b) (g : b -1-> c) : right_unitor_2mor f ;h; identity g = inv_from_z_iso (associator f (identity1 b) g) ;v; (identity _ ;h; left_unitor_2mor _). Proof. refine (!_). use z_iso_inv_on_right. apply triangle_axiom. Qed.
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.