Lemma id_2mor_left {C : prebicategory} {b c : C} {g g' : b -1-> c} (β : g -2-> g') : identity (identity1 b) ;h; β = left_unitor g ;v; β ;v; inv_from_z_iso (left_unitor g'). Proof. apply z_iso_inv_on_left. apply pathsinv0. apply (nat_trans_ax (left_unitor_trans b c)). 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.