Lemma whisker_left_id_inj {C : prebicategory} {b c : C} {g h : b -1-> c} (alpha alpha' : g -2-> h) : whisker_left (identity1 _) alpha = whisker_left (identity1 _) alpha' -> alpha = alpha'. Proof. intros w. intermediate_path (inv_from_z_iso (left_unitor _) ;v; whisker_left (identity1 _) alpha ;v; left_unitor _ ). apply pathsinv0. apply z_iso_inv_to_right. apply z_iso_inv_on_right. rewrite assoc. apply whisker_left_id_1mor. intermediate_path (inv_from_z_iso (left_unitor _) ;v; whisker_left (identity1 _) alpha' ;v; left_unitor _ ). apply cancel_postcomposition. apply cancel_precomposition. assumption. apply z_iso_inv_to_right. apply z_iso_inv_on_right. rewrite assoc. apply whisker_left_id_1mor. Defined.
Require Import UniMath.Foundations.PartD. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.Categories.StandardCategories. Require Import UniMath.CategoryTheory.HorizontalComposition. Require Import UniMath.CategoryTheory.Equivalences.Core. Require Import UniMath.Bicategories.WkCatEnrichment.prebicategory. Require Import UniMath.Bicategories.WkCatEnrichment.Notations.