Lemma whisker_right_id_inj {C : prebicategory} {a b : C} {f g : a -1-> b} (alpha alpha' : f -2-> g) : whisker_right alpha (identity1 _) = whisker_right alpha' (identity1 _) -> alpha = alpha'. Proof. intros w. intermediate_path (inv_from_z_iso (right_unitor _) ;v; whisker_right alpha (identity1 _) ;v; right_unitor _ ). apply pathsinv0. apply z_iso_inv_to_right. apply z_iso_inv_on_right. rewrite assoc. apply whisker_right_id_1mor. intermediate_path (inv_from_z_iso (right_unitor _) ;v; whisker_right alpha' (identity1 _) ;v; right_unitor _ ). apply cancel_postcomposition. apply cancel_precomposition. assumption. apply z_iso_inv_to_right. apply z_iso_inv_on_right. rewrite assoc. apply whisker_right_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.