Lemma whisker_right_inv {C : prebicategory} {a b c : C} {f g : a -1-> b} (alpha : z_iso f g) (h : b -1-> c) : whisker_right (inv_from_z_iso alpha) h = inv_from_z_iso (whisker_right_iso alpha h). Proof. unfold whisker_right. intermediate_path (inv_from_z_iso alpha ;h; inv_from_iso (identity_iso h)). set (W := maponpaths pr1 (iso_inv_of_iso_id h)). simpl in W. rewrite <- W. reflexivity. apply (maponpaths pr1 (inv_horizontal_comp alpha (identity_z_iso h))). 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.