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