Lemma whisker_left_on_comp {C : prebicategory} {a b c : C} (f : a -1-> b) {g h i : b -1-> c} (alpha : g -2-> h) (alpha' : h -2-> i) : whisker_left f (alpha ;v; alpha') = whisker_left f alpha ;v; whisker_left f alpha'. Proof. unfold whisker_left. intermediate_path ((identity f;v; identity f);h;(alpha;v;alpha')). rewrite id_left. reflexivity. now apply interchange. 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.