Lemma twomor_naturality {C : prebicategory} {a b c : C} {f g : a -1-> b} {h k : b -1-> c} (gamma : f -2-> g) (delta : h -2-> k) : (whisker_right gamma h) ;v; (whisker_left g delta) = (whisker_left f delta) ;v; (whisker_right gamma k). Proof. unfold whisker_left, whisker_right. intermediate_path ((gamma ;v; identity g);h;(identity h ;v; delta)). apply pathsinv0. apply interchange. intermediate_path ((identity f ;v; gamma);h;(delta ;v; identity k)). rewrite !id_left, !id_right. reflexivity. 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.