Lemma rwhisker_rwhisker_CAT {A B C D : category} {F G : [A, B]} {H : [B, C]} {I : [C, D]} (α : [A, B]⟦F, G⟧) : lassociator_CAT _ _ _ · rwhisker_CAT I (rwhisker_CAT H α) = rwhisker_CAT (functor_compose H I) α · lassociator_CAT _ _ _. Proof. apply (nat_trans_eq D); intro c. cbn. rewrite id_left, id_right. apply idpath. Qed.
Require Import UniMath.Foundations.PartD. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.whiskering.