Lemma rwhisker_lwhisker_rassociator (a b c d : C) (f : C⟦a, b⟧) (g h : C⟦b, c⟧) (i : c --> d) (x : g ==> h) : rassociator _ _ _ • (f ◃ (x ▹ i)) = ((f ◃ x) ▹ i) • rassociator _ _ _ . Proof. apply (vcomp_lcancel (lassociator f g i)). { apply is_invertible_2cell_lassociator. } etrans. { etrans; [ apply vassocr |]. apply maponpaths_2. apply lassociator_rassociator. } etrans; [ apply id2_left |]. apply (vcomp_rcancel (lassociator f h i)). { apply is_invertible_2cell_lassociator. } apply pathsinv0. etrans; [ apply vassocl |]. etrans. { apply maponpaths. apply vassocl. } etrans. { do 2 apply maponpaths. apply rassociator_lassociator. } etrans. { apply maponpaths. apply id2_right. } apply pathsinv0, rwhisker_lwhisker. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.PrecategoryBinProduct.