Lemma lwhisker_lwhisker_rassociator (a b c d : C) (f : C⟦a, b⟧) (g : C⟦b, c⟧) (h i : c --> d) (x : h ==> i) : rassociator f g h • (f ◃ (g ◃ x)) = (f · g ◃ x) • rassociator _ _ _ . Proof. apply (vcomp_lcancel (lassociator f g h)). { apply is_invertible_2cell_lassociator. } etrans. { etrans; [ apply vassocr |]. apply maponpaths_2. apply lassociator_rassociator. } etrans; [ apply id2_left |]. apply (vcomp_rcancel (lassociator f g 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, lwhisker_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.