Lemma whisker_left_left {C : prebicategory} {a b c d : C} (f : a -1-> b) (g : b -1-> c) {h i : c -1-> d} (x : h -2-> i) : whisker_left f (whisker_left g x) ;v; associator_2mor f g i = associator_2mor f g h ;v; whisker_left (f ;1; g) x. Proof. unfold whisker_left. etrans; [ apply associator_naturality | idtac]. apply maponpaths. apply maponpaths_2. exact horizontal_comp_id. Defined.
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.Univalence. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.HorizontalComposition. Require Import UniMath.Bicategories.WkCatEnrichment.prebicategory. Require Import UniMath.Bicategories.WkCatEnrichment.whiskering. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.WkCatEnrichment.Notations.