Lemma left_unitor_id_is_right_unitor_id {C : prebicategory} {a : C} : left_unitor_2mor (identity1 a) = right_unitor_2mor (identity1 a). Proof. apply whisker_right_id_inj. use (pre_comp_with_z_iso_is_inj (associator _ _ _)). intermediate_path (left_unitor_2mor ((identity1 a) ;1; (identity1 a))). apply pathsinv0. apply kelly_left. intermediate_path (whisker_left (identity1 a) (left_unitor (identity1 a))). apply pathsinv0. apply left_unitor_on_id. apply (triangle_axiom (identity1 a) (identity1 a)). 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.