Lemma lwhisker_id_inj {a b : C} (f g : C⟦a, b⟧) (x y : f ==> g) : identity a ◃ x = identity a ◃ y → x = y. Proof. intro H. apply (vcomp_lcancel (lunitor _)). - apply is_invertible_2cell_lunitor. - etrans. { apply pathsinv0, vcomp_lunitor. } etrans. 2: apply vcomp_lunitor. apply maponpaths_2. apply H. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.Examples.OpMorBicat. Require Import UniMath.Bicategories.Core.Examples.OpCellBicat.