Lemma rinvunitor_natural {X Y : C} {f g : C⟦X, Y⟧} (η : f ==> g) : rinvunitor g o η = (id₂ (id₁ Y) ⋆⋆ η) o rinvunitor f. Proof. use (vcomp_rcancel (runitor _ )). { apply is_invertible_2cell_runitor. } rewrite vassocl. rewrite rinvunitor_runitor. use (vcomp_lcancel (runitor _ )). { apply is_invertible_2cell_runitor. } repeat rewrite vassocr. rewrite runitor_rinvunitor. rewrite id2_left, id2_right. apply (! runitor_natural _ _ _ _ _ ). 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.Unitors.