Lemma linvunitor_assoc {X Y Z : C} (g : C⟦Y,Z⟧) (f : C⟦X,Y⟧) : linvunitor (g ∘ f) = rassociator (id₁ X) f g o (g ◅ (linvunitor f)). Proof. use vcomp_move_L_pM. { is_iso. } cbn. use vcomp_move_R_Mp. { is_iso. } cbn. rewrite <- lunitor_triangle. rewrite vassocr. rewrite rassociator_lassociator. rewrite id2_left. apply idpath. 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.