proposition: Lemma linvunitor_natural {X Y : C} {f g : C⟦X, Y⟧} (η : f ==> g) : linvunitor g o η = (η ⋆⋆ id₂ (id₁ X)) o linvunitor f.
proof: Proof. use (vcomp_rcancel (lunitor _ )). { apply is_invertible_2cell_lunitor. } rewrite vassocl. rewrite linvunitor_lunitor. use (vcomp_lcancel (lunitor _ )). { apply is_invertible_2cell_lunitor. } repeat rewrite vassocr. rewrite lunitor_linvunitor. rewrite id2_left, id2_right. apply (! lunitor_natural _ _ _ _ _ ). Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.Bicategories.Core.Bicat UniMath.Bicategories.Core.Invertible_2cells UniMath.Bicategories.Core.Unitors