Lemma vcomp_move_L_Mp {C : bicat} {X Y : C} {f g h : C⟦X,Y⟧} (η₁ : f ==> h) (η₂ : f ==> g) (ε : g ==> h) (Hε : is_invertible_2cell ε) : Hε^-1 o η₁ = η₂ -> η₁ = ε o η₂. Proof. intros. rewrite <- (id2_right η₁). rewrite <- (vcomp_linv Hε). rewrite vassocr. apply maponpaths_2. assumption. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations.