proposition: Lemma transport_two_cell_FlFr {C : bicat} {A : Type} {X Y : C} (F G : A -> C⟦X,Y⟧) {a₁ a₂ : A} (p : a₁ = a₂) (α : F a₁ ==> G a₁) : transportf (λ z, F z ==> G z) p α = idtoiso_2_1 _ _ (maponpaths G p) o α o (idtoiso_2_1 _ _ (maponpaths F p))^-1.
proof: Proof. induction p ; cbn. rewrite id2_right, id2_left. apply idpath. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.Bicategories.Core.Bicat UniMath.Bicategories.Core.Unitors UniMath.Bicategories.Core.Invertible_2cells UniMath.Bicategories.Morphisms.Adjunctions UniMath.Bicategories.Core.Univalence