case nil =>
  dsimp [appendF.naturatorLax]
  rw [Category.comp_id (Y:=(mapF.obj F).obj bs₂)]
  rw [Category.id_comp (X:=(mapF.obj F).obj as₂)]
  rfl
α : Type u
inst✝¹ : Category α
β : Type v
inst✝ : Category β
F : α ⥤ β
as₁ as₂ bs₁ bs₂ : List α
gs : as₂ ⟶ bs₂
⊢ (Prefunctor.map (Prefunctor.obj mapF.toPrefunctor F).toPrefunctor DVect2.nil ++
        Prefunctor.map (Prefunctor.obj mapF.toPrefunctor F).toPrefunctor gs) ≫
      appendF.naturatorLax F [] bs₂ =
    appendF.naturatorLax F [] as₂ ≫ Prefunctor.map (Prefunctor.obj mapF.toPrefunctor F).toPrefunctor (DVect2.nil ++ gs)
no goals