∀ {𝒮 : Type u_6} [inst : CategoryTheory.Category.{u_5, u_6} 𝒮] {𝒳 : CategoryTheory.BasedCategory 𝒮}
  {𝒴 : CategoryTheory.BasedCategory 𝒮} {F G : CategoryTheory.BasedFunctor 𝒳 𝒴} (α : F.toFunctor ≅ G.toFunctor)
  (isHomLift' : ∀ (a : 𝒳.obj), 𝒴.p.IsHomLift (CategoryTheory.CategoryStruct.id (𝒳.p.obj a)) (α.hom.app a)),
  CategoryTheory.CategoryStruct.comp
      (let __NatTrans := α.inv;
      { toNatTrans := __NatTrans, isHomLift' := ⋯ })
      (let __NatTrans := α.hom;
      { toNatTrans := __NatTrans, isHomLift' := ⋯ }) =
    CategoryTheory.CategoryStruct.id G