∀ {X Y : FintypeCat} (f : X ⟶ Y),
  CategoryTheory.CategoryStruct.comp ((CategoryTheory.Functor.id FintypeCat).map f)
      ((fun X => (FintypeCat.equivEquivIso ((FintypeCat.uSwitch.obj X).uSwitchEquiv.trans X.uSwitchEquiv)).symm)
          Y).hom =
    CategoryTheory.CategoryStruct.comp
      ((fun X => (FintypeCat.equivEquivIso ((FintypeCat.uSwitch.obj X).uSwitchEquiv.trans X.uSwitchEquiv)).symm) X).hom
      ((FintypeCat.uSwitch.comp FintypeCat.uSwitch).map f)