object Fix2 {
  type Fix2_1[F1[_, _], F2[_, _]]
  type Fix2_2[F1[_, _], F2[_, _]]

  final class Subst[F1[_, _], F2[_, _]] {
    type Apply[H[_, _]]  = H[F1, F2]
    type ApplyF[H[_, _]] = H[Apply[Fix2_1], Apply[Fix2_2]]

    def _1[H[_]](f: H[Apply[Fix2_1]]): H[ApplyF[F1]] = f.asInstanceOf[H[ApplyF[F1]]]
    def _2[H[_]](f: H[Apply[Fix2_2]]): H[ApplyF[F2]] = f.asInstanceOf[H[ApplyF[F2]]]
  }

  private[this] val _subst = new Subst[Any, Any]
  def subst[F1[_, _], F2[_, _]]: Subst[F1, F2] = _subst.asInstanceOf[Subst[F1, F2]]
}

object Fix3 {
  type Fix3_1[F1[_, _, _], F2[_, _, _], F3[_, _, _]]
  type Fix3_2[F1[_, _, _], F2[_, _, _], F3[_, _, _]]
  type Fix3_3[F1[_, _, _], F2[_, _, _], F3[_, _, _]]

  final class Subst[F1[_, _, _], F2[_, _, _], F3[_, _, _]] {
    type Apply[H[_, _, _]]  = H[F1, F2, F3]
    type ApplyF[H[_, _, _]] = H[Apply[Fix3_1], Apply[Fix3_2], Apply[Fix3_3]]

    def _1[H[_]](f: H[Apply[Fix3_1]]): H[ApplyF[F1]] = f.asInstanceOf[H[ApplyF[F1]]]
    def _2[H[_]](f: H[Apply[Fix3_2]]): H[ApplyF[F2]] = f.asInstanceOf[H[ApplyF[F2]]]
    def _3[H[_]](f: H[Apply[Fix3_3]]): H[ApplyF[F3]] = f.asInstanceOf[H[ApplyF[F3]]]
  }

  private[this] val _subst = new Subst[Any, Any, Any]
  def subst[F1[_, _, _], F2[_, _, _], F3[_, _, _]]: Subst[F1, F2, F3]
  = _subst.asInstanceOf[Subst[F1, F2, F3]]
}