∀ {α : Type u_2} [inst : Monoid α],
  Set.monoid =
    { toSemigroup := Set.semigroup, toOne := Set.mulOneClass.toOne, one_mul := ⋯, mul_one := ⋯, npow := npowRecAuto,
      npow_zero := ⋯, npow_succ := ⋯ }