Zeta transform

This is Inclusion-Exclusion.

Then, this is the Zeta transform.

Moreover, this is the inversion.

You prove this.

At first, you use the Zeta transform.

You put the inversion.

You remove the gray area.

You divide S and R.

This is Inclusion-Exclusion.

You got f(R).

Therefore, the Zeta transform is feasible.