I think it's by definition that the unique elements of a set is a subset. Nonetheless, the clarification is a good point. To take a stab at a yet more correct

I think it's by definition that the unique elements of a set is a subset. Nonetheless, the clarification is a good point. To take a stab at a yet more correct statement, maybe something like the follows captures it: In the algorithm noted, we are extrapolating the size of the unique elements by looking at additional subsets, which themselves are an equivalence class.