Originally Posted by
Overlord265 Assume that there is a mapping from X to some Y, and a partial function from B to Y. Using the definition of a subset, which states that for every a from A , a belongs to B, I can further assume that set B can be expressed as a union of set A and difference of sets A and B. Now substituting B for the sum in the earlier defined partial function, we can see that the original statement is true in both cases whether A is a proper subset or not. Anyway, I doubt it can be considered as the solid proof.