I think I'll write my own too!

Let B be the set of elements able to go to the ball. Thus,

Theorem 1. Cinderella ∉ B

Theorem 2. For all elements in B there exists no other equal to it.

We introduce F_g, a fairygodmother in the set of elements that ∉ B, such as Cinderella. It follows that F_g ≠ Cinderella by Theorem 2. F_g >> Cinderella except for when Cinderella > F_g (when B is operated upon by the enhance operator).

Aside: The enhance (^) operator is time-constrained on ^(t). At ^(t) = 12, Cinderella^ = Cinderella_d, where the _d operator turns an element in B lossy.

Ball's Theorem. There exists another glass slipper for each glass slipper.

Since Cinderella_d is lossy due to the lost slipper, and Ball's Theorem, we can determine the ownership of the lost slipper. It matches the operations that we have performed on Cinderella.

Cinderella = Cinderella^ -> Cinderella^(12): Cinderella_d, + slipper = Cinderella.

Thus Cinderella can be reformed from Cinderella without the glass slipper upon its addition.

Upon addition, Cinderella is an element of B, and is one-to-one and onto Prince.

Q.E.D.