If an even number is subtracted from an even number, then the remainder is even.

Let the even number *BC* be subtracted from the even number *AB.*

I say that the remainder *CA* is even.

Since *AB* is even, therefore it has a half part. For the same reason *BC* also has a half part, so that the remainder *CA* also has a half part, and *CA* is therefore even.

Therefore, *if an even number is subtracted from an even number, then the remainder is even.*

Q.E.D.