Multiplying N * N bit unsigneds creates an N+N bit unsigned.
This is a common case of lousy-unsigned-byte-p-of-*-mixed, but it also rarely unifies with anything. See also basic-unsigned-byte-p-of-*.
Theorem:
(defthm lousy-unsigned-byte-p-of-* (implies (and (unsigned-byte-p n a) (unsigned-byte-p n b)) (unsigned-byte-p (+ n n) (* a b))))