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• Bitops/signed-byte-p

Lousy-signed-byte-p-of-mixed-*

Multiplying N-bit signed * N-bit unsigned creates an N+N bit signed.

This is a nice and general theorem but it rarely unifies automatically. See also basic-signed-byte-p-of-mixed-*. Also see lousy-signed-byte-p-of-*.

Definitions and Theorems

Theorem: lousy-signed-byte-p-of-mixed-*

(defthm lousy-signed-byte-p-of-mixed-*
  (implies (and (signed-byte-p n a)
                (unsigned-byte-p n b))
           (signed-byte-p (+ n n) (* a b))))