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• Bitops/signed-byte-p

Basic-signed-byte-p-of-*

Multiplying constant N * N bit signeds creates an N+N bit signed.

This is a less general but more automatic version of lousy-signed-byte-p-of-*. It's good for constant widths.

The use of division here looks awful, but note the syntaxp hyp: we'll only do these divisions when we know n is a constant, e.g., this will let us know that 16-bit multiplication gives us a 32-bit result.

See also basic-signed-byte-p-of-mixed-*.

Definitions and Theorems

Theorem: basic-signed-byte-p-of-*

(defthm basic-signed-byte-p-of-*
  (implies (and (syntaxp (quotep n))
                (natp n)
                (signed-byte-p (/ n 2) a)
                (signed-byte-p (/ n 2) b))
           (signed-byte-p n (* a b))))