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• Bitops/signed-byte-p

Basic-unsigned-byte-p-of-*

Multiplying constant N * N bit unsigneds creates an N+N bit unsigned.

This is a less general but more automatic lousy-unsigned-byte-p-of-* for reasoning about constant widths. The use of division here looks awful, but note the syntaxp hyp. This will let us get us things like:

(unsigned-byte-p 32 (* a b))

When we know that (unsigned-byte-p 16 a) and (unsigned-byte-p 16 b).

Definitions and Theorems

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

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