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• Bitops/signed-byte-p

Basic-signed-byte-p-of-+-with-cin

Adding N+1 bit signeds with a carry bit creates an N+1 bit signed.

ACL2's fancy unification stuff means this works fine in the common case that you're dealing with quoted constants for N and N+1. See also basic-signed-byte-p-of-+.

Definitions and Theorems

Theorem: basic-signed-byte-p-of-+-with-cin

(defthm basic-signed-byte-p-of-+-with-cin
  (implies (and (bitp cin)
                (signed-byte-p n a)
                (signed-byte-p n b))
           (signed-byte-p (+ 1 n) (+ cin a b)))
  :rule-classes
  ((:rewrite)
   (:rewrite
        :corollary (implies (and (bitp cin)
                                 (signed-byte-p n a)
                                 (signed-byte-p n b))
                            (signed-byte-p (+ 1 n) (+ cin a b))))))