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• Bitops/signed-byte-p

Basic-signed-byte-p-of-floor-split

Floor of an N-bit signed by an integer is usually an N-bit signed. (Strong form, case splitting, disabled by default).

See also basic-signed-byte-p-of-floor.

Definitions and Theorems

Theorem: basic-signed-byte-p-of-floor-split

(defthm basic-signed-byte-p-of-floor-split
  (implies (and (signed-byte-p n a) (integerp b))
           (equal (signed-byte-p n (floor a b))
                  (not (and (equal a (- (expt 2 (- n 1))))
                            (equal b -1))))))