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Byte

Bytep

Recognizer for byte.

Signature
(bytep x) → yes/no
Returns: yes/no — Type (booleanp yes/no).

Definitions and Theorems

Function: bytep

(defun bytep (x)
  (declare (xargs :guard t))
  (mbe :logic (unsigned-byte-p (char-bit) x)
       :exec (and (integerp x)
                  (<= 0 x)
                  (< x (expt 2 (char-bit))))))

Theorem: booleanp-of-bytep

(defthm booleanp-of-bytep
  (b* ((yes/no (bytep x)))
    (booleanp yes/no))
  :rule-classes :rewrite)

Theorem: bytep-forward-unsigned-byte-p

(defthm bytep-forward-unsigned-byte-p
  (implies (bytep x)
           (unsigned-byte-p (char-bit) x))
  :rule-classes :forward-chaining)

Theorem: unsigned-byte-p-rewrite-bytep

(defthm unsigned-byte-p-rewrite-bytep
  (equal (unsigned-byte-p (char-bit) x)
         (bytep x)))

Theorem: natp-when-bytep

(defthm natp-when-bytep
  (implies (bytep x) (natp x))
  :rule-classes :compound-recognizer)