		Search-engine friendly clone of the ACL2 documentation.

Uchar-integer

Uchar-integerp

Recognizer for uchar-integer.

Signature
(uchar-integerp x) → yes/no
Returns: yes/no — Type (booleanp yes/no).

Definitions and Theorems

Function: uchar-integerp

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

Theorem: booleanp-of-uchar-integerp

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

Theorem: uchar-integerp-forward-unsigned-byte-p

(defthm uchar-integerp-forward-unsigned-byte-p
  (implies (uchar-integerp x)
           (unsigned-byte-p (char-bits) x))
  :rule-classes :forward-chaining)

Theorem: unsigned-byte-p-rewrite-uchar-integerp

(defthm unsigned-byte-p-rewrite-uchar-integerp
  (equal (unsigned-byte-p (char-bits) x)
         (uchar-integerp x)))

Theorem: natp-when-uchar-integerp

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