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Word

Wordp

Recognizer for word.

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

Definitions and Theorems

Function: wordp

(defun wordp (x)
 (declare (xargs :guard t))
 (mbe
  :logic (unsigned-byte-p 256 x)
  :exec
  (and
   (integerp x)
   (<= 0 x)
   (<
    x
    115792089237316195423570985008687907853269984665640564039457584007913129639936))))

Theorem: booleanp-of-wordp

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

Theorem: wordp-forward-unsigned-byte-p

(defthm wordp-forward-unsigned-byte-p
  (implies (wordp x)
           (unsigned-byte-p 256 x))
  :rule-classes :forward-chaining)

Theorem: unsigned-byte-p-rewrite-wordp

(defthm unsigned-byte-p-rewrite-wordp
  (equal (unsigned-byte-p 256 x)
         (wordp x)))

Theorem: natp-when-wordp

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