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Ullong-integer

Ullong-integerp

Recognizer for ullong-integer.

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

Definitions and Theorems

Function: ullong-integerp

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

Theorem: booleanp-of-ullong-integerp

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

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

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

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

(defthm unsigned-byte-p-rewrite-ullong-integerp
  (equal (unsigned-byte-p (llong-bits) x)
         (ullong-integerp x)))

Theorem: natp-when-ullong-integerp

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