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Ubyte16

Ubyte16p

Recognizer for ubyte16.

Signature
(ubyte16p x) → yes/no
Returns: yes/no — Type (booleanp yes/no).

Definitions and Theorems

Function: ubyte16p

(defun ubyte16p (x)
  (declare (xargs :guard t))
  (mbe :logic (unsigned-byte-p 16 x)
       :exec (and (integerp x)
                  (<= 0 x)
                  (< x 65536))))

Theorem: booleanp-of-ubyte16p

(defthm booleanp-of-ubyte16p
  (b* ((yes/no (ubyte16p x)))
    (booleanp yes/no))
  :rule-classes :rewrite)

Theorem: ubyte16p-forward-unsigned-byte-p

(defthm ubyte16p-forward-unsigned-byte-p
  (implies (ubyte16p x)
           (unsigned-byte-p 16 x))
  :rule-classes :forward-chaining)

Theorem: unsigned-byte-p-rewrite-ubyte16p

(defthm unsigned-byte-p-rewrite-ubyte16p
  (equal (unsigned-byte-p 16 x)
         (ubyte16p x)))

Theorem: natp-when-ubyte16p

(defthm natp-when-ubyte16p
  (implies (ubyte16p x) (natp x))
  :rule-classes :compound-recognizer)