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Ubyte2p

Recognizer for ubyte2.

Function: ubyte2p

(defun ubyte2p (x)
  (declare (xargs :guard t))
  (mbe :logic (unsigned-byte-p 2 x)
       :exec (and (integerp x) (<= 0 x) (< x 4))))

Theorem: booleanp-of-ubyte2p

(defthm booleanp-of-ubyte2p
  (b* ((yes/no (ubyte2p x)))
    (booleanp yes/no))
  :rule-classes :rewrite)

Theorem: ubyte2p-forward-unsigned-byte-p

(defthm ubyte2p-forward-unsigned-byte-p
  (implies (ubyte2p x)
           (unsigned-byte-p 2 x))
  :rule-classes :forward-chaining)

Theorem: unsigned-byte-p-rewrite-ubyte2p

(defthm unsigned-byte-p-rewrite-ubyte2p
  (equal (unsigned-byte-p 2 x)
         (ubyte2p x)))

Theorem: natp-when-ubyte2p

(defthm natp-when-ubyte2p
  (implies (ubyte2p x) (natp x))
  :rule-classes :compound-recognizer)