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Ubyte1p

Recognizer for ubyte1.

Function: ubyte1p

(defun ubyte1p (x)
  (declare (xargs :guard t))
  (mbe :logic (unsigned-byte-p 1 x)
       :exec (and (integerp x) (<= 0 x) (< x 2))))

Theorem: booleanp-of-ubyte1p

(defthm booleanp-of-ubyte1p
  (b* ((yes/no (ubyte1p x)))
    (booleanp yes/no))
  :rule-classes :rewrite)

Theorem: ubyte1p-forward-unsigned-byte-p

(defthm ubyte1p-forward-unsigned-byte-p
  (implies (ubyte1p x)
           (unsigned-byte-p 1 x))
  :rule-classes :forward-chaining)

Theorem: unsigned-byte-p-rewrite-ubyte1p

(defthm unsigned-byte-p-rewrite-ubyte1p
  (equal (unsigned-byte-p 1 x)
         (ubyte1p x)))

Theorem: natp-when-ubyte1p

(defthm natp-when-ubyte1p
  (implies (ubyte1p x) (natp x))
  :rule-classes :compound-recognizer)