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Polarity4

Polarity4-p

Recognizer for polarity4 bit structures.

Signature
(polarity4-p x) → *

Definitions and Theorems

Function: polarity4-p

(defun polarity4-p (x)
  (declare (xargs :guard t))
  (let ((__function__ 'polarity4-p))
    (declare (ignorable __function__))
    (mbe :logic (unsigned-byte-p 4 x)
         :exec (and (natp x) (< x 16)))))

Theorem: polarity4-p-when-unsigned-byte-p

(defthm polarity4-p-when-unsigned-byte-p
  (implies (unsigned-byte-p 4 x)
           (polarity4-p x)))

Theorem: unsigned-byte-p-when-polarity4-p

(defthm unsigned-byte-p-when-polarity4-p
  (implies (polarity4-p x)
           (unsigned-byte-p 4 x)))

Theorem: polarity4-p-compound-recognizer

(defthm polarity4-p-compound-recognizer
  (implies (polarity4-p x) (natp x))
  :rule-classes :compound-recognizer)