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S4vecs

S3vec-p

Signature
(s3vec-p x) → bool
Arguments: x — Guard (s4vec-p x).

Definitions and Theorems

Function: s3vec-p

(defun s3vec-p (x)
 (declare (xargs :guard (s4vec-p x)))
 (let ((__function__ 's3vec-p))
  (declare (ignorable __function__))
  (mbe
    :logic
    (b* (((s4vec x)))
      (not (sparseint-test-bitandc2 x.lower x.upper)))
    :exec (or (s2vec-p x)
              (b* (((s4vec x)))
                (not (sparseint-test-bitandc2 x.lower x.upper)))))))

Theorem: s3vec-p-correct

(defthm s3vec-p-correct
  (b* ((?bool (s3vec-p x)))
    (equal bool (3vec-p (s4vec->4vec x)))))

Theorem: s3vec-p-of-s4vec-fix-x

(defthm s3vec-p-of-s4vec-fix-x
  (equal (s3vec-p (s4vec-fix x))
         (s3vec-p x)))

Theorem: s3vec-p-s4vec-equiv-congruence-on-x

(defthm s3vec-p-s4vec-equiv-congruence-on-x
  (implies (s4vec-equiv x x-equiv)
           (equal (s3vec-p x) (s3vec-p x-equiv)))
  :rule-classes :congruence)