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S4vecs

S3vec-reduction-and

Signature
(s3vec-reduction-and x) → res
Arguments: x — Guard (s4vec-p x).
Returns: res — Type (s4vec-p res).

Definitions and Theorems

Function: s3vec-reduction-and

(defun s3vec-reduction-and (x)
 (declare (xargs :guard (s4vec-p x)))
 (let ((__function__ 's3vec-reduction-and))
  (declare (ignorable __function__))
  (if-s2vec-p
   (x)
   (s2vec (int-to-sparseint
               (bool->vec (sparseint-equal (s2vec->val x) -1))))
   (b* (((s4vec x)))
    (s4vec
         (int-to-sparseint (bool->vec (sparseint-equal x.upper -1)))
         (int-to-sparseint
              (bool->vec (sparseint-equal x.lower -1))))))))

Theorem: s4vec-p-of-s3vec-reduction-and

(defthm s4vec-p-of-s3vec-reduction-and
  (b* ((res (s3vec-reduction-and x)))
    (s4vec-p res))
  :rule-classes :rewrite)

Theorem: s3vec-reduction-and-correct

(defthm s3vec-reduction-and-correct
  (b* ((?res (s3vec-reduction-and x)))
    (equal (s4vec->4vec res)
           (3vec-reduction-and (s4vec->4vec x)))))

Theorem: s3vec-reduction-and-of-s4vec-fix-x

(defthm s3vec-reduction-and-of-s4vec-fix-x
  (equal (s3vec-reduction-and (s4vec-fix x))
         (s3vec-reduction-and x)))

Theorem: s3vec-reduction-and-s4vec-equiv-congruence-on-x

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