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S4vecs

S3vec-reduction-or

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

Definitions and Theorems

Function: s3vec-reduction-or

(defun s3vec-reduction-or (x)
 (declare (xargs :guard (s4vec-p x)))
 (let ((__function__ 's3vec-reduction-or))
  (declare (ignorable __function__))
  (if-s2vec-p
   (x)
   (s2vec
        (int-to-sparseint
             (bool->vec (not (sparseint-equal (s2vec->val x) 0)))))
   (b* (((s4vec x)))
     (s4vec (int-to-sparseint
                 (bool->vec (not (sparseint-equal x.upper 0))))
            (int-to-sparseint
                 (bool->vec (not (sparseint-equal x.lower 0)))))))))

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

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

Theorem: s3vec-reduction-or-correct

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

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

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

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

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