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S4vecs

S3vec-bitnot

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

Definitions and Theorems

Function: s3vec-bitnot

(defun s3vec-bitnot (x)
  (declare (xargs :guard (s4vec-p x)))
  (let ((__function__ 's3vec-bitnot))
    (declare (ignorable __function__))
    (if-s2vec-p (x)
                (s2vec (sparseint-bitnot (s2vec->val x)))
                (b* (((s4vec x)))
                  (s4vec (sparseint-bitnot x.lower)
                         (sparseint-bitnot x.upper))))))

Theorem: s4vec-p-of-s3vec-bitnot

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

Theorem: s3vec-bitnot-correct

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

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

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

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

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