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S4vecs

S4vec-offset

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

Definitions and Theorems

Function: s4vec-offset

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

Theorem: s4vec-p-of-s4vec-offset

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

Theorem: s4vec-offset-correct

(defthm s4vec-offset-correct
  (b* ((?res (s4vec-offset x)))
    (equal (s4vec->4vec res)
           (4vec-offset (s4vec->4vec x)))))

Theorem: s4vec-offset-of-s4vec-fix-x

(defthm s4vec-offset-of-s4vec-fix-x
  (equal (s4vec-offset (s4vec-fix x))
         (s4vec-offset x)))

Theorem: s4vec-offset-s4vec-equiv-congruence-on-x

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