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3vec-operations

3vec-bitnot

Bitwise logical NOT of a 3vec.

Signature
(3vec-bitnot x) → ~x
Arguments: x — Guard (4vec-p x).
Returns: ~x — Type (4vec-p ~x).

Definitions and Theorems

Function: 3vec-bitnot

(defun 3vec-bitnot (x)
  (declare (xargs :guard (4vec-p x)))
  (let ((__function__ '3vec-bitnot))
    (declare (ignorable __function__))
    (if-2vec-p (x)
               (2vec (lognot (2vec->val x)))
               (b* (((4vec x)))
                 (4vec (lognot x.lower)
                       (lognot x.upper))))))

Theorem: 4vec-p-of-3vec-bitnot

(defthm 4vec-p-of-3vec-bitnot
  (b* ((~x (3vec-bitnot x))) (4vec-p ~x))
  :rule-classes :rewrite)

Theorem: 3vec-p-of-3vec-bitnot

(defthm 3vec-p-of-3vec-bitnot
  (b* ((?~x (3vec-bitnot x)))
    (implies (3vec-p x) (3vec-p ~x))))

Theorem: 3vec-bitnot-bits

(defthm 3vec-bitnot-bits
  (implies (3vec-p x)
           (equal (4vec-idx->4v n (3vec-bitnot x))
                  (acl2::4v-not (4vec-idx->4v n x)))))

Theorem: 3vec-bitnot-of-4vec-fix-x

(defthm 3vec-bitnot-of-4vec-fix-x
  (equal (3vec-bitnot (4vec-fix x))
         (3vec-bitnot x)))

Theorem: 3vec-bitnot-4vec-equiv-congruence-on-x

(defthm 3vec-bitnot-4vec-equiv-congruence-on-x
  (implies (4vec-equiv x x-equiv)
           (equal (3vec-bitnot x)
                  (3vec-bitnot x-equiv)))
  :rule-classes :congruence)