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4vec-operations

4vec-bitnot

Bitwise logical NOT of a 4vec.

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

Definitions and Theorems

Function: 4vec-bitnot

(defun 4vec-bitnot (x)
  (declare (xargs :guard (4vec-p x)))
  (let ((__function__ '4vec-bitnot))
    (declare (ignorable __function__))
    (3vec-bitnot (3vec-fix x))))

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

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

Main correctness theorem: each result bit is just the ACL2::4v-not of the corresponding input bit.

Theorem: 4vec-bitnot-bits

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

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

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

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

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