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3vec-operations

3vec-bitand

Bitwise logical AND of 3vecs.

Signature
(3vec-bitand x y) → x&y
Arguments: x — Guard (4vec-p x).; y — Guard (4vec-p y).
Returns: x&y — Type (4vec-p x&y).

Definitions and Theorems

Function: 3vec-bitand

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

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

(defthm 4vec-p-of-3vec-bitand
  (b* ((x&y (3vec-bitand x y)))
    (4vec-p x&y))
  :rule-classes :rewrite)

Theorem: 3vec-p-of-3vec-bitand

(defthm 3vec-p-of-3vec-bitand
  (b* ((?x&y (3vec-bitand x y)))
    (implies (and (3vec-p x) (3vec-p y))
             (3vec-p x&y))))

Theorem: 3vec-bitand-bits

(defthm 3vec-bitand-bits
  (implies (and (3vec-p! x) (3vec-p! y))
           (equal (4vec-idx->4v n (3vec-bitand x y))
                  (acl2::4v-and (4vec-idx->4v n (3vec-fix x))
                                (4vec-idx->4v n (3vec-fix y))))))

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

(defthm 3vec-bitand-of-4vec-fix-x
  (equal (3vec-bitand (4vec-fix x) y)
         (3vec-bitand x y)))

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

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

Theorem: 3vec-bitand-of-4vec-fix-y

(defthm 3vec-bitand-of-4vec-fix-y
  (equal (3vec-bitand x (4vec-fix y))
         (3vec-bitand x y)))

Theorem: 3vec-bitand-4vec-equiv-congruence-on-y

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