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4vec-operations

4vec-symwildeq

Symmetric wildcard equality: true if for every pair of corresponding bits of a and b, either they are equal or the bit from either a or b is Z.

Signature
(4vec-symwildeq a b) → res
Arguments: a — Guard (4vec-p a).; b — Guard (4vec-p b).
Returns: res — Type (4vec-p res).

Definitions and Theorems

Function: 4vec-symwildeq

(defun 4vec-symwildeq (a b)
  (declare (xargs :guard (and (4vec-p a) (4vec-p b))))
  (let ((__function__ '4vec-symwildeq))
    (declare (ignorable __function__))
    (b* ((eq (3vec-bitnot (4vec-bitxor a b)))
         ((4vec a))
         ((4vec b))
         (zmask (logior (logand (lognot b.upper) b.lower)
                        (logand (lognot a.upper) a.lower))))
      (3vec-reduction-and (3vec-bitor eq (2vec zmask))))))

Theorem: 4vec-p-of-4vec-symwildeq

(defthm 4vec-p-of-4vec-symwildeq
  (b* ((res (4vec-symwildeq a b)))
    (4vec-p res))
  :rule-classes :rewrite)

Theorem: 4vec-symwildeq-of-4vec-fix-a

(defthm 4vec-symwildeq-of-4vec-fix-a
  (equal (4vec-symwildeq (4vec-fix a) b)
         (4vec-symwildeq a b)))

Theorem: 4vec-symwildeq-4vec-equiv-congruence-on-a

(defthm 4vec-symwildeq-4vec-equiv-congruence-on-a
  (implies (4vec-equiv a a-equiv)
           (equal (4vec-symwildeq a b)
                  (4vec-symwildeq a-equiv b)))
  :rule-classes :congruence)

Theorem: 4vec-symwildeq-of-4vec-fix-b

(defthm 4vec-symwildeq-of-4vec-fix-b
  (equal (4vec-symwildeq a (4vec-fix b))
         (4vec-symwildeq a b)))

Theorem: 4vec-symwildeq-4vec-equiv-congruence-on-b

(defthm 4vec-symwildeq-4vec-equiv-congruence-on-b
  (implies (4vec-equiv b b-equiv)
           (equal (4vec-symwildeq a b)
                  (4vec-symwildeq a b-equiv)))
  :rule-classes :congruence)