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4vec-operations

4vec-wildeq-safe

True if for every pair of corresponding bits of a and b, either they are equal or the bit from b is Z.

Signature
(4vec-wildeq-safe 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-wildeq-safe

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

Theorem: 4vec-p-of-4vec-wildeq-safe

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

Theorem: 4vec-wildeq-safe-of-3vec-fix-a

(defthm 4vec-wildeq-safe-of-3vec-fix-a
  (equal (4vec-wildeq-safe (3vec-fix a) b)
         (4vec-wildeq-safe a b)))

Theorem: 4vec-wildeq-safe-3vec-equiv-congruence-on-a

(defthm 4vec-wildeq-safe-3vec-equiv-congruence-on-a
  (implies (3vec-equiv a a-equiv)
           (equal (4vec-wildeq-safe a b)
                  (4vec-wildeq-safe a-equiv b)))
  :rule-classes :congruence)

Theorem: 4vec-wildeq-safe-of-4vec-fix-b

(defthm 4vec-wildeq-safe-of-4vec-fix-b
  (equal (4vec-wildeq-safe a (4vec-fix b))
         (4vec-wildeq-safe a b)))

Theorem: 4vec-wildeq-safe-4vec-equiv-congruence-on-b

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