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S4vecs

S4vec-wildeq

Signature
(s4vec-wildeq a b) → res
Arguments: a — Guard (s4vec-p a).; b — Guard (s4vec-p b).
Returns: res — Type (s4vec-p res).

Definitions and Theorems

Function: s4vec-wildeq

(defun s4vec-wildeq (a b)
  (declare (xargs :guard (and (s4vec-p a) (s4vec-p b))))
  (let ((__function__ 's4vec-wildeq))
    (declare (ignorable __function__))
    (b* ((eq (s3vec-bitnot (s4vec-bitxor a b)))
         ((s4vec b))
         (zxmask (sparseint-bitxor b.upper b.lower)))
      (s3vec-reduction-and (s3vec-bitor eq (s2vec zxmask))))))

Theorem: s4vec-p-of-s4vec-wildeq

(defthm s4vec-p-of-s4vec-wildeq
  (b* ((res (s4vec-wildeq a b)))
    (s4vec-p res))
  :rule-classes :rewrite)

Theorem: s4vec-wildeq-correct

(defthm s4vec-wildeq-correct
  (b* ((?res (s4vec-wildeq a b)))
    (equal (s4vec->4vec res)
           (4vec-wildeq (s4vec->4vec a)
                        (s4vec->4vec b)))))

Theorem: s4vec-wildeq-of-s4vec-fix-a

(defthm s4vec-wildeq-of-s4vec-fix-a
  (equal (s4vec-wildeq (s4vec-fix a) b)
         (s4vec-wildeq a b)))

Theorem: s4vec-wildeq-s4vec-equiv-congruence-on-a

(defthm s4vec-wildeq-s4vec-equiv-congruence-on-a
  (implies (s4vec-equiv a a-equiv)
           (equal (s4vec-wildeq a b)
                  (s4vec-wildeq a-equiv b)))
  :rule-classes :congruence)

Theorem: s4vec-wildeq-of-s4vec-fix-b

(defthm s4vec-wildeq-of-s4vec-fix-b
  (equal (s4vec-wildeq a (s4vec-fix b))
         (s4vec-wildeq a b)))

Theorem: s4vec-wildeq-s4vec-equiv-congruence-on-b

(defthm s4vec-wildeq-s4vec-equiv-congruence-on-b
  (implies (s4vec-equiv b b-equiv)
           (equal (s4vec-wildeq a b)
                  (s4vec-wildeq a b-equiv)))
  :rule-classes :congruence)