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A4vec-operations

A4vec-symwildeq

Symbolic version of 4vec-symwildeq.

Signature
(a4vec-symwildeq a b) → res
Arguments: a — Guard (a4vec-p a).; b — Guard (a4vec-p b).
Returns: res — Type (a4vec-p res).

Definitions and Theorems

Function: a4vec-symwildeq

(defun a4vec-symwildeq (a b)
  (declare (xargs :guard (and (a4vec-p a) (a4vec-p b))))
  (let ((__function__ 'a4vec-symwildeq))
    (declare (ignorable __function__))
    (b* (((a4vec a))
         ((a4vec b))
         (eq (a3vec-bitnot (a3vec-bitxor (a3vec-fix a)
                                         (a3vec-fix b))))
         (zmask (aig-logior-ss (aig-logandc1-ss b.upper b.lower)
                               (aig-logandc1-ss a.upper a.lower))))
      (a3vec-reduction-and (a3vec-bitor eq (a4vec zmask zmask))))))

Theorem: a4vec-p-of-a4vec-symwildeq

(defthm a4vec-p-of-a4vec-symwildeq
  (b* ((res (a4vec-symwildeq a b)))
    (a4vec-p res))
  :rule-classes :rewrite)

Theorem: a4vec-symwildeq-correct

(defthm a4vec-symwildeq-correct
  (equal (a4vec-eval (a4vec-symwildeq a b) env)
         (4vec-symwildeq (a4vec-eval a env)
                         (a4vec-eval b env))))

Theorem: a4vec-symwildeq-of-a4vec-fix-a

(defthm a4vec-symwildeq-of-a4vec-fix-a
  (equal (a4vec-symwildeq (a4vec-fix a) b)
         (a4vec-symwildeq a b)))

Theorem: a4vec-symwildeq-a4vec-equiv-congruence-on-a

(defthm a4vec-symwildeq-a4vec-equiv-congruence-on-a
  (implies (a4vec-equiv a a-equiv)
           (equal (a4vec-symwildeq a b)
                  (a4vec-symwildeq a-equiv b)))
  :rule-classes :congruence)

Theorem: a4vec-symwildeq-of-a4vec-fix-b

(defthm a4vec-symwildeq-of-a4vec-fix-b
  (equal (a4vec-symwildeq a (a4vec-fix b))
         (a4vec-symwildeq a b)))

Theorem: a4vec-symwildeq-a4vec-equiv-congruence-on-b

(defthm a4vec-symwildeq-a4vec-equiv-congruence-on-b
  (implies (a4vec-equiv b b-equiv)
           (equal (a4vec-symwildeq a b)
                  (a4vec-symwildeq a b-equiv)))
  :rule-classes :congruence)