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A4vec-operations

A3vec-reduction-or

Signature
(a3vec-reduction-or x) → res
Arguments: x — Guard (a4vec-p x).
Returns: res — Type (a4vec-p res).

Definitions and Theorems

Function: a3vec-reduction-or

(defun a3vec-reduction-or (x)
 (declare (xargs :guard (a4vec-p x)))
 (let ((__function__ 'a3vec-reduction-or))
  (declare (ignorable __function__))
  (b* (((a4vec x)))
   (a4vec
        (aig-sterm (aig-not (aig-=-ss x.upper (aig-sterm nil))))
        (aig-sterm (aig-not (aig-=-ss x.lower (aig-sterm nil))))))))

Theorem: a4vec-p-of-a3vec-reduction-or

(defthm a4vec-p-of-a3vec-reduction-or
  (b* ((res (a3vec-reduction-or x)))
    (a4vec-p res))
  :rule-classes :rewrite)

Theorem: a3vec-reduction-or-correct

(defthm a3vec-reduction-or-correct
  (equal (a4vec-eval (a3vec-reduction-or x) env)
         (3vec-reduction-or (a4vec-eval x env))))

Theorem: a3vec-reduction-or-of-a4vec-fix-x

(defthm a3vec-reduction-or-of-a4vec-fix-x
  (equal (a3vec-reduction-or (a4vec-fix x))
         (a3vec-reduction-or x)))

Theorem: a3vec-reduction-or-a4vec-equiv-congruence-on-x

(defthm a3vec-reduction-or-a4vec-equiv-congruence-on-x
  (implies (a4vec-equiv x x-equiv)
           (equal (a3vec-reduction-or x)
                  (a3vec-reduction-or x-equiv)))
  :rule-classes :congruence)