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A4vec-operations

A3vec-reduction-and

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

Definitions and Theorems

Function: a3vec-reduction-and

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

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

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

Theorem: a3vec-reduction-and-correct

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

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

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

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

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