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A4vec-operations

A3vec-bitxor

Symbolic version of 3vec-bitxor.

Signature
(a3vec-bitxor x y) → res
Arguments: x — Guard (a4vec-p x).; y — Guard (a4vec-p y).
Returns: res — Type (a4vec-p res).

Definitions and Theorems

Function: a3vec-bitxor

(defun a3vec-bitxor (x y)
  (declare (xargs :guard (and (a4vec-p x) (a4vec-p y))))
  (let ((__function__ 'a3vec-bitxor))
    (declare (ignorable __function__))
    (b* (((a4vec x))
         ((a4vec y))
         (xmask (aig-logior-ss (aig-logandc2-ss x.upper x.lower)
                               (aig-logandc2-ss y.upper y.lower))))
      (a4vec (aig-logior-ss xmask (aig-logxor-ss x.upper y.upper))
             (aig-logandc1-ss xmask
                              (aig-logxor-ss x.lower y.lower))))))

Theorem: a4vec-p-of-a3vec-bitxor

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

Theorem: a3vec-bitxor-correct

(defthm a3vec-bitxor-correct
  (equal (a4vec-eval (a3vec-bitxor x y) env)
         (3vec-bitxor (a4vec-eval x env)
                      (a4vec-eval y env))))

Theorem: a3vec-bitxor-of-a4vec-fix-x

(defthm a3vec-bitxor-of-a4vec-fix-x
  (equal (a3vec-bitxor (a4vec-fix x) y)
         (a3vec-bitxor x y)))

Theorem: a3vec-bitxor-a4vec-equiv-congruence-on-x

(defthm a3vec-bitxor-a4vec-equiv-congruence-on-x
  (implies (a4vec-equiv x x-equiv)
           (equal (a3vec-bitxor x y)
                  (a3vec-bitxor x-equiv y)))
  :rule-classes :congruence)

Theorem: a3vec-bitxor-of-a4vec-fix-y

(defthm a3vec-bitxor-of-a4vec-fix-y
  (equal (a3vec-bitxor x (a4vec-fix y))
         (a3vec-bitxor x y)))

Theorem: a3vec-bitxor-a4vec-equiv-congruence-on-y

(defthm a3vec-bitxor-a4vec-equiv-congruence-on-y
  (implies (a4vec-equiv y y-equiv)
           (equal (a3vec-bitxor x y)
                  (a3vec-bitxor x y-equiv)))
  :rule-classes :congruence)