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A4vec-operations

A3vec-bitand

Symbolic version of 3vec-bitand.

Signature
(a3vec-bitand 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-bitand

(defun a3vec-bitand (x y)
  (declare (xargs :guard (and (a4vec-p x) (a4vec-p y))))
  (let ((__function__ 'a3vec-bitand))
    (declare (ignorable __function__))
    (b* (((a4vec x)) ((a4vec y)))
      (a4vec (aig-logand-ss x.upper y.upper)
             (aig-logand-ss x.lower y.lower)))))

Theorem: a4vec-p-of-a3vec-bitand

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

Theorem: a3vec-bitand-correct

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

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

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

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

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

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

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

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

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