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S4vecs

S4vec-res

Signature
(s4vec-res x y) → res
Arguments: x — Guard (s4vec-p x).; y — Guard (s4vec-p y).
Returns: res — Type (s4vec-p res).

Definitions and Theorems

Function: s4vec-res

(defun s4vec-res (x y)
  (declare (xargs :guard (and (s4vec-p x) (s4vec-p y))))
  (let ((__function__ 's4vec-res))
    (declare (ignorable __function__))
    (b* (((s4vec x)) ((s4vec y)))
      (s4vec (sparseint-bitor x.upper y.upper)
             (sparseint-bitand x.lower y.lower)))))

Theorem: s4vec-p-of-s4vec-res

(defthm s4vec-p-of-s4vec-res
  (b* ((res (s4vec-res x y)))
    (s4vec-p res))
  :rule-classes :rewrite)

Theorem: s4vec-res-correct

(defthm s4vec-res-correct
  (b* ((?res (s4vec-res x y)))
    (equal (s4vec->4vec res)
           (4vec-res (s4vec->4vec x)
                     (s4vec->4vec y)))))

Theorem: s4vec-res-of-s4vec-fix-x

(defthm s4vec-res-of-s4vec-fix-x
  (equal (s4vec-res (s4vec-fix x) y)
         (s4vec-res x y)))

Theorem: s4vec-res-s4vec-equiv-congruence-on-x

(defthm s4vec-res-s4vec-equiv-congruence-on-x
  (implies (s4vec-equiv x x-equiv)
           (equal (s4vec-res x y)
                  (s4vec-res x-equiv y)))
  :rule-classes :congruence)

Theorem: s4vec-res-of-s4vec-fix-y

(defthm s4vec-res-of-s4vec-fix-y
  (equal (s4vec-res x (s4vec-fix y))
         (s4vec-res x y)))

Theorem: s4vec-res-s4vec-equiv-congruence-on-y

(defthm s4vec-res-s4vec-equiv-congruence-on-y
  (implies (s4vec-equiv y y-equiv)
           (equal (s4vec-res x y)
                  (s4vec-res x y-equiv)))
  :rule-classes :congruence)