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S4vecs

S4vec-resor

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

Definitions and Theorems

Function: s4vec-resor

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

Theorem: s4vec-p-of-s4vec-resor

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

Theorem: s4vec-resor-correct

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

Theorem: s4vec-resor-of-s4vec-fix-x

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

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

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

Theorem: s4vec-resor-of-s4vec-fix-y

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

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

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