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• Obags

Difference

Remove from the first obag all (the occurrences of) the elements of the second obag.

Signature

(difference bag1 bag2) → bag

Arguments

bag1 — Guard (bagp bag1).

bag2 — Guard (bagp bag2).

Returns

bag — Type (bagp bag).

Definitions and Theorems

Function: difference

(defun difference (bag1 bag2)
  (declare (xargs :guard (and (bagp bag1) (bagp bag2))))
  (let ((__function__ 'difference))
    (declare (ignorable __function__))
    (cond ((emptyp bag1) nil)
          ((in (head bag1) bag2)
           (difference (tail bag1) bag2))
          (t (insert (head bag1)
                     (difference (tail bag1) bag2))))))

Theorem: bagp-of-difference

(defthm bagp-of-difference
  (b* ((bag (difference bag1 bag2)))
    (bagp bag))
  :rule-classes :rewrite)