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• Obags

Intersect

Intersection of all (the occurrences of) all the elements of two obags.

Signature

(intersect bag1 bag2) → bag

Arguments

bag1 — Guard (bagp bag1).

bag2 — Guard (bagp bag2).

Returns

bag — Type (bagp bag).

This is similar to set::intersect for osets.

Definitions and Theorems

Function: intersect

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

Theorem: bagp-of-intersect

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