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• Obags

Union

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

Signature

(union bag1 bag2) → bag

Arguments

bag1 — Guard (bagp bag1).

bag2 — Guard (bagp bag2).

Returns

bag — Type (bagp bag).

This is similar to set::union for osets.

Definitions and Theorems

Function: union

(defun union (bag1 bag2)
  (declare (xargs :guard (and (bagp bag1) (bagp bag2))))
  (let ((__function__ 'union))
    (declare (ignorable __function__))
    (if (emptyp bag1)
        (bfix bag2)
      (insert (head bag1)
              (union (tail bag1) bag2)))))

Theorem: bagp-of-union

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