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• Obags

Cardinality

Number of (occurrences of) elements in an obag.

Signature

(cardinality bag) → card

Arguments

bag — Guard (bagp bag).

Returns

card — Type (natp card).

This is similar to set::cardinality on osets.

Definitions and Theorems

Function: cardinality

(defun cardinality (bag)
       (declare (xargs :guard (bagp bag)))
       (let ((__function__ 'cardinality))
            (declare (ignorable __function__))
            (if (empty bag)
                0 (1+ (cardinality (tail bag))))))

Theorem: natp-of-cardinality

(defthm natp-of-cardinality
        (b* ((card (cardinality bag)))
            (natp card))
        :rule-classes :rewrite)