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• Obags

Subbag

Check if (every occurrence of) every value in the first obag is also (an occurrence of) a value in the second obag.

Signature

(subbag sub sup) → yes/no

Arguments

sub — Guard (bagp sub).

sup — Guard (bagp sup).

Returns

yes/no — Type (booleanp yes/no).

This is similar to subset for osets.

Definitions and Theorems

Function: subbag

(defun subbag (sub sup)
       (declare (xargs :guard (and (bagp sub) (bagp sup))))
       (let ((__function__ 'subbag))
            (declare (ignorable __function__))
            (or (empty sub)
                (and (in (head sub) sup)
                     (subbag (tail sub)
                             (delete (head sub) sup))))))

Theorem: booleanp-of-subbag

(defthm booleanp-of-subbag
        (b* ((yes/no (subbag sub sup)))
            (booleanp yes/no))
        :rule-classes :rewrite)