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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 (emptyp 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)