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Obags

Empty

Check if an obag is empty.

Signature
(empty bag) → yes/no
Arguments: bag — Guard (bagp bag).
Returns: yes/no — Type (booleanp yes/no).

This is similar to set::empty for osets.

Definitions and Theorems

Function: empty

(defun empty (bag)
       (declare (xargs :guard (bagp bag)))
       (let ((__function__ 'empty))
            (declare (ignorable __function__))
            (null (bfix bag))))

Theorem: booleanp-of-empty

(defthm booleanp-of-empty
        (b* ((yes/no (empty bag)))
            (booleanp yes/no))
        :rule-classes :rewrite)

Theorem: bagp-when-not-empty

(defthm bagp-when-not-empty
        (implies (not (empty bag)) (bagp bag)))

Theorem: bfix-when-empty

(defthm bfix-when-empty
        (implies (empty x)
                 (equal (bfix x) nil)))