		Search-engine friendly clone of the ACL2 documentation.

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)))