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Obags

Emptyp

Check if an obag is empty.

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

This is similar to set::emptyp for osets.

Definitions and Theorems

Function: emptyp

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

Theorem: booleanp-of-emptyp

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

Theorem: bagp-when-not-emptyp

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

Theorem: bfix-when-emptyp

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