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Obags

In

Check if a values occurs in an obag.

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

This is similar to set::in on osets.

Definitions and Theorems

Function: in

(defun in (x bag)
       (declare (xargs :guard (bagp bag)))
       (let ((__function__ 'in))
            (declare (ignorable __function__))
            (and (not (empty bag))
                 (or (equal x (head bag))
                     (in x (tail bag))))))

Theorem: booleanp-of-in

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