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• Primitives

Empty

(empty x) recognizes empty sets.

This function is like endp for lists, but it respects the non-set convention and always returns true for ill-formed sets.

Definitions and Theorems

Function: empty

(defun empty (x)
       (declare (xargs :guard (setp x)))
       (mbe :logic (or (null x) (not (setp x)))
            :exec (null x)))

Theorem: empty-type

(defthm empty-type
        (or (equal (empty x) t)
            (equal (empty x) nil))
        :rule-classes :type-prescription)

Theorem: nonempty-means-set

(defthm nonempty-means-set
        (implies (not (empty x)) (setp x)))

Theorem: empty-sfix-cancel

(defthm empty-sfix-cancel
        (equal (empty (sfix x)) (empty x)))