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• Primitives

Emptyp

(emptyp 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: emptyp

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

Theorem: emptyp-type

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

Theorem: nonempty-means-set

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

Theorem: emptyp-sfix-cancel

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