		Search-engine friendly clone of the ACL2 documentation.

Name-set

Name-setp

Recognizer for name-set.

Signature
(name-setp x) → *

Definitions and Theorems

Function: name-setp

(defun name-setp (x)
  (declare (xargs :guard t))
  (if (atom x)
      (null x)
    (and (namep (car x))
         (or (null (cdr x))
             (and (consp (cdr x))
                  (acl2::fast-<< (car x) (cadr x))
                  (name-setp (cdr x)))))))

Theorem: booleanp-ofname-setp

(defthm booleanp-ofname-setp
  (booleanp (name-setp x)))

Theorem: setp-when-name-setp

(defthm setp-when-name-setp
  (implies (name-setp x) (setp x))
  :rule-classes (:rewrite))

Theorem: namep-of-head-when-name-setp

(defthm namep-of-head-when-name-setp
  (implies (name-setp x)
           (equal (namep (head x))
                  (not (emptyp x)))))

Theorem: name-setp-of-tail-when-name-setp

(defthm name-setp-of-tail-when-name-setp
  (implies (name-setp x)
           (name-setp (tail x))))

Theorem: name-setp-of-insert

(defthm name-setp-of-insert
  (equal (name-setp (insert a x))
         (and (namep a) (name-setp (sfix x)))))

Theorem: namep-when-in-name-setp-binds-free-x

(defthm namep-when-in-name-setp-binds-free-x
  (implies (and (in a x) (name-setp x))
           (namep a)))

Theorem: not-in-name-setp-when-not-namep

(defthm not-in-name-setp-when-not-namep
  (implies (and (name-setp x) (not (namep a)))
           (not (in a x))))

Theorem: name-setp-of-union

(defthm name-setp-of-union
  (equal (name-setp (union x y))
         (and (name-setp (sfix x))
              (name-setp (sfix y)))))

Theorem: name-setp-of-intersect

(defthm name-setp-of-intersect
  (implies (and (name-setp x) (name-setp y))
           (name-setp (intersect x y))))

Theorem: name-setp-of-difference

(defthm name-setp-of-difference
  (implies (name-setp x)
           (name-setp (difference x y))))

Theorem: name-setp-of-delete

(defthm name-setp-of-delete
  (implies (name-setp x)
           (name-setp (delete a x))))