		Search-engine friendly clone of the ACL2 documentation.

Identifier-set

Identifier-setp

Recognizer for identifier-set.

Signature
(identifier-setp x) → *

Definitions and Theorems

Function: identifier-setp

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

Theorem: booleanp-ofidentifier-setp

(defthm booleanp-ofidentifier-setp
  (booleanp (identifier-setp x)))

Theorem: setp-when-identifier-setp

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

Theorem: identifierp-of-head-when-identifier-setp

(defthm identifierp-of-head-when-identifier-setp
  (implies (identifier-setp x)
           (equal (identifierp (head x))
                  (not (emptyp x)))))

Theorem: identifier-setp-of-tail-when-identifier-setp

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

Theorem: identifier-setp-of-insert

(defthm identifier-setp-of-insert
  (equal (identifier-setp (insert a x))
         (and (identifierp a)
              (identifier-setp (sfix x)))))

Theorem: identifierp-when-in-identifier-setp-binds-free-x

(defthm identifierp-when-in-identifier-setp-binds-free-x
  (implies (and (in a x) (identifier-setp x))
           (identifierp a)))

Theorem: not-in-identifier-setp-when-not-identifierp

(defthm not-in-identifier-setp-when-not-identifierp
  (implies (and (identifier-setp x)
                (not (identifierp a)))
           (not (in a x))))

Theorem: identifier-setp-of-union

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

Theorem: identifier-setp-of-intersect

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

Theorem: identifier-setp-of-difference

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

Theorem: identifier-setp-of-delete

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