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Message-set

Message-setp

Recognizer for message-set.

Signature
(message-setp x) → *

Definitions and Theorems

Function: message-setp

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

Theorem: booleanp-ofmessage-setp

(defthm booleanp-ofmessage-setp
  (booleanp (message-setp x)))

Theorem: setp-when-message-setp

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

Theorem: messagep-of-head-when-message-setp

(defthm messagep-of-head-when-message-setp
  (implies (message-setp x)
           (equal (messagep (head x))
                  (not (emptyp x)))))

Theorem: message-setp-of-tail-when-message-setp

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

Theorem: message-setp-of-insert

(defthm message-setp-of-insert
  (equal (message-setp (insert a x))
         (and (messagep a)
              (message-setp (sfix x)))))

Theorem: messagep-when-in-message-setp-binds-free-x

(defthm messagep-when-in-message-setp-binds-free-x
  (implies (and (in a x) (message-setp x))
           (messagep a)))

Theorem: not-in-message-setp-when-not-messagep

(defthm not-in-message-setp-when-not-messagep
  (implies (and (message-setp x)
                (not (messagep a)))
           (not (in a x))))

Theorem: message-setp-of-union

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

Theorem: message-setp-of-intersect

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

Theorem: message-setp-of-difference

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

Theorem: message-setp-of-delete

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