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• Messages

Message-set->certificate-set

Lift message->certificate to sets.

Signature

(message-set->certificate-set msgs) → certs

Arguments

msgs — Guard (message-setp msgs).

Returns

certs — Type (certificate-setp certs).

Definitions and Theorems

Function: message-set->certificate-set

(defun message-set->certificate-set (msgs)
  (declare (xargs :guard (message-setp msgs)))
  (let ((__function__ 'message-set->certificate-set))
    (declare (ignorable __function__))
    (cond ((emptyp msgs) nil)
          (t (insert (message->certificate (head msgs))
                     (message-set->certificate-set (tail msgs)))))))

Theorem: certificate-setp-of-message-set->certificate-set

(defthm certificate-setp-of-message-set->certificate-set
  (b* ((certs (message-set->certificate-set msgs)))
    (certificate-setp certs))
  :rule-classes :rewrite)

Theorem: message->certificate-in-message-set->certificate-set

(defthm message->certificate-in-message-set->certificate-set
  (implies (in msg msgs)
           (in (message->certificate msg)
               (message-set->certificate-set msgs))))

Theorem: message-set->certificate-set-of-insert

(defthm message-set->certificate-set-of-insert
  (equal (message-set->certificate-set (insert msg msgs))
         (insert (message->certificate msg)
                 (message-set->certificate-set msgs))))

Theorem: message-set->certificate-set-of-union

(defthm message-set->certificate-set-of-union
  (equal (message-set->certificate-set (union msgs1 msgs2))
         (union (message-set->certificate-set msgs1)
                (message-set->certificate-set (sfix msgs2)))))

Theorem: message-set->certificate-set-monotone

(defthm message-set->certificate-set-monotone
  (implies (subset msgs1 msgs2)
           (subset (message-set->certificate-set msgs1)
                   (message-set->certificate-set msgs2))))

Theorem: in-of-message-set->certificate-set-of-delete

(defthm in-of-message-set->certificate-set-of-delete
  (implies (and (certificatep cert)
                (message-setp msgs)
                (in cert
                    (message-set->certificate-set msgs))
                (not (equal (message->certificate msg)
                            cert)))
           (in cert
               (message-set->certificate-set (delete msg msgs)))))