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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)))))