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Certificates

Certs-with-round

Retrieve, from a set of certificates, the subset of certificates with a given round.

Signature
(certs-with-round round certs) → certs-with-round
Arguments: round — Guard (posp round).; certs — Guard (certificate-setp certs).
Returns: certs-with-round — Type (certificate-setp certs-with-round).

Definitions and Theorems

Function: certs-with-round

(defun certs-with-round (round certs)
  (declare (xargs :guard (and (posp round)
                              (certificate-setp certs))))
  (let ((__function__ 'certs-with-round))
    (declare (ignorable __function__))
    (b* (((when (emptyp (certificate-set-fix certs)))
          nil)
         (cert (head certs)))
      (if (equal (certificate->round cert)
                 (pos-fix round))
          (insert (certificate-fix cert)
                  (certs-with-round round (tail certs)))
        (certs-with-round round (tail certs))))))

Theorem: certificate-setp-of-certs-with-round

(defthm certificate-setp-of-certs-with-round
  (b* ((certs-with-round (certs-with-round round certs)))
    (certificate-setp certs-with-round))
  :rule-classes :rewrite)

Theorem: cert-set->round-set-of-certs-with-round

(defthm cert-set->round-set-of-certs-with-round
  (equal (cert-set->round-set (certs-with-round round certs))
         (if (emptyp (certs-with-round round certs))
             nil
           (insert (pos-fix round) nil))))

Theorem: certs-with-round-of-pos-fix-round

(defthm certs-with-round-of-pos-fix-round
  (equal (certs-with-round (pos-fix round) certs)
         (certs-with-round round certs)))

Theorem: certs-with-round-pos-equiv-congruence-on-round

(defthm certs-with-round-pos-equiv-congruence-on-round
  (implies (acl2::pos-equiv round round-equiv)
           (equal (certs-with-round round certs)
                  (certs-with-round round-equiv certs)))
  :rule-classes :congruence)

Theorem: certs-with-round-of-certificate-set-fix-certs

(defthm certs-with-round-of-certificate-set-fix-certs
  (equal (certs-with-round round (certificate-set-fix certs))
         (certs-with-round round certs)))

Theorem: certs-with-round-certificate-set-equiv-congruence-on-certs

(defthm certs-with-round-certificate-set-equiv-congruence-on-certs
  (implies (certificate-set-equiv certs certs-equiv)
           (equal (certs-with-round round certs)
                  (certs-with-round round certs-equiv)))
  :rule-classes :congruence)