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Certificate

Certificate->round

Get the round field from a certificate.

Signature
(certificate->round x) → round
Arguments: x — Guard (certificatep x).
Returns: round — Type (posp round).

This is an ordinary field accessor created by fty::defprod.

Definitions and Theorems

Function: certificate->round$inline

(defun certificate->round$inline (x)
  (declare (xargs :guard (certificatep x)))
  (declare (xargs :guard t))
  (let ((__function__ 'certificate->round))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and t x)))
           (pos-fix (cdr (std::da-nth 1 x))))
         :exec (cdr (std::da-nth 1 x)))))

Theorem: posp-of-certificate->round

(defthm posp-of-certificate->round
  (b* ((round (certificate->round$inline x)))
    (posp round))
  :rule-classes :rewrite)

Theorem: certificate->round$inline-of-certificate-fix-x

(defthm certificate->round$inline-of-certificate-fix-x
  (equal (certificate->round$inline (certificate-fix x))
         (certificate->round$inline x)))

Theorem: certificate->round$inline-certificate-equiv-congruence-on-x

(defthm certificate->round$inline-certificate-equiv-congruence-on-x
  (implies (certificate-equiv x x-equiv)
           (equal (certificate->round$inline x)
                  (certificate->round$inline x-equiv)))
  :rule-classes :congruence)