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Certificate

Certificate-fix

Fixing function for certificate structures.

Signature
(certificate-fix x) → new-x
Arguments: x — Guard (certificatep x).
Returns: new-x — Type (certificatep new-x).

Definitions and Theorems

Function: certificate-fix$inline

(defun certificate-fix$inline (x)
 (declare (xargs :guard (certificatep x)))
 (let ((__function__ 'certificate-fix))
  (declare (ignorable __function__))
  (mbe
    :logic
    (b*
      ((author (address-fix (cdr (std::da-nth 0 x))))
       (round (pos-fix (cdr (std::da-nth 1 x))))
       (transactions (transaction-list-fix (cdr (std::da-nth 2 x))))
       (previous (address-set-fix (cdr (std::da-nth 3 x))))
       (endorsers (address-set-fix (cdr (std::da-nth 4 x)))))
      (list (cons 'author author)
            (cons 'round round)
            (cons 'transactions transactions)
            (cons 'previous previous)
            (cons 'endorsers endorsers)))
    :exec x)))

Theorem: certificatep-of-certificate-fix

(defthm certificatep-of-certificate-fix
  (b* ((new-x (certificate-fix$inline x)))
    (certificatep new-x))
  :rule-classes :rewrite)

Theorem: certificate-fix-when-certificatep

(defthm certificate-fix-when-certificatep
  (implies (certificatep x)
           (equal (certificate-fix x) x)))

Function: certificate-equiv$inline

(defun certificate-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (certificatep acl2::x)
                              (certificatep acl2::y))))
  (equal (certificate-fix acl2::x)
         (certificate-fix acl2::y)))

Theorem: certificate-equiv-is-an-equivalence

(defthm certificate-equiv-is-an-equivalence
  (and (booleanp (certificate-equiv x y))
       (certificate-equiv x x)
       (implies (certificate-equiv x y)
                (certificate-equiv y x))
       (implies (and (certificate-equiv x y)
                     (certificate-equiv y z))
                (certificate-equiv x z)))
  :rule-classes (:equivalence))

Theorem: certificate-equiv-implies-equal-certificate-fix-1

(defthm certificate-equiv-implies-equal-certificate-fix-1
  (implies (certificate-equiv acl2::x x-equiv)
           (equal (certificate-fix acl2::x)
                  (certificate-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: certificate-fix-under-certificate-equiv

(defthm certificate-fix-under-certificate-equiv
  (certificate-equiv (certificate-fix acl2::x)
                     acl2::x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-certificate-fix-1-forward-to-certificate-equiv

(defthm equal-of-certificate-fix-1-forward-to-certificate-equiv
  (implies (equal (certificate-fix acl2::x)
                  acl2::y)
           (certificate-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: equal-of-certificate-fix-2-forward-to-certificate-equiv

(defthm equal-of-certificate-fix-2-forward-to-certificate-equiv
  (implies (equal acl2::x (certificate-fix acl2::y))
           (certificate-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: certificate-equiv-of-certificate-fix-1-forward

(defthm certificate-equiv-of-certificate-fix-1-forward
  (implies (certificate-equiv (certificate-fix acl2::x)
                              acl2::y)
           (certificate-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: certificate-equiv-of-certificate-fix-2-forward

(defthm certificate-equiv-of-certificate-fix-2-forward
  (implies (certificate-equiv acl2::x (certificate-fix acl2::y))
           (certificate-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)