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Validator-state

Validator-state-fix

Fixing function for validator-state structures.

Signature
(validator-state-fix x) → new-x
Arguments: x — Guard (validator-statep x).
Returns: new-x — Type (validator-statep new-x).

Definitions and Theorems

Function: validator-state-fix$inline

(defun validator-state-fix$inline (x)
 (declare (xargs :guard (validator-statep x)))
 (let ((__function__ 'validator-state-fix))
  (declare (ignorable __function__))
  (mbe
      :logic
      (b* ((round (pos-fix (cdr (std::da-nth 0 x))))
           (dag (certificate-set-fix (cdr (std::da-nth 1 x))))
           (buffer (certificate-set-fix (cdr (std::da-nth 2 x))))
           (endorsed (address+pos-set-fix (cdr (std::da-nth 3 x))))
           (last (nfix (cdr (std::da-nth 4 x))))
           (blockchain (block-list-fix (cdr (std::da-nth 5 x))))
           (committed (certificate-set-fix (cdr (std::da-nth 6 x))))
           (timer (timer-fix (cdr (std::da-nth 7 x)))))
        (list (cons 'round round)
              (cons 'dag dag)
              (cons 'buffer buffer)
              (cons 'endorsed endorsed)
              (cons 'last last)
              (cons 'blockchain blockchain)
              (cons 'committed committed)
              (cons 'timer timer)))
      :exec x)))

Theorem: validator-statep-of-validator-state-fix

(defthm validator-statep-of-validator-state-fix
  (b* ((new-x (validator-state-fix$inline x)))
    (validator-statep new-x))
  :rule-classes :rewrite)

Theorem: validator-state-fix-when-validator-statep

(defthm validator-state-fix-when-validator-statep
  (implies (validator-statep x)
           (equal (validator-state-fix x) x)))

Function: validator-state-equiv$inline

(defun validator-state-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (validator-statep acl2::x)
                              (validator-statep acl2::y))))
  (equal (validator-state-fix acl2::x)
         (validator-state-fix acl2::y)))

Theorem: validator-state-equiv-is-an-equivalence

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

Theorem: validator-state-equiv-implies-equal-validator-state-fix-1

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

Theorem: validator-state-fix-under-validator-state-equiv

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

Theorem: equal-of-validator-state-fix-1-forward-to-validator-state-equiv

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

Theorem: equal-of-validator-state-fix-2-forward-to-validator-state-equiv

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

Theorem: validator-state-equiv-of-validator-state-fix-1-forward

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

Theorem: validator-state-equiv-of-validator-state-fix-2-forward

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