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Committed-redundant-def-and-init-and-next

Committed-redundant-p

Definition of the invariant: the set of committed certificates of each correct validator is redundant, equal to the causal history of the last committed anchor.

Definitions and Theorems

Theorem: committed-redundant-p-necc

(defthm committed-redundant-p-necc
  (implies (committed-redundant-p systate)
           (implies (in val (correct-addresses systate))
                    (validator-committed-redundant-p
                         (get-validator-state val systate)))))

Theorem: booleanp-of-committed-redundant-p

(defthm booleanp-of-committed-redundant-p
  (b* ((yes/no (committed-redundant-p systate)))
    (booleanp yes/no))
  :rule-classes :rewrite)

Theorem: committed-redundant-p-of-system-state-fix-systate

(defthm committed-redundant-p-of-system-state-fix-systate
  (equal (committed-redundant-p (system-state-fix systate))
         (committed-redundant-p systate)))

Theorem: committed-redundant-p-system-state-equiv-congruence-on-systate

(defthm
     committed-redundant-p-system-state-equiv-congruence-on-systate
  (implies (system-state-equiv systate systate-equiv)
           (equal (committed-redundant-p systate)
                  (committed-redundant-p systate-equiv)))
  :rule-classes :congruence)