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Blockchain-redundant-def-and-init-and-next

Blockchain-redundant-p

Definition of the invariant: the blockchain of each validator is redundant, equal to its calculation from the committed anchors and DAG.

Definitions and Theorems

Theorem: blockchain-redundant-p-necc

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

Theorem: booleanp-of-blockchain-redundant-p

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

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

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

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

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