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• Committees

Same-active-committees-p

Check if two blockchains calculate consistent active committees.

The two blockchains may differ, in particular in length, but the predicate checks that, when they both calculate a active committeed at a round, they calculate the same committee. It allows only one blockchain to calculate the active committee for a round, with the other blockchain being too short for that.

Definitions and Theorems

Theorem: same-active-committees-p-necc

(defthm same-active-committees-p-necc
 (implies
  (same-active-committees-p blocks1 blocks2)
  (implies (posp round)
           (b* ((commtt1 (active-committee-at-round round blocks1))
                (commtt2 (active-committee-at-round round blocks2)))
             (implies (and commtt1 commtt2)
                      (equal commtt1 commtt2))))))

Theorem: booleanp-of-same-active-committees-p

(defthm booleanp-of-same-active-committees-p
  (b* ((yes/no (same-active-committees-p blocks1 blocks2)))
    (booleanp yes/no))
  :rule-classes :rewrite)

Theorem: same-active-committees-p-of-block-list-fix-blocks1

(defthm same-active-committees-p-of-block-list-fix-blocks1
  (equal (same-active-committees-p (block-list-fix blocks1)
                                   blocks2)
         (same-active-committees-p blocks1 blocks2)))

Theorem: same-active-committees-p-block-list-equiv-congruence-on-blocks1

(defthm
    same-active-committees-p-block-list-equiv-congruence-on-blocks1
  (implies (block-list-equiv blocks1 blocks1-equiv)
           (equal (same-active-committees-p blocks1 blocks2)
                  (same-active-committees-p blocks1-equiv blocks2)))
  :rule-classes :congruence)

Theorem: same-active-committees-p-of-block-list-fix-blocks2

(defthm same-active-committees-p-of-block-list-fix-blocks2
  (equal (same-active-committees-p blocks1 (block-list-fix blocks2))
         (same-active-committees-p blocks1 blocks2)))

Theorem: same-active-committees-p-block-list-equiv-congruence-on-blocks2

(defthm
    same-active-committees-p-block-list-equiv-congruence-on-blocks2
  (implies (block-list-equiv blocks2 blocks2-equiv)
           (equal (same-active-committees-p blocks1 blocks2)
                  (same-active-committees-p blocks1 blocks2-equiv)))
  :rule-classes :congruence)