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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)