• Top
    • Documentation
    • Books
    • Boolean-reasoning
    • Projects
      • Apt
      • Zfc
      • Acre
      • Milawa
      • Smtlink
      • Abnf
      • Vwsim
      • Isar
      • Pfcs
      • Wp-gen
      • Dimacs-reader
      • Legacy-defrstobj
      • Proof-checker-array
      • Soft
      • C
      • Farray
      • Rp-rewriter
      • Riscv
      • Instant-runoff-voting
      • Imp-language
      • Sidekick
      • Leftist-trees
      • Java
      • Taspi
      • Bitcoin
      • Des
      • Ethereum
      • X86isa
      • Sha-2
      • Yul
      • Zcash
      • Proof-checker-itp13
      • Regex
      • ACL2-programming-language
      • Json
      • Jfkr
      • Equational
      • Cryptography
      • Poseidon
      • Where-do-i-place-my-book
      • Axe
      • Aleo
        • Aleobft
          • Correctness
          • Definition
            • Initialization
            • Transitions
            • States
              • Committees
              • System-states
              • Certificates
                • Certificate-set-unequivocalp
                • Certificate-sets-unequivocalp
                • Cert-with-author+round
                • Certs-with-authors+round
                • Certs-with-author
                • Certs-with-round
                • Unequivocal-certs-with-authors+round
                • Unequivocal-cert-with-author+round
                • Certificate
                • Cert-set->author-set
                  • Certificate-option
                  • Cert-set->round-set
                  • Certs-with-authors
                  • Certificate-list-orderedp
                  • Certs-with-signer
                  • Certificate->signers
                  • Certificate-list-evenp
                  • Certificate->transactions
                  • Certificate->previous
                  • Certificate->author
                  • Certificate->round
                  • Certificate-set
                  • Certificate-list
                • Messages
                • Transactions
                • Proposals
                • Validator-states
                • Blocks
                • Addresses
              • Events
              • Reachability
            • Library-extensions
          • Aleovm
          • Leo
        • Bigmems
        • Builtins
        • Execloader
        • Solidity
        • Paco
        • Concurrent-programs
        • Bls12-377-curves
      • Debugging
      • Std
      • Community
      • Proof-automation
      • Macro-libraries
      • ACL2
      • Interfacing-tools
      • Hardware-verification
      • Software-verification
      • Math
      • Testing-utilities
    • Certificates

    Cert-set->author-set

    Lift certificate->author to sets.

    Signature
    (cert-set->author-set certs) → addrs
    Arguments
    certs — Guard (certificate-setp certs).
    Returns
    addrs — Type (address-setp addrs).

    Definitions and Theorems

    Function: cert-set->author-set

    (defun cert-set->author-set (certs)
      (declare (xargs :guard (certificate-setp certs)))
      (let ((__function__ 'cert-set->author-set))
        (declare (ignorable __function__))
        (cond ((emptyp (certificate-set-fix certs))
               nil)
              (t (insert (certificate->author (head certs))
                         (cert-set->author-set (tail certs)))))))

    Theorem: address-setp-of-cert-set->author-set

    (defthm address-setp-of-cert-set->author-set
      (b* ((addrs (cert-set->author-set certs)))
        (address-setp addrs))
      :rule-classes :rewrite)

    Theorem: emptyp-of-cert-set->author-set

    (defthm emptyp-of-cert-set->author-set
      (equal (emptyp (cert-set->author-set certs))
             (emptyp (certificate-set-fix certs))))

    Theorem: certificate->author-in-cert-set->author-set

    (defthm certificate->author-in-cert-set->author-set
      (implies (in (certificate-fix cert)
                   (certificate-set-fix certs))
               (in (certificate->author cert)
                   (cert-set->author-set certs))))

    Theorem: cert-set->author-set-monotone

    (defthm cert-set->author-set-monotone
      (implies (subset certs1 (certificate-set-fix certs2))
               (subset (cert-set->author-set certs1)
                       (cert-set->author-set certs2))))

    Theorem: cert-set->author-set-of-insert

    (defthm cert-set->author-set-of-insert
      (implies (and (certificatep cert)
                    (certificate-setp certs))
               (equal (cert-set->author-set (insert cert certs))
                      (insert (certificate->author cert)
                              (cert-set->author-set certs)))))

    Theorem: cert-set->author-set-of-union

    (defthm cert-set->author-set-of-union
      (implies (and (certificate-setp certs1)
                    (certificate-setp certs2))
               (equal (cert-set->author-set (union certs1 certs2))
                      (union (cert-set->author-set certs1)
                             (cert-set->author-set certs2)))))

    Theorem: same-certificate-author-when-cardinality-leq-1

    (defthm same-certificate-author-when-cardinality-leq-1
      (implies (and (<= (cardinality (cert-set->author-set certs))
                        1)
                    (in cert1 (certificate-set-fix certs))
                    (in cert2 (certificate-set-fix certs)))
               (equal (certificate->author cert1)
                      (certificate->author cert2))))

    Theorem: cert-set->author-set-of-certificate-set-fix-certs

    (defthm cert-set->author-set-of-certificate-set-fix-certs
      (equal (cert-set->author-set (certificate-set-fix certs))
             (cert-set->author-set certs)))

    Theorem: cert-set->author-set-certificate-set-equiv-congruence-on-certs

    (defthm
         cert-set->author-set-certificate-set-equiv-congruence-on-certs
      (implies (certificate-set-equiv certs certs-equiv)
               (equal (cert-set->author-set certs)
                      (cert-set->author-set certs-equiv)))
      :rule-classes :congruence)