• Top
  • Documentation
  • Books
  • Boolean-reasoning
  • Projects
    • Apt
    • Aleobft
      • Aleobft-static
      • Aleobft-stake2
      • Aleobft-dynamic
      • Aleobft-stake
      • Aleobft-proposals
        • Definition
          • Initialization
          • Transitions
          • States
            • Committees
            • System-states
            • Certificates
            • Transactions
            • Messages
            • Proposals
              • Proposal
                • Proposal-fix
                • Proposalp
                • Proposal-equiv
                • Make-proposal
                • Proposal->transactions
                • Change-proposal
                • Proposal->previous
                • Proposal->round
                • Proposal->author
              • Props-with-author+round
              • Proposal-option
              • Props-with-round
              • Proposal-set
            • Validator-states
            • Addresses
            • Blocks
          • Events
          • Reachability
        • Correctness
      • Library-extensions
    • Acre
    • Milawa
    • Smtlink
    • Abnf
    • Vwsim
    • Isar
    • Wp-gen
    • Dimacs-reader
    • Pfcs
    • Legacy-defrstobj
    • Proof-checker-array
    • Soft
    • Farray
    • Rp-rewriter
    • Instant-runoff-voting
    • Imp-language
    • Sidekick
    • Leftist-trees
    • C
    • Java
    • Taspi
    • Bitcoin
    • Riscv
    • 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
    • Bigmems
    • Builtins
    • Axe
    • Execloader
    • Solidity
    • Leo
    • Paco
    • Concurrent-programs
  • Debugging
  • Std
  • Proof-automation
  • Macro-libraries
  • ACL2
  • Interfacing-tools
  • Hardware-verification
  • Software-verification
  • Math
  • Testing-utilities

• Proposal

Proposal-fix

Fixing function for proposal structures.

Signature

(proposal-fix x) → new-x

Arguments

x — Guard (proposalp x).

Returns

new-x — Type (proposalp new-x).

Definitions and Theorems

Function: proposal-fix$inline

(defun proposal-fix$inline (x)
 (declare (xargs :guard (proposalp x)))
 (let ((__function__ 'proposal-fix))
  (declare (ignorable __function__))
  (mbe
    :logic
    (b*
      ((author (address-fix (cdr (std::da-nth 0 x))))
       (round (pos-fix (cdr (std::da-nth 1 x))))
       (transactions (transaction-list-fix (cdr (std::da-nth 2 x))))
       (previous (address-set-fix (cdr (std::da-nth 3 x)))))
      (list (cons 'author author)
            (cons 'round round)
            (cons 'transactions transactions)
            (cons 'previous previous)))
    :exec x)))

Theorem: proposalp-of-proposal-fix

(defthm proposalp-of-proposal-fix
  (b* ((new-x (proposal-fix$inline x)))
    (proposalp new-x))
  :rule-classes :rewrite)

Theorem: proposal-fix-when-proposalp

(defthm proposal-fix-when-proposalp
  (implies (proposalp x)
           (equal (proposal-fix x) x)))

Function: proposal-equiv$inline

(defun proposal-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (proposalp acl2::x)
                              (proposalp acl2::y))))
  (equal (proposal-fix acl2::x)
         (proposal-fix acl2::y)))

Theorem: proposal-equiv-is-an-equivalence

(defthm proposal-equiv-is-an-equivalence
  (and (booleanp (proposal-equiv x y))
       (proposal-equiv x x)
       (implies (proposal-equiv x y)
                (proposal-equiv y x))
       (implies (and (proposal-equiv x y)
                     (proposal-equiv y z))
                (proposal-equiv x z)))
  :rule-classes (:equivalence))

Theorem: proposal-equiv-implies-equal-proposal-fix-1

(defthm proposal-equiv-implies-equal-proposal-fix-1
  (implies (proposal-equiv acl2::x x-equiv)
           (equal (proposal-fix acl2::x)
                  (proposal-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: proposal-fix-under-proposal-equiv

(defthm proposal-fix-under-proposal-equiv
  (proposal-equiv (proposal-fix acl2::x)
                  acl2::x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-proposal-fix-1-forward-to-proposal-equiv

(defthm equal-of-proposal-fix-1-forward-to-proposal-equiv
  (implies (equal (proposal-fix acl2::x) acl2::y)
           (proposal-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: equal-of-proposal-fix-2-forward-to-proposal-equiv

(defthm equal-of-proposal-fix-2-forward-to-proposal-equiv
  (implies (equal acl2::x (proposal-fix acl2::y))
           (proposal-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: proposal-equiv-of-proposal-fix-1-forward

(defthm proposal-equiv-of-proposal-fix-1-forward
  (implies (proposal-equiv (proposal-fix acl2::x)
                           acl2::y)
           (proposal-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: proposal-equiv-of-proposal-fix-2-forward

(defthm proposal-equiv-of-proposal-fix-2-forward
  (implies (proposal-equiv acl2::x (proposal-fix acl2::y))
           (proposal-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)