• Top
  • Documentation
  • Books
  • Boolean-reasoning
  • Projects
    • Apt
    • Zfc
    • Acre
    • Milawa
    • Smtlink
    • Abnf
    • Vwsim
    • Isar
    • Wp-gen
    • Dimacs-reader
    • Pfcs
    • Legacy-defrstobj
    • Proof-checker-array
    • Soft
    • C
    • Farray
    • Rp-rewriter
    • Instant-runoff-voting
    • Imp-language
    • Sidekick
    • Leftist-trees
    • Java
    • Taspi
    • Bitcoin
    • Riscv
    • Des
    • Ethereum
      • Mmp-trees
      • Semaphore
      • Database
      • Cryptography
      • Rlp
        • Rlp-tree
        • Rlp-decoding-executable
          • Rlp-error
            • Rlp-error-fix
            • Rlp-error-p
            • Rlp-error-case
            • Rlp-error-equiv
            • Rlp-error-count
            • Rlp-error-fewer-bytes-than-short-length
            • Rlp-error-fewer-bytes-than-long-length
            • Rlp-error-fewer-bytes-than-length-of-length
            • Rlp-error-kind
            • Rlp-error-subtree
            • Rlp-error-non-optimal-short-length
            • Rlp-error-non-optimal-long-length
            • Rlp-error-leading-zeros-in-scalar
            • Rlp-error-leading-zeros-in-long-length
            • Rlp-error-extra-bytes
            • Rlp-error-branch-tree
            • Rlp-error-no-bytes
          • Rlp-parse-tree
          • Rlp-decodex-tree
          • Maybe-rlp-error
          • Rlp-decodex-bytes
          • Rlp-decodex-scalar
        • Rlp-decodability
        • Rlp-encoding
        • Rlp-decoding-declarative
        • Rlp-big-endian-representations
      • Transactions
      • Hex-prefix
      • Basics
      • Addresses
    • X86isa
    • Sha-2
    • Yul
    • Zcash
    • Proof-checker-itp13
    • Regex
    • ACL2-programming-language
    • Json
    • Jfkr
    • Equational
    • Cryptography
    • Poseidon
    • Where-do-i-place-my-book
    • Axe
    • Bigmems
    • Builtins
    • Execloader
    • Aleo
    • Solidity
    • Paco
    • Concurrent-programs
    • Bls12-377-curves
  • Debugging
  • Std
  • Proof-automation
  • Macro-libraries
  • ACL2
  • Interfacing-tools
  • Hardware-verification
  • Software-verification
  • Math
  • Testing-utilities

• Rlp-error

Rlp-error-equiv

Basic equivalence relation for rlp-error structures.

Definitions and Theorems

Function: rlp-error-equiv$inline

(defun rlp-error-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (rlp-error-p acl2::x)
                              (rlp-error-p acl2::y))))
  (equal (rlp-error-fix acl2::x)
         (rlp-error-fix acl2::y)))

Theorem: rlp-error-equiv-is-an-equivalence

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

Theorem: rlp-error-equiv-implies-equal-rlp-error-fix-1

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

Theorem: rlp-error-fix-under-rlp-error-equiv

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

Theorem: equal-of-rlp-error-fix-1-forward-to-rlp-error-equiv

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

Theorem: equal-of-rlp-error-fix-2-forward-to-rlp-error-equiv

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

Theorem: rlp-error-equiv-of-rlp-error-fix-1-forward

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

Theorem: rlp-error-equiv-of-rlp-error-fix-2-forward

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