• Top
  • Documentation
  • Books
  • Boolean-reasoning
  • Projects
    • Apt
    • Zfc
    • Acre
    • Milawa
    • Smtlink
    • Abnf
    • Vwsim
    • Isar
    • Wp-gen
    • Dimacs-reader
    • Pfcs
    • Legacy-defrstobj
    • C
    • Proof-checker-array
    • Soft
    • Farray
    • Rp-rewriter
    • Instant-runoff-voting
    • Imp-language
    • Sidekick
    • Ethereum
      • Mmp-trees
        • Mmp-encode-n/c
        • Mmp-encode-c-max
        • Mmp-encode
        • Mmp-write
        • Mmp-decode
        • Mmp-encode-u-map
        • Nibblelist-bytelist-map-sup-len-key
        • Mmp-encode-c-forall
        • Mmp-read
        • Mmp-encoding-p
        • Bytelist-to-nibblelist-keys
        • Mmp-encode-c-exists
        • Bytelist-bytelist-map
        • Nibblelist-bytelist-map
          • Nibblelist-bytelist-mfix
          • Nibblelist-bytelist-mapp
          • Nibblelist-bytelist-mequiv
      • Semaphore
      • Database
      • Cryptography
      • Rlp
      • Transactions
      • Hex-prefix
      • Basics
      • Addresses
    • Leftist-trees
    • Java
    • Riscv
    • Taspi
    • Bitcoin
    • Zcash
    • Des
    • X86isa
    • Sha-2
    • Yul
    • Proof-checker-itp13
    • Regex
    • ACL2-programming-language
    • Json
    • Jfkr
    • Equational
    • Cryptography
    • Axe
    • Poseidon
    • Where-do-i-place-my-book
    • Aleo
    • Bigmems
    • Builtins
    • Execloader
    • Solidity
    • Paco
    • Concurrent-programs
    • Bls12-377-curves
  • Debugging
  • Community
  • Std
  • Proof-automation
  • Macro-libraries
  • ACL2
  • Interfacing-tools
  • Hardware-verification
  • Software-verification
  • Math
  • Testing-utilities

• Nibblelist-bytelist-map

Nibblelist-bytelist-mequiv

Basic equivalence relation for nibblelist-bytelist-map structures.

Definitions and Theorems

Function: nibblelist-bytelist-mequiv$inline

(defun nibblelist-bytelist-mequiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (nibblelist-bytelist-mapp acl2::x)
                              (nibblelist-bytelist-mapp acl2::y))))
  (equal (nibblelist-bytelist-mfix acl2::x)
         (nibblelist-bytelist-mfix acl2::y)))

Theorem: nibblelist-bytelist-mequiv-is-an-equivalence

(defthm nibblelist-bytelist-mequiv-is-an-equivalence
  (and (booleanp (nibblelist-bytelist-mequiv x y))
       (nibblelist-bytelist-mequiv x x)
       (implies (nibblelist-bytelist-mequiv x y)
                (nibblelist-bytelist-mequiv y x))
       (implies (and (nibblelist-bytelist-mequiv x y)
                     (nibblelist-bytelist-mequiv y z))
                (nibblelist-bytelist-mequiv x z)))
  :rule-classes (:equivalence))

Theorem: nibblelist-bytelist-mequiv-implies-equal-nibblelist-bytelist-mfix-1

(defthm
 nibblelist-bytelist-mequiv-implies-equal-nibblelist-bytelist-mfix-1
 (implies (nibblelist-bytelist-mequiv acl2::x x-equiv)
          (equal (nibblelist-bytelist-mfix acl2::x)
                 (nibblelist-bytelist-mfix x-equiv)))
 :rule-classes (:congruence))

Theorem: nibblelist-bytelist-mfix-under-nibblelist-bytelist-mequiv

(defthm nibblelist-bytelist-mfix-under-nibblelist-bytelist-mequiv
  (nibblelist-bytelist-mequiv (nibblelist-bytelist-mfix acl2::x)
                              acl2::x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-nibblelist-bytelist-mfix-1-forward-to-nibblelist-bytelist-mequiv

(defthm
 equal-of-nibblelist-bytelist-mfix-1-forward-to-nibblelist-bytelist-mequiv
 (implies (equal (nibblelist-bytelist-mfix acl2::x)
                 acl2::y)
          (nibblelist-bytelist-mequiv acl2::x acl2::y))
 :rule-classes :forward-chaining)

Theorem: equal-of-nibblelist-bytelist-mfix-2-forward-to-nibblelist-bytelist-mequiv

(defthm
 equal-of-nibblelist-bytelist-mfix-2-forward-to-nibblelist-bytelist-mequiv
 (implies (equal acl2::x
                 (nibblelist-bytelist-mfix acl2::y))
          (nibblelist-bytelist-mequiv acl2::x acl2::y))
 :rule-classes :forward-chaining)

Theorem: nibblelist-bytelist-mequiv-of-nibblelist-bytelist-mfix-1-forward

(defthm
   nibblelist-bytelist-mequiv-of-nibblelist-bytelist-mfix-1-forward
 (implies
      (nibblelist-bytelist-mequiv (nibblelist-bytelist-mfix acl2::x)
                                  acl2::y)
      (nibblelist-bytelist-mequiv acl2::x acl2::y))
 :rule-classes :forward-chaining)

Theorem: nibblelist-bytelist-mequiv-of-nibblelist-bytelist-mfix-2-forward

(defthm
   nibblelist-bytelist-mequiv-of-nibblelist-bytelist-mfix-2-forward
 (implies
     (nibblelist-bytelist-mequiv acl2::x
                                 (nibblelist-bytelist-mfix acl2::y))
     (nibblelist-bytelist-mequiv acl2::x acl2::y))
 :rule-classes :forward-chaining)