• 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
      • Instructions
        • Instr
        • Op-funct
        • Op-32-funct
        • Op-imm-funct
        • Load-funct
        • Branch-funct
        • Op-imms-funct
        • Store-funct
          • Store-funct-fix
          • Store-funct-case
          • Store-funct-equiv
          • Store-funct-p
          • Store-funct-sw
          • Store-funct-sh
          • Store-funct-sd
          • Store-funct-sb
          • Store-funct-kind
        • Op-imms-32-funct
        • Instr-validp
        • Instr-option
        • Op-imm-32-funct
      • States
      • Decoding
      • Encoding
      • Features
      • Semantics
      • Execution
    • 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
    • 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

• Store-funct

Store-funct-equiv

Basic equivalence relation for store-funct structures.

Definitions and Theorems

Function: store-funct-equiv$inline

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

Theorem: store-funct-equiv-is-an-equivalence

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

Theorem: store-funct-equiv-implies-equal-store-funct-fix-1

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

Theorem: store-funct-fix-under-store-funct-equiv

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

Theorem: equal-of-store-funct-fix-1-forward-to-store-funct-equiv

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

Theorem: equal-of-store-funct-fix-2-forward-to-store-funct-equiv

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

Theorem: store-funct-equiv-of-store-funct-fix-1-forward

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

Theorem: store-funct-equiv-of-store-funct-fix-2-forward

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