• 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
    • Instant-runoff-voting
    • Imp-language
    • Sidekick
    • Leftist-trees
    • Java
    • Taspi
    • Riscv
    • 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
      • Aleovm
        • Circuits
        • Language
          • Grammar
          • Early-version
            • Abstract-syntax
              • Binary-op
              • Literal
              • Instruction
              • Hash-op
              • Literal-type
              • Operand
              • Unary-op
              • Identifier
              • Commit-op
              • Mapping
              • Function
              • Programdef
              • Finalize-type
              • Closure
              • Register-type
              • Finalizer
              • Value-type
              • Record-type
              • Command
              • Plaintext-type
              • Finalization-option
              • Visibility
              • Register
              • Reference
              • Programid
              • Locator
              • Finalization
              • Entry-type
              • Regaccess
                • Regaccess-fix
                • Regaccess-equiv
                • Make-regaccess
                • Regaccess->comps
                • Change-regaccess
                • Regaccess->base
                • Regaccessp
              • Program
              • Interface-type
              • Ident+ptype
              • Ident+etype
              • Function-output
              • Finalize-output
              • Finalize-input
              • Closure-output
              • Closure-input
              • Assert-op
              • Function-input
              • Equal-op
              • Finalize-command
              • Ternary-op
              • Import
              • Ident+ptype-list
              • Operand-list
              • Ident+etype-list
              • Programdef-list
              • Instruction-list
              • Import-list
              • Identifier-list
              • Function-output-list
              • Function-input-list
              • Finalize-output-list
              • Finalize-input-list
              • Command-list
              • Closure-output-list
              • Closure-input-list
            • Parser
            • Concrete-syntax
          • Concrete-syntax
      • Leo
    • Bigmems
    • Builtins
    • Execloader
    • Solidity
    • Paco
    • Concurrent-programs
    • Bls12-377-curves
  • Debugging
  • Std
  • Community
  • Proof-automation
  • ACL2
  • Macro-libraries
  • Interfacing-tools
  • Hardware-verification
  • Software-verification
  • Math
  • Testing-utilities

• Regaccess

Regaccess-equiv

Basic equivalence relation for regaccess structures.

Definitions and Theorems

Function: regaccess-equiv$inline

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

Theorem: regaccess-equiv-is-an-equivalence

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

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

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

Theorem: regaccess-fix-under-regaccess-equiv

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

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

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

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

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

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

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

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

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