• Top
  • Documentation
  • Books
  • Boolean-reasoning
  • Projects
  • Debugging
  • Std
  • Proof-automation
  • Macro-libraries
  • ACL2
  • Interfacing-tools
  • Hardware-verification
  • Software-verification
    • Kestrel-books
      • Crypto-hdwallet
      • Apt
      • Error-checking
      • Fty-extensions
      • Isar
      • Kestrel-utilities
      • Soft
      • Bv
      • Imp-language
      • C
      • Event-macros
      • Java
        • Atj
          • Atj-implementation
            • Atj-types
            • Atj-java-primitive-array-model
            • Atj-java-abstract-syntax
              • Jbinop
              • Jmethod
              • Jtype
              • Jfield
              • Jexprs
              • Jliteral
              • Junop
              • Jlocvar
              • Jcunit
              • Jaccess
              • Maybe-jexpr
              • Jparam
              • Jimport
                • Jimport-fix
                • Jimport-equiv
                • Make-jimport
                • Change-jimport
                • Jimport->target
                • Jimport->static?
                • Jimportp
              • Jcinitializer
              • Jresult
              • Jstatems+jblocks
              • Jexpr-get-field
              • Jliteral-long-dec-nouscores
              • Nat-to-dec-chars-theorems
              • Jmethods-to-jcbody-elements
              • Jclasses-to-jcbody-elements
              • Jblock-locvar-final
              • Jblock-locvar
              • Jliteral-int-dec-nouscores
              • Jfields-to-jcbody-elements
              • Jblock-for
              • Jblock-smethod
              • Jblock-imethod
              • Jblock-ifelse
              • Jblock-asg-name
              • Jparam-list->types
              • Jparam-list->names
              • Jexpr-lit-long-dec-nouscores
              • Jexpr-lit-int-dec-nouscores
              • Jexpr-literal-string
              • Jexpr-literal-floating
              • Jexpr-literal-character
              • Jblock-while
              • Jblock-method
              • Jblock-if
              • Jblock-expr
              • Jblock-do
              • Jblock-asg
              • Jexpr-name-list
              • Jblock-throw
              • Jblock-return
              • Jparam-list
              • Jimport-list
              • Jexpr-literal-true
              • Jexpr-literal-null
              • Jexpr-literal-false
              • Jexpr-literal-1
              • Jexpr-literal-0
              • Jclass-list
              • Jblock-continue
              • Jtype-short
              • Jtype-long
              • Jtype-list
              • Jtype-int
              • Jtype-float
              • Jtype-double
              • Jtype-char
              • Jtype-byte
              • Jtype-boolean
              • Jmethod-list
              • Jliteral-list
              • Jfield-list
              • Jblock-list
              • Jblock-break
              • Jclasses+jcmembers
            • Atj-input-processing
            • Atj-java-pretty-printer
            • Atj-code-generation
            • Atj-java-primitives
            • Atj-java-primitive-arrays
            • Atj-type-macros
            • Atj-java-syntax-operations
            • Atj-fn
            • Atj-library-extensions
            • Atj-java-input-types
            • Atj-test-structures
            • Aij-notions
            • Atj-macro-definition
          • Atj-tutorial
        • Aij
        • Language
      • Bitcoin
      • Ethereum
      • Yul
      • Zcash
      • ACL2-programming-language
      • Prime-fields
      • Json
      • Syntheto
      • File-io-light
      • Number-theory
      • Cryptography
      • Lists-light
      • Builtins
      • Axe
      • Solidity
      • Helpers
      • Htclient
      • Typed-lists-light
      • Arithmetic-light
    • X86isa
    • Axe
    • Execloader
  • Math
  • Testing-utilities

• Jimport

Jimport-equiv

Basic equivalence relation for jimport structures.

Definitions and Theorems

Function: jimport-equiv$inline

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

Theorem: jimport-equiv-is-an-equivalence

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

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

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

Theorem: jimport-fix-under-jimport-equiv

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

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

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

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

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

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

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

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

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