• 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
      • Set
      • Soft
      • C
        • Syntax-for-tools
          • Disambiguator
          • Abstract-syntax
          • Parser
          • Validator
          • Printer
          • Formalized-subset
          • Mapping-to-language-definition
          • Input-files
          • Defpred
          • Output-files
          • Abstract-syntax-operations
          • Validation-information
            • Abstract-syntax-annop
            • Types
            • Valid-ord-info
            • Lifetime
            • Valid-defstatus
            • Valid-table
            • Valid-ord-info-option
            • Linkage-option
            • Linkage
              • Linkage-case
              • Linkage-fix
              • Linkagep
              • Linkage-equiv
              • Linkage-none
              • Linkage-internal
              • Linkage-external
              • Linkage-kind
            • Lifetime-option
            • Iconst-info
            • Var-info
            • Valid-scope
            • Stmt-type
            • Expr-null-pointer-constp
            • Transunit-info
            • Expr-type
            • Const-expr-null-pointer-constp
            • Unary-info
            • Binary-info
            • Block-item-list-type
            • Block-item-type
            • Valid-ord-scope
            • Coerce-transunit-info
            • Coerce-var-info
            • Coerce-unary-info
            • Coerce-iconst-info
            • Coerce-binary-info
            • Irr-transunit-info
            • Irr-iconst-info
            • Irr-binary-info
            • Irr-var-info
            • Irr-valid-table
            • Irr-unary-info
            • Valid-scope-list
            • Irr-linkage
            • Irr-lifetime
          • Implementation-environments
          • Concrete-syntax
          • Unambiguity
          • Ascii-identifiers
          • Preprocessing
          • Abstraction-mapping
        • Atc
        • Language
        • Representation
        • Transformation-tools
        • Insertion-sort
        • Pack
      • Bv
      • Imp-language
      • Event-macros
      • Java
      • Bitcoin
      • Ethereum
      • Yul
      • Zcash
      • ACL2-programming-language
      • Prime-fields
      • Json
      • Syntheto
      • File-io-light
      • Cryptography
      • Number-theory
      • Lists-light
      • Axe
      • Builtins
      • Solidity
      • Helpers
      • Htclient
      • Typed-lists-light
      • Arithmetic-light
    • X86isa
    • Axe
    • Execloader
  • Math
  • Testing-utilities

• Linkage

Linkage-equiv

Basic equivalence relation for linkage structures.

Definitions and Theorems

Function: linkage-equiv$inline

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

Theorem: linkage-equiv-is-an-equivalence

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

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

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

Theorem: linkage-fix-under-linkage-equiv

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

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

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

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

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

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

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

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

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