• 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
      • Bitcoin
      • Ethereum
      • Yul
      • Zcash
      • ACL2-programming-language
        • Primitive-functions
        • Translated-terms
        • Values
        • Evaluation
        • Program-equivalence
        • Functions
        • Packages
          • Lift-package-list
          • Import-lookup
          • Package-option
          • Package-lookup
          • Package
          • Lift-package
          • Package-list
            • Package-list-fix
            • Package-list-equiv
            • Package-listp
        • Programs
        • Interpreter
        • Evaluation-states
      • 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

• Package-list

Package-list-equiv

Basic equivalence relation for package-list structures.

Definitions and Theorems

Function: package-list-equiv$inline

(defun package-list-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (package-listp acl2::x)
                              (package-listp acl2::y))))
  (equal (package-list-fix acl2::x)
         (package-list-fix acl2::y)))

Theorem: package-list-equiv-is-an-equivalence

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

Theorem: package-list-equiv-implies-equal-package-list-fix-1

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

Theorem: package-list-fix-under-package-list-equiv

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

Theorem: equal-of-package-list-fix-1-forward-to-package-list-equiv

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

Theorem: equal-of-package-list-fix-2-forward-to-package-list-equiv

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

Theorem: package-list-equiv-of-package-list-fix-1-forward

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

Theorem: package-list-equiv-of-package-list-fix-2-forward

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