• 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
      • Bv
      • Imp-language
      • Event-macros
      • Java
      • Bitcoin
      • Ethereum
      • Yul
        • Transformations
        • Language
          • Abstract-syntax
            • Escape
            • Swcase-list->value-list
            • Hex-digit-list->chars
            • Fundef-list->name-list
            • Literal
            • Path
            • Hex-string-rest-element
            • Plain-string
            • String-element
            • Hex-string-content-option
            • Hex-string-content
            • Identifier
            • Funcall-option
            • Expression-option
            • Statement-option
            • Literal-option
            • Identifier-option
            • Hex-string
            • Hex-quad
            • Hex-digit
            • Hex-pair
            • Data-value
            • Data-item
            • Statements-to-fundefs
            • String-element-list-result
            • Identifier-identifier-map-result
            • Swcase-result
            • String-element-result
            • Statement-result
            • Literal-result
            • Identifier-set-result
            • Identifier-result
            • Identifier-list-result
            • Fundef-result
            • Funcall-result
            • Expression-result
            • Escape-result
            • Path-result
            • Block-result
            • Objects
            • Statements/blocks/cases/fundefs
              • Statement
              • Fundef
                • Fundefp
                • Make-fundef
                • Fundef-equiv
                • Fundef->outputs
                • Fundef->name
                • Change-fundef
                • Fundef->inputs
                • Fundef->body
                • Fundef-fix
                • Fundef-count
              • Block-option
              • Block
              • Swcase
              • Swcase-list
              • Statement-list
            • Identifier-list
            • Identifier-set
            • Identifier-identifier-map
            • Identifier-identifier-alist
            • Hex-string-rest-element-list
            • String-element-list
            • Path-list
            • Hex-digit-list
            • Literal-list
            • Fundef-list
            • Expressions/funcalls
            • Abstract-syntax-induction-schemas
          • Dynamic-semantics
          • Concrete-syntax
          • Static-soundness
          • Static-semantics
          • Errors
        • Yul-json
      • 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

• Fundef

Fundef-equiv

Basic equivalence relation for fundef structures.

Definitions and Theorems

Function: fundef-equiv$inline

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

Theorem: fundef-equiv-is-an-equivalence

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

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

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

Theorem: fundef-fix-under-fundef-equiv

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

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

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

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

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

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

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

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

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