• 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
        • Atc
        • Language
          • Abstract-syntax
          • Integer-ranges
          • Implementation-environments
          • Dynamic-semantics
          • Static-semantics
          • Grammar
          • Integer-formats
          • Types
          • Portable-ascii-identifiers
          • Values
          • Integer-operations
          • Computation-states
            • Write-object
            • Objdesign-of-var
            • Compustate-scopes-numbers
            • Create-var
            • Read-object
            • Compustate
            • Frame
            • Enter-scope
            • Compustate-scopes-numbers-aux
            • Compustate-option
            • Push-frame
            • Exit-scope
            • Compustate-frames-number
            • Compustate-option-result
            • Scope-list-result
            • Pop-frame
            • Compustate-result
              • Compustate-result-fix
              • Compustate-result-equiv
              • Compustate-resultp
              • Compustate-result-ok
              • Compustate-result-err
              • Compustate-result-kind
            • Scope-result
            • Compustate-top-frame-scopes-number
            • Top-frame
            • Heap
            • Scope
            • Scope-list
            • Frame-list
          • Object-designators
          • Operations
          • Errors
          • Tag-environments
          • Function-environments
          • Character-sets
          • Flexible-array-member-removal
          • Arithmetic-operations
          • Pointer-operations
          • Bytes
          • Keywords
          • Real-operations
          • Array-operations
          • Scalar-operations
          • Structure-operations
        • 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

• Compustate-result

Compustate-result-equiv

Basic equivalence relation for compustate-result structures.

Definitions and Theorems

Function: compustate-result-equiv$inline

(defun compustate-result-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (compustate-resultp acl2::x)
                              (compustate-resultp acl2::y))))
  (equal (compustate-result-fix acl2::x)
         (compustate-result-fix acl2::y)))

Theorem: compustate-result-equiv-is-an-equivalence

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

Theorem: compustate-result-equiv-implies-equal-compustate-result-fix-1

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

Theorem: compustate-result-fix-under-compustate-result-equiv

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

Theorem: equal-of-compustate-result-fix-1-forward-to-compustate-result-equiv

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

Theorem: equal-of-compustate-result-fix-2-forward-to-compustate-result-equiv

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

Theorem: compustate-result-equiv-of-compustate-result-fix-1-forward

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

Theorem: compustate-result-equiv-of-compustate-result-fix-2-forward

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