• 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
        • Syntax-for-tools
        • Atc
        • Language
          • Abstract-syntax
            • Tyspecseq
            • Expr
            • Binop
            • Fileset
            • Obj-declor
            • Ident
            • Iconst
            • Obj-adeclor
            • Const
            • Fundef
            • Unop
            • File
            • Tag-declon
            • Fun-declor
            • Obj-declon
            • Iconst-length
            • Abstract-syntax-operations
            • Label
            • Struct-declon
            • Initer
            • Ext-declon
            • Fun-adeclor
            • Expr-option
            • Iconst-base
            • Initer-option
            • Iconst-option
              • Iconst-option-fix
              • Iconst-option-case
              • Iconst-option-equiv
              • Iconst-option-some
              • Iconst-option-none
              • Iconst-optionp
            • Tyspecseq-option
            • Stmt-option
            • Scspecseq
            • Param-declon
            • Obj-declon-option
            • File-option
            • Tyname
            • Transunit
            • Fun-declon
            • Transunit-result
            • Param-declon-list
            • Struct-declon-list
            • Expr-list
            • Tyspecseq-list
            • Ident-set
            • Ident-list
            • Ext-declon-list
            • Unop-list
            • Tyname-list
            • Fundef-list
            • Fun-declon-list
            • Binop-list
            • Stmt-fixtypes
            • Expr-fixtypes
          • Integer-ranges
          • Dynamic-semantics
          • Static-semantics
          • Grammar
          • Integer-formats
          • Types
          • Portable-ascii-identifiers
          • Values
          • Integer-operations
          • Computation-states
          • Object-designators
          • Implementation-environments
          • 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
        • Pack
      • Event-macros
      • Java
      • 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

• Iconst-option

Iconst-option-equiv

Basic equivalence relation for iconst-option structures.

Definitions and Theorems

Function: iconst-option-equiv$inline

(defun iconst-option-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (iconst-optionp acl2::x)
                              (iconst-optionp acl2::y))))
  (equal (iconst-option-fix acl2::x)
         (iconst-option-fix acl2::y)))

Theorem: iconst-option-equiv-is-an-equivalence

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

Theorem: iconst-option-equiv-implies-equal-iconst-option-fix-1

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

Theorem: iconst-option-fix-under-iconst-option-equiv

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

Theorem: equal-of-iconst-option-fix-1-forward-to-iconst-option-equiv

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

Theorem: equal-of-iconst-option-fix-2-forward-to-iconst-option-equiv

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

Theorem: iconst-option-equiv-of-iconst-option-fix-1-forward

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

Theorem: iconst-option-equiv-of-iconst-option-fix-2-forward

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