• 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
          • Disambiguator
          • Abstract-syntax
            • Expr
            • Exprs/decls/stmts
            • Type-spec
            • Binop
            • Stmt
            • Amb-expr/tyname
            • Dirdeclor
            • Unop
            • Asm-stmt
            • Dec/oct/hex-const
            • Simple-escape
            • Attrib
            • Amb-decl/stmt
            • Dirabsdeclor
            • Ident
            • Decl-spec
            • Structdecl
            • Fundef
            • Asm-name-spec
            • Amb-declor/absdeclor
            • Transunit-ensemble
            • Paramdeclor
            • Declor
            • Type-qual
            • Absdeclor
            • Stor-spec
            • Keyword-uscores
            • Strunispec
            • Align-spec
            • Lsuffix
            • Label
            • Expr-option
            • Spec/qual
            • Hex-frac-const
            • Dec-frac-const
            • Dec-core-fconst
            • Tyname
            • Dirabsdeclor-option
            • Desiniter
            • Extdecl
            • Amb?-declor/absdeclor
            • Isuffix
            • Attrib-spec
            • Initdeclor
            • Hex-core-fconst
            • Escape
            • Decl
            • Const-expr-option
            • Amb?-expr/tyname
            • Structdeclor
            • Bin-expo
            • Statassert
            • Ident-option
            • Fsuffix
            • Enumspec
            • Absdeclor-option
            • Paramdecl
            • Member-designor
            • Initer-option
            • Initer
            • Declor-option
            • Const
            • Block-item
            • Oct-escape
            • Inc/dec-op
            • Iconst
            • Hex-quad
            • Fun-spec
            • Eprefix
            • Dec-expo
            • Cprefix-option
            • Const-expr
            • Asm-name-spec-option
            • Amb?-decl/stmt
            • S-char
            • Isuffix-option
            • Fundef-option
            • Fsuffix-option
            • Fconst
              • Fconst-case
              • Fconst-fix
              • Fconst-equiv
              • Fconst-hex
              • Fconstp
              • Fconst-dec
              • Fconst-kind
            • Eprefix-option
            • Dec-expo-option
            • Cprefix
            • C-char
            • Sign-option
            • Iconst-option
            • Genassoc
            • Asm-output
            • Asm-input
            • Const-option
            • Usuffix
            • Univ-char-name
            • Designor
            • Attrib-name
            • Sign
            • Hprefix
            • Asm-qual
            • Typequal/attribspec
            • Enumer
            • Dec-expo-prefix
            • Bin-expo-prefix
            • Stringlit
            • Transunit
            • Cconst
            • Expr/tyname
            • Decl/stmt
            • Declor/absdeclor
            • Asm-clobber
            • Typequal/attribspec-list
            • Stringlit-list
            • Inc/dec-op-list
            • Decl-spec-list
            • Spec/qual-list
            • S-char-list
            • Decl-list
            • C-char-list
            • Typequal/attribspec-list-list
            • Structdeclor-list
            • Structdecl-list
            • Paramdecl-list
            • Initdeclor-list
            • Genassoc-list
            • Filepath-transunit-map
            • Extdecl-list
            • Desiniter-list
            • Enumer-list
            • Block-item-list
            • Attrib-spec-list
            • Type-spec-list
            • Ident-list
            • Expr-list
            • Asm-qual-list
            • Asm-output-list
            • Asm-input-list
            • Asm-clobber-list
            • Stor-spec-list
            • Ident-set
            • Ident-option-set
            • Eprefix-option-list
            • Designor-list
            • Attrib-list
          • Parser
          • Validator
          • Printer
          • Formalized-subset
          • Mapping-to-language-definition
          • Defpred
          • Output-files
          • Input-files
          • Abstract-syntax-operations
          • Implementation-environments
          • Concrete-syntax
          • Unambiguity
          • Preprocessing
          • Abstraction-mapping
          • Annotation
        • Atc
        • Language
        • 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

• Fconst

Fconst-equiv

Basic equivalence relation for fconst structures.

Definitions and Theorems

Function: fconst-equiv$inline

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

Theorem: fconst-equiv-is-an-equivalence

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

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

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

Theorem: fconst-fix-under-fconst-equiv

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

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

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

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

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

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

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

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

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