• Top
  • Documentation
  • Books
  • Boolean-reasoning
  • Projects
    • Apt
    • Acre
    • Milawa
    • Smtlink
    • Aleobft
    • Abnf
    • Vwsim
    • Isar
    • Wp-gen
    • Dimacs-reader
    • Pfcs
    • Legacy-defrstobj
    • Proof-checker-array
    • Soft
    • Farray
    • Rp-rewriter
    • Instant-runoff-voting
    • Imp-language
    • Sidekick
    • Leftist-trees
    • 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
            • Iconst-base-fix
            • Iconst-base-case
            • Iconst-base-equiv
            • Iconst-basep
            • Iconst-base-oct
            • Iconst-base-kind
            • Iconst-base-hex
            • Iconst-base-dec
          • Initer-option
          • Iconst-option
          • 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
    • Java
    • Taspi
    • Bitcoin
    • Des
    • Ethereum
    • X86isa
    • Sha-2
    • Yul
    • Riscv
    • Zcash
    • Proof-checker-itp13
    • Regex
    • ACL2-programming-language
    • Json
    • Jfkr
    • Equational
    • Cryptography
    • Poseidon
    • Where-do-i-place-my-book
    • Bigmems
    • Builtins
    • Axe
    • Execloader
    • Solidity
    • Leo
    • Paco
    • Concurrent-programs
  • Debugging
  • Std
  • Proof-automation
  • Macro-libraries
  • ACL2
  • Interfacing-tools
  • Hardware-verification
  • Software-verification
  • Math
  • Testing-utilities

• Iconst-base

Iconst-base-equiv

Basic equivalence relation for iconst-base structures.

Definitions and Theorems

Function: iconst-base-equiv$inline

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

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

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

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

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

Theorem: iconst-base-fix-under-iconst-base-equiv

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

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

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

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

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

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

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

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

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