• 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
          • Integer-ranges
            • Def-integer-range
            • Integer-type-rangep
            • Ushort-integer
            • Ullong-integer
            • Sshort-integer
            • Sllong-integer
            • Ulong-integer
              • Ulong-integerp
              • Ulong-integer-fix
            • Uint-integer
            • Uchar-integer
            • Slong-integer
            • Sint-integer
            • Schar-integer
            • Ushort-max
            • Slong-max
            • Integer-type-max
            • Sllong-max
            • Integer-type-min
            • Uint-max
            • Sint-max
            • Ulong-max
            • Uchar-max
            • Def-integer-range-loop
            • Sshort-min
            • Sshort-max
            • Slong-min
            • Sint-min
            • Ullong-max
            • Sllong-min
            • Schar-min
            • Schar-max
            • Ushort-integer-list
            • Ulong-integer-list
            • Ullong-integer-list
            • Uint-integer-list
            • Uchar-integer-list
            • Sshort-integer-list
            • Slong-integer-list
            • Sllong-integer-list
            • Sint-integer-list
            • Schar-integer-list
            • Uchar-integerp-alt-def
            • Ushort-integerp-alt-def
            • Ulong-integerp-alt-def
            • Ullong-integerp-alt-def
            • Uint-integerp-alt-def
            • Sshort-integerp-alt-def
            • Slong-integerp-alt-def
            • Sllong-integerp-alt-def
            • Sint-integerp-alt-def
            • Schar-integerp-alt-def
          • 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

• Integer-ranges

Ulong-integer

Fixtype of ACL2 integers in the range of type unsigned long.

Definitions and Theorems

Function: ulong-integer-equiv$inline

(defun ulong-integer-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (ulong-integerp acl2::x)
                              (ulong-integerp acl2::y))))
  (equal (ulong-integer-fix acl2::x)
         (ulong-integer-fix acl2::y)))

Theorem: ulong-integer-equiv-is-an-equivalence

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

Theorem: ulong-integer-equiv-implies-equal-ulong-integer-fix-1

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

Theorem: ulong-integer-fix-under-ulong-integer-equiv

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

Theorem: equal-of-ulong-integer-fix-1-forward-to-ulong-integer-equiv

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

Theorem: equal-of-ulong-integer-fix-2-forward-to-ulong-integer-equiv

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

Theorem: ulong-integer-equiv-of-ulong-integer-fix-1-forward

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

Theorem: ulong-integer-equiv-of-ulong-integer-fix-2-forward

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

Subtopics

Ulong-integerp

Recognizer for ulong-integer.

Ulong-integer-fix

Fixer for ulong-integer.