• Top
  • Documentation
  • Books
  • Boolean-reasoning
  • Projects
  • Debugging
  • Std
  • Community
  • 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
      • Bv
      • Imp-language
      • Event-macros
      • Java
        • Atj
        • Aij
        • Language
          • Syntax
            • Grammar
            • Unicode-escapes
            • Unicode-input-char
            • Escape-sequence
            • Identifiers
            • Primitive-types
            • Reference-types
            • Keywords
            • Unicode-characters
            • Integer-literals
              • Optional-integer-type-suffix
              • Integer-literal
              • Octal-integer-literals
              • Hexadecimal-integer-literals
              • Decimal-integer-literals
                • Decdig/uscore-digit-list
                • Dec-integer-literal
                  • Dec-integer-literal-fix
                  • Dec-integer-literal-equiv
                  • Make-dec-integer-literal
                  • Dec-integer-literal->digits/uscores
                  • Dec-integer-literal->suffix?
                  • Change-dec-integer-literal
                  • Dec-integer-literalp
                • Decdig/uscore-list-wfp
                • Decdig/uscore
                • Decdig/uscores-to-digits
                • Decdig/uscore-list
              • Binary-integer-literals
            • String-literals
            • Octal-digits
            • Hexadecimal-digits
            • Decimal-digits
            • Binary-digits
            • Character-literals
            • Null-literal
            • Floating-point-literals
            • Boolean-literals
            • Package-names
            • Literals
          • Semantics
      • 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

• Dec-integer-literal

Dec-integer-literal-equiv

Basic equivalence relation for dec-integer-literal structures.

Definitions and Theorems

Function: dec-integer-literal-equiv$inline

(defun dec-integer-literal-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (dec-integer-literalp acl2::x)
                              (dec-integer-literalp acl2::y))))
  (equal (dec-integer-literal-fix acl2::x)
         (dec-integer-literal-fix acl2::y)))

Theorem: dec-integer-literal-equiv-is-an-equivalence

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

Theorem: dec-integer-literal-equiv-implies-equal-dec-integer-literal-fix-1

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

Theorem: dec-integer-literal-fix-under-dec-integer-literal-equiv

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

Theorem: equal-of-dec-integer-literal-fix-1-forward-to-dec-integer-literal-equiv

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

Theorem: equal-of-dec-integer-literal-fix-2-forward-to-dec-integer-literal-equiv

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

Theorem: dec-integer-literal-equiv-of-dec-integer-literal-fix-1-forward

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

Theorem: dec-integer-literal-equiv-of-dec-integer-literal-fix-2-forward

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