• 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
              • Unicode
              • Ascii
              • String=>unicode
              • Ascii=>string
              • Ascii-list
              • Unicode-list
                • Unicode-list-fix
                • Unicode-list-equiv
                • Unicode-listp
            • 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

• Unicode-list

Unicode-list-equiv

Basic equivalence relation for unicode-list structures.

Definitions and Theorems

Function: unicode-list-equiv$inline

(defun unicode-list-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (unicode-listp acl2::x)
                              (unicode-listp acl2::y))))
  (equal (unicode-list-fix acl2::x)
         (unicode-list-fix acl2::y)))

Theorem: unicode-list-equiv-is-an-equivalence

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

Theorem: unicode-list-equiv-implies-equal-unicode-list-fix-1

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

Theorem: unicode-list-fix-under-unicode-list-equiv

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

Theorem: equal-of-unicode-list-fix-1-forward-to-unicode-list-equiv

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

Theorem: equal-of-unicode-list-fix-2-forward-to-unicode-list-equiv

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

Theorem: unicode-list-equiv-of-unicode-list-fix-1-forward

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

Theorem: unicode-list-equiv-of-unicode-list-fix-2-forward

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