• 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
          • 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
            • Source-character-set
              • Source-char-recognizer+fixer+mappings+fixtype
              • Ascii-basic-source-charp
              • Ascii-basic-source-char
              • Ascii-to-source-char-number
              • Ascii-basic-source-char-fix
              • Basic-source-charp
              • Ext-source-charp
            • Exec-character-set
          • 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

• Source-character-set

Ascii-basic-source-char

Fixtype for ascii-basic-source-charp.

Definitions and Theorems

Function: ascii-basic-source-char-equiv$inline

(defun ascii-basic-source-char-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (ascii-basic-source-charp acl2::x)
                              (ascii-basic-source-charp acl2::y))))
  (equal (ascii-basic-source-char-fix acl2::x)
         (ascii-basic-source-char-fix acl2::y)))

Theorem: ascii-basic-source-char-equiv-is-an-equivalence

(defthm ascii-basic-source-char-equiv-is-an-equivalence
  (and (booleanp (ascii-basic-source-char-equiv x y))
       (ascii-basic-source-char-equiv x x)
       (implies (ascii-basic-source-char-equiv x y)
                (ascii-basic-source-char-equiv y x))
       (implies (and (ascii-basic-source-char-equiv x y)
                     (ascii-basic-source-char-equiv y z))
                (ascii-basic-source-char-equiv x z)))
  :rule-classes (:equivalence))

Theorem: ascii-basic-source-char-equiv-implies-equal-ascii-basic-source-char-fix-1

(defthm
 ascii-basic-source-char-equiv-implies-equal-ascii-basic-source-char-fix-1
 (implies (ascii-basic-source-char-equiv acl2::x x-equiv)
          (equal (ascii-basic-source-char-fix acl2::x)
                 (ascii-basic-source-char-fix x-equiv)))
 :rule-classes (:congruence))

Theorem: ascii-basic-source-char-fix-under-ascii-basic-source-char-equiv

(defthm
    ascii-basic-source-char-fix-under-ascii-basic-source-char-equiv
  (ascii-basic-source-char-equiv
       (ascii-basic-source-char-fix acl2::x)
       acl2::x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-ascii-basic-source-char-fix-1-forward-to-ascii-basic-source-char-equiv

(defthm
 equal-of-ascii-basic-source-char-fix-1-forward-to-ascii-basic-source-char-equiv
 (implies (equal (ascii-basic-source-char-fix acl2::x)
                 acl2::y)
          (ascii-basic-source-char-equiv acl2::x acl2::y))
 :rule-classes :forward-chaining)

Theorem: equal-of-ascii-basic-source-char-fix-2-forward-to-ascii-basic-source-char-equiv

(defthm
 equal-of-ascii-basic-source-char-fix-2-forward-to-ascii-basic-source-char-equiv
 (implies (equal acl2::x
                 (ascii-basic-source-char-fix acl2::y))
          (ascii-basic-source-char-equiv acl2::x acl2::y))
 :rule-classes :forward-chaining)

Theorem: ascii-basic-source-char-equiv-of-ascii-basic-source-char-fix-1-forward

(defthm
 ascii-basic-source-char-equiv-of-ascii-basic-source-char-fix-1-forward
 (implies (ascii-basic-source-char-equiv
               (ascii-basic-source-char-fix acl2::x)
               acl2::y)
          (ascii-basic-source-char-equiv acl2::x acl2::y))
 :rule-classes :forward-chaining)

Theorem: ascii-basic-source-char-equiv-of-ascii-basic-source-char-fix-2-forward

(defthm
 ascii-basic-source-char-equiv-of-ascii-basic-source-char-fix-2-forward
 (implies (ascii-basic-source-char-equiv
               acl2::x
               (ascii-basic-source-char-fix acl2::y))
          (ascii-basic-source-char-equiv acl2::x acl2::y))
 :rule-classes :forward-chaining)