• Top
  • Documentation
  • Books
  • Boolean-reasoning
  • Projects
    • Apt
    • Zfc
    • Acre
    • Milawa
    • Smtlink
    • Abnf
    • Vwsim
    • Isar
    • Wp-gen
    • Dimacs-reader
    • Pfcs
    • Legacy-defrstobj
    • Proof-checker-array
    • Soft
    • C
    • Farray
    • Rp-rewriter
    • Instant-runoff-voting
    • Imp-language
    • Sidekick
    • Leftist-trees
    • Java
      • Atj
      • Aij
      • Language
        • Syntax
          • Grammar
          • Unicode-escapes
          • Unicode-input-char
          • Escape-sequence
          • Identifiers
          • Primitive-types
          • Reference-types
          • Keywords
          • Unicode-characters
          • Integer-literals
          • String-literals
          • Octal-digits
            • Oct-digit
              • Oct-digitp
              • Oct-digit-fix
            • Octal-digits-grammar-validation
            • Oct-digit-value
            • Oct-digit-list
            • Octal-digits-std/strings-theorems
          • Hexadecimal-digits
          • Decimal-digits
          • Binary-digits
          • Character-literals
          • Null-literal
          • Floating-point-literals
          • Boolean-literals
          • Package-names
          • Literals
        • Semantics
    • Taspi
    • Riscv
    • Bitcoin
    • Des
    • Ethereum
    • X86isa
    • Sha-2
    • Yul
    • Zcash
    • Proof-checker-itp13
    • Regex
    • ACL2-programming-language
    • Json
    • Jfkr
    • Equational
    • Cryptography
    • Poseidon
    • Where-do-i-place-my-book
    • Axe
    • Aleo
    • Bigmems
    • Builtins
    • Execloader
    • Solidity
    • Paco
    • Concurrent-programs
    • Bls12-377-curves
  • Debugging
  • Std
  • Community
  • Proof-automation
  • ACL2
  • Macro-libraries
  • Interfacing-tools
  • Hardware-verification
  • Software-verification
  • Math
  • Testing-utilities

• Oct-digit

Oct-digit-fix

Fixer for oct-digit.

Signature

(oct-digit-fix x) → fixed-x

Arguments

x — Guard (oct-digitp x).

Returns

fixed-x — Type (oct-digitp fixed-x).

Definitions and Theorems

Function: oct-digit-fix

(defun oct-digit-fix (x)
  (declare (xargs :guard (oct-digitp x)))
  (mbe :logic (if (oct-digitp x) x (char-code #\0))
       :exec x))

Theorem: oct-digitp-of-oct-digit-fix

(defthm oct-digitp-of-oct-digit-fix
  (b* ((fixed-x (oct-digit-fix x)))
    (oct-digitp fixed-x))
  :rule-classes :rewrite)

Theorem: oct-digit-fix-when-oct-digitp

(defthm oct-digit-fix-when-oct-digitp
  (implies (oct-digitp x)
           (equal (oct-digit-fix x) x)))