• 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
        • Defbyte
        • Defresult
        • Defsubtype
        • Defset
        • Specific-types
        • Defflatsum
        • Deflist-of-len
        • Pos-list
        • Defbytelist
        • Defbyte-standard-instances
          • Ubyte5
          • Ubyte8
          • Ubyte32
          • Ubyte12
          • Ubyte64
          • Ubyte16
          • Ubyte128
          • Sbyte8
          • Sbyte64
          • Sbyte32
          • Sbyte16
          • Sbyte128
          • Ubyte20
          • Ubyte11
          • Ubyte4
          • Ubyte256
          • Sbyte256
          • Ubyte7
          • Ubyte6
          • Ubyte3
          • Ubyte2
          • Ubyte1
          • Sbyte4
          • Sbyte3
          • Sbyte2
            • Sbyte2p
            • Sbyte2-fix
          • Sbyte1
          • Defbyte-standard-instances-ihs-theorems
          • Defubyte
          • Defsbyte
        • Defomap
        • Deffixtype-alias
        • Defbytelist-standard-instances
        • Defunit
        • Byte-list
        • Byte
        • Pos-option
        • Nibble
        • Nat-option
        • String-option
        • Byte-list20
        • Byte-list32
        • Byte-list64
        • Pseudo-event-form
        • Natoption/natoptionlist
        • Nati
        • Character-list
        • Nat/natlist
        • Maybe-string
        • Nibble-list
        • Natoption/natoptionlist-result
        • Nat/natlist-result
        • Nat-option-list-result
        • Set
        • String-result
        • String-list-result
        • Nat-result
        • Nat-option-result
        • Nat-list-result
        • Maybe-string-result
        • Integer-result
        • Character-result
        • Character-list-result
        • Boolean-result
        • Map
        • Bag
        • Pos-set
        • Hex-digit-char-list
        • Dec-digit-char-list
        • Nat-option-list
        • Symbol-set
        • String-set
        • Pseudo-event-form-list
        • Nat-set
        • Oct-digit-char-list
        • Bin-digit-char-list
        • Bit-list
      • Isar
      • Kestrel-utilities
      • Soft
      • Bv
      • Imp-language
      • C
      • 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

• Sbyte2

Sbyte2-fix

Fixer for sbyte2.

Signature

(sbyte2-fix x) → fixed-x

Arguments

x — Guard (sbyte2p x).

Returns

fixed-x — Type (sbyte2p fixed-x).

Definitions and Theorems

Function: sbyte2-fix

(defun sbyte2-fix (x)
  (declare (xargs :guard (sbyte2p x)))
  (mbe :logic (if (sbyte2p x) x 0)
       :exec x))

Theorem: sbyte2p-of-sbyte2-fix

(defthm sbyte2p-of-sbyte2-fix
  (b* ((fixed-x (sbyte2-fix x)))
    (sbyte2p fixed-x))
  :rule-classes :rewrite)

Theorem: sbyte2-fix-when-sbyte2p

(defthm sbyte2-fix-when-sbyte2p
  (implies (sbyte2p x)
           (equal (sbyte2-fix x) x)))