• Top
  • Documentation
  • Books
  • Boolean-reasoning
  • Projects
  • Debugging
  • Std
  • Proof-automation
  • Macro-libraries
  • ACL2
    • Theories
    • Rule-classes
    • Proof-builder
    • Recursion-and-induction
    • Hons-and-memoization
    • Events
    • Parallelism
    • History
    • Programming
      • Defun
      • Declare
      • System-utilities
      • Stobj
      • State
      • Mutual-recursion
      • Memoize
      • Mbe
      • Io
      • Defpkg
      • Apply$
      • Loop$
      • Programming-with-state
      • Arrays
      • Characters
      • Time$
      • Defmacro
      • Loop$-primer
      • Fast-alists
      • Defconst
      • Evaluation
      • Guard
      • Equality-variants
      • Compilation
      • Hons
      • ACL2-built-ins
      • Developers-guide
      • System-attachments
      • Advanced-features
      • Set-check-invariant-risk
      • Numbers
        • Df
        • Unsigned-byte-p
        • Posp
        • Natp
        • <
        • +
        • Bitp
        • Zero-test-idioms
        • Nat-listp
        • Integerp
        • *
        • -
        • Zp
        • Signed-byte-p
        • Logbitp
        • Sharp-f-reader
        • Expt
        • <=
        • Ash
        • Rationalp
        • =
        • Nfix
        • Logand
        • Floor
        • Random$
        • Integer-listp
        • Complex
        • Numbers-introduction
        • Truncate
        • Code-char
        • Char-code
        • Integer-length
        • Zip
        • Logior
        • Sharp-u-reader
        • Mod
        • Unary--
        • Boole$
        • /
        • Logxor
        • Ifix
        • Lognot
        • Integer-range-p
        • Allocate-fixnum-range
        • ACL2-numberp
        • Sharp-d-reader
        • Mod-expt
        • Ceiling
        • Round
        • Logeqv
        • Fix
        • Explode-nonnegative-integer
        • Max
        • Evenp
        • Zerop
        • Abs
        • Nonnegative-integer-quotient
        • Rfix
        • 1+
        • Pos-listp
        • Signum
        • Rem
        • Real/rationalp
        • Rational-listp
        • >=
        • >
        • Logcount
        • ACL2-number-listp
        • /=
        • Unary-/
        • Realfix
          • Std/basic/realfix
        • Complex/complex-rationalp
        • Logtest
        • Logandc1
        • Logorc1
        • Logandc2
        • Denominator
        • 1-
        • Numerator
        • Logorc2
        • The-number
        • Int=
        • Complex-rationalp
        • Min
        • Lognor
        • Zpf
        • Oddp
        • Minusp
        • Lognand
        • Imagpart
        • Conjugate
        • Realpart
        • Plusp
      • Efficiency
      • Irrelevant-formals
      • Introduction-to-programming-in-ACL2-for-those-who-know-lisp
      • Redefining-programs
      • Lists
      • Invariant-risk
      • Errors
      • Defabbrev
      • Conses
      • Alists
      • Set-register-invariant-risk
      • Strings
      • Program-wrapper
      • Get-internal-time
      • Basics
      • Packages
      • Oracle-eval
      • Defmacro-untouchable
      • <<
      • Primitive
      • Revert-world
      • Unmemoize
      • Set-duplicate-keys-action
      • Symbols
      • Def-list-constructor
      • Easy-simplify-term
      • Defiteration
      • Fake-oracle-eval
      • Defopen
      • Sleep
    • Operational-semantics
    • Real
    • Start-here
    • Debugging
    • Miscellaneous
    • Output-controls
    • Macros
    • Interfacing-tools
  • Interfacing-tools
  • Hardware-verification
  • Software-verification
  • Math
  • Testing-utilities

• Std/basic
• Realfix

Std/basic/realfix

Rules about realfix.

Definitions and Theorems

Theorem: realfix-when-real/rationalp

(defthm realfix-when-real/rationalp
  (implies (real/rationalp x)
           (equal (realfix x) x)))

Theorem: real/rationalp-of-realfix

(defthm real/rationalp-of-realfix
  (real/rationalp (realfix x)))