• Top
  • Documentation
  • Books
  • Boolean-reasoning
  • Debugging
  • Projects
  • 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
      • Memoize
      • Mbe
      • Io
      • Defpkg
      • Apply$
      • Mutual-recursion
      • Loop$
      • Programming-with-state
      • Arrays
      • Characters
      • Time$
      • Loop$-primer
      • Fast-alists
      • Defmacro
      • Defconst
      • Evaluation
      • Guard
      • Equality-variants
      • Compilation
      • Hons
      • ACL2-built-ins
      • Developers-guide
      • System-attachments
      • Advanced-features
      • Set-check-invariant-risk
      • Numbers
      • Irrelevant-formals
      • Efficiency
      • Introduction-to-programming-in-ACL2-for-those-who-know-lisp
      • Redefining-programs
      • Lists
        • Member
        • Append
        • Nth
        • Len
        • List
        • True-listp
        • String-listp
        • Nat-listp
        • Character-listp
        • Symbol-listp
        • True-list-listp
        • Length
        • Search
        • Intersection$
        • Union$
        • Remove-duplicates
        • Position
        • Take
        • Update-nth
        • Set-difference$
        • Subsetp
        • No-duplicatesp
        • Nthcdr
        • Concatenate
        • Remove
        • Remove1
        • Intersectp
        • Endp
        • Keyword-value-listp
        • Reverse
        • List-utilities
        • Add-to-set
        • Set-size
        • Integer-listp
        • Revappend
        • Subseq
        • Make-list
        • Lists-light
        • Butlast
        • Pairlis$
        • Boolean-listp
        • Substitute
        • Count
        • Keyword-listp
        • List*
        • Eqlable-listp
        • Last
        • Pos-listp
        • Integer-range-listp
          • Integer-range-listp-basics
          • Integer-range-list-fix
        • Rational-listp
        • Evens
        • Atom-listp
        • ACL2-number-listp
        • Typed-list-utilities
        • Listp
        • Odds
        • Standard-char-listp
        • Last-cdr
        • Pairlis
        • Proper-consp
        • Improper-consp
        • Pairlis-x2
        • Pairlis-x1
        • Merge-sort-lexorder
        • Fix-true-list
        • Real-listp
      • 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
      • Set-duplicate-keys-action
      • Unmemoize
      • Symbols
      • Def-list-constructor
      • Easy-simplify-term
      • Defiteration
      • Fake-oracle-eval
      • Defopen
      • Sleep
    • Real
    • Start-here
    • Debugging
    • Miscellaneous
    • Output-controls
    • Macros
    • Interfacing-tools
  • Interfacing-tools
  • Hardware-verification
  • Software-verification
  • Math
  • Testing-utilities

• Integer-range-listp

Integer-range-list-fix

Fixing function for integer-range-listp.

Signature

(integer-range-list-fix lower upper x) → fixed-x

Arguments

lower — Guard (integerp lower).

upper — Guard (integerp upper).

x — Guard (integer-range-listp (ifix lower) (ifix upper) x).

Returns

fixed-x — Type (integer-range-listp lower upper fixed-x), given (and (integerp lower) (integerp upper) (< lower upper)).

This lifts integer-range-fix to lists. See that function for more information, in particular about the fixing of lower and upper to integers and the treatment of empty ranges.

Definitions and Theorems

Function: integer-range-list-fix

(defun integer-range-list-fix (lower upper x)
 (declare (xargs :guard (and (integerp lower)
                             (integerp upper)
                             (integer-range-listp (ifix lower)
                                                  (ifix upper)
                                                  x))))
 (let ((__function__ 'integer-range-list-fix))
  (declare (ignorable __function__))
  (mbe
      :logic
      (cond ((atom x) nil)
            (t (cons (integer-range-fix lower upper (car x))
                     (integer-range-list-fix lower upper (cdr x)))))
      :exec x)))

Theorem: return-type-of-integer-range-list-fix

(defthm return-type-of-integer-range-list-fix
  (implies (and (integerp lower)
                (integerp upper)
                (< lower upper))
           (b* ((fixed-x (integer-range-list-fix lower upper x)))
             (integer-range-listp lower upper fixed-x)))
  :rule-classes :rewrite)

Theorem: integer-listp-of-integer-range-list-fix

(defthm integer-listp-of-integer-range-list-fix
  (b* ((fixed-x (integer-range-list-fix lower upper x)))
    (integer-listp fixed-x))
  :rule-classes :rewrite)

Theorem: integer-range-list-fix-when-integer-range-p

(defthm integer-range-list-fix-when-integer-range-p
  (implies (and (integer-range-listp (ifix lower)
                                     (ifix upper)
                                     x)
                (< (ifix lower) (ifix upper)))
           (equal (integer-range-list-fix lower upper x)
                  x)))

Theorem: integer-range-list-fix-of-nil

(defthm integer-range-list-fix-of-nil
  (equal (integer-range-list-fix lower upper nil)
         nil))

Theorem: integer-range-list-fix-of-cons

(defthm integer-range-list-fix-of-cons
  (equal (integer-range-list-fix lower upper (cons x y))
         (cons (integer-range-fix lower upper x)
               (integer-range-list-fix lower upper y))))

Theorem: integer-range-list-fix-of-append

(defthm integer-range-list-fix-of-append
  (equal (integer-range-list-fix lower upper (append x y))
         (append (integer-range-list-fix lower upper x)
                 (integer-range-list-fix lower upper y))))

Theorem: len-of-integer-range-list-fix

(defthm len-of-integer-range-list-fix
  (equal (len (integer-range-list-fix lower upper x))
         (len x)))

Theorem: consp-of-integer-range-list-fix

(defthm consp-of-integer-range-list-fix
  (equal (consp (integer-range-list-fix lower upper x))
         (consp x)))

Theorem: car-of-integer-range-list-fix

(defthm car-of-integer-range-list-fix
  (implies (consp x)
           (equal (car (integer-range-list-fix lower upper x))
                  (integer-range-fix lower upper (car x)))))

Theorem: cdr-of-integer-range-list-fix

(defthm cdr-of-integer-range-list-fix
  (implies (consp x)
           (equal (cdr (integer-range-list-fix lower upper x))
                  (integer-range-list-fix lower upper (cdr x)))))

Theorem: rev-of-integer-range-list-fix

(defthm rev-of-integer-range-list-fix
  (equal (rev (integer-range-list-fix lower upper x))
         (integer-range-list-fix lower upper (rev x))))

Theorem: integer-range-list-fix-of-ifix-lower

(defthm integer-range-list-fix-of-ifix-lower
  (equal (integer-range-list-fix (ifix lower)
                                 upper x)
         (integer-range-list-fix lower upper x)))

Theorem: integer-range-list-fix-int-equiv-congruence-on-lower

(defthm integer-range-list-fix-int-equiv-congruence-on-lower
  (implies (int-equiv lower lower-equiv)
           (equal (integer-range-list-fix lower upper x)
                  (integer-range-list-fix lower-equiv upper x)))
  :rule-classes :congruence)

Theorem: integer-range-list-fix-of-ifix-upper

(defthm integer-range-list-fix-of-ifix-upper
  (equal (integer-range-list-fix lower (ifix upper)
                                 x)
         (integer-range-list-fix lower upper x)))

Theorem: integer-range-list-fix-int-equiv-congruence-on-upper

(defthm integer-range-list-fix-int-equiv-congruence-on-upper
  (implies (int-equiv upper upper-equiv)
           (equal (integer-range-list-fix lower upper x)
                  (integer-range-list-fix lower upper-equiv x)))
  :rule-classes :congruence)