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Char-fix

Charlist-fix

(charlist-fix x) maps ACL2::char-fix across a list.

Signature
(charlist-fix x) → *

This is an ordinary defprojection.

Definitions and Theorems

Function: charlist-fix-exec

(defun charlist-fix-exec (x acc)
  (declare (xargs :guard t))
  (let ((__function__ 'charlist-fix-exec))
    (declare (ignorable __function__))
    (if (consp x)
        (charlist-fix-exec (cdr x)
                           (cons (acl2::char-fix (car x)) acc))
      acc)))

Function: charlist-fix-nrev

(defun charlist-fix-nrev (x acl2::nrev)
  (declare (xargs :stobjs (acl2::nrev)))
  (declare (xargs :guard t))
  (let ((__function__ 'charlist-fix-nrev))
    (declare (ignorable __function__))
    (if (atom x)
        (acl2::nrev-fix acl2::nrev)
      (let ((acl2::nrev (acl2::nrev-push (acl2::char-fix (car x))
                                         acl2::nrev)))
        (charlist-fix-nrev (cdr x)
                           acl2::nrev)))))

Function: charlist-fix

(defun charlist-fix (x)
 (declare (xargs :guard t))
 (let ((__function__ 'charlist-fix))
  (declare (ignorable __function__))
  (mbe
      :logic
      (if (consp x)
          (cons (acl2::char-fix (car x))
                (charlist-fix (cdr x)))
        nil)
      :exec
      (if (atom x)
          nil
        (acl2::with-local-nrev (charlist-fix-nrev x acl2::nrev))))))

Theorem: charlist-fix-of-rev

(defthm charlist-fix-of-rev
  (equal (charlist-fix (acl2::rev acl2::x))
         (acl2::rev (charlist-fix acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: charlist-fix-nrev-removal

(defthm charlist-fix-nrev-removal
  (equal (charlist-fix-nrev acl2::x acl2::nrev)
         (append acl2::nrev (charlist-fix acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: charlist-fix-exec-removal

(defthm charlist-fix-exec-removal
  (equal (charlist-fix-exec acl2::x acl2::acc)
         (revappend (charlist-fix acl2::x)
                    acl2::acc))
  :rule-classes ((:rewrite)))

Theorem: charlist-fix-of-list-fix

(defthm charlist-fix-of-list-fix
  (equal (charlist-fix (list-fix acl2::x))
         (charlist-fix acl2::x))
  :rule-classes ((:rewrite)))

Theorem: charlist-fix-of-append

(defthm charlist-fix-of-append
  (equal (charlist-fix (append acl2::a acl2::b))
         (append (charlist-fix acl2::a)
                 (charlist-fix acl2::b)))
  :rule-classes ((:rewrite)))

Theorem: cdr-of-charlist-fix

(defthm cdr-of-charlist-fix
  (equal (cdr (charlist-fix acl2::x))
         (charlist-fix (cdr acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: car-of-charlist-fix

(defthm car-of-charlist-fix
  (equal (car (charlist-fix acl2::x))
         (and (consp acl2::x)
              (acl2::char-fix (car acl2::x))))
  :rule-classes ((:rewrite)))

Theorem: charlist-fix-under-iff

(defthm charlist-fix-under-iff
  (iff (charlist-fix acl2::x)
       (consp acl2::x))
  :rule-classes ((:rewrite)))

Theorem: consp-of-charlist-fix

(defthm consp-of-charlist-fix
  (equal (consp (charlist-fix acl2::x))
         (consp acl2::x))
  :rule-classes ((:rewrite)))

Theorem: len-of-charlist-fix

(defthm len-of-charlist-fix
  (equal (len (charlist-fix acl2::x))
         (len acl2::x))
  :rule-classes ((:rewrite)))

Theorem: true-listp-of-charlist-fix

(defthm true-listp-of-charlist-fix
  (true-listp (charlist-fix acl2::x))
  :rule-classes :type-prescription)

Theorem: charlist-fix-when-not-consp

(defthm charlist-fix-when-not-consp
  (implies (not (consp acl2::x))
           (equal (charlist-fix acl2::x) nil))
  :rule-classes ((:rewrite)))

Theorem: charlist-fix-of-cons

(defthm charlist-fix-of-cons
  (equal (charlist-fix (cons acl2::a acl2::b))
         (cons (acl2::char-fix acl2::a)
               (charlist-fix acl2::b)))
  :rule-classes ((:rewrite)))