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• Lint-stmt-rewrite

Vl-initiallist-lint-stmt-rewrite

(vl-initiallist-lint-stmt-rewrite x) maps vl-initial-lint-stmt-rewrite across a list.

Signature

(vl-initiallist-lint-stmt-rewrite x) → new-x

Arguments

x — Guard (vl-initiallist-p x).

Returns

new-x — Type (vl-initiallist-p new-x).

This is an ordinary defprojection.

Definitions and Theorems

Function: vl-initiallist-lint-stmt-rewrite-exec

(defun vl-initiallist-lint-stmt-rewrite-exec (x acc)
  (declare (xargs :guard (vl-initiallist-p x)))
  (declare (xargs :guard t))
  (let ((__function__ 'vl-initiallist-lint-stmt-rewrite-exec))
    (declare (ignorable __function__))
    (if (consp x)
        (vl-initiallist-lint-stmt-rewrite-exec
             (cdr x)
             (cons (vl-initial-lint-stmt-rewrite (car x))
                   acc))
      acc)))

Function: vl-initiallist-lint-stmt-rewrite-nrev

(defun vl-initiallist-lint-stmt-rewrite-nrev (x nrev)
  (declare (xargs :stobjs (nrev)))
  (declare (xargs :guard (vl-initiallist-p x)))
  (declare (xargs :guard t))
  (let ((__function__ 'vl-initiallist-lint-stmt-rewrite-nrev))
    (declare (ignorable __function__))
    (if (atom x)
        (nrev-fix nrev)
      (let ((nrev (nrev-push (vl-initial-lint-stmt-rewrite (car x))
                             nrev)))
        (vl-initiallist-lint-stmt-rewrite-nrev (cdr x)
                                               nrev)))))

Function: vl-initiallist-lint-stmt-rewrite

(defun vl-initiallist-lint-stmt-rewrite (x)
  (declare (xargs :guard (vl-initiallist-p x)))
  (declare (xargs :guard t))
  (let ((__function__ 'vl-initiallist-lint-stmt-rewrite))
    (declare (ignorable __function__))
    (mbe :logic
         (if (consp x)
             (cons (vl-initial-lint-stmt-rewrite (car x))
                   (vl-initiallist-lint-stmt-rewrite (cdr x)))
           nil)
         :exec
         (if (atom x)
             nil
           (with-local-nrev
                (vl-initiallist-lint-stmt-rewrite-nrev x nrev))))))

Theorem: vl-initiallist-p-of-vl-initiallist-lint-stmt-rewrite

(defthm vl-initiallist-p-of-vl-initiallist-lint-stmt-rewrite
  (b* ((new-x (vl-initiallist-lint-stmt-rewrite x)))
    (vl-initiallist-p new-x))
  :rule-classes :rewrite)

Theorem: vl-initiallist-lint-stmt-rewrite-of-vl-initiallist-fix-x

(defthm vl-initiallist-lint-stmt-rewrite-of-vl-initiallist-fix-x
  (equal (vl-initiallist-lint-stmt-rewrite (vl-initiallist-fix x))
         (vl-initiallist-lint-stmt-rewrite x)))

Theorem: vl-initiallist-lint-stmt-rewrite-vl-initiallist-equiv-congruence-on-x

(defthm
 vl-initiallist-lint-stmt-rewrite-vl-initiallist-equiv-congruence-on-x
 (implies (vl-initiallist-equiv x x-equiv)
          (equal (vl-initiallist-lint-stmt-rewrite x)
                 (vl-initiallist-lint-stmt-rewrite x-equiv)))
 :rule-classes :congruence)

Theorem: vl-initiallist-lint-stmt-rewrite-of-update-nth

(defthm vl-initiallist-lint-stmt-rewrite-of-update-nth
 (implies
    (<= (nfix acl2::n) (len acl2::x))
    (equal (vl-initiallist-lint-stmt-rewrite
                (update-nth acl2::n acl2::v acl2::x))
           (update-nth acl2::n
                       (vl-initial-lint-stmt-rewrite acl2::v)
                       (vl-initiallist-lint-stmt-rewrite acl2::x))))
 :rule-classes ((:rewrite)))

Theorem: vl-initiallist-lint-stmt-rewrite-of-revappend

(defthm vl-initiallist-lint-stmt-rewrite-of-revappend
 (equal
      (vl-initiallist-lint-stmt-rewrite (revappend acl2::x acl2::y))
      (revappend (vl-initiallist-lint-stmt-rewrite acl2::x)
                 (vl-initiallist-lint-stmt-rewrite acl2::y)))
 :rule-classes ((:rewrite)))

Theorem: nthcdr-of-vl-initiallist-lint-stmt-rewrite

(defthm nthcdr-of-vl-initiallist-lint-stmt-rewrite
 (equal (nthcdr acl2::n
                (vl-initiallist-lint-stmt-rewrite acl2::x))
        (vl-initiallist-lint-stmt-rewrite (nthcdr acl2::n acl2::x)))
 :rule-classes ((:rewrite)))

Theorem: nth-of-vl-initiallist-lint-stmt-rewrite

(defthm nth-of-vl-initiallist-lint-stmt-rewrite
  (equal (nth acl2::n
              (vl-initiallist-lint-stmt-rewrite acl2::x))
         (and (< (nfix acl2::n) (len acl2::x))
              (vl-initial-lint-stmt-rewrite (nth acl2::n acl2::x))))
  :rule-classes ((:rewrite)))

Theorem: vl-initiallist-lint-stmt-rewrite-nrev-removal

(defthm vl-initiallist-lint-stmt-rewrite-nrev-removal
  (equal (vl-initiallist-lint-stmt-rewrite-nrev acl2::x nrev)
         (append nrev
                 (vl-initiallist-lint-stmt-rewrite acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: vl-initiallist-lint-stmt-rewrite-exec-removal

(defthm vl-initiallist-lint-stmt-rewrite-exec-removal
  (equal (vl-initiallist-lint-stmt-rewrite-exec acl2::x acl2::acc)
         (revappend (vl-initiallist-lint-stmt-rewrite acl2::x)
                    acl2::acc))
  :rule-classes ((:rewrite)))

Theorem: vl-initiallist-lint-stmt-rewrite-of-take

(defthm vl-initiallist-lint-stmt-rewrite-of-take
 (implies
    (<= (nfix acl2::n) (len acl2::x))
    (equal (vl-initiallist-lint-stmt-rewrite (take acl2::n acl2::x))
           (take acl2::n
                 (vl-initiallist-lint-stmt-rewrite acl2::x))))
 :rule-classes ((:rewrite)))

Theorem: set-equiv-congruence-over-vl-initiallist-lint-stmt-rewrite

(defthm set-equiv-congruence-over-vl-initiallist-lint-stmt-rewrite
  (implies (set-equiv acl2::x acl2::y)
           (set-equiv (vl-initiallist-lint-stmt-rewrite acl2::x)
                      (vl-initiallist-lint-stmt-rewrite acl2::y)))
  :rule-classes ((:congruence)))

Theorem: subsetp-of-vl-initiallist-lint-stmt-rewrite-when-subsetp

(defthm subsetp-of-vl-initiallist-lint-stmt-rewrite-when-subsetp
  (implies (subsetp acl2::x acl2::y)
           (subsetp (vl-initiallist-lint-stmt-rewrite acl2::x)
                    (vl-initiallist-lint-stmt-rewrite acl2::y)))
  :rule-classes ((:rewrite)))

Theorem: member-of-vl-initial-lint-stmt-rewrite-in-vl-initiallist-lint-stmt-rewrite

(defthm
 member-of-vl-initial-lint-stmt-rewrite-in-vl-initiallist-lint-stmt-rewrite
 (implies (member acl2::k acl2::x)
          (member (vl-initial-lint-stmt-rewrite acl2::k)
                  (vl-initiallist-lint-stmt-rewrite acl2::x)))
 :rule-classes ((:rewrite)))

Theorem: vl-initiallist-lint-stmt-rewrite-of-rev

(defthm vl-initiallist-lint-stmt-rewrite-of-rev
  (equal (vl-initiallist-lint-stmt-rewrite (rev acl2::x))
         (rev (vl-initiallist-lint-stmt-rewrite acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: vl-initiallist-lint-stmt-rewrite-of-list-fix

(defthm vl-initiallist-lint-stmt-rewrite-of-list-fix
  (equal (vl-initiallist-lint-stmt-rewrite (list-fix acl2::x))
         (vl-initiallist-lint-stmt-rewrite acl2::x))
  :rule-classes ((:rewrite)))

Theorem: vl-initiallist-lint-stmt-rewrite-of-append

(defthm vl-initiallist-lint-stmt-rewrite-of-append
  (equal (vl-initiallist-lint-stmt-rewrite (append acl2::a acl2::b))
         (append (vl-initiallist-lint-stmt-rewrite acl2::a)
                 (vl-initiallist-lint-stmt-rewrite acl2::b)))
  :rule-classes ((:rewrite)))

Theorem: cdr-of-vl-initiallist-lint-stmt-rewrite

(defthm cdr-of-vl-initiallist-lint-stmt-rewrite
  (equal (cdr (vl-initiallist-lint-stmt-rewrite acl2::x))
         (vl-initiallist-lint-stmt-rewrite (cdr acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: car-of-vl-initiallist-lint-stmt-rewrite

(defthm car-of-vl-initiallist-lint-stmt-rewrite
  (equal (car (vl-initiallist-lint-stmt-rewrite acl2::x))
         (and (consp acl2::x)
              (vl-initial-lint-stmt-rewrite (car acl2::x))))
  :rule-classes ((:rewrite)))

Theorem: vl-initiallist-lint-stmt-rewrite-under-iff

(defthm vl-initiallist-lint-stmt-rewrite-under-iff
  (iff (vl-initiallist-lint-stmt-rewrite acl2::x)
       (consp acl2::x))
  :rule-classes ((:rewrite)))

Theorem: consp-of-vl-initiallist-lint-stmt-rewrite

(defthm consp-of-vl-initiallist-lint-stmt-rewrite
  (equal (consp (vl-initiallist-lint-stmt-rewrite acl2::x))
         (consp acl2::x))
  :rule-classes ((:rewrite)))

Theorem: len-of-vl-initiallist-lint-stmt-rewrite

(defthm len-of-vl-initiallist-lint-stmt-rewrite
  (equal (len (vl-initiallist-lint-stmt-rewrite acl2::x))
         (len acl2::x))
  :rule-classes ((:rewrite)))

Theorem: true-listp-of-vl-initiallist-lint-stmt-rewrite

(defthm true-listp-of-vl-initiallist-lint-stmt-rewrite
  (true-listp (vl-initiallist-lint-stmt-rewrite acl2::x))
  :rule-classes :type-prescription)

Theorem: vl-initiallist-lint-stmt-rewrite-when-not-consp

(defthm vl-initiallist-lint-stmt-rewrite-when-not-consp
  (implies (not (consp acl2::x))
           (equal (vl-initiallist-lint-stmt-rewrite acl2::x)
                  nil))
  :rule-classes ((:rewrite)))

Theorem: vl-initiallist-lint-stmt-rewrite-of-cons

(defthm vl-initiallist-lint-stmt-rewrite-of-cons
  (equal (vl-initiallist-lint-stmt-rewrite (cons acl2::a acl2::b))
         (cons (vl-initial-lint-stmt-rewrite acl2::a)
               (vl-initiallist-lint-stmt-rewrite acl2::b)))
  :rule-classes ((:rewrite)))