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• Elimalways

Vl-modulelist-elimalways

(vl-modulelist-elimalways x) maps vl-module-elimalways across a list.

Signature

(vl-modulelist-elimalways x) → new-x

Arguments

x — Guard (vl-modulelist-p x).

Returns

new-x — Type (vl-modulelist-p new-x).

This is an ordinary defprojection.

Definitions and Theorems

Function: vl-modulelist-elimalways-exec

(defun vl-modulelist-elimalways-exec (x acc)
  (declare (xargs :guard (vl-modulelist-p x)))
  (declare (xargs :guard t))
  (let ((__function__ 'vl-modulelist-elimalways-exec))
    (declare (ignorable __function__))
    (if (consp x)
        (vl-modulelist-elimalways-exec
             (cdr x)
             (cons (vl-module-elimalways (car x))
                   acc))
      acc)))

Function: vl-modulelist-elimalways-nrev

(defun vl-modulelist-elimalways-nrev (x nrev)
  (declare (xargs :stobjs (nrev)))
  (declare (xargs :guard (vl-modulelist-p x)))
  (declare (xargs :guard t))
  (let ((__function__ 'vl-modulelist-elimalways-nrev))
    (declare (ignorable __function__))
    (if (atom x)
        (nrev-fix nrev)
      (let ((nrev (nrev-push (vl-module-elimalways (car x))
                             nrev)))
        (vl-modulelist-elimalways-nrev (cdr x)
                                       nrev)))))

Function: vl-modulelist-elimalways

(defun vl-modulelist-elimalways (x)
 (declare (xargs :guard (vl-modulelist-p x)))
 (declare (xargs :guard t))
 (let ((__function__ 'vl-modulelist-elimalways))
  (declare (ignorable __function__))
  (mbe
      :logic
      (if (consp x)
          (cons (vl-module-elimalways (car x))
                (vl-modulelist-elimalways (cdr x)))
        nil)
      :exec
      (if (atom x)
          nil
        (with-local-nrev (vl-modulelist-elimalways-nrev x nrev))))))

Theorem: vl-modulelist-p-of-vl-modulelist-elimalways

(defthm vl-modulelist-p-of-vl-modulelist-elimalways
  (b* ((new-x (vl-modulelist-elimalways x)))
    (vl-modulelist-p new-x))
  :rule-classes :rewrite)

Theorem: vl-modulelist-elimalways-of-vl-modulelist-fix-x

(defthm vl-modulelist-elimalways-of-vl-modulelist-fix-x
  (equal (vl-modulelist-elimalways (vl-modulelist-fix x))
         (vl-modulelist-elimalways x)))

Theorem: vl-modulelist-elimalways-vl-modulelist-equiv-congruence-on-x

(defthm vl-modulelist-elimalways-vl-modulelist-equiv-congruence-on-x
  (implies (vl-modulelist-equiv x x-equiv)
           (equal (vl-modulelist-elimalways x)
                  (vl-modulelist-elimalways x-equiv)))
  :rule-classes :congruence)

Theorem: vl-modulelist-elimalways-of-update-nth

(defthm vl-modulelist-elimalways-of-update-nth
 (implies
  (<= (nfix acl2::n) (len acl2::x))
  (equal
     (vl-modulelist-elimalways (update-nth acl2::n acl2::v acl2::x))
     (update-nth acl2::n (vl-module-elimalways acl2::v)
                 (vl-modulelist-elimalways acl2::x))))
 :rule-classes ((:rewrite)))

Theorem: vl-modulelist-elimalways-of-revappend

(defthm vl-modulelist-elimalways-of-revappend
  (equal (vl-modulelist-elimalways (revappend acl2::x acl2::y))
         (revappend (vl-modulelist-elimalways acl2::x)
                    (vl-modulelist-elimalways acl2::y)))
  :rule-classes ((:rewrite)))

Theorem: nthcdr-of-vl-modulelist-elimalways

(defthm nthcdr-of-vl-modulelist-elimalways
  (equal (nthcdr acl2::n
                 (vl-modulelist-elimalways acl2::x))
         (vl-modulelist-elimalways (nthcdr acl2::n acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: nth-of-vl-modulelist-elimalways

(defthm nth-of-vl-modulelist-elimalways
  (equal (nth acl2::n
              (vl-modulelist-elimalways acl2::x))
         (and (< (nfix acl2::n) (len acl2::x))
              (vl-module-elimalways (nth acl2::n acl2::x))))
  :rule-classes ((:rewrite)))

Theorem: vl-modulelist-elimalways-nrev-removal

(defthm vl-modulelist-elimalways-nrev-removal
  (equal (vl-modulelist-elimalways-nrev acl2::x nrev)
         (append nrev
                 (vl-modulelist-elimalways acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: vl-modulelist-elimalways-exec-removal

(defthm vl-modulelist-elimalways-exec-removal
  (equal (vl-modulelist-elimalways-exec acl2::x acl2::acc)
         (revappend (vl-modulelist-elimalways acl2::x)
                    acl2::acc))
  :rule-classes ((:rewrite)))

Theorem: vl-modulelist-elimalways-of-take

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

Theorem: set-equiv-congruence-over-vl-modulelist-elimalways

(defthm set-equiv-congruence-over-vl-modulelist-elimalways
  (implies (set-equiv acl2::x acl2::y)
           (set-equiv (vl-modulelist-elimalways acl2::x)
                      (vl-modulelist-elimalways acl2::y)))
  :rule-classes ((:congruence)))

Theorem: subsetp-of-vl-modulelist-elimalways-when-subsetp

(defthm subsetp-of-vl-modulelist-elimalways-when-subsetp
  (implies (subsetp acl2::x acl2::y)
           (subsetp (vl-modulelist-elimalways acl2::x)
                    (vl-modulelist-elimalways acl2::y)))
  :rule-classes ((:rewrite)))

Theorem: member-of-vl-module-elimalways-in-vl-modulelist-elimalways

(defthm member-of-vl-module-elimalways-in-vl-modulelist-elimalways
  (implies (member acl2::k acl2::x)
           (member (vl-module-elimalways acl2::k)
                   (vl-modulelist-elimalways acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: vl-modulelist-elimalways-of-rev

(defthm vl-modulelist-elimalways-of-rev
  (equal (vl-modulelist-elimalways (rev acl2::x))
         (rev (vl-modulelist-elimalways acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: vl-modulelist-elimalways-of-list-fix

(defthm vl-modulelist-elimalways-of-list-fix
  (equal (vl-modulelist-elimalways (list-fix acl2::x))
         (vl-modulelist-elimalways acl2::x))
  :rule-classes ((:rewrite)))

Theorem: vl-modulelist-elimalways-of-append

(defthm vl-modulelist-elimalways-of-append
  (equal (vl-modulelist-elimalways (append acl2::a acl2::b))
         (append (vl-modulelist-elimalways acl2::a)
                 (vl-modulelist-elimalways acl2::b)))
  :rule-classes ((:rewrite)))

Theorem: cdr-of-vl-modulelist-elimalways

(defthm cdr-of-vl-modulelist-elimalways
  (equal (cdr (vl-modulelist-elimalways acl2::x))
         (vl-modulelist-elimalways (cdr acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: car-of-vl-modulelist-elimalways

(defthm car-of-vl-modulelist-elimalways
  (equal (car (vl-modulelist-elimalways acl2::x))
         (and (consp acl2::x)
              (vl-module-elimalways (car acl2::x))))
  :rule-classes ((:rewrite)))

Theorem: vl-modulelist-elimalways-under-iff

(defthm vl-modulelist-elimalways-under-iff
  (iff (vl-modulelist-elimalways acl2::x)
       (consp acl2::x))
  :rule-classes ((:rewrite)))

Theorem: consp-of-vl-modulelist-elimalways

(defthm consp-of-vl-modulelist-elimalways
  (equal (consp (vl-modulelist-elimalways acl2::x))
         (consp acl2::x))
  :rule-classes ((:rewrite)))

Theorem: len-of-vl-modulelist-elimalways

(defthm len-of-vl-modulelist-elimalways
  (equal (len (vl-modulelist-elimalways acl2::x))
         (len acl2::x))
  :rule-classes ((:rewrite)))

Theorem: true-listp-of-vl-modulelist-elimalways

(defthm true-listp-of-vl-modulelist-elimalways
  (true-listp (vl-modulelist-elimalways acl2::x))
  :rule-classes :type-prescription)

Theorem: vl-modulelist-elimalways-when-not-consp

(defthm vl-modulelist-elimalways-when-not-consp
  (implies (not (consp acl2::x))
           (equal (vl-modulelist-elimalways acl2::x)
                  nil))
  :rule-classes ((:rewrite)))

Theorem: vl-modulelist-elimalways-of-cons

(defthm vl-modulelist-elimalways-of-cons
  (equal (vl-modulelist-elimalways (cons acl2::a acl2::b))
         (cons (vl-module-elimalways acl2::a)
               (vl-modulelist-elimalways acl2::b)))
  :rule-classes ((:rewrite)))