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• Udp-elim

Vl-udps-to-modules

(vl-udps-to-modules x) maps vl-udp-to-module across a list.

Signature

(vl-udps-to-modules x) → mods

Arguments

x — Guard (vl-udplist-p x).

Returns

mods — Type (vl-modulelist-p mods).

This is an ordinary defprojection.

Definitions and Theorems

Function: vl-udps-to-modules-exec

(defun vl-udps-to-modules-exec (x acc)
 (declare (xargs :guard (vl-udplist-p x)))
 (declare (xargs :guard t))
 (let ((__function__ 'vl-udps-to-modules-exec))
   (declare (ignorable __function__))
   (if
     (consp x)
     (vl-udps-to-modules-exec (cdr x)
                              (cons (vl-udp-to-module (car x)) acc))
     acc)))

Function: vl-udps-to-modules-nrev

(defun vl-udps-to-modules-nrev (x nrev)
  (declare (xargs :stobjs (nrev)))
  (declare (xargs :guard (vl-udplist-p x)))
  (declare (xargs :guard t))
  (let ((__function__ 'vl-udps-to-modules-nrev))
    (declare (ignorable __function__))
    (if (atom x)
        (nrev-fix nrev)
      (let ((nrev (nrev-push (vl-udp-to-module (car x))
                             nrev)))
        (vl-udps-to-modules-nrev (cdr x)
                                 nrev)))))

Function: vl-udps-to-modules

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

Theorem: vl-modulelist-p-of-vl-udps-to-modules

(defthm vl-modulelist-p-of-vl-udps-to-modules
  (b* ((mods (vl-udps-to-modules x)))
    (vl-modulelist-p mods))
  :rule-classes :rewrite)

Theorem: vl-udps-to-modules-of-update-nth

(defthm vl-udps-to-modules-of-update-nth
 (implies
    (<= (nfix acl2::n) (len acl2::x))
    (equal (vl-udps-to-modules (update-nth acl2::n acl2::v acl2::x))
           (update-nth acl2::n (vl-udp-to-module acl2::v)
                       (vl-udps-to-modules acl2::x))))
 :rule-classes ((:rewrite)))

Theorem: vl-udps-to-modules-of-revappend

(defthm vl-udps-to-modules-of-revappend
  (equal (vl-udps-to-modules (revappend acl2::x acl2::y))
         (revappend (vl-udps-to-modules acl2::x)
                    (vl-udps-to-modules acl2::y)))
  :rule-classes ((:rewrite)))

Theorem: nthcdr-of-vl-udps-to-modules

(defthm nthcdr-of-vl-udps-to-modules
  (equal (nthcdr acl2::n (vl-udps-to-modules acl2::x))
         (vl-udps-to-modules (nthcdr acl2::n acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: nth-of-vl-udps-to-modules

(defthm nth-of-vl-udps-to-modules
  (equal (nth acl2::n (vl-udps-to-modules acl2::x))
         (and (< (nfix acl2::n) (len acl2::x))
              (vl-udp-to-module (nth acl2::n acl2::x))))
  :rule-classes ((:rewrite)))

Theorem: vl-udps-to-modules-of-take

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

Theorem: set-equiv-congruence-over-vl-udps-to-modules

(defthm set-equiv-congruence-over-vl-udps-to-modules
  (implies (set-equiv acl2::x acl2::y)
           (set-equiv (vl-udps-to-modules acl2::x)
                      (vl-udps-to-modules acl2::y)))
  :rule-classes ((:congruence)))

Theorem: subsetp-of-vl-udps-to-modules-when-subsetp

(defthm subsetp-of-vl-udps-to-modules-when-subsetp
  (implies (subsetp acl2::x acl2::y)
           (subsetp (vl-udps-to-modules acl2::x)
                    (vl-udps-to-modules acl2::y)))
  :rule-classes ((:rewrite)))

Theorem: member-of-vl-udp-to-module-in-vl-udps-to-modules

(defthm member-of-vl-udp-to-module-in-vl-udps-to-modules
  (implies (member acl2::k acl2::x)
           (member (vl-udp-to-module acl2::k)
                   (vl-udps-to-modules acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: vl-udps-to-modules-nrev-removal

(defthm vl-udps-to-modules-nrev-removal
  (equal (vl-udps-to-modules-nrev acl2::x nrev)
         (append nrev (vl-udps-to-modules acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: vl-udps-to-modules-exec-removal

(defthm vl-udps-to-modules-exec-removal
  (equal (vl-udps-to-modules-exec acl2::x acl2::acc)
         (revappend (vl-udps-to-modules acl2::x)
                    acl2::acc))
  :rule-classes ((:rewrite)))

Theorem: vl-udps-to-modules-of-rev

(defthm vl-udps-to-modules-of-rev
  (equal (vl-udps-to-modules (rev acl2::x))
         (rev (vl-udps-to-modules acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: vl-udps-to-modules-of-list-fix

(defthm vl-udps-to-modules-of-list-fix
  (equal (vl-udps-to-modules (list-fix acl2::x))
         (vl-udps-to-modules acl2::x))
  :rule-classes ((:rewrite)))

Theorem: vl-udps-to-modules-of-append

(defthm vl-udps-to-modules-of-append
  (equal (vl-udps-to-modules (append acl2::a acl2::b))
         (append (vl-udps-to-modules acl2::a)
                 (vl-udps-to-modules acl2::b)))
  :rule-classes ((:rewrite)))

Theorem: cdr-of-vl-udps-to-modules

(defthm cdr-of-vl-udps-to-modules
  (equal (cdr (vl-udps-to-modules acl2::x))
         (vl-udps-to-modules (cdr acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: car-of-vl-udps-to-modules

(defthm car-of-vl-udps-to-modules
  (equal (car (vl-udps-to-modules acl2::x))
         (and (consp acl2::x)
              (vl-udp-to-module (car acl2::x))))
  :rule-classes ((:rewrite)))

Theorem: vl-udps-to-modules-under-iff

(defthm vl-udps-to-modules-under-iff
  (iff (vl-udps-to-modules acl2::x)
       (consp acl2::x))
  :rule-classes ((:rewrite)))

Theorem: consp-of-vl-udps-to-modules

(defthm consp-of-vl-udps-to-modules
  (equal (consp (vl-udps-to-modules acl2::x))
         (consp acl2::x))
  :rule-classes ((:rewrite)))

Theorem: len-of-vl-udps-to-modules

(defthm len-of-vl-udps-to-modules
  (equal (len (vl-udps-to-modules acl2::x))
         (len acl2::x))
  :rule-classes ((:rewrite)))

Theorem: true-listp-of-vl-udps-to-modules

(defthm true-listp-of-vl-udps-to-modules
  (true-listp (vl-udps-to-modules acl2::x))
  :rule-classes :type-prescription)

Theorem: vl-udps-to-modules-when-not-consp

(defthm vl-udps-to-modules-when-not-consp
  (implies (not (consp acl2::x))
           (equal (vl-udps-to-modules acl2::x)
                  nil))
  :rule-classes ((:rewrite)))

Theorem: vl-udps-to-modules-of-cons

(defthm vl-udps-to-modules-of-cons
  (equal (vl-udps-to-modules (cons acl2::a acl2::b))
         (cons (vl-udp-to-module acl2::a)
               (vl-udps-to-modules acl2::b)))
  :rule-classes ((:rewrite)))