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• Eliminitial

Vl-modulelist-eliminitial

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

Signature

(vl-modulelist-eliminitial 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-eliminitial-exec

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

Function: vl-modulelist-eliminitial-nrev

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

Function: vl-modulelist-eliminitial

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

Theorem: vl-modulelist-p-of-vl-modulelist-eliminitial

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

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

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

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

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

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

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

Theorem: vl-modulelist-eliminitial-of-revappend

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

Theorem: nthcdr-of-vl-modulelist-eliminitial

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

Theorem: nth-of-vl-modulelist-eliminitial

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

Theorem: vl-modulelist-eliminitial-of-take

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

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

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

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

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

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

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

Theorem: vl-modulelist-eliminitial-nrev-removal

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

Theorem: vl-modulelist-eliminitial-exec-removal

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

Theorem: vl-modulelist-eliminitial-of-rev

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

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

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

Theorem: vl-modulelist-eliminitial-of-append

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

Theorem: cdr-of-vl-modulelist-eliminitial

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

Theorem: car-of-vl-modulelist-eliminitial

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

Theorem: vl-modulelist-eliminitial-under-iff

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

Theorem: consp-of-vl-modulelist-eliminitial

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

Theorem: len-of-vl-modulelist-eliminitial

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

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

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

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

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

Theorem: vl-modulelist-eliminitial-of-cons

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