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• Nedgeflop

Vl-make-same-bitselect-from-each

(vl-make-same-bitselect-from-each x index) maps vl-make-bitselect across a list.

Signature

(vl-make-same-bitselect-from-each x index) → *

This is an ordinary defprojection.

Definitions and Theorems

Function: vl-make-same-bitselect-from-each-exec

(defun vl-make-same-bitselect-from-each-exec (x index acc)
  (declare (xargs :guard (and (vl-exprlist-p x) (natp index))))
  (let ((__function__ 'vl-make-same-bitselect-from-each-exec))
    (declare (ignorable __function__))
    (if (consp x)
        (vl-make-same-bitselect-from-each-exec
             (cdr x)
             index
             (cons (vl-make-bitselect (car x) index)
                   acc))
      acc)))

Function: vl-make-same-bitselect-from-each-nrev

(defun vl-make-same-bitselect-from-each-nrev (x index nrev)
  (declare (xargs :stobjs (nrev)))
  (declare (xargs :guard (and (vl-exprlist-p x) (natp index))))
  (let ((__function__ 'vl-make-same-bitselect-from-each-nrev))
    (declare (ignorable __function__))
    (if (atom x)
        (nrev-fix nrev)
      (let ((nrev (nrev-push (vl-make-bitselect (car x) index)
                             nrev)))
        (vl-make-same-bitselect-from-each-nrev (cdr x)
                                               index nrev)))))

Function: vl-make-same-bitselect-from-each

(defun vl-make-same-bitselect-from-each (x index)
 (declare (xargs :guard (and (vl-exprlist-p x) (natp index))))
 (let ((__function__ 'vl-make-same-bitselect-from-each))
  (declare (ignorable __function__))
  (mbe
    :logic
    (if (consp x)
        (cons (vl-make-bitselect (car x) index)
              (vl-make-same-bitselect-from-each (cdr x)
                                                index))
      nil)
    :exec
    (if (atom x)
        nil
      (with-local-nrev
           (vl-make-same-bitselect-from-each-nrev x index nrev))))))

Theorem: vl-make-same-bitselect-from-each-of-update-nth

(defthm vl-make-same-bitselect-from-each-of-update-nth
 (implies
  (<= (nfix acl2::n) (len acl2::x))
  (equal
     (vl-make-same-bitselect-from-each
          (update-nth acl2::n acl2::v acl2::x)
          index)
     (update-nth acl2::n
                 (vl-make-bitselect acl2::v index)
                 (vl-make-same-bitselect-from-each acl2::x index))))
 :rule-classes ((:rewrite)))

Theorem: vl-make-same-bitselect-from-each-of-revappend

(defthm vl-make-same-bitselect-from-each-of-revappend
  (equal
       (vl-make-same-bitselect-from-each (revappend acl2::x acl2::y)
                                         index)
       (revappend (vl-make-same-bitselect-from-each acl2::x index)
                  (vl-make-same-bitselect-from-each acl2::y index)))
  :rule-classes ((:rewrite)))

Theorem: nthcdr-of-vl-make-same-bitselect-from-each

(defthm nthcdr-of-vl-make-same-bitselect-from-each
  (equal (nthcdr acl2::n
                 (vl-make-same-bitselect-from-each acl2::x index))
         (vl-make-same-bitselect-from-each (nthcdr acl2::n acl2::x)
                                           index))
  :rule-classes ((:rewrite)))

Theorem: nth-of-vl-make-same-bitselect-from-each

(defthm nth-of-vl-make-same-bitselect-from-each
  (equal (nth acl2::n
              (vl-make-same-bitselect-from-each acl2::x index))
         (and (< (nfix acl2::n) (len acl2::x))
              (vl-make-bitselect (nth acl2::n acl2::x)
                                 index)))
  :rule-classes ((:rewrite)))

Theorem: vl-make-same-bitselect-from-each-nrev-removal

(defthm vl-make-same-bitselect-from-each-nrev-removal
  (equal (vl-make-same-bitselect-from-each-nrev acl2::x index nrev)
         (append nrev
                 (vl-make-same-bitselect-from-each acl2::x index)))
  :rule-classes ((:rewrite)))

Theorem: vl-make-same-bitselect-from-each-exec-removal

(defthm vl-make-same-bitselect-from-each-exec-removal
 (equal
     (vl-make-same-bitselect-from-each-exec acl2::x index acl2::acc)
     (revappend (vl-make-same-bitselect-from-each acl2::x index)
                acl2::acc))
 :rule-classes ((:rewrite)))

Theorem: vl-make-same-bitselect-from-each-of-take

(defthm vl-make-same-bitselect-from-each-of-take
 (implies
    (<= (nfix acl2::n) (len acl2::x))
    (equal (vl-make-same-bitselect-from-each (take acl2::n acl2::x)
                                             index)
           (take acl2::n
                 (vl-make-same-bitselect-from-each acl2::x index))))
 :rule-classes ((:rewrite)))

Theorem: set-equiv-congruence-over-vl-make-same-bitselect-from-each

(defthm set-equiv-congruence-over-vl-make-same-bitselect-from-each
  (implies
       (set-equiv acl2::x acl2::y)
       (set-equiv (vl-make-same-bitselect-from-each acl2::x index)
                  (vl-make-same-bitselect-from-each acl2::y index)))
  :rule-classes ((:congruence)))

Theorem: subsetp-of-vl-make-same-bitselect-from-each-when-subsetp

(defthm subsetp-of-vl-make-same-bitselect-from-each-when-subsetp
  (implies
       (subsetp acl2::x acl2::y)
       (subsetp (vl-make-same-bitselect-from-each acl2::x index)
                (vl-make-same-bitselect-from-each acl2::y index)))
  :rule-classes ((:rewrite)))

Theorem: member-of-vl-make-bitselect-in-vl-make-same-bitselect-from-each

(defthm
    member-of-vl-make-bitselect-in-vl-make-same-bitselect-from-each
 (implies (member acl2::k acl2::x)
          (member (vl-make-bitselect acl2::k index)
                  (vl-make-same-bitselect-from-each acl2::x index)))
 :rule-classes ((:rewrite)))

Theorem: vl-make-same-bitselect-from-each-of-rev

(defthm vl-make-same-bitselect-from-each-of-rev
  (equal (vl-make-same-bitselect-from-each (rev acl2::x)
                                           index)
         (rev (vl-make-same-bitselect-from-each acl2::x index)))
  :rule-classes ((:rewrite)))

Theorem: vl-make-same-bitselect-from-each-of-list-fix

(defthm vl-make-same-bitselect-from-each-of-list-fix
  (equal (vl-make-same-bitselect-from-each (list-fix acl2::x)
                                           index)
         (vl-make-same-bitselect-from-each acl2::x index))
  :rule-classes ((:rewrite)))

Theorem: vl-make-same-bitselect-from-each-of-append

(defthm vl-make-same-bitselect-from-each-of-append
  (equal (vl-make-same-bitselect-from-each (append acl2::a acl2::b)
                                           index)
         (append (vl-make-same-bitselect-from-each acl2::a index)
                 (vl-make-same-bitselect-from-each acl2::b index)))
  :rule-classes ((:rewrite)))

Theorem: cdr-of-vl-make-same-bitselect-from-each

(defthm cdr-of-vl-make-same-bitselect-from-each
  (equal (cdr (vl-make-same-bitselect-from-each acl2::x index))
         (vl-make-same-bitselect-from-each (cdr acl2::x)
                                           index))
  :rule-classes ((:rewrite)))

Theorem: car-of-vl-make-same-bitselect-from-each

(defthm car-of-vl-make-same-bitselect-from-each
  (equal (car (vl-make-same-bitselect-from-each acl2::x index))
         (and (consp acl2::x)
              (vl-make-bitselect (car acl2::x)
                                 index)))
  :rule-classes ((:rewrite)))

Theorem: vl-make-same-bitselect-from-each-under-iff

(defthm vl-make-same-bitselect-from-each-under-iff
  (iff (vl-make-same-bitselect-from-each acl2::x index)
       (consp acl2::x))
  :rule-classes ((:rewrite)))

Theorem: consp-of-vl-make-same-bitselect-from-each

(defthm consp-of-vl-make-same-bitselect-from-each
  (equal (consp (vl-make-same-bitselect-from-each acl2::x index))
         (consp acl2::x))
  :rule-classes ((:rewrite)))

Theorem: len-of-vl-make-same-bitselect-from-each

(defthm len-of-vl-make-same-bitselect-from-each
  (equal (len (vl-make-same-bitselect-from-each acl2::x index))
         (len acl2::x))
  :rule-classes ((:rewrite)))

Theorem: true-listp-of-vl-make-same-bitselect-from-each

(defthm true-listp-of-vl-make-same-bitselect-from-each
  (true-listp (vl-make-same-bitselect-from-each acl2::x index))
  :rule-classes :type-prescription)

Theorem: vl-make-same-bitselect-from-each-when-not-consp

(defthm vl-make-same-bitselect-from-each-when-not-consp
  (implies (not (consp acl2::x))
           (equal (vl-make-same-bitselect-from-each acl2::x index)
                  nil))
  :rule-classes ((:rewrite)))

Theorem: vl-make-same-bitselect-from-each-of-cons

(defthm vl-make-same-bitselect-from-each-of-cons
  (equal (vl-make-same-bitselect-from-each (cons acl2::a acl2::b)
                                           index)
         (cons (vl-make-bitselect acl2::a index)
               (vl-make-same-bitselect-from-each acl2::b index)))
  :rule-classes ((:rewrite)))

Theorem: vl-exprlist-p-of-vl-make-same-bitselect-from-each

(defthm vl-exprlist-p-of-vl-make-same-bitselect-from-each
  (implies
       (force (vl-exprlist-p x))
       (vl-exprlist-p (vl-make-same-bitselect-from-each x index))))

Theorem: vl-exprlist->finalwidths-of-vl-make-same-bitselect-from-each

(defthm vl-exprlist->finalwidths-of-vl-make-same-bitselect-from-each
  (equal (vl-exprlist->finalwidths
              (vl-make-same-bitselect-from-each x index))
         (replicate (len x) 1)))

Theorem: vl-exprlist->finaltypes-of-vl-make-same-bitselect-from-each

(defthm vl-exprlist->finaltypes-of-vl-make-same-bitselect-from-each
  (equal (vl-exprlist->finaltypes
              (vl-make-same-bitselect-from-each x index))
         (replicate (len x) :vl-unsigned)))