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• Basic-bind-elim

Vl-interfacelist-apply-binddelta

(vl-interfacelist-apply-binddelta x delta) maps vl-interface-apply-binddelta across a list.

Signature

(vl-interfacelist-apply-binddelta x delta) → new-x

Arguments

x — Guard (vl-interfacelist-p x).

delta — Guard (vl-binddelta-p delta).

Returns

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

This is an ordinary defprojection.

Definitions and Theorems

Function: vl-interfacelist-apply-binddelta-exec

(defun vl-interfacelist-apply-binddelta-exec (x delta acc)
  (declare (xargs :guard (and (vl-interfacelist-p x)
                              (vl-binddelta-p delta))))
  (declare (xargs :guard t))
  (let ((__function__ 'vl-interfacelist-apply-binddelta-exec))
    (declare (ignorable __function__))
    (if (consp x)
        (vl-interfacelist-apply-binddelta-exec
             (cdr x)
             delta
             (cons (vl-interface-apply-binddelta (car x)
                                                 delta)
                   acc))
      acc)))

Function: vl-interfacelist-apply-binddelta-nrev

(defun vl-interfacelist-apply-binddelta-nrev (x delta nrev)
  (declare (xargs :stobjs (nrev)))
  (declare (xargs :guard (and (vl-interfacelist-p x)
                              (vl-binddelta-p delta))))
  (declare (xargs :guard t))
  (let ((__function__ 'vl-interfacelist-apply-binddelta-nrev))
    (declare (ignorable __function__))
    (if (atom x)
        (nrev-fix nrev)
      (let ((nrev (nrev-push (vl-interface-apply-binddelta (car x)
                                                           delta)
                             nrev)))
        (vl-interfacelist-apply-binddelta-nrev (cdr x)
                                               delta nrev)))))

Function: vl-interfacelist-apply-binddelta

(defun vl-interfacelist-apply-binddelta (x delta)
 (declare (xargs :guard (and (vl-interfacelist-p x)
                             (vl-binddelta-p delta))))
 (declare (xargs :guard t))
 (let ((__function__ 'vl-interfacelist-apply-binddelta))
  (declare (ignorable __function__))
  (mbe
    :logic
    (if (consp x)
        (cons (vl-interface-apply-binddelta (car x)
                                            delta)
              (vl-interfacelist-apply-binddelta (cdr x)
                                                delta))
      nil)
    :exec
    (if (atom x)
        nil
      (with-local-nrev
           (vl-interfacelist-apply-binddelta-nrev x delta nrev))))))

Theorem: vl-interfacelist-p-of-vl-interfacelist-apply-binddelta

(defthm vl-interfacelist-p-of-vl-interfacelist-apply-binddelta
  (b* ((new-x (vl-interfacelist-apply-binddelta x delta)))
    (vl-interfacelist-p new-x))
  :rule-classes :rewrite)

Theorem: vl-interfacelist-apply-binddelta-of-vl-interfacelist-fix-x

(defthm vl-interfacelist-apply-binddelta-of-vl-interfacelist-fix-x
  (equal (vl-interfacelist-apply-binddelta (vl-interfacelist-fix x)
                                           delta)
         (vl-interfacelist-apply-binddelta x delta)))

Theorem: vl-interfacelist-apply-binddelta-vl-interfacelist-equiv-congruence-on-x

(defthm
 vl-interfacelist-apply-binddelta-vl-interfacelist-equiv-congruence-on-x
 (implies (vl-interfacelist-equiv x x-equiv)
          (equal (vl-interfacelist-apply-binddelta x delta)
                 (vl-interfacelist-apply-binddelta x-equiv delta)))
 :rule-classes :congruence)

Theorem: vl-interfacelist-apply-binddelta-of-vl-binddelta-fix-delta

(defthm vl-interfacelist-apply-binddelta-of-vl-binddelta-fix-delta
  (equal
       (vl-interfacelist-apply-binddelta x (vl-binddelta-fix delta))
       (vl-interfacelist-apply-binddelta x delta)))

Theorem: vl-interfacelist-apply-binddelta-vl-binddelta-equiv-congruence-on-delta

(defthm
 vl-interfacelist-apply-binddelta-vl-binddelta-equiv-congruence-on-delta
 (implies (vl-binddelta-equiv delta delta-equiv)
          (equal (vl-interfacelist-apply-binddelta x delta)
                 (vl-interfacelist-apply-binddelta x delta-equiv)))
 :rule-classes :congruence)

Theorem: vl-interfacelist-apply-binddelta-of-update-nth

(defthm vl-interfacelist-apply-binddelta-of-update-nth
 (implies
  (<= (nfix acl2::n) (len acl2::x))
  (equal
     (vl-interfacelist-apply-binddelta
          (update-nth acl2::n acl2::v acl2::x)
          delta)
     (update-nth acl2::n
                 (vl-interface-apply-binddelta acl2::v delta)
                 (vl-interfacelist-apply-binddelta acl2::x delta))))
 :rule-classes ((:rewrite)))

Theorem: vl-interfacelist-apply-binddelta-of-revappend

(defthm vl-interfacelist-apply-binddelta-of-revappend
  (equal
       (vl-interfacelist-apply-binddelta (revappend acl2::x acl2::y)
                                         delta)
       (revappend (vl-interfacelist-apply-binddelta acl2::x delta)
                  (vl-interfacelist-apply-binddelta acl2::y delta)))
  :rule-classes ((:rewrite)))

Theorem: nthcdr-of-vl-interfacelist-apply-binddelta

(defthm nthcdr-of-vl-interfacelist-apply-binddelta
  (equal (nthcdr acl2::n
                 (vl-interfacelist-apply-binddelta acl2::x delta))
         (vl-interfacelist-apply-binddelta (nthcdr acl2::n acl2::x)
                                           delta))
  :rule-classes ((:rewrite)))

Theorem: nth-of-vl-interfacelist-apply-binddelta

(defthm nth-of-vl-interfacelist-apply-binddelta
  (equal (nth acl2::n
              (vl-interfacelist-apply-binddelta acl2::x delta))
         (and (< (nfix acl2::n) (len acl2::x))
              (vl-interface-apply-binddelta (nth acl2::n acl2::x)
                                            delta)))
  :rule-classes ((:rewrite)))

Theorem: vl-interfacelist-apply-binddelta-of-take

(defthm vl-interfacelist-apply-binddelta-of-take
 (implies
    (<= (nfix acl2::n) (len acl2::x))
    (equal (vl-interfacelist-apply-binddelta (take acl2::n acl2::x)
                                             delta)
           (take acl2::n
                 (vl-interfacelist-apply-binddelta acl2::x delta))))
 :rule-classes ((:rewrite)))

Theorem: set-equiv-congruence-over-vl-interfacelist-apply-binddelta

(defthm set-equiv-congruence-over-vl-interfacelist-apply-binddelta
  (implies
       (set-equiv acl2::x acl2::y)
       (set-equiv (vl-interfacelist-apply-binddelta acl2::x delta)
                  (vl-interfacelist-apply-binddelta acl2::y delta)))
  :rule-classes ((:congruence)))

Theorem: subsetp-of-vl-interfacelist-apply-binddelta-when-subsetp

(defthm subsetp-of-vl-interfacelist-apply-binddelta-when-subsetp
  (implies
       (subsetp acl2::x acl2::y)
       (subsetp (vl-interfacelist-apply-binddelta acl2::x delta)
                (vl-interfacelist-apply-binddelta acl2::y delta)))
  :rule-classes ((:rewrite)))

Theorem: member-of-vl-interface-apply-binddelta-in-vl-interfacelist-apply-binddelta

(defthm
 member-of-vl-interface-apply-binddelta-in-vl-interfacelist-apply-binddelta
 (implies (member acl2::k acl2::x)
          (member (vl-interface-apply-binddelta acl2::k delta)
                  (vl-interfacelist-apply-binddelta acl2::x delta)))
 :rule-classes ((:rewrite)))

Theorem: vl-interfacelist-apply-binddelta-nrev-removal

(defthm vl-interfacelist-apply-binddelta-nrev-removal
  (equal (vl-interfacelist-apply-binddelta-nrev acl2::x delta nrev)
         (append nrev
                 (vl-interfacelist-apply-binddelta acl2::x delta)))
  :rule-classes ((:rewrite)))

Theorem: vl-interfacelist-apply-binddelta-exec-removal

(defthm vl-interfacelist-apply-binddelta-exec-removal
 (equal
     (vl-interfacelist-apply-binddelta-exec acl2::x delta acl2::acc)
     (revappend (vl-interfacelist-apply-binddelta acl2::x delta)
                acl2::acc))
 :rule-classes ((:rewrite)))

Theorem: vl-interfacelist-apply-binddelta-of-rev

(defthm vl-interfacelist-apply-binddelta-of-rev
  (equal (vl-interfacelist-apply-binddelta (rev acl2::x)
                                           delta)
         (rev (vl-interfacelist-apply-binddelta acl2::x delta)))
  :rule-classes ((:rewrite)))

Theorem: vl-interfacelist-apply-binddelta-of-list-fix

(defthm vl-interfacelist-apply-binddelta-of-list-fix
  (equal (vl-interfacelist-apply-binddelta (list-fix acl2::x)
                                           delta)
         (vl-interfacelist-apply-binddelta acl2::x delta))
  :rule-classes ((:rewrite)))

Theorem: vl-interfacelist-apply-binddelta-of-append

(defthm vl-interfacelist-apply-binddelta-of-append
  (equal (vl-interfacelist-apply-binddelta (append acl2::a acl2::b)
                                           delta)
         (append (vl-interfacelist-apply-binddelta acl2::a delta)
                 (vl-interfacelist-apply-binddelta acl2::b delta)))
  :rule-classes ((:rewrite)))

Theorem: cdr-of-vl-interfacelist-apply-binddelta

(defthm cdr-of-vl-interfacelist-apply-binddelta
  (equal (cdr (vl-interfacelist-apply-binddelta acl2::x delta))
         (vl-interfacelist-apply-binddelta (cdr acl2::x)
                                           delta))
  :rule-classes ((:rewrite)))

Theorem: car-of-vl-interfacelist-apply-binddelta

(defthm car-of-vl-interfacelist-apply-binddelta
  (equal (car (vl-interfacelist-apply-binddelta acl2::x delta))
         (and (consp acl2::x)
              (vl-interface-apply-binddelta (car acl2::x)
                                            delta)))
  :rule-classes ((:rewrite)))

Theorem: vl-interfacelist-apply-binddelta-under-iff

(defthm vl-interfacelist-apply-binddelta-under-iff
  (iff (vl-interfacelist-apply-binddelta acl2::x delta)
       (consp acl2::x))
  :rule-classes ((:rewrite)))

Theorem: consp-of-vl-interfacelist-apply-binddelta

(defthm consp-of-vl-interfacelist-apply-binddelta
  (equal (consp (vl-interfacelist-apply-binddelta acl2::x delta))
         (consp acl2::x))
  :rule-classes ((:rewrite)))

Theorem: len-of-vl-interfacelist-apply-binddelta

(defthm len-of-vl-interfacelist-apply-binddelta
  (equal (len (vl-interfacelist-apply-binddelta acl2::x delta))
         (len acl2::x))
  :rule-classes ((:rewrite)))

Theorem: true-listp-of-vl-interfacelist-apply-binddelta

(defthm true-listp-of-vl-interfacelist-apply-binddelta
  (true-listp (vl-interfacelist-apply-binddelta acl2::x delta))
  :rule-classes :type-prescription)

Theorem: vl-interfacelist-apply-binddelta-when-not-consp

(defthm vl-interfacelist-apply-binddelta-when-not-consp
  (implies (not (consp acl2::x))
           (equal (vl-interfacelist-apply-binddelta acl2::x delta)
                  nil))
  :rule-classes ((:rewrite)))

Theorem: vl-interfacelist-apply-binddelta-of-cons

(defthm vl-interfacelist-apply-binddelta-of-cons
  (equal (vl-interfacelist-apply-binddelta (cons acl2::a acl2::b)
                                           delta)
         (cons (vl-interface-apply-binddelta acl2::a delta)
               (vl-interfacelist-apply-binddelta acl2::b delta)))
  :rule-classes ((:rewrite)))