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• Scopesubst

Vl-namedparamvaluelist-scopesubst

(vl-namedparamvaluelist-scopesubst x ss) maps vl-namedparamvalue-scopesubst across a list.

Signature

(vl-namedparamvaluelist-scopesubst x ss) → new-x

Arguments

x — Guard (vl-namedparamvaluelist-p x).

ss — Guard (vl-scopestack-p ss).

Returns

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

This is an ordinary defprojection.

Definitions and Theorems

Function: vl-namedparamvaluelist-scopesubst-exec

(defun vl-namedparamvaluelist-scopesubst-exec (x ss acc)
  (declare (xargs :guard (and (vl-namedparamvaluelist-p x)
                              (vl-scopestack-p ss))))
  (declare (xargs :guard t))
  (let ((__function__ 'vl-namedparamvaluelist-scopesubst-exec))
    (declare (ignorable __function__))
    (if (consp x)
        (vl-namedparamvaluelist-scopesubst-exec
             (cdr x)
             ss
             (cons (vl-namedparamvalue-scopesubst (car x)
                                                  ss)
                   acc))
      acc)))

Function: vl-namedparamvaluelist-scopesubst-nrev

(defun vl-namedparamvaluelist-scopesubst-nrev (x ss nrev)
  (declare (xargs :stobjs (nrev)))
  (declare (xargs :guard (and (vl-namedparamvaluelist-p x)
                              (vl-scopestack-p ss))))
  (declare (xargs :guard t))
  (let ((__function__ 'vl-namedparamvaluelist-scopesubst-nrev))
    (declare (ignorable __function__))
    (if (atom x)
        (nrev-fix nrev)
      (let ((nrev (nrev-push (vl-namedparamvalue-scopesubst (car x)
                                                            ss)
                             nrev)))
        (vl-namedparamvaluelist-scopesubst-nrev (cdr x)
                                                ss nrev)))))

Function: vl-namedparamvaluelist-scopesubst

(defun vl-namedparamvaluelist-scopesubst (x ss)
 (declare (xargs :guard (and (vl-namedparamvaluelist-p x)
                             (vl-scopestack-p ss))))
 (declare (xargs :guard t))
 (let ((__function__ 'vl-namedparamvaluelist-scopesubst))
  (declare (ignorable __function__))
  (mbe
      :logic
      (if (consp x)
          (cons (vl-namedparamvalue-scopesubst (car x)
                                               ss)
                (vl-namedparamvaluelist-scopesubst (cdr x)
                                                   ss))
        nil)
      :exec
      (if (atom x)
          nil
        (with-local-nrev
             (vl-namedparamvaluelist-scopesubst-nrev x ss nrev))))))

Theorem: vl-namedparamvaluelist-p-of-vl-namedparamvaluelist-scopesubst

(defthm
      vl-namedparamvaluelist-p-of-vl-namedparamvaluelist-scopesubst
  (b* ((new-x (vl-namedparamvaluelist-scopesubst x ss)))
    (vl-namedparamvaluelist-p new-x))
  :rule-classes :rewrite)

Theorem: vl-namedparamvaluelist-scopesubst-of-vl-namedparamvaluelist-fix-x

(defthm
  vl-namedparamvaluelist-scopesubst-of-vl-namedparamvaluelist-fix-x
 (equal
   (vl-namedparamvaluelist-scopesubst (vl-namedparamvaluelist-fix x)
                                      ss)
   (vl-namedparamvaluelist-scopesubst x ss)))

Theorem: vl-namedparamvaluelist-scopesubst-vl-namedparamvaluelist-equiv-congruence-on-x

(defthm
 vl-namedparamvaluelist-scopesubst-vl-namedparamvaluelist-equiv-congruence-on-x
 (implies (vl-namedparamvaluelist-equiv x x-equiv)
          (equal (vl-namedparamvaluelist-scopesubst x ss)
                 (vl-namedparamvaluelist-scopesubst x-equiv ss)))
 :rule-classes :congruence)

Theorem: vl-namedparamvaluelist-scopesubst-of-vl-scopestack-fix-ss

(defthm vl-namedparamvaluelist-scopesubst-of-vl-scopestack-fix-ss
 (equal (vl-namedparamvaluelist-scopesubst x (vl-scopestack-fix ss))
        (vl-namedparamvaluelist-scopesubst x ss)))

Theorem: vl-namedparamvaluelist-scopesubst-vl-scopestack-equiv-congruence-on-ss

(defthm
 vl-namedparamvaluelist-scopesubst-vl-scopestack-equiv-congruence-on-ss
 (implies (vl-scopestack-equiv ss ss-equiv)
          (equal (vl-namedparamvaluelist-scopesubst x ss)
                 (vl-namedparamvaluelist-scopesubst x ss-equiv)))
 :rule-classes :congruence)

Theorem: vl-namedparamvaluelist-scopesubst-of-update-nth

(defthm vl-namedparamvaluelist-scopesubst-of-update-nth
 (implies
  (<= (nfix acl2::n) (len acl2::x))
  (equal
       (vl-namedparamvaluelist-scopesubst
            (update-nth acl2::n acl2::v acl2::x)
            ss)
       (update-nth acl2::n
                   (vl-namedparamvalue-scopesubst acl2::v ss)
                   (vl-namedparamvaluelist-scopesubst acl2::x ss))))
 :rule-classes ((:rewrite)))

Theorem: vl-namedparamvaluelist-scopesubst-of-revappend

(defthm vl-namedparamvaluelist-scopesubst-of-revappend
 (equal
      (vl-namedparamvaluelist-scopesubst (revappend acl2::x acl2::y)
                                         ss)
      (revappend (vl-namedparamvaluelist-scopesubst acl2::x ss)
                 (vl-namedparamvaluelist-scopesubst acl2::y ss)))
 :rule-classes ((:rewrite)))

Theorem: nthcdr-of-vl-namedparamvaluelist-scopesubst

(defthm nthcdr-of-vl-namedparamvaluelist-scopesubst
  (equal (nthcdr acl2::n
                 (vl-namedparamvaluelist-scopesubst acl2::x ss))
         (vl-namedparamvaluelist-scopesubst (nthcdr acl2::n acl2::x)
                                            ss))
  :rule-classes ((:rewrite)))

Theorem: nth-of-vl-namedparamvaluelist-scopesubst

(defthm nth-of-vl-namedparamvaluelist-scopesubst
  (equal (nth acl2::n
              (vl-namedparamvaluelist-scopesubst acl2::x ss))
         (and (< (nfix acl2::n) (len acl2::x))
              (vl-namedparamvalue-scopesubst (nth acl2::n acl2::x)
                                             ss)))
  :rule-classes ((:rewrite)))

Theorem: vl-namedparamvaluelist-scopesubst-nrev-removal

(defthm vl-namedparamvaluelist-scopesubst-nrev-removal
  (equal (vl-namedparamvaluelist-scopesubst-nrev acl2::x ss nrev)
         (append nrev
                 (vl-namedparamvaluelist-scopesubst acl2::x ss)))
  :rule-classes ((:rewrite)))

Theorem: vl-namedparamvaluelist-scopesubst-exec-removal

(defthm vl-namedparamvaluelist-scopesubst-exec-removal
  (equal
       (vl-namedparamvaluelist-scopesubst-exec acl2::x ss acl2::acc)
       (revappend (vl-namedparamvaluelist-scopesubst acl2::x ss)
                  acl2::acc))
  :rule-classes ((:rewrite)))

Theorem: vl-namedparamvaluelist-scopesubst-of-take

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

Theorem: set-equiv-congruence-over-vl-namedparamvaluelist-scopesubst

(defthm set-equiv-congruence-over-vl-namedparamvaluelist-scopesubst
  (implies
       (set-equiv acl2::x acl2::y)
       (set-equiv (vl-namedparamvaluelist-scopesubst acl2::x ss)
                  (vl-namedparamvaluelist-scopesubst acl2::y ss)))
  :rule-classes ((:congruence)))

Theorem: subsetp-of-vl-namedparamvaluelist-scopesubst-when-subsetp

(defthm subsetp-of-vl-namedparamvaluelist-scopesubst-when-subsetp
  (implies (subsetp acl2::x acl2::y)
           (subsetp (vl-namedparamvaluelist-scopesubst acl2::x ss)
                    (vl-namedparamvaluelist-scopesubst acl2::y ss)))
  :rule-classes ((:rewrite)))

Theorem: member-of-vl-namedparamvalue-scopesubst-in-vl-namedparamvaluelist-scopesubst

(defthm
 member-of-vl-namedparamvalue-scopesubst-in-vl-namedparamvaluelist-scopesubst
 (implies (member acl2::k acl2::x)
          (member (vl-namedparamvalue-scopesubst acl2::k ss)
                  (vl-namedparamvaluelist-scopesubst acl2::x ss)))
 :rule-classes ((:rewrite)))

Theorem: vl-namedparamvaluelist-scopesubst-of-rev

(defthm vl-namedparamvaluelist-scopesubst-of-rev
  (equal (vl-namedparamvaluelist-scopesubst (rev acl2::x)
                                            ss)
         (rev (vl-namedparamvaluelist-scopesubst acl2::x ss)))
  :rule-classes ((:rewrite)))

Theorem: vl-namedparamvaluelist-scopesubst-of-list-fix

(defthm vl-namedparamvaluelist-scopesubst-of-list-fix
  (equal (vl-namedparamvaluelist-scopesubst (list-fix acl2::x)
                                            ss)
         (vl-namedparamvaluelist-scopesubst acl2::x ss))
  :rule-classes ((:rewrite)))

Theorem: vl-namedparamvaluelist-scopesubst-of-append

(defthm vl-namedparamvaluelist-scopesubst-of-append
  (equal (vl-namedparamvaluelist-scopesubst (append acl2::a acl2::b)
                                            ss)
         (append (vl-namedparamvaluelist-scopesubst acl2::a ss)
                 (vl-namedparamvaluelist-scopesubst acl2::b ss)))
  :rule-classes ((:rewrite)))

Theorem: cdr-of-vl-namedparamvaluelist-scopesubst

(defthm cdr-of-vl-namedparamvaluelist-scopesubst
  (equal (cdr (vl-namedparamvaluelist-scopesubst acl2::x ss))
         (vl-namedparamvaluelist-scopesubst (cdr acl2::x)
                                            ss))
  :rule-classes ((:rewrite)))

Theorem: car-of-vl-namedparamvaluelist-scopesubst

(defthm car-of-vl-namedparamvaluelist-scopesubst
  (equal (car (vl-namedparamvaluelist-scopesubst acl2::x ss))
         (and (consp acl2::x)
              (vl-namedparamvalue-scopesubst (car acl2::x)
                                             ss)))
  :rule-classes ((:rewrite)))

Theorem: vl-namedparamvaluelist-scopesubst-under-iff

(defthm vl-namedparamvaluelist-scopesubst-under-iff
  (iff (vl-namedparamvaluelist-scopesubst acl2::x ss)
       (consp acl2::x))
  :rule-classes ((:rewrite)))

Theorem: consp-of-vl-namedparamvaluelist-scopesubst

(defthm consp-of-vl-namedparamvaluelist-scopesubst
  (equal (consp (vl-namedparamvaluelist-scopesubst acl2::x ss))
         (consp acl2::x))
  :rule-classes ((:rewrite)))

Theorem: len-of-vl-namedparamvaluelist-scopesubst

(defthm len-of-vl-namedparamvaluelist-scopesubst
  (equal (len (vl-namedparamvaluelist-scopesubst acl2::x ss))
         (len acl2::x))
  :rule-classes ((:rewrite)))

Theorem: true-listp-of-vl-namedparamvaluelist-scopesubst

(defthm true-listp-of-vl-namedparamvaluelist-scopesubst
  (true-listp (vl-namedparamvaluelist-scopesubst acl2::x ss))
  :rule-classes :type-prescription)

Theorem: vl-namedparamvaluelist-scopesubst-when-not-consp

(defthm vl-namedparamvaluelist-scopesubst-when-not-consp
  (implies (not (consp acl2::x))
           (equal (vl-namedparamvaluelist-scopesubst acl2::x ss)
                  nil))
  :rule-classes ((:rewrite)))

Theorem: vl-namedparamvaluelist-scopesubst-of-cons

(defthm vl-namedparamvaluelist-scopesubst-of-cons
  (equal (vl-namedparamvaluelist-scopesubst (cons acl2::a acl2::b)
                                            ss)
         (cons (vl-namedparamvalue-scopesubst acl2::a ss)
               (vl-namedparamvaluelist-scopesubst acl2::b ss)))
  :rule-classes ((:rewrite)))