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Vl-expr-scopesubst

Vl-exprlist-scopesubst

Signature
(vl-exprlist-scopesubst x ss) → new-x
Arguments: x — Guard (vl-exprlist-p x).; ss — Guard (vl-scopestack-p ss).
Returns: new-x — Type (and (vl-exprlist-p new-x) (equal (len new-x) (len x))).

Definitions and Theorems

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

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

Theorem: vl-exprlist-scopesubst-of-revappend

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

Theorem: nthcdr-of-vl-exprlist-scopesubst

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

Theorem: nth-of-vl-exprlist-scopesubst

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

Theorem: vl-exprlist-scopesubst-of-take

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

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

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

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

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

Theorem: member-of-vl-expr-scopesubst-in-vl-exprlist-scopesubst

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

Theorem: vl-exprlist-scopesubst-of-rev

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

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

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

Theorem: vl-exprlist-scopesubst-of-append

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

Theorem: cdr-of-vl-exprlist-scopesubst

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

Theorem: car-of-vl-exprlist-scopesubst

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

Theorem: vl-exprlist-scopesubst-under-iff

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

Theorem: consp-of-vl-exprlist-scopesubst

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

Theorem: len-of-vl-exprlist-scopesubst

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

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

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

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

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

Theorem: vl-exprlist-scopesubst-of-cons

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