		Search-engine friendly clone of the ACL2 documentation.

Scopesubst

Vl-expr-scopesubst

Substitute resolved parameters into an expression.

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

We assume that the parameters have already been processed so that their overrides are compatible with thier types.

Theorem: return-type-of-vl-expr-scopesubst.new-x

(defthm return-type-of-vl-expr-scopesubst.new-x
  (b* ((?new-x (vl-expr-scopesubst x ss)))
    (vl-expr-p new-x))
  :rule-classes :rewrite)

Theorem: return-type-of-vl-exprlist-scopesubst.new-x

(defthm return-type-of-vl-exprlist-scopesubst.new-x
  (b* ((?new-x (vl-exprlist-scopesubst x ss)))
    (and (vl-exprlist-p new-x)
         (equal (len new-x) (len x))))
  :rule-classes :rewrite)

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)))

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Subtopics

Vl-exprlist-scopesubst