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• Clean-selects

Vl-stmt-clean-selects

Signature

(vl-stmt-clean-selects x ss) → new-x

Arguments

x — Guard (vl-stmt-p x).

ss — Guard (vl-scopestack-p ss).

Returns

new-x — Type (vl-stmt-p new-x).

Theorem: return-type-of-vl-stmt-clean-selects.new-x

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

Theorem: return-type-of-vl-stmtlist-clean-selects.new-x

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

Theorem: vl-stmt-clean-selects-of-vl-stmt-fix-x

(defthm vl-stmt-clean-selects-of-vl-stmt-fix-x
  (equal (vl-stmt-clean-selects (vl-stmt-fix x)
                                ss)
         (vl-stmt-clean-selects x ss)))

Theorem: vl-stmt-clean-selects-of-vl-scopestack-fix-ss

(defthm vl-stmt-clean-selects-of-vl-scopestack-fix-ss
  (equal (vl-stmt-clean-selects x (vl-scopestack-fix ss))
         (vl-stmt-clean-selects x ss)))

Theorem: vl-stmtlist-clean-selects-of-vl-stmtlist-fix-x

(defthm vl-stmtlist-clean-selects-of-vl-stmtlist-fix-x
  (equal (vl-stmtlist-clean-selects (vl-stmtlist-fix x)
                                    ss)
         (vl-stmtlist-clean-selects x ss)))

Theorem: vl-stmtlist-clean-selects-of-vl-scopestack-fix-ss

(defthm vl-stmtlist-clean-selects-of-vl-scopestack-fix-ss
  (equal (vl-stmtlist-clean-selects x (vl-scopestack-fix ss))
         (vl-stmtlist-clean-selects x ss)))

Theorem: vl-stmt-clean-selects-vl-stmt-equiv-congruence-on-x

(defthm vl-stmt-clean-selects-vl-stmt-equiv-congruence-on-x
  (implies (vl-stmt-equiv x x-equiv)
           (equal (vl-stmt-clean-selects x ss)
                  (vl-stmt-clean-selects x-equiv ss)))
  :rule-classes :congruence)

Theorem: vl-stmt-clean-selects-vl-scopestack-equiv-congruence-on-ss

(defthm vl-stmt-clean-selects-vl-scopestack-equiv-congruence-on-ss
  (implies (vl-scopestack-equiv ss ss-equiv)
           (equal (vl-stmt-clean-selects x ss)
                  (vl-stmt-clean-selects x ss-equiv)))
  :rule-classes :congruence)

Theorem: vl-stmtlist-clean-selects-vl-stmtlist-equiv-congruence-on-x

(defthm vl-stmtlist-clean-selects-vl-stmtlist-equiv-congruence-on-x
  (implies (vl-stmtlist-equiv x x-equiv)
           (equal (vl-stmtlist-clean-selects x ss)
                  (vl-stmtlist-clean-selects x-equiv ss)))
  :rule-classes :congruence)

Theorem: vl-stmtlist-clean-selects-vl-scopestack-equiv-congruence-on-ss

(defthm
     vl-stmtlist-clean-selects-vl-scopestack-equiv-congruence-on-ss
  (implies (vl-scopestack-equiv ss ss-equiv)
           (equal (vl-stmtlist-clean-selects x ss)
                  (vl-stmtlist-clean-selects x ss-equiv)))
  :rule-classes :congruence)

Theorem: vl-stmtlist-clean-selects-of-update-nth

(defthm vl-stmtlist-clean-selects-of-update-nth
 (implies
  (<= (nfix acl2::n) (len acl2::x))
  (equal
     (vl-stmtlist-clean-selects (update-nth acl2::n acl2::v acl2::x)
                                ss)
     (update-nth acl2::n
                 (vl-stmt-clean-selects acl2::v ss)
                 (vl-stmtlist-clean-selects acl2::x ss))))
 :rule-classes ((:rewrite)))

Theorem: vl-stmtlist-clean-selects-of-revappend

(defthm vl-stmtlist-clean-selects-of-revappend
  (equal (vl-stmtlist-clean-selects (revappend acl2::x acl2::y)
                                    ss)
         (revappend (vl-stmtlist-clean-selects acl2::x ss)
                    (vl-stmtlist-clean-selects acl2::y ss)))
  :rule-classes ((:rewrite)))

Theorem: nthcdr-of-vl-stmtlist-clean-selects

(defthm nthcdr-of-vl-stmtlist-clean-selects
  (equal (nthcdr acl2::n
                 (vl-stmtlist-clean-selects acl2::x ss))
         (vl-stmtlist-clean-selects (nthcdr acl2::n acl2::x)
                                    ss))
  :rule-classes ((:rewrite)))

Theorem: nth-of-vl-stmtlist-clean-selects

(defthm nth-of-vl-stmtlist-clean-selects
  (equal (nth acl2::n
              (vl-stmtlist-clean-selects acl2::x ss))
         (and (< (nfix acl2::n) (len acl2::x))
              (vl-stmt-clean-selects (nth acl2::n acl2::x)
                                     ss)))
  :rule-classes ((:rewrite)))

Theorem: vl-stmtlist-clean-selects-of-take

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

Theorem: set-equiv-congruence-over-vl-stmtlist-clean-selects

(defthm set-equiv-congruence-over-vl-stmtlist-clean-selects
  (implies (set-equiv acl2::x acl2::y)
           (set-equiv (vl-stmtlist-clean-selects acl2::x ss)
                      (vl-stmtlist-clean-selects acl2::y ss)))
  :rule-classes ((:congruence)))

Theorem: subsetp-of-vl-stmtlist-clean-selects-when-subsetp

(defthm subsetp-of-vl-stmtlist-clean-selects-when-subsetp
  (implies (subsetp acl2::x acl2::y)
           (subsetp (vl-stmtlist-clean-selects acl2::x ss)
                    (vl-stmtlist-clean-selects acl2::y ss)))
  :rule-classes ((:rewrite)))

Theorem: member-of-vl-stmt-clean-selects-in-vl-stmtlist-clean-selects

(defthm member-of-vl-stmt-clean-selects-in-vl-stmtlist-clean-selects
  (implies (member acl2::k acl2::x)
           (member (vl-stmt-clean-selects acl2::k ss)
                   (vl-stmtlist-clean-selects acl2::x ss)))
  :rule-classes ((:rewrite)))

Theorem: vl-stmtlist-clean-selects-of-rev

(defthm vl-stmtlist-clean-selects-of-rev
  (equal (vl-stmtlist-clean-selects (rev acl2::x)
                                    ss)
         (rev (vl-stmtlist-clean-selects acl2::x ss)))
  :rule-classes ((:rewrite)))

Theorem: vl-stmtlist-clean-selects-of-list-fix

(defthm vl-stmtlist-clean-selects-of-list-fix
  (equal (vl-stmtlist-clean-selects (list-fix acl2::x)
                                    ss)
         (vl-stmtlist-clean-selects acl2::x ss))
  :rule-classes ((:rewrite)))

Theorem: vl-stmtlist-clean-selects-of-append

(defthm vl-stmtlist-clean-selects-of-append
  (equal (vl-stmtlist-clean-selects (append acl2::a acl2::b)
                                    ss)
         (append (vl-stmtlist-clean-selects acl2::a ss)
                 (vl-stmtlist-clean-selects acl2::b ss)))
  :rule-classes ((:rewrite)))

Theorem: cdr-of-vl-stmtlist-clean-selects

(defthm cdr-of-vl-stmtlist-clean-selects
  (equal (cdr (vl-stmtlist-clean-selects acl2::x ss))
         (vl-stmtlist-clean-selects (cdr acl2::x)
                                    ss))
  :rule-classes ((:rewrite)))

Theorem: car-of-vl-stmtlist-clean-selects

(defthm car-of-vl-stmtlist-clean-selects
  (equal (car (vl-stmtlist-clean-selects acl2::x ss))
         (and (consp acl2::x)
              (vl-stmt-clean-selects (car acl2::x)
                                     ss)))
  :rule-classes ((:rewrite)))

Theorem: vl-stmtlist-clean-selects-under-iff

(defthm vl-stmtlist-clean-selects-under-iff
  (iff (vl-stmtlist-clean-selects acl2::x ss)
       (consp acl2::x))
  :rule-classes ((:rewrite)))

Theorem: consp-of-vl-stmtlist-clean-selects

(defthm consp-of-vl-stmtlist-clean-selects
  (equal (consp (vl-stmtlist-clean-selects acl2::x ss))
         (consp acl2::x))
  :rule-classes ((:rewrite)))

Theorem: len-of-vl-stmtlist-clean-selects

(defthm len-of-vl-stmtlist-clean-selects
  (equal (len (vl-stmtlist-clean-selects acl2::x ss))
         (len acl2::x))
  :rule-classes ((:rewrite)))

Theorem: true-listp-of-vl-stmtlist-clean-selects

(defthm true-listp-of-vl-stmtlist-clean-selects
  (true-listp (vl-stmtlist-clean-selects acl2::x ss))
  :rule-classes :type-prescription)

Theorem: vl-stmtlist-clean-selects-when-not-consp

(defthm vl-stmtlist-clean-selects-when-not-consp
  (implies (not (consp acl2::x))
           (equal (vl-stmtlist-clean-selects acl2::x ss)
                  nil))
  :rule-classes ((:rewrite)))

Theorem: vl-stmtlist-clean-selects-of-cons

(defthm vl-stmtlist-clean-selects-of-cons
  (equal (vl-stmtlist-clean-selects (cons acl2::a acl2::b)
                                    ss)
         (cons (vl-stmt-clean-selects acl2::a ss)
               (vl-stmtlist-clean-selects acl2::b ss)))
  :rule-classes ((:rewrite)))

Subtopics

Vl-stmtlist-clean-selects