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Vl-atts

Vl-atts-p

Recognizer for vl-atts.

Signature
(vl-atts-p x) → *

Definitions and Theorems

Theorem: vl-atts-p-of-nthcdr

(defthm vl-atts-p-of-nthcdr
  (implies (vl-atts-p (double-rewrite acl2::x))
           (vl-atts-p (nthcdr acl2::n acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: vl-atts-p-of-repeat

(defthm vl-atts-p-of-repeat
  (iff (vl-atts-p (repeat acl2::n acl2::x))
       (or (and (consp acl2::x)
                (stringp (car acl2::x))
                (vl-maybe-expr-p (cdr acl2::x)))
           (zp acl2::n)))
  :rule-classes ((:rewrite)))

Theorem: vl-atts-p-of-take

(defthm vl-atts-p-of-take
  (implies (vl-atts-p (double-rewrite acl2::x))
           (iff (vl-atts-p (take acl2::n acl2::x))
                (or (and (consp nil)
                         (stringp (car nil))
                         (vl-maybe-expr-p (cdr nil)))
                    (<= (nfix acl2::n) (len acl2::x)))))
  :rule-classes ((:rewrite)))

Theorem: vl-atts-p-of-append

(defthm vl-atts-p-of-append
  (equal (vl-atts-p (append acl2::a acl2::b))
         (and (vl-atts-p (list-fix acl2::a))
              (vl-atts-p acl2::b)))
  :rule-classes ((:rewrite)))

Theorem: vl-atts-p-of-rev

(defthm vl-atts-p-of-rev
  (equal (vl-atts-p (rev acl2::x))
         (vl-atts-p (list-fix acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: vl-atts-p-of-list-fix

(defthm vl-atts-p-of-list-fix
  (implies (vl-atts-p acl2::x)
           (vl-atts-p (list-fix acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: true-listp-when-vl-atts-p-compound-recognizer

(defthm true-listp-when-vl-atts-p-compound-recognizer
  (implies (vl-atts-p acl2::x)
           (true-listp acl2::x))
  :rule-classes :compound-recognizer)

Theorem: vl-atts-p-when-not-consp

(defthm vl-atts-p-when-not-consp
  (implies (not (consp acl2::x))
           (equal (vl-atts-p acl2::x)
                  (not acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: vl-atts-p-of-cdr-when-vl-atts-p

(defthm vl-atts-p-of-cdr-when-vl-atts-p
  (implies (vl-atts-p (double-rewrite acl2::x))
           (vl-atts-p (cdr acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: vl-atts-p-of-cons

(defthm vl-atts-p-of-cons
  (equal (vl-atts-p (cons acl2::a acl2::x))
         (and (and (consp acl2::a)
                   (stringp (car acl2::a))
                   (vl-maybe-expr-p (cdr acl2::a)))
              (vl-atts-p acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: vl-atts-p-of-remove-assoc

(defthm vl-atts-p-of-remove-assoc
  (implies (vl-atts-p acl2::x)
           (vl-atts-p (remove-assoc-equal acl2::name acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: vl-atts-p-of-put-assoc

(defthm vl-atts-p-of-put-assoc
 (implies
     (and (vl-atts-p acl2::x))
     (iff (vl-atts-p (put-assoc-equal acl2::name acl2::val acl2::x))
          (and (stringp acl2::name)
               (vl-maybe-expr-p acl2::val))))
 :rule-classes ((:rewrite)))

Theorem: vl-atts-p-of-fast-alist-clean

(defthm vl-atts-p-of-fast-alist-clean
  (implies (vl-atts-p acl2::x)
           (vl-atts-p (fast-alist-clean acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: vl-atts-p-of-hons-shrink-alist

(defthm vl-atts-p-of-hons-shrink-alist
  (implies (and (vl-atts-p acl2::x)
                (vl-atts-p acl2::y))
           (vl-atts-p (hons-shrink-alist acl2::x acl2::y)))
  :rule-classes ((:rewrite)))

Theorem: vl-atts-p-of-hons-acons

(defthm vl-atts-p-of-hons-acons
  (equal (vl-atts-p (hons-acons acl2::a acl2::n acl2::x))
         (and (stringp acl2::a)
              (vl-maybe-expr-p acl2::n)
              (vl-atts-p acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: vl-maybe-expr-p-of-cdr-of-hons-assoc-equal-when-vl-atts-p

(defthm vl-maybe-expr-p-of-cdr-of-hons-assoc-equal-when-vl-atts-p
 (implies
     (vl-atts-p acl2::x)
     (iff (vl-maybe-expr-p (cdr (hons-assoc-equal acl2::k acl2::x)))
          (or (hons-assoc-equal acl2::k acl2::x)
              (vl-maybe-expr-p nil))))
 :rule-classes ((:rewrite)))

Theorem: alistp-when-vl-atts-p-rewrite

(defthm alistp-when-vl-atts-p-rewrite
  (implies (vl-atts-p acl2::x)
           (alistp acl2::x))
  :rule-classes ((:rewrite)))

Theorem: alistp-when-vl-atts-p

(defthm alistp-when-vl-atts-p
  (implies (vl-atts-p acl2::x)
           (alistp acl2::x))
  :rule-classes :tau-system)

Theorem: vl-maybe-expr-p-of-cdar-when-vl-atts-p

(defthm vl-maybe-expr-p-of-cdar-when-vl-atts-p
  (implies (vl-atts-p acl2::x)
           (iff (vl-maybe-expr-p (cdar acl2::x))
                (or (consp acl2::x)
                    (vl-maybe-expr-p nil))))
  :rule-classes ((:rewrite)))

Theorem: stringp-of-caar-when-vl-atts-p

(defthm stringp-of-caar-when-vl-atts-p
  (implies (vl-atts-p acl2::x)
           (iff (stringp (caar acl2::x))
                (or (consp acl2::x) (stringp nil))))
  :rule-classes ((:rewrite)))