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• Attributes

Attributes-p

Recognizer for attributes.

Signature

(attributes-p x) → *

Definitions and Theorems

Function: attributes-p

(defun attributes-p (x)
  (declare (xargs :guard t))
  (let ((__function__ 'attributes-p))
    (declare (ignorable __function__))
    (if (atom x)
        (eq x nil)
      (and (consp (car x))
           (stringp (caar x))
           (maybe-svex-p (cdar x))
           (attributes-p (cdr x))))))

Theorem: attributes-p-of-butlast

(defthm attributes-p-of-butlast
  (implies (attributes-p (double-rewrite x))
           (attributes-p (butlast x acl2::n)))
  :rule-classes ((:rewrite)))

Theorem: attributes-p-of-take

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

Theorem: attributes-p-of-append

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

Theorem: attributes-p-of-repeat

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

Theorem: attributes-p-of-rev

(defthm attributes-p-of-rev
  (equal (attributes-p (rev x))
         (attributes-p (list-fix x)))
  :rule-classes ((:rewrite)))

Theorem: attributes-p-of-list-fix

(defthm attributes-p-of-list-fix
  (implies (attributes-p x)
           (attributes-p (list-fix x)))
  :rule-classes ((:rewrite)))

Theorem: true-listp-when-attributes-p-compound-recognizer

(defthm true-listp-when-attributes-p-compound-recognizer
  (implies (attributes-p x)
           (true-listp x))
  :rule-classes :compound-recognizer)

Theorem: attributes-p-when-not-consp

(defthm attributes-p-when-not-consp
  (implies (not (consp x))
           (equal (attributes-p x) (not x)))
  :rule-classes ((:rewrite)))

Theorem: attributes-p-of-cdr-when-attributes-p

(defthm attributes-p-of-cdr-when-attributes-p
  (implies (attributes-p (double-rewrite x))
           (attributes-p (cdr x)))
  :rule-classes ((:rewrite)))

Theorem: attributes-p-of-cons

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

Theorem: attributes-p-of-remove-assoc

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

Theorem: attributes-p-of-put-assoc

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

Theorem: attributes-p-of-fast-alist-clean

(defthm attributes-p-of-fast-alist-clean
  (implies (attributes-p x)
           (attributes-p (fast-alist-clean x)))
  :rule-classes ((:rewrite)))

Theorem: attributes-p-of-hons-shrink-alist

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

Theorem: attributes-p-of-hons-acons

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

Theorem: maybe-svex-p-of-cdr-of-hons-assoc-equal-when-attributes-p

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

Theorem: alistp-when-attributes-p-rewrite

(defthm alistp-when-attributes-p-rewrite
  (implies (attributes-p x) (alistp x))
  :rule-classes ((:rewrite)))

Theorem: alistp-when-attributes-p

(defthm alistp-when-attributes-p
  (implies (attributes-p x) (alistp x))
  :rule-classes :tau-system)

Theorem: maybe-svex-p-of-cdar-when-attributes-p

(defthm maybe-svex-p-of-cdar-when-attributes-p
  (implies (attributes-p x)
           (iff (maybe-svex-p (cdar x))
                (or (consp x) (maybe-svex-p nil))))
  :rule-classes ((:rewrite)))

Theorem: stringp-of-caar-when-attributes-p

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