		Search-engine friendly clone of the ACL2 documentation.

Svar-proplist

Svar-proplist-p

Signature
(svar-proplist-p x) → *

Definitions and Theorems

Function: svar-proplist-p

(defun svar-proplist-p (x)
  (declare (xargs :guard t))
  (let ((__function__ 'svar-proplist-p))
    (declare (ignorable __function__))
    (if (atom x)
        (eq x nil)
      (and (consp (car x))
           (symbolp (caar x))
           (svar-proplist-p (cdr x))))))

Theorem: true-listp-when-svar-proplist-p-compound-recognizer

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

Theorem: svar-proplist-p-when-not-consp

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

Theorem: svar-proplist-p-of-cdr-when-svar-proplist-p

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

Theorem: svar-proplist-p-of-cons

(defthm svar-proplist-p-of-cons
  (equal (svar-proplist-p (cons acl2::a x))
         (and (and (consp acl2::a)
                   (symbolp (car acl2::a)))
              (svar-proplist-p x)))
  :rule-classes ((:rewrite)))

Theorem: svar-proplist-p-of-remove-assoc

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

Theorem: svar-proplist-p-of-put-assoc

(defthm svar-proplist-p-of-put-assoc
 (implies
     (and (svar-proplist-p x))
     (iff (svar-proplist-p (put-assoc-equal acl2::name acl2::val x))
          (and (symbolp acl2::name) t)))
 :rule-classes ((:rewrite)))

Theorem: svar-proplist-p-of-fast-alist-clean

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

Theorem: svar-proplist-p-of-hons-shrink-alist

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

Theorem: svar-proplist-p-of-hons-acons

(defthm svar-proplist-p-of-hons-acons
  (equal (svar-proplist-p (hons-acons acl2::a acl2::n x))
         (and (symbolp acl2::a)
              t (svar-proplist-p x)))
  :rule-classes ((:rewrite)))

Theorem: alistp-when-svar-proplist-p-rewrite

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

Theorem: alistp-when-svar-proplist-p

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

Theorem: symbolp-of-caar-when-svar-proplist-p

(defthm symbolp-of-caar-when-svar-proplist-p
  (implies (svar-proplist-p x)
           (iff (symbolp (caar x))
                (or (consp x) (symbolp nil))))
  :rule-classes ((:rewrite)))