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Svexl-node-array

Svexl-node-array-p

Signature
(svexl-node-array-p x) → *

Definitions and Theorems

Function: svexl-node-array-p

(defun svexl-node-array-p (x)
  (declare (xargs :guard t))
  (let ((acl2::__function__ 'svexl-node-array-p))
    (declare (ignorable acl2::__function__))
    (if (atom x)
        (eq x nil)
      (and (consp (car x))
           (natp (caar x))
           (svexl-node-p (cdar x))
           (svexl-node-array-p (cdr x))))))

Theorem: svexl-node-array-p-of-butlast

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

Theorem: svexl-node-array-p-of-append

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

Theorem: svexl-node-array-p-of-repeat

(defthm svexl-node-array-p-of-repeat
  (iff (svexl-node-array-p (repeat acl2::n acl2::x))
       (or (and (consp acl2::x)
                (natp (car acl2::x))
                (svexl-node-p (cdr acl2::x)))
           (zp acl2::n)))
  :rule-classes ((:rewrite)))

Theorem: svexl-node-array-p-of-rev

(defthm svexl-node-array-p-of-rev
  (equal (svexl-node-array-p (rev acl2::x))
         (svexl-node-array-p (list-fix acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: svexl-node-array-p-of-list-fix

(defthm svexl-node-array-p-of-list-fix
  (implies (svexl-node-array-p acl2::x)
           (svexl-node-array-p (list-fix acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: true-listp-when-svexl-node-array-p-compound-recognizer

(defthm true-listp-when-svexl-node-array-p-compound-recognizer
  (implies (svexl-node-array-p acl2::x)
           (true-listp acl2::x))
  :rule-classes :compound-recognizer)

Theorem: svexl-node-array-p-when-not-consp

(defthm svexl-node-array-p-when-not-consp
  (implies (not (consp acl2::x))
           (equal (svexl-node-array-p acl2::x)
                  (not acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: svexl-node-array-p-of-cdr-when-svexl-node-array-p

(defthm svexl-node-array-p-of-cdr-when-svexl-node-array-p
  (implies (svexl-node-array-p (double-rewrite acl2::x))
           (svexl-node-array-p (cdr acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: svexl-node-array-p-of-cons

(defthm svexl-node-array-p-of-cons
  (equal (svexl-node-array-p (cons acl2::a acl2::x))
         (and (and (consp acl2::a)
                   (natp (car acl2::a))
                   (svexl-node-p (cdr acl2::a)))
              (svexl-node-array-p acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: svexl-node-array-p-of-remove-assoc

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

Theorem: svexl-node-array-p-of-put-assoc

(defthm svexl-node-array-p-of-put-assoc
  (implies (and (svexl-node-array-p acl2::x))
           (iff (svexl-node-array-p
                     (put-assoc-equal acl2::name acl2::val acl2::x))
                (and (natp acl2::name)
                     (svexl-node-p acl2::val))))
  :rule-classes ((:rewrite)))

Theorem: svexl-node-array-p-of-fast-alist-clean

(defthm svexl-node-array-p-of-fast-alist-clean
  (implies (svexl-node-array-p acl2::x)
           (svexl-node-array-p (fast-alist-clean acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: svexl-node-array-p-of-hons-shrink-alist

(defthm svexl-node-array-p-of-hons-shrink-alist
  (implies (and (svexl-node-array-p acl2::x)
                (svexl-node-array-p acl2::y))
           (svexl-node-array-p (hons-shrink-alist acl2::x acl2::y)))
  :rule-classes ((:rewrite)))

Theorem: svexl-node-array-p-of-hons-acons

(defthm svexl-node-array-p-of-hons-acons
  (equal (svexl-node-array-p (hons-acons acl2::a acl2::n acl2::x))
         (and (natp acl2::a)
              (svexl-node-p acl2::n)
              (svexl-node-array-p acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: svexl-node-p-of-cdr-of-hons-assoc-equal-when-svexl-node-array-p

(defthm
    svexl-node-p-of-cdr-of-hons-assoc-equal-when-svexl-node-array-p
  (implies
       (svexl-node-array-p acl2::x)
       (iff (svexl-node-p (cdr (hons-assoc-equal acl2::k acl2::x)))
            (or (hons-assoc-equal acl2::k acl2::x)
                (svexl-node-p nil))))
  :rule-classes ((:rewrite)))

Theorem: alistp-when-svexl-node-array-p-rewrite

(defthm alistp-when-svexl-node-array-p-rewrite
  (implies (svexl-node-array-p acl2::x)
           (alistp acl2::x))
  :rule-classes ((:rewrite)))

Theorem: alistp-when-svexl-node-array-p

(defthm alistp-when-svexl-node-array-p
  (implies (svexl-node-array-p acl2::x)
           (alistp acl2::x))
  :rule-classes :tau-system)

Theorem: svexl-node-p-of-cdar-when-svexl-node-array-p

(defthm svexl-node-p-of-cdar-when-svexl-node-array-p
  (implies (svexl-node-array-p acl2::x)
           (iff (svexl-node-p (cdar acl2::x))
                (or (consp acl2::x)
                    (svexl-node-p nil))))
  :rule-classes ((:rewrite)))

Theorem: natp-of-caar-when-svexl-node-array-p

(defthm natp-of-caar-when-svexl-node-array-p
  (implies (svexl-node-array-p acl2::x)
           (iff (natp (caar acl2::x))
                (or (consp acl2::x) (natp nil))))
  :rule-classes ((:rewrite)))