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Neteval-ordering

Neteval-ordering-p

Signature
(neteval-ordering-p x) → *

Definitions and Theorems

Theorem: neteval-ordering-p-of-union-equal

(defthm neteval-ordering-p-of-union-equal
  (equal (neteval-ordering-p (union-equal x y))
         (and (neteval-ordering-p (list-fix x))
              (neteval-ordering-p (double-rewrite y))))
  :rule-classes ((:rewrite)))

Theorem: neteval-ordering-p-of-intersection-equal-2

(defthm neteval-ordering-p-of-intersection-equal-2
  (implies (neteval-ordering-p (double-rewrite y))
           (neteval-ordering-p (intersection-equal x y)))
  :rule-classes ((:rewrite)))

Theorem: neteval-ordering-p-of-intersection-equal-1

(defthm neteval-ordering-p-of-intersection-equal-1
  (implies (neteval-ordering-p (double-rewrite x))
           (neteval-ordering-p (intersection-equal x y)))
  :rule-classes ((:rewrite)))

Theorem: neteval-ordering-p-of-set-difference-equal

(defthm neteval-ordering-p-of-set-difference-equal
  (implies (neteval-ordering-p x)
           (neteval-ordering-p (set-difference-equal x y)))
  :rule-classes ((:rewrite)))

Theorem: neteval-ordering-p-when-subsetp-equal

(defthm neteval-ordering-p-when-subsetp-equal
  (and (implies (and (subsetp-equal x y)
                     (neteval-ordering-p y))
                (equal (neteval-ordering-p x)
                       (true-listp x)))
       (implies (and (neteval-ordering-p y)
                     (subsetp-equal x y))
                (equal (neteval-ordering-p x)
                       (true-listp x))))
  :rule-classes ((:rewrite)))

Theorem: neteval-ordering-p-of-rcons

(defthm neteval-ordering-p-of-rcons
  (iff (neteval-ordering-p (acl2::rcons acl2::a x))
       (and (and (consp acl2::a)
                 (svar-p (car acl2::a))
                 (neteval-sigordering-p (cdr acl2::a)))
            (neteval-ordering-p (list-fix x))))
  :rule-classes ((:rewrite)))

Theorem: neteval-ordering-p-of-append

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

Theorem: neteval-ordering-p-of-repeat

(defthm neteval-ordering-p-of-repeat
  (iff (neteval-ordering-p (repeat acl2::n x))
       (or (and (consp x)
                (svar-p (car x))
                (neteval-sigordering-p (cdr x)))
           (zp acl2::n)))
  :rule-classes ((:rewrite)))

Theorem: neteval-ordering-p-of-rev

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

Theorem: neteval-ordering-p-of-list-fix

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

Theorem: true-listp-when-neteval-ordering-p-compound-recognizer

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

Theorem: neteval-ordering-p-when-not-consp

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

Theorem: neteval-ordering-p-of-cdr-when-neteval-ordering-p

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

Theorem: neteval-ordering-p-of-cons

(defthm neteval-ordering-p-of-cons
  (equal (neteval-ordering-p (cons acl2::a x))
         (and (and (consp acl2::a)
                   (svar-p (car acl2::a))
                   (neteval-sigordering-p (cdr acl2::a)))
              (neteval-ordering-p x)))
  :rule-classes ((:rewrite)))

Theorem: neteval-ordering-p-of-remove-assoc

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

Theorem: neteval-ordering-p-of-put-assoc

(defthm neteval-ordering-p-of-put-assoc
 (implies
  (and (neteval-ordering-p x))
  (iff (neteval-ordering-p (put-assoc-equal acl2::name acl2::val x))
       (and (svar-p acl2::name)
            (neteval-sigordering-p acl2::val))))
 :rule-classes ((:rewrite)))

Theorem: neteval-ordering-p-of-fast-alist-clean

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

Theorem: neteval-ordering-p-of-hons-shrink-alist

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

Theorem: neteval-ordering-p-of-hons-acons

(defthm neteval-ordering-p-of-hons-acons
  (equal (neteval-ordering-p (hons-acons acl2::a acl2::n x))
         (and (svar-p acl2::a)
              (neteval-sigordering-p acl2::n)
              (neteval-ordering-p x)))
  :rule-classes ((:rewrite)))

Theorem: neteval-sigordering-p-of-cdr-of-hons-assoc-equal-when-neteval-ordering-p

(defthm
 neteval-sigordering-p-of-cdr-of-hons-assoc-equal-when-neteval-ordering-p
 (implies
     (neteval-ordering-p x)
     (iff (neteval-sigordering-p (cdr (hons-assoc-equal acl2::k x)))
          (or (hons-assoc-equal acl2::k x)
              (neteval-sigordering-p nil))))
 :rule-classes ((:rewrite)))

Theorem: alistp-when-neteval-ordering-p-rewrite

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

Theorem: alistp-when-neteval-ordering-p

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

Theorem: neteval-sigordering-p-of-cdar-when-neteval-ordering-p

(defthm neteval-sigordering-p-of-cdar-when-neteval-ordering-p
  (implies (neteval-ordering-p x)
           (iff (neteval-sigordering-p (cdar x))
                (or (consp x)
                    (neteval-sigordering-p nil))))
  :rule-classes ((:rewrite)))

Theorem: svar-p-of-caar-when-neteval-ordering-p

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