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• Ubdd-to-aignet-memo

Ubdd-to-aignet-memo-p

Recognizer for ubdd-to-aignet-memo.

Signature

(ubdd-to-aignet-memo-p x) → *

Definitions and Theorems

Function: ubdd-to-aignet-memo-p

(defun ubdd-to-aignet-memo-p (x)
  (declare (xargs :guard t))
  (let ((__function__ 'ubdd-to-aignet-memo-p))
    (declare (ignorable __function__))
    (if (atom x)
        (eq x nil)
      (and (consp (car x))
           (ubdd/level-p (caar x))
           (litp (cdar x))
           (ubdd-to-aignet-memo-p (cdr x))))))

Theorem: ubdd-to-aignet-memo-p-of-revappend

(defthm ubdd-to-aignet-memo-p-of-revappend
  (equal (ubdd-to-aignet-memo-p (revappend x acl2::y))
         (and (ubdd-to-aignet-memo-p (acl2::list-fix x))
              (ubdd-to-aignet-memo-p acl2::y)))
  :rule-classes ((:rewrite)))

Theorem: ubdd-to-aignet-memo-p-of-remove

(defthm ubdd-to-aignet-memo-p-of-remove
  (implies (ubdd-to-aignet-memo-p x)
           (ubdd-to-aignet-memo-p (remove acl2::a x)))
  :rule-classes ((:rewrite)))

Theorem: ubdd-to-aignet-memo-p-of-last

(defthm ubdd-to-aignet-memo-p-of-last
  (implies (ubdd-to-aignet-memo-p (double-rewrite x))
           (ubdd-to-aignet-memo-p (last x)))
  :rule-classes ((:rewrite)))

Theorem: ubdd-to-aignet-memo-p-of-nthcdr

(defthm ubdd-to-aignet-memo-p-of-nthcdr
  (implies (ubdd-to-aignet-memo-p (double-rewrite x))
           (ubdd-to-aignet-memo-p (nthcdr acl2::n x)))
  :rule-classes ((:rewrite)))

Theorem: ubdd-to-aignet-memo-p-of-butlast

(defthm ubdd-to-aignet-memo-p-of-butlast
  (implies (ubdd-to-aignet-memo-p (double-rewrite x))
           (ubdd-to-aignet-memo-p (butlast x acl2::n)))
  :rule-classes ((:rewrite)))

Theorem: ubdd-to-aignet-memo-p-of-update-nth

(defthm ubdd-to-aignet-memo-p-of-update-nth
  (implies
       (ubdd-to-aignet-memo-p (double-rewrite x))
       (iff (ubdd-to-aignet-memo-p (update-nth acl2::n acl2::y x))
            (and (and (consp acl2::y)
                      (ubdd/level-p (car acl2::y))
                      (litp (cdr acl2::y)))
                 (or (<= (nfix acl2::n) (len x))
                     (and (consp nil)
                          (ubdd/level-p (car nil))
                          (litp (cdr nil)))))))
  :rule-classes ((:rewrite)))

Theorem: ubdd-to-aignet-memo-p-of-repeat

(defthm ubdd-to-aignet-memo-p-of-repeat
  (iff (ubdd-to-aignet-memo-p (acl2::repeat acl2::n x))
       (or (and (consp x)
                (ubdd/level-p (car x))
                (litp (cdr x)))
           (zp acl2::n)))
  :rule-classes ((:rewrite)))

Theorem: ubdd-to-aignet-memo-p-of-take

(defthm ubdd-to-aignet-memo-p-of-take
  (implies (ubdd-to-aignet-memo-p (double-rewrite x))
           (iff (ubdd-to-aignet-memo-p (take acl2::n x))
                (or (and (consp nil)
                         (ubdd/level-p (car nil))
                         (litp (cdr nil)))
                    (<= (nfix acl2::n) (len x)))))
  :rule-classes ((:rewrite)))

Theorem: ubdd-to-aignet-memo-p-of-union-equal

(defthm ubdd-to-aignet-memo-p-of-union-equal
  (equal (ubdd-to-aignet-memo-p (union-equal x acl2::y))
         (and (ubdd-to-aignet-memo-p (acl2::list-fix x))
              (ubdd-to-aignet-memo-p (double-rewrite acl2::y))))
  :rule-classes ((:rewrite)))

Theorem: ubdd-to-aignet-memo-p-of-intersection-equal-2

(defthm ubdd-to-aignet-memo-p-of-intersection-equal-2
  (implies (ubdd-to-aignet-memo-p (double-rewrite acl2::y))
           (ubdd-to-aignet-memo-p (intersection-equal x acl2::y)))
  :rule-classes ((:rewrite)))

Theorem: ubdd-to-aignet-memo-p-of-intersection-equal-1

(defthm ubdd-to-aignet-memo-p-of-intersection-equal-1
  (implies (ubdd-to-aignet-memo-p (double-rewrite x))
           (ubdd-to-aignet-memo-p (intersection-equal x acl2::y)))
  :rule-classes ((:rewrite)))

Theorem: ubdd-to-aignet-memo-p-of-set-difference-equal

(defthm ubdd-to-aignet-memo-p-of-set-difference-equal
  (implies (ubdd-to-aignet-memo-p x)
           (ubdd-to-aignet-memo-p (set-difference-equal x acl2::y)))
  :rule-classes ((:rewrite)))

Theorem: ubdd-to-aignet-memo-p-when-subsetp-equal

(defthm ubdd-to-aignet-memo-p-when-subsetp-equal
  (and (implies (and (subsetp-equal x acl2::y)
                     (ubdd-to-aignet-memo-p acl2::y))
                (equal (ubdd-to-aignet-memo-p x)
                       (true-listp x)))
       (implies (and (ubdd-to-aignet-memo-p acl2::y)
                     (subsetp-equal x acl2::y))
                (equal (ubdd-to-aignet-memo-p x)
                       (true-listp x))))
  :rule-classes ((:rewrite)))

Theorem: ubdd-to-aignet-memo-p-of-rcons

(defthm ubdd-to-aignet-memo-p-of-rcons
  (iff (ubdd-to-aignet-memo-p (acl2::rcons acl2::a x))
       (and (and (consp acl2::a)
                 (ubdd/level-p (car acl2::a))
                 (litp (cdr acl2::a)))
            (ubdd-to-aignet-memo-p (acl2::list-fix x))))
  :rule-classes ((:rewrite)))

Theorem: ubdd-to-aignet-memo-p-of-append

(defthm ubdd-to-aignet-memo-p-of-append
  (equal (ubdd-to-aignet-memo-p (append acl2::a acl2::b))
         (and (ubdd-to-aignet-memo-p (acl2::list-fix acl2::a))
              (ubdd-to-aignet-memo-p acl2::b)))
  :rule-classes ((:rewrite)))

Theorem: ubdd-to-aignet-memo-p-of-rev

(defthm ubdd-to-aignet-memo-p-of-rev
  (equal (ubdd-to-aignet-memo-p (acl2::rev x))
         (ubdd-to-aignet-memo-p (acl2::list-fix x)))
  :rule-classes ((:rewrite)))

Theorem: ubdd-to-aignet-memo-p-of-duplicated-members

(defthm ubdd-to-aignet-memo-p-of-duplicated-members
  (implies (ubdd-to-aignet-memo-p x)
           (ubdd-to-aignet-memo-p (acl2::duplicated-members x)))
  :rule-classes ((:rewrite)))

Theorem: ubdd-to-aignet-memo-p-of-difference

(defthm ubdd-to-aignet-memo-p-of-difference
  (implies (ubdd-to-aignet-memo-p x)
           (ubdd-to-aignet-memo-p (set::difference x acl2::y)))
  :rule-classes ((:rewrite)))

Theorem: ubdd-to-aignet-memo-p-of-intersect-2

(defthm ubdd-to-aignet-memo-p-of-intersect-2
  (implies (ubdd-to-aignet-memo-p acl2::y)
           (ubdd-to-aignet-memo-p (set::intersect x acl2::y)))
  :rule-classes ((:rewrite)))

Theorem: ubdd-to-aignet-memo-p-of-intersect-1

(defthm ubdd-to-aignet-memo-p-of-intersect-1
  (implies (ubdd-to-aignet-memo-p x)
           (ubdd-to-aignet-memo-p (set::intersect x acl2::y)))
  :rule-classes ((:rewrite)))

Theorem: ubdd-to-aignet-memo-p-of-union

(defthm ubdd-to-aignet-memo-p-of-union
  (iff (ubdd-to-aignet-memo-p (set::union x acl2::y))
       (and (ubdd-to-aignet-memo-p (set::sfix x))
            (ubdd-to-aignet-memo-p (set::sfix acl2::y))))
  :rule-classes ((:rewrite)))

Theorem: ubdd-to-aignet-memo-p-of-mergesort

(defthm ubdd-to-aignet-memo-p-of-mergesort
  (iff (ubdd-to-aignet-memo-p (set::mergesort x))
       (ubdd-to-aignet-memo-p (acl2::list-fix x)))
  :rule-classes ((:rewrite)))

Theorem: ubdd-to-aignet-memo-p-of-delete

(defthm ubdd-to-aignet-memo-p-of-delete
  (implies (ubdd-to-aignet-memo-p x)
           (ubdd-to-aignet-memo-p (set::delete acl2::k x)))
  :rule-classes ((:rewrite)))

Theorem: ubdd-to-aignet-memo-p-of-insert

(defthm ubdd-to-aignet-memo-p-of-insert
  (iff (ubdd-to-aignet-memo-p (set::insert acl2::a x))
       (and (ubdd-to-aignet-memo-p (set::sfix x))
            (and (consp acl2::a)
                 (ubdd/level-p (car acl2::a))
                 (litp (cdr acl2::a)))))
  :rule-classes ((:rewrite)))

Theorem: ubdd-to-aignet-memo-p-of-sfix

(defthm ubdd-to-aignet-memo-p-of-sfix
  (iff (ubdd-to-aignet-memo-p (set::sfix x))
       (or (ubdd-to-aignet-memo-p x)
           (not (set::setp x))))
  :rule-classes ((:rewrite)))

Theorem: ubdd-to-aignet-memo-p-of-list-fix

(defthm ubdd-to-aignet-memo-p-of-list-fix
  (implies (ubdd-to-aignet-memo-p x)
           (ubdd-to-aignet-memo-p (acl2::list-fix x)))
  :rule-classes ((:rewrite)))

Theorem: true-listp-when-ubdd-to-aignet-memo-p-compound-recognizer

(defthm true-listp-when-ubdd-to-aignet-memo-p-compound-recognizer
  (implies (ubdd-to-aignet-memo-p x)
           (true-listp x))
  :rule-classes :compound-recognizer)

Theorem: ubdd-to-aignet-memo-p-when-not-consp

(defthm ubdd-to-aignet-memo-p-when-not-consp
  (implies (not (consp x))
           (equal (ubdd-to-aignet-memo-p x)
                  (not x)))
  :rule-classes ((:rewrite)))

Theorem: ubdd-to-aignet-memo-p-of-cdr-when-ubdd-to-aignet-memo-p

(defthm ubdd-to-aignet-memo-p-of-cdr-when-ubdd-to-aignet-memo-p
  (implies (ubdd-to-aignet-memo-p (double-rewrite x))
           (ubdd-to-aignet-memo-p (cdr x)))
  :rule-classes ((:rewrite)))

Theorem: ubdd-to-aignet-memo-p-of-cons

(defthm ubdd-to-aignet-memo-p-of-cons
  (equal (ubdd-to-aignet-memo-p (cons acl2::a x))
         (and (and (consp acl2::a)
                   (ubdd/level-p (car acl2::a))
                   (litp (cdr acl2::a)))
              (ubdd-to-aignet-memo-p x)))
  :rule-classes ((:rewrite)))

Theorem: ubdd-to-aignet-memo-p-of-remove-assoc

(defthm ubdd-to-aignet-memo-p-of-remove-assoc
 (implies (ubdd-to-aignet-memo-p x)
          (ubdd-to-aignet-memo-p (remove-assoc-equal acl2::name x)))
 :rule-classes ((:rewrite)))

Theorem: ubdd-to-aignet-memo-p-of-put-assoc

(defthm ubdd-to-aignet-memo-p-of-put-assoc
 (implies
  (and (ubdd-to-aignet-memo-p x))
  (iff
    (ubdd-to-aignet-memo-p (put-assoc-equal acl2::name acl2::val x))
    (and (ubdd/level-p acl2::name)
         (litp acl2::val))))
 :rule-classes ((:rewrite)))

Theorem: ubdd-to-aignet-memo-p-of-fast-alist-clean

(defthm ubdd-to-aignet-memo-p-of-fast-alist-clean
  (implies (ubdd-to-aignet-memo-p x)
           (ubdd-to-aignet-memo-p (fast-alist-clean x)))
  :rule-classes ((:rewrite)))

Theorem: ubdd-to-aignet-memo-p-of-hons-shrink-alist

(defthm ubdd-to-aignet-memo-p-of-hons-shrink-alist
  (implies (and (ubdd-to-aignet-memo-p x)
                (ubdd-to-aignet-memo-p acl2::y))
           (ubdd-to-aignet-memo-p (hons-shrink-alist x acl2::y)))
  :rule-classes ((:rewrite)))

Theorem: ubdd-to-aignet-memo-p-of-hons-acons

(defthm ubdd-to-aignet-memo-p-of-hons-acons
  (equal (ubdd-to-aignet-memo-p (hons-acons acl2::a acl2::n x))
         (and (ubdd/level-p acl2::a)
              (litp acl2::n)
              (ubdd-to-aignet-memo-p x)))
  :rule-classes ((:rewrite)))

Theorem: litp-of-cdr-of-hons-assoc-equal-when-ubdd-to-aignet-memo-p

(defthm litp-of-cdr-of-hons-assoc-equal-when-ubdd-to-aignet-memo-p
  (implies (ubdd-to-aignet-memo-p x)
           (iff (litp (cdr (hons-assoc-equal acl2::k x)))
                (or (hons-assoc-equal acl2::k x)
                    (litp nil))))
  :rule-classes ((:rewrite)))

Theorem: alistp-when-ubdd-to-aignet-memo-p-rewrite

(defthm alistp-when-ubdd-to-aignet-memo-p-rewrite
  (implies (ubdd-to-aignet-memo-p x)
           (alistp x))
  :rule-classes ((:rewrite)))

Theorem: alistp-when-ubdd-to-aignet-memo-p

(defthm alistp-when-ubdd-to-aignet-memo-p
  (implies (ubdd-to-aignet-memo-p x)
           (alistp x))
  :rule-classes :tau-system)

Theorem: litp-of-cdar-when-ubdd-to-aignet-memo-p

(defthm litp-of-cdar-when-ubdd-to-aignet-memo-p
  (implies (ubdd-to-aignet-memo-p x)
           (iff (litp (cdar x))
                (or (consp x) (litp nil))))
  :rule-classes ((:rewrite)))

Theorem: ubdd/level-p-of-caar-when-ubdd-to-aignet-memo-p

(defthm ubdd/level-p-of-caar-when-ubdd-to-aignet-memo-p
  (implies (ubdd-to-aignet-memo-p x)
           (iff (ubdd/level-p (caar x))
                (or (consp x) (ubdd/level-p nil))))
  :rule-classes ((:rewrite)))