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    • 4vmask-alist

    4vmask-alist-p

    Recognizer for 4vmask-alist.

    Signature
    (4vmask-alist-p x) → *

    Definitions and Theorems

    Function: 4vmask-alist-p

    (defun 4vmask-alist-p (x)
      (declare (xargs :guard t))
      (let ((__function__ '4vmask-alist-p))
        (declare (ignorable __function__))
        (if (atom x)
            (eq x nil)
          (and (consp (car x))
               (svar-p (caar x))
               (4vmask-p (cdar x))
               (4vmask-alist-p (cdr x))))))

    Theorem: 4vmask-alist-p-of-repeat

    (defthm 4vmask-alist-p-of-repeat
      (iff (4vmask-alist-p (repeat acl2::n x))
           (or (and (consp x)
                    (svar-p (car x))
                    (4vmask-p (cdr x)))
               (zp acl2::n)))
      :rule-classes ((:rewrite)))

    Theorem: 4vmask-alist-p-of-rev

    (defthm 4vmask-alist-p-of-rev
      (equal (4vmask-alist-p (rev x))
             (4vmask-alist-p (list-fix x)))
      :rule-classes ((:rewrite)))

    Theorem: 4vmask-alist-p-of-list-fix

    (defthm 4vmask-alist-p-of-list-fix
      (implies (4vmask-alist-p x)
               (4vmask-alist-p (list-fix x)))
      :rule-classes ((:rewrite)))

    Theorem: true-listp-when-4vmask-alist-p-compound-recognizer

    (defthm true-listp-when-4vmask-alist-p-compound-recognizer
      (implies (4vmask-alist-p x)
               (true-listp x))
      :rule-classes :compound-recognizer)

    Theorem: 4vmask-alist-p-when-not-consp

    (defthm 4vmask-alist-p-when-not-consp
      (implies (not (consp x))
               (equal (4vmask-alist-p x) (not x)))
      :rule-classes ((:rewrite)))

    Theorem: 4vmask-alist-p-of-cdr-when-4vmask-alist-p

    (defthm 4vmask-alist-p-of-cdr-when-4vmask-alist-p
      (implies (4vmask-alist-p (double-rewrite x))
               (4vmask-alist-p (cdr x)))
      :rule-classes ((:rewrite)))

    Theorem: 4vmask-alist-p-of-cons

    (defthm 4vmask-alist-p-of-cons
      (equal (4vmask-alist-p (cons acl2::a x))
             (and (and (consp acl2::a)
                       (svar-p (car acl2::a))
                       (4vmask-p (cdr acl2::a)))
                  (4vmask-alist-p x)))
      :rule-classes ((:rewrite)))

    Theorem: 4vmask-alist-p-of-remove-assoc

    (defthm 4vmask-alist-p-of-remove-assoc
      (implies (4vmask-alist-p x)
               (4vmask-alist-p (remove-assoc-equal acl2::name x)))
      :rule-classes ((:rewrite)))

    Theorem: 4vmask-alist-p-of-put-assoc

    (defthm 4vmask-alist-p-of-put-assoc
     (implies
          (and (4vmask-alist-p x))
          (iff (4vmask-alist-p (put-assoc-equal acl2::name acl2::val x))
               (and (svar-p acl2::name)
                    (4vmask-p acl2::val))))
     :rule-classes ((:rewrite)))

    Theorem: 4vmask-alist-p-of-fast-alist-clean

    (defthm 4vmask-alist-p-of-fast-alist-clean
      (implies (4vmask-alist-p x)
               (4vmask-alist-p (fast-alist-clean x)))
      :rule-classes ((:rewrite)))

    Theorem: 4vmask-alist-p-of-hons-shrink-alist

    (defthm 4vmask-alist-p-of-hons-shrink-alist
      (implies (and (4vmask-alist-p x)
                    (4vmask-alist-p y))
               (4vmask-alist-p (hons-shrink-alist x y)))
      :rule-classes ((:rewrite)))

    Theorem: 4vmask-alist-p-of-hons-acons

    (defthm 4vmask-alist-p-of-hons-acons
      (equal (4vmask-alist-p (hons-acons acl2::a acl2::n x))
             (and (svar-p acl2::a)
                  (4vmask-p acl2::n)
                  (4vmask-alist-p x)))
      :rule-classes ((:rewrite)))

    Theorem: 4vmask-p-of-cdr-of-hons-assoc-equal-when-4vmask-alist-p

    (defthm 4vmask-p-of-cdr-of-hons-assoc-equal-when-4vmask-alist-p
      (implies (4vmask-alist-p x)
               (iff (4vmask-p (cdr (hons-assoc-equal acl2::k x)))
                    (or (hons-assoc-equal acl2::k x)
                        (4vmask-p nil))))
      :rule-classes ((:rewrite)))

    Theorem: alistp-when-4vmask-alist-p-rewrite

    (defthm alistp-when-4vmask-alist-p-rewrite
      (implies (4vmask-alist-p x) (alistp x))
      :rule-classes ((:rewrite)))

    Theorem: alistp-when-4vmask-alist-p

    (defthm alistp-when-4vmask-alist-p
      (implies (4vmask-alist-p x) (alistp x))
      :rule-classes :tau-system)

    Theorem: 4vmask-p-of-cdar-when-4vmask-alist-p

    (defthm 4vmask-p-of-cdar-when-4vmask-alist-p
      (implies (4vmask-alist-p x)
               (iff (4vmask-p (cdar x))
                    (or (consp x) (4vmask-p nil))))
      :rule-classes ((:rewrite)))

    Theorem: svar-p-of-caar-when-4vmask-alist-p

    (defthm svar-p-of-caar-when-4vmask-alist-p
      (implies (4vmask-alist-p x)
               (iff (svar-p (caar x))
                    (or (consp x) (svar-p nil))))
      :rule-classes ((:rewrite)))