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    • Svex-svex-memo

    Svex-svex-memo-p

    Recognizer for svex-svex-memo.

    Signature
    (svex-svex-memo-p x) → *

    Definitions and Theorems

    Function: svex-svex-memo-p

    (defun svex-svex-memo-p (x)
      (declare (xargs :guard t))
      (let ((__function__ 'svex-svex-memo-p))
        (declare (ignorable __function__))
        (if (atom x)
            t
          (and (consp (car x))
               (svex-p (caar x))
               (svex-p (cdar x))
               (svex-svex-memo-p (cdr x))))))

    Theorem: svex-svex-memo-p-of-union-equal

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

    Theorem: svex-svex-memo-p-of-intersection-equal-2

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

    Theorem: svex-svex-memo-p-of-intersection-equal-1

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

    Theorem: svex-svex-memo-p-of-set-difference-equal

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

    Theorem: svex-svex-memo-p-set-equiv-congruence

    (defthm svex-svex-memo-p-set-equiv-congruence
      (implies (set-equiv x y)
               (equal (svex-svex-memo-p x)
                      (svex-svex-memo-p y)))
      :rule-classes :congruence)

    Theorem: svex-svex-memo-p-when-subsetp-equal

    (defthm svex-svex-memo-p-when-subsetp-equal
      (and (implies (and (subsetp-equal x y)
                         (svex-svex-memo-p y))
                    (svex-svex-memo-p x))
           (implies (and (svex-svex-memo-p y)
                         (subsetp-equal x y))
                    (svex-svex-memo-p x)))
      :rule-classes ((:rewrite)))

    Theorem: svex-svex-memo-p-of-rcons

    (defthm svex-svex-memo-p-of-rcons
      (iff (svex-svex-memo-p (acl2::rcons acl2::a x))
           (and (and (consp acl2::a)
                     (svex-p (car acl2::a))
                     (svex-p (cdr acl2::a)))
                (svex-svex-memo-p (list-fix x))))
      :rule-classes ((:rewrite)))

    Theorem: svex-svex-memo-p-of-repeat

    (defthm svex-svex-memo-p-of-repeat
      (iff (svex-svex-memo-p (repeat acl2::n x))
           (or (and (consp x)
                    (svex-p (car x))
                    (svex-p (cdr x)))
               (zp acl2::n)))
      :rule-classes ((:rewrite)))

    Theorem: svex-svex-memo-p-of-rev

    (defthm svex-svex-memo-p-of-rev
      (equal (svex-svex-memo-p (rev x))
             (svex-svex-memo-p (list-fix x)))
      :rule-classes ((:rewrite)))

    Theorem: svex-svex-memo-p-of-list-fix

    (defthm svex-svex-memo-p-of-list-fix
      (equal (svex-svex-memo-p (list-fix x))
             (svex-svex-memo-p x))
      :rule-classes ((:rewrite)))

    Theorem: svex-svex-memo-p-of-append

    (defthm svex-svex-memo-p-of-append
      (equal (svex-svex-memo-p (append acl2::a acl2::b))
             (and (svex-svex-memo-p acl2::a)
                  (svex-svex-memo-p acl2::b)))
      :rule-classes ((:rewrite)))

    Theorem: svex-svex-memo-p-when-not-consp

    (defthm svex-svex-memo-p-when-not-consp
      (implies (not (consp x))
               (svex-svex-memo-p x))
      :rule-classes ((:rewrite)))

    Theorem: svex-svex-memo-p-of-cdr-when-svex-svex-memo-p

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

    Theorem: svex-svex-memo-p-of-cons

    (defthm svex-svex-memo-p-of-cons
      (equal (svex-svex-memo-p (cons acl2::a x))
             (and (and (consp acl2::a)
                       (svex-p (car acl2::a))
                       (svex-p (cdr acl2::a)))
                  (svex-svex-memo-p x)))
      :rule-classes ((:rewrite)))

    Theorem: svex-svex-memo-p-of-fast-alist-clean

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

    Theorem: svex-svex-memo-p-of-hons-shrink-alist

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

    Theorem: svex-svex-memo-p-of-hons-acons

    (defthm svex-svex-memo-p-of-hons-acons
      (equal (svex-svex-memo-p (hons-acons acl2::a acl2::n x))
             (and (svex-p acl2::a)
                  (svex-p acl2::n)
                  (svex-svex-memo-p x)))
      :rule-classes ((:rewrite)))

    Theorem: svex-p-of-cdr-of-hons-assoc-equal-when-svex-svex-memo-p

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

    Theorem: svex-p-of-cdar-when-svex-svex-memo-p

    (defthm svex-p-of-cdar-when-svex-svex-memo-p
      (implies (svex-svex-memo-p x)
               (iff (svex-p (cdar x))
                    (or (consp x) (svex-p nil))))
      :rule-classes ((:rewrite)))

    Theorem: svex-p-of-caar-when-svex-svex-memo-p

    (defthm svex-p-of-caar-when-svex-svex-memo-p
      (implies (svex-svex-memo-p x)
               (iff (svex-p (caar x))
                    (or (consp x) (svex-p nil))))
      :rule-classes ((:rewrite)))