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• Svtv-outentrylist-p

Svtv-outentrylist-p-basics

Basic theorems about svtv-outentrylist-p, generated by std::deflist.

Definitions and Theorems

Theorem: svtv-outentrylist-p-of-cons

(defthm svtv-outentrylist-p-of-cons
  (equal (svtv-outentrylist-p (cons acl2::a x))
         (and (svtv-outentry-p acl2::a)
              (svtv-outentrylist-p x)))
  :rule-classes ((:rewrite)))

Theorem: svtv-outentrylist-p-of-cdr-when-svtv-outentrylist-p

(defthm svtv-outentrylist-p-of-cdr-when-svtv-outentrylist-p
  (implies (svtv-outentrylist-p (double-rewrite x))
           (svtv-outentrylist-p (cdr x)))
  :rule-classes ((:rewrite)))

Theorem: svtv-outentrylist-p-when-not-consp

(defthm svtv-outentrylist-p-when-not-consp
  (implies (not (consp x))
           (equal (svtv-outentrylist-p x) (not x)))
  :rule-classes ((:rewrite)))

Theorem: svtv-outentry-p-of-car-when-svtv-outentrylist-p

(defthm svtv-outentry-p-of-car-when-svtv-outentrylist-p
  (implies (svtv-outentrylist-p x)
           (iff (svtv-outentry-p (car x))
                (or (consp x) (svtv-outentry-p nil))))
  :rule-classes ((:rewrite)))

Theorem: true-listp-when-svtv-outentrylist-p-compound-recognizer

(defthm true-listp-when-svtv-outentrylist-p-compound-recognizer
  (implies (svtv-outentrylist-p x)
           (true-listp x))
  :rule-classes :compound-recognizer)

Theorem: svtv-outentrylist-p-of-list-fix

(defthm svtv-outentrylist-p-of-list-fix
  (implies (svtv-outentrylist-p x)
           (svtv-outentrylist-p (list-fix x)))
  :rule-classes ((:rewrite)))

Theorem: svtv-outentrylist-p-of-rev

(defthm svtv-outentrylist-p-of-rev
  (equal (svtv-outentrylist-p (rev x))
         (svtv-outentrylist-p (list-fix x)))
  :rule-classes ((:rewrite)))

Theorem: svtv-outentrylist-p-of-repeat

(defthm svtv-outentrylist-p-of-repeat
  (iff (svtv-outentrylist-p (repeat acl2::n x))
       (or (svtv-outentry-p x) (zp acl2::n)))
  :rule-classes ((:rewrite)))

Theorem: svtv-outentrylist-p-of-append

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