Basic theorems about segment-driverlist-p, generated by std::deflist.
Theorem:
(defthm segment-driverlist-p-of-cons (equal (segment-driverlist-p (cons acl2::a x)) (and (segment-driver-p acl2::a) (segment-driverlist-p x))) :rule-classes ((:rewrite)))
Theorem:
(defthm segment-driverlist-p-of-cdr-when-segment-driverlist-p (implies (segment-driverlist-p (double-rewrite x)) (segment-driverlist-p (cdr x))) :rule-classes ((:rewrite)))
Theorem:
(defthm segment-driverlist-p-when-not-consp (implies (not (consp x)) (equal (segment-driverlist-p x) (not x))) :rule-classes ((:rewrite)))
Theorem:
(defthm segment-driver-p-of-car-when-segment-driverlist-p (implies (segment-driverlist-p x) (iff (segment-driver-p (car x)) (consp x))) :rule-classes ((:rewrite)))
Theorem:
(defthm true-listp-when-segment-driverlist-p-compound-recognizer (implies (segment-driverlist-p x) (true-listp x)) :rule-classes :compound-recognizer)
Theorem:
(defthm segment-driverlist-p-of-list-fix (implies (segment-driverlist-p x) (segment-driverlist-p (list-fix x))) :rule-classes ((:rewrite)))
Theorem:
(defthm segment-driverlist-p-of-rev (equal (segment-driverlist-p (rev x)) (segment-driverlist-p (list-fix x))) :rule-classes ((:rewrite)))
Theorem:
(defthm segment-driverlist-p-of-repeat (iff (segment-driverlist-p (repeat acl2::n x)) (or (segment-driver-p x) (zp acl2::n))) :rule-classes ((:rewrite)))
Theorem:
(defthm segment-driverlist-p-of-append (equal (segment-driverlist-p (append acl2::a acl2::b)) (and (segment-driverlist-p (list-fix acl2::a)) (segment-driverlist-p acl2::b))) :rule-classes ((:rewrite)))