Basic theorems about driverlist-p, generated by std::deflist.
Theorem:
(defthm driverlist-p-of-cons (equal (driverlist-p (cons acl2::a x)) (and (driver-p acl2::a) (driverlist-p x))) :rule-classes ((:rewrite)))
Theorem:
(defthm driverlist-p-of-cdr-when-driverlist-p (implies (driverlist-p (double-rewrite x)) (driverlist-p (cdr x))) :rule-classes ((:rewrite)))
Theorem:
(defthm driverlist-p-when-not-consp (implies (not (consp x)) (driverlist-p x)) :rule-classes ((:rewrite)))
Theorem:
(defthm driver-p-of-car-when-driverlist-p (implies (driverlist-p x) (iff (driver-p (car x)) (or (consp x) (driver-p nil)))) :rule-classes ((:rewrite)))
Theorem:
(defthm driverlist-p-of-append (equal (driverlist-p (append acl2::a acl2::b)) (and (driverlist-p acl2::a) (driverlist-p acl2::b))) :rule-classes ((:rewrite)))
Theorem:
(defthm driverlist-p-of-list-fix (equal (driverlist-p (list-fix x)) (driverlist-p x)) :rule-classes ((:rewrite)))
Theorem:
(defthm driverlist-p-of-rev (equal (driverlist-p (rev x)) (driverlist-p (list-fix x))) :rule-classes ((:rewrite)))
Theorem:
(defthm driverlist-p-of-repeat (iff (driverlist-p (repeat acl2::n x)) (or (driver-p x) (zp acl2::n))) :rule-classes ((:rewrite)))
Theorem:
(defthm driverlist-p-of-rcons (iff (driverlist-p (acl2::rcons acl2::a x)) (and (driver-p acl2::a) (driverlist-p (list-fix x)))) :rule-classes ((:rewrite)))
Theorem:
(defthm driver-p-when-member-equal-of-driverlist-p (and (implies (and (member-equal acl2::a x) (driverlist-p x)) (driver-p acl2::a)) (implies (and (driverlist-p x) (member-equal acl2::a x)) (driver-p acl2::a))) :rule-classes ((:rewrite)))
Theorem:
(defthm driverlist-p-when-subsetp-equal (and (implies (and (subsetp-equal x y) (driverlist-p y)) (driverlist-p x)) (implies (and (driverlist-p y) (subsetp-equal x y)) (driverlist-p x))) :rule-classes ((:rewrite)))
Theorem:
(defthm driverlist-p-set-equiv-congruence (implies (set-equiv x y) (equal (driverlist-p x) (driverlist-p y))) :rule-classes :congruence)
Theorem:
(defthm driverlist-p-of-set-difference-equal (implies (driverlist-p x) (driverlist-p (set-difference-equal x y))) :rule-classes ((:rewrite)))
Theorem:
(defthm driverlist-p-of-intersection-equal-1 (implies (driverlist-p (double-rewrite x)) (driverlist-p (intersection-equal x y))) :rule-classes ((:rewrite)))
Theorem:
(defthm driverlist-p-of-intersection-equal-2 (implies (driverlist-p (double-rewrite y)) (driverlist-p (intersection-equal x y))) :rule-classes ((:rewrite)))
Theorem:
(defthm driverlist-p-of-union-equal (equal (driverlist-p (union-equal x y)) (and (driverlist-p (list-fix x)) (driverlist-p (double-rewrite y)))) :rule-classes ((:rewrite)))
Theorem:
(defthm driverlist-p-of-update-nth (implies (driverlist-p (double-rewrite x)) (iff (driverlist-p (update-nth acl2::n y x)) (and (driver-p y) (or (<= (nfix acl2::n) (len x)) (driver-p nil))))) :rule-classes ((:rewrite)))
Theorem:
(defthm driverlist-p-of-butlast (implies (driverlist-p (double-rewrite x)) (driverlist-p (butlast x acl2::n))) :rule-classes ((:rewrite)))