Basic theorems about wirelist-p, generated by std::deflist.
Theorem:
(defthm wirelist-p-of-cons (equal (wirelist-p (cons acl2::a x)) (and (wire-p acl2::a) (wirelist-p x))) :rule-classes ((:rewrite)))
Theorem:
(defthm wirelist-p-of-cdr-when-wirelist-p (implies (wirelist-p (double-rewrite x)) (wirelist-p (cdr x))) :rule-classes ((:rewrite)))
Theorem:
(defthm wirelist-p-when-not-consp (implies (not (consp x)) (equal (wirelist-p x) (not x))) :rule-classes ((:rewrite)))
Theorem:
(defthm wire-p-of-car-when-wirelist-p (implies (wirelist-p x) (iff (wire-p (car x)) (or (consp x) (wire-p nil)))) :rule-classes ((:rewrite)))
Theorem:
(defthm true-listp-when-wirelist-p-compound-recognizer (implies (wirelist-p x) (true-listp x)) :rule-classes :compound-recognizer)
Theorem:
(defthm wirelist-p-of-list-fix (implies (wirelist-p x) (wirelist-p (list-fix x))) :rule-classes ((:rewrite)))
Theorem:
(defthm wirelist-p-of-rev (equal (wirelist-p (rev x)) (wirelist-p (list-fix x))) :rule-classes ((:rewrite)))
Theorem:
(defthm wirelist-p-of-repeat (iff (wirelist-p (repeat acl2::n x)) (or (wire-p x) (zp acl2::n))) :rule-classes ((:rewrite)))
Theorem:
(defthm wirelist-p-of-append (equal (wirelist-p (append acl2::a acl2::b)) (and (wirelist-p (list-fix acl2::a)) (wirelist-p acl2::b))) :rule-classes ((:rewrite)))
Theorem:
(defthm wirelist-p-of-take (implies (wirelist-p (double-rewrite x)) (iff (wirelist-p (take acl2::n x)) (or (wire-p nil) (<= (nfix acl2::n) (len x))))) :rule-classes ((:rewrite)))
Theorem:
(defthm wirelist-p-of-butlast (implies (wirelist-p (double-rewrite x)) (wirelist-p (butlast x acl2::n))) :rule-classes ((:rewrite)))