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