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