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