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