Basic theorems about node-listp, generated by deflist.
Theorem:
(defthm node-listp-of-cons (equal (node-listp (cons acl2::a x)) (and (node-p acl2::a) (node-listp x))) :rule-classes ((:rewrite)))
Theorem:
(defthm node-listp-of-cdr-when-node-listp (implies (node-listp (double-rewrite x)) (node-listp (cdr x))) :rule-classes ((:rewrite)))
Theorem:
(defthm node-listp-when-not-consp (implies (not (consp x)) (equal (node-listp x) (not x))) :rule-classes ((:rewrite)))
Theorem:
(defthm node-p-of-car-when-node-listp (implies (node-listp x) (node-p (car x))) :rule-classes ((:rewrite)))
Theorem:
(defthm true-listp-when-node-listp-compound-recognizer (implies (node-listp x) (true-listp x)) :rule-classes :compound-recognizer)
Theorem:
(defthm node-listp-of-list-fix (implies (node-listp x) (node-listp (acl2::list-fix x))) :rule-classes ((:rewrite)))
Theorem:
(defthm node-listp-of-append (equal (node-listp (append acl2::a acl2::b)) (and (node-listp (acl2::list-fix acl2::a)) (node-listp acl2::b))) :rule-classes ((:rewrite)))
Theorem:
(defthm node-listp-of-rev (equal (node-listp (acl2::rev x)) (node-listp (acl2::list-fix x))) :rule-classes ((:rewrite)))