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