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