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