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