Basic theorems about rulelistp, generated by std::deflist.
Theorem:
(defthm rulelistp-of-cons (equal (rulelistp (cons acl2::a acl2::x)) (and (rulep acl2::a) (rulelistp acl2::x))) :rule-classes ((:rewrite)))
Theorem:
(defthm rulelistp-of-cdr-when-rulelistp (implies (rulelistp (double-rewrite acl2::x)) (rulelistp (cdr acl2::x))) :rule-classes ((:rewrite)))
Theorem:
(defthm rulelistp-when-not-consp (implies (not (consp acl2::x)) (equal (rulelistp acl2::x) (not acl2::x))) :rule-classes ((:rewrite)))
Theorem:
(defthm rulep-of-car-when-rulelistp (implies (rulelistp acl2::x) (iff (rulep (car acl2::x)) (consp acl2::x))) :rule-classes ((:rewrite)))
Theorem:
(defthm true-listp-when-rulelistp-compound-recognizer (implies (rulelistp acl2::x) (true-listp acl2::x)) :rule-classes :compound-recognizer)
Theorem:
(defthm rulelistp-of-list-fix (implies (rulelistp acl2::x) (rulelistp (list-fix acl2::x))) :rule-classes ((:rewrite)))
Theorem:
(defthm rulelistp-of-rev (equal (rulelistp (rev acl2::x)) (rulelistp (list-fix acl2::x))) :rule-classes ((:rewrite)))
Theorem:
(defthm rulelistp-of-append (equal (rulelistp (append acl2::a acl2::b)) (and (rulelistp (list-fix acl2::a)) (rulelistp acl2::b))) :rule-classes ((:rewrite)))
Theorem:
(defthm rulelistp-of-last (implies (rulelistp (double-rewrite acl2::x)) (rulelistp (last acl2::x))) :rule-classes ((:rewrite)))
Theorem:
(defthm rulep-of-nth-when-rulelistp (implies (rulelistp acl2::x) (iff (rulep (nth acl2::n acl2::x)) (< (nfix acl2::n) (len acl2::x)))) :rule-classes ((:rewrite)))
Theorem:
(defthm rulelistp-of-nthcdr (implies (rulelistp (double-rewrite acl2::x)) (rulelistp (nthcdr acl2::n acl2::x))) :rule-classes ((:rewrite)))
Theorem:
(defthm rulelistp-of-remove (implies (rulelistp acl2::x) (rulelistp (remove acl2::a acl2::x))) :rule-classes ((:rewrite)))
Theorem:
(defthm rulelistp-of-repeat (iff (rulelistp (repeat acl2::n acl2::x)) (or (rulep acl2::x) (zp acl2::n))) :rule-classes ((:rewrite)))
Theorem:
(defthm rulelistp-of-revappend (equal (rulelistp (revappend acl2::x acl2::y)) (and (rulelistp (list-fix acl2::x)) (rulelistp acl2::y))) :rule-classes ((:rewrite)))
Theorem:
(defthm rulelistp-of-rcons (iff (rulelistp (rcons acl2::a acl2::x)) (and (rulep acl2::a) (rulelistp (list-fix acl2::x)))) :rule-classes ((:rewrite)))
Theorem:
(defthm rulep-when-member-equal-of-rulelistp (and (implies (and (member-equal acl2::a acl2::x) (rulelistp acl2::x)) (rulep acl2::a)) (implies (and (rulelistp acl2::x) (member-equal acl2::a acl2::x)) (rulep acl2::a))) :rule-classes ((:rewrite)))
Theorem:
(defthm rulelistp-when-subsetp-equal (and (implies (and (subsetp-equal acl2::x acl2::y) (rulelistp acl2::y)) (equal (rulelistp acl2::x) (true-listp acl2::x))) (implies (and (rulelistp acl2::y) (subsetp-equal acl2::x acl2::y)) (equal (rulelistp acl2::x) (true-listp acl2::x)))) :rule-classes ((:rewrite)))
Theorem:
(defthm rulelistp-of-set-difference-equal (implies (rulelistp acl2::x) (rulelistp (set-difference-equal acl2::x acl2::y))) :rule-classes ((:rewrite)))
Theorem:
(defthm rulelistp-of-intersection-equal-1 (implies (rulelistp (double-rewrite acl2::x)) (rulelistp (intersection-equal acl2::x acl2::y))) :rule-classes ((:rewrite)))
Theorem:
(defthm rulelistp-of-intersection-equal-2 (implies (rulelistp (double-rewrite acl2::y)) (rulelistp (intersection-equal acl2::x acl2::y))) :rule-classes ((:rewrite)))
Theorem:
(defthm rulelistp-of-union-equal (equal (rulelistp (union-equal acl2::x acl2::y)) (and (rulelistp (list-fix acl2::x)) (rulelistp (double-rewrite acl2::y)))) :rule-classes ((:rewrite)))
Theorem:
(defthm rulelistp-of-take (implies (rulelistp (double-rewrite acl2::x)) (iff (rulelistp (take acl2::n acl2::x)) (or (rulep nil) (<= (nfix acl2::n) (len acl2::x))))) :rule-classes ((:rewrite)))
Theorem:
(defthm rulelistp-of-update-nth (implies (rulelistp (double-rewrite acl2::x)) (iff (rulelistp (update-nth acl2::n acl2::y acl2::x)) (and (rulep acl2::y) (or (<= (nfix acl2::n) (len acl2::x)) (rulep nil))))) :rule-classes ((:rewrite)))