Basic theorems about vl-rangelist-p, generated by deflist.
Theorem:
(defthm vl-rangelist-p-of-cons (equal (vl-rangelist-p (cons acl2::a acl2::x)) (and (vl-range-p acl2::a) (vl-rangelist-p acl2::x))) :rule-classes ((:rewrite)))
Theorem:
(defthm vl-rangelist-p-of-cdr-when-vl-rangelist-p (implies (vl-rangelist-p (double-rewrite acl2::x)) (vl-rangelist-p (cdr acl2::x))) :rule-classes ((:rewrite)))
Theorem:
(defthm vl-rangelist-p-when-not-consp (implies (not (consp acl2::x)) (vl-rangelist-p acl2::x)) :rule-classes ((:rewrite)))
Theorem:
(defthm vl-range-p-of-car-when-vl-rangelist-p (implies (vl-rangelist-p acl2::x) (iff (vl-range-p (car acl2::x)) (or (consp acl2::x) (vl-range-p nil)))) :rule-classes ((:rewrite)))
Theorem:
(defthm vl-rangelist-p-of-append (equal (vl-rangelist-p (append acl2::a acl2::b)) (and (vl-rangelist-p acl2::a) (vl-rangelist-p acl2::b))) :rule-classes ((:rewrite)))
Theorem:
(defthm vl-rangelist-p-of-list-fix (equal (vl-rangelist-p (list-fix acl2::x)) (vl-rangelist-p acl2::x)) :rule-classes ((:rewrite)))
Theorem:
(defthm vl-rangelist-p-of-rev (equal (vl-rangelist-p (rev acl2::x)) (vl-rangelist-p (list-fix acl2::x))) :rule-classes ((:rewrite)))
Theorem:
(defthm vl-rangelist-p-of-take (implies (vl-rangelist-p (double-rewrite acl2::x)) (iff (vl-rangelist-p (take acl2::n acl2::x)) (or (vl-range-p nil) (<= (nfix acl2::n) (len acl2::x))))) :rule-classes ((:rewrite)))
Theorem:
(defthm vl-rangelist-p-of-repeat (iff (vl-rangelist-p (repeat acl2::n acl2::x)) (or (vl-range-p acl2::x) (zp acl2::n))) :rule-classes ((:rewrite)))
Theorem:
(defthm vl-rangelist-p-of-nthcdr (implies (vl-rangelist-p (double-rewrite acl2::x)) (vl-rangelist-p (nthcdr acl2::n acl2::x))) :rule-classes ((:rewrite)))