Basic theorems about vcd-scopelist-p, generated by std::deflist.
Theorem:
(defthm vcd-scopelist-p-of-cons (equal (vcd-scopelist-p (cons acl2::a x)) (and (vcd-scope-p acl2::a) (vcd-scopelist-p x))) :rule-classes ((:rewrite)))
Theorem:
(defthm vcd-scopelist-p-of-cdr-when-vcd-scopelist-p (implies (vcd-scopelist-p (double-rewrite x)) (vcd-scopelist-p (cdr x))) :rule-classes ((:rewrite)))
Theorem:
(defthm vcd-scopelist-p-when-not-consp (implies (not (consp x)) (vcd-scopelist-p x)) :rule-classes ((:rewrite)))
Theorem:
(defthm vcd-scope-p-of-car-when-vcd-scopelist-p (implies (vcd-scopelist-p x) (iff (vcd-scope-p (car x)) (or (consp x) (vcd-scope-p nil)))) :rule-classes ((:rewrite)))
Theorem:
(defthm vcd-scopelist-p-of-append (equal (vcd-scopelist-p (append acl2::a acl2::b)) (and (vcd-scopelist-p acl2::a) (vcd-scopelist-p acl2::b))) :rule-classes ((:rewrite)))
Theorem:
(defthm vcd-scopelist-p-of-list-fix (equal (vcd-scopelist-p (list-fix x)) (vcd-scopelist-p x)) :rule-classes ((:rewrite)))
Theorem:
(defthm vcd-scopelist-p-of-rev (equal (vcd-scopelist-p (rev x)) (vcd-scopelist-p (list-fix x))) :rule-classes ((:rewrite)))
Theorem:
(defthm vcd-scopelist-p-of-repeat (iff (vcd-scopelist-p (repeat acl2::n x)) (or (vcd-scope-p x) (zp acl2::n))) :rule-classes ((:rewrite)))