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