Basic theorems about 4veclistlist-p, generated by std::deflist.
Theorem:
(defthm 4veclistlist-p-of-cons (equal (4veclistlist-p (cons acl2::a x)) (and (4veclist-p acl2::a) (4veclistlist-p x))) :rule-classes ((:rewrite)))
Theorem:
(defthm 4veclistlist-p-of-cdr-when-4veclistlist-p (implies (4veclistlist-p (double-rewrite x)) (4veclistlist-p (cdr x))) :rule-classes ((:rewrite)))
Theorem:
(defthm 4veclistlist-p-when-not-consp (implies (not (consp x)) (equal (4veclistlist-p x) (not x))) :rule-classes ((:rewrite)))
Theorem:
(defthm 4veclist-p-of-car-when-4veclistlist-p (implies (4veclistlist-p x) (4veclist-p (car x))) :rule-classes ((:rewrite)))
Theorem:
(defthm true-listp-when-4veclistlist-p-compound-recognizer (implies (4veclistlist-p x) (true-listp x)) :rule-classes :compound-recognizer)
Theorem:
(defthm 4veclistlist-p-of-list-fix (implies (4veclistlist-p x) (4veclistlist-p (list-fix x))) :rule-classes ((:rewrite)))
Theorem:
(defthm 4veclistlist-p-of-rev (equal (4veclistlist-p (rev x)) (4veclistlist-p (list-fix x))) :rule-classes ((:rewrite)))
Theorem:
(defthm 4veclistlist-p-of-repeat (iff (4veclistlist-p (repeat acl2::n x)) (or (4veclist-p x) (zp acl2::n))) :rule-classes ((:rewrite)))
Theorem:
(defthm 4veclistlist-p-of-take (implies (4veclistlist-p (double-rewrite x)) (iff (4veclistlist-p (take acl2::n x)) (or (4veclist-p nil) (<= (nfix acl2::n) (len x))))) :rule-classes ((:rewrite)))
Theorem:
(defthm 4veclistlist-p-of-nthcdr (implies (4veclistlist-p (double-rewrite x)) (4veclistlist-p (nthcdr acl2::n x))) :rule-classes ((:rewrite)))