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