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