Basic theorems about hex-digit-char-list*p, generated by std::deflist.
Theorem:
(defthm hex-digit-char-list*p-of-cons (equal (hex-digit-char-list*p (cons a x)) (and (hex-digit-char-p a) (hex-digit-char-list*p x))) :rule-classes ((:rewrite)))
Theorem:
(defthm hex-digit-char-list*p-of-cdr-when-hex-digit-char-list*p (implies (hex-digit-char-list*p (double-rewrite x)) (hex-digit-char-list*p (cdr x))) :rule-classes ((:rewrite)))
Theorem:
(defthm hex-digit-char-list*p-when-not-consp (implies (not (consp x)) (hex-digit-char-list*p x)) :rule-classes ((:rewrite)))
Theorem:
(defthm hex-digit-char-p-of-car-when-hex-digit-char-list*p (implies (hex-digit-char-list*p x) (iff (hex-digit-char-p (car x)) (or (consp x) (hex-digit-char-p nil)))) :rule-classes ((:rewrite)))
Theorem:
(defthm hex-digit-char-list*p-of-append (equal (hex-digit-char-list*p (append a b)) (and (hex-digit-char-list*p a) (hex-digit-char-list*p b))) :rule-classes ((:rewrite)))
Theorem:
(defthm hex-digit-char-list*p-of-list-fix (equal (hex-digit-char-list*p (list-fix x)) (hex-digit-char-list*p x)) :rule-classes ((:rewrite)))
Theorem:
(defthm hex-digit-char-list*p-of-sfix (iff (hex-digit-char-list*p (set::sfix x)) (or (hex-digit-char-list*p x) (not (set::setp x)))) :rule-classes ((:rewrite)))
Theorem:
(defthm hex-digit-char-list*p-of-insert (iff (hex-digit-char-list*p (set::insert a x)) (and (hex-digit-char-list*p (set::sfix x)) (hex-digit-char-p a))) :rule-classes ((:rewrite)))
Theorem:
(defthm hex-digit-char-list*p-of-delete (implies (hex-digit-char-list*p x) (hex-digit-char-list*p (set::delete k x))) :rule-classes ((:rewrite)))
Theorem:
(defthm hex-digit-char-list*p-of-mergesort (iff (hex-digit-char-list*p (set::mergesort x)) (hex-digit-char-list*p (list-fix x))) :rule-classes ((:rewrite)))
Theorem:
(defthm hex-digit-char-list*p-of-union (iff (hex-digit-char-list*p (set::union x y)) (and (hex-digit-char-list*p (set::sfix x)) (hex-digit-char-list*p (set::sfix y)))) :rule-classes ((:rewrite)))
Theorem:
(defthm hex-digit-char-list*p-of-intersect-1 (implies (hex-digit-char-list*p x) (hex-digit-char-list*p (set::intersect x y))) :rule-classes ((:rewrite)))
Theorem:
(defthm hex-digit-char-list*p-of-intersect-2 (implies (hex-digit-char-list*p y) (hex-digit-char-list*p (set::intersect x y))) :rule-classes ((:rewrite)))
Theorem:
(defthm hex-digit-char-list*p-of-difference (implies (hex-digit-char-list*p x) (hex-digit-char-list*p (set::difference x y))) :rule-classes ((:rewrite)))
Theorem:
(defthm hex-digit-char-list*p-of-duplicated-members (implies (hex-digit-char-list*p x) (hex-digit-char-list*p (acl2::duplicated-members x))) :rule-classes ((:rewrite)))
Theorem:
(defthm hex-digit-char-list*p-of-rev (equal (hex-digit-char-list*p (rev x)) (hex-digit-char-list*p (list-fix x))) :rule-classes ((:rewrite)))
Theorem:
(defthm hex-digit-char-list*p-of-rcons (iff (hex-digit-char-list*p (acl2::rcons a x)) (and (hex-digit-char-p a) (hex-digit-char-list*p (list-fix x)))) :rule-classes ((:rewrite)))
Theorem:
(defthm hex-digit-char-p-when-member-equal-of-hex-digit-char-list*p (and (implies (and (member-equal a x) (hex-digit-char-list*p x)) (hex-digit-char-p a)) (implies (and (hex-digit-char-list*p x) (member-equal a x)) (hex-digit-char-p a))) :rule-classes ((:rewrite)))
Theorem:
(defthm hex-digit-char-list*p-when-subsetp-equal (and (implies (and (subsetp-equal x y) (hex-digit-char-list*p y)) (hex-digit-char-list*p x)) (implies (and (hex-digit-char-list*p y) (subsetp-equal x y)) (hex-digit-char-list*p x))) :rule-classes ((:rewrite)))
Theorem:
(defthm hex-digit-char-list*p-set-equiv-congruence (implies (acl2::set-equiv x y) (equal (hex-digit-char-list*p x) (hex-digit-char-list*p y))) :rule-classes :congruence)
Theorem:
(defthm hex-digit-char-list*p-of-set-difference-equal (implies (hex-digit-char-list*p x) (hex-digit-char-list*p (set-difference-equal x y))) :rule-classes ((:rewrite)))
Theorem:
(defthm hex-digit-char-list*p-of-intersection-equal-1 (implies (hex-digit-char-list*p (double-rewrite x)) (hex-digit-char-list*p (intersection-equal x y))) :rule-classes ((:rewrite)))
Theorem:
(defthm hex-digit-char-list*p-of-intersection-equal-2 (implies (hex-digit-char-list*p (double-rewrite y)) (hex-digit-char-list*p (intersection-equal x y))) :rule-classes ((:rewrite)))
Theorem:
(defthm hex-digit-char-list*p-of-union-equal (equal (hex-digit-char-list*p (union-equal x y)) (and (hex-digit-char-list*p (list-fix x)) (hex-digit-char-list*p (double-rewrite y)))) :rule-classes ((:rewrite)))
Theorem:
(defthm hex-digit-char-list*p-of-take (implies (hex-digit-char-list*p (double-rewrite x)) (iff (hex-digit-char-list*p (take n x)) (or (hex-digit-char-p nil) (<= (nfix n) (len x))))) :rule-classes ((:rewrite)))
Theorem:
(defthm hex-digit-char-list*p-of-repeat (iff (hex-digit-char-list*p (repeat n x)) (or (hex-digit-char-p x) (zp n))) :rule-classes ((:rewrite)))
Theorem:
(defthm hex-digit-char-p-of-nth-when-hex-digit-char-list*p (implies (and (hex-digit-char-list*p x) (< (nfix n) (len x))) (hex-digit-char-p (nth n x))) :rule-classes ((:rewrite)))
Theorem:
(defthm hex-digit-char-list*p-of-update-nth (implies (hex-digit-char-list*p (double-rewrite x)) (iff (hex-digit-char-list*p (update-nth n y x)) (and (hex-digit-char-p y) (or (<= (nfix n) (len x)) (hex-digit-char-p nil))))) :rule-classes ((:rewrite)))
Theorem:
(defthm hex-digit-char-list*p-of-butlast (implies (hex-digit-char-list*p (double-rewrite x)) (hex-digit-char-list*p (butlast x n))) :rule-classes ((:rewrite)))
Theorem:
(defthm hex-digit-char-list*p-of-nthcdr (implies (hex-digit-char-list*p (double-rewrite x)) (hex-digit-char-list*p (nthcdr n x))) :rule-classes ((:rewrite)))
Theorem:
(defthm hex-digit-char-list*p-of-last (implies (hex-digit-char-list*p (double-rewrite x)) (hex-digit-char-list*p (last x))) :rule-classes ((:rewrite)))
Theorem:
(defthm hex-digit-char-list*p-of-remove (implies (hex-digit-char-list*p x) (hex-digit-char-list*p (remove a x))) :rule-classes ((:rewrite)))
Theorem:
(defthm hex-digit-char-list*p-of-revappend (equal (hex-digit-char-list*p (revappend x y)) (and (hex-digit-char-list*p (list-fix x)) (hex-digit-char-list*p y))) :rule-classes ((:rewrite)))