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