Basic theorems about svarlist-addr-p, generated by std::deflist.
Theorem:
(defthm svarlist-addr-p-of-cons (equal (svarlist-addr-p (cons acl2::a x)) (and (svar-addr-p acl2::a) (svarlist-addr-p x))) :rule-classes ((:rewrite)))
Theorem:
(defthm svarlist-addr-p-of-cdr-when-svarlist-addr-p (implies (svarlist-addr-p (double-rewrite x)) (svarlist-addr-p (cdr x))) :rule-classes ((:rewrite)))
Theorem:
(defthm svarlist-addr-p-when-not-consp (implies (not (consp x)) (svarlist-addr-p x)) :rule-classes ((:rewrite)))
Theorem:
(defthm svar-addr-p-of-car-when-svarlist-addr-p (implies (svarlist-addr-p x) (iff (svar-addr-p (car x)) (or (consp x) (svar-addr-p nil)))) :rule-classes ((:rewrite)))
Theorem:
(defthm svarlist-addr-p-of-append (equal (svarlist-addr-p (append acl2::a acl2::b)) (and (svarlist-addr-p acl2::a) (svarlist-addr-p acl2::b))) :rule-classes ((:rewrite)))
Theorem:
(defthm svarlist-addr-p-of-list-fix (equal (svarlist-addr-p (list-fix x)) (svarlist-addr-p x)) :rule-classes ((:rewrite)))
Theorem:
(defthm svarlist-addr-p-of-rev (equal (svarlist-addr-p (rev x)) (svarlist-addr-p (list-fix x))) :rule-classes ((:rewrite)))
Theorem:
(defthm svarlist-addr-p-of-repeat (iff (svarlist-addr-p (repeat acl2::n x)) (or (svar-addr-p x) (zp acl2::n))) :rule-classes ((:rewrite)))
Theorem:
(defthm svarlist-addr-p-of-rcons (iff (svarlist-addr-p (acl2::rcons acl2::a x)) (and (svar-addr-p acl2::a) (svarlist-addr-p (list-fix x)))) :rule-classes ((:rewrite)))
Theorem:
(defthm svar-addr-p-when-member-equal-of-svarlist-addr-p (and (implies (and (member-equal acl2::a x) (svarlist-addr-p x)) (svar-addr-p acl2::a)) (implies (and (svarlist-addr-p x) (member-equal acl2::a x)) (svar-addr-p acl2::a))) :rule-classes ((:rewrite)))
Theorem:
(defthm svarlist-addr-p-when-subsetp-equal (and (implies (and (subsetp-equal x y) (svarlist-addr-p y)) (svarlist-addr-p x)) (implies (and (svarlist-addr-p y) (subsetp-equal x y)) (svarlist-addr-p x))) :rule-classes ((:rewrite)))
Theorem:
(defthm svarlist-addr-p-set-equiv-congruence (implies (set-equiv x y) (equal (svarlist-addr-p x) (svarlist-addr-p y))) :rule-classes :congruence)
Theorem:
(defthm svarlist-addr-p-of-set-difference-equal (implies (svarlist-addr-p x) (svarlist-addr-p (set-difference-equal x y))) :rule-classes ((:rewrite)))
Theorem:
(defthm svarlist-addr-p-of-intersection-equal-1 (implies (svarlist-addr-p (double-rewrite x)) (svarlist-addr-p (intersection-equal x y))) :rule-classes ((:rewrite)))
Theorem:
(defthm svarlist-addr-p-of-intersection-equal-2 (implies (svarlist-addr-p (double-rewrite y)) (svarlist-addr-p (intersection-equal x y))) :rule-classes ((:rewrite)))
Theorem:
(defthm svarlist-addr-p-of-union-equal (equal (svarlist-addr-p (union-equal x y)) (and (svarlist-addr-p (list-fix x)) (svarlist-addr-p (double-rewrite y)))) :rule-classes ((:rewrite)))
Theorem:
(defthm svarlist-addr-p-of-sfix (iff (svarlist-addr-p (sfix x)) (or (svarlist-addr-p x) (not (setp x)))) :rule-classes ((:rewrite)))
Theorem:
(defthm svarlist-addr-p-of-insert (iff (svarlist-addr-p (insert acl2::a x)) (and (svarlist-addr-p (sfix x)) (svar-addr-p acl2::a))) :rule-classes ((:rewrite)))
Theorem:
(defthm svarlist-addr-p-of-delete (implies (svarlist-addr-p x) (svarlist-addr-p (delete acl2::k x))) :rule-classes ((:rewrite)))
Theorem:
(defthm svarlist-addr-p-of-mergesort (iff (svarlist-addr-p (mergesort x)) (svarlist-addr-p (list-fix x))) :rule-classes ((:rewrite)))
Theorem:
(defthm svarlist-addr-p-of-union (iff (svarlist-addr-p (union x y)) (and (svarlist-addr-p (sfix x)) (svarlist-addr-p (sfix y)))) :rule-classes ((:rewrite)))
Theorem:
(defthm svarlist-addr-p-of-intersect-1 (implies (svarlist-addr-p x) (svarlist-addr-p (intersect x y))) :rule-classes ((:rewrite)))
Theorem:
(defthm svarlist-addr-p-of-intersect-2 (implies (svarlist-addr-p y) (svarlist-addr-p (intersect x y))) :rule-classes ((:rewrite)))
Theorem:
(defthm svarlist-addr-p-of-difference (implies (svarlist-addr-p x) (svarlist-addr-p (difference x y))) :rule-classes ((:rewrite)))