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