Basic theorems about bindinglist-p, generated by std::deflist.
Theorem:
(defthm bindinglist-p-of-cons (equal (bindinglist-p (cons a x)) (and (binding-p a) (bindinglist-p x))) :rule-classes ((:rewrite)))
Theorem:
(defthm bindinglist-p-of-cdr-when-bindinglist-p (implies (bindinglist-p (double-rewrite x)) (bindinglist-p (cdr x))) :rule-classes ((:rewrite)))
Theorem:
(defthm bindinglist-p-when-not-consp (implies (not (consp x)) (equal (bindinglist-p x) (not x))) :rule-classes ((:rewrite)))
Theorem:
(defthm binding-p-of-car-when-bindinglist-p (implies (bindinglist-p x) (iff (binding-p (car x)) (or (consp x) (binding-p nil)))) :rule-classes ((:rewrite)))
Theorem:
(defthm true-listp-when-bindinglist-p-compound-recognizer (implies (bindinglist-p x) (true-listp x)) :rule-classes :compound-recognizer)
Theorem:
(defthm bindinglist-p-of-list-fix (implies (bindinglist-p x) (bindinglist-p (list-fix x))) :rule-classes ((:rewrite)))
Theorem:
(defthm bindinglist-p-of-rev (equal (bindinglist-p (acl2::rev x)) (bindinglist-p (list-fix x))) :rule-classes ((:rewrite)))
Theorem:
(defthm bindinglist-p-of-append (equal (bindinglist-p (append a b)) (and (bindinglist-p (list-fix a)) (bindinglist-p b))) :rule-classes ((:rewrite)))
Theorem:
(defthm bindinglist-p-of-rcons (iff (bindinglist-p (acl2::rcons a x)) (and (binding-p a) (bindinglist-p (list-fix x)))) :rule-classes ((:rewrite)))
Theorem:
(defthm binding-p-when-member-equal-of-bindinglist-p (and (implies (and (member-equal a x) (bindinglist-p x)) (binding-p a)) (implies (and (bindinglist-p x) (member-equal a x)) (binding-p a))) :rule-classes ((:rewrite)))
Theorem:
(defthm bindinglist-p-when-subsetp-equal (and (implies (and (subsetp-equal x y) (bindinglist-p y)) (equal (bindinglist-p x) (true-listp x))) (implies (and (bindinglist-p y) (subsetp-equal x y)) (equal (bindinglist-p x) (true-listp x)))) :rule-classes ((:rewrite)))
Theorem:
(defthm bindinglist-p-of-set-difference-equal (implies (bindinglist-p x) (bindinglist-p (set-difference-equal x y))) :rule-classes ((:rewrite)))
Theorem:
(defthm bindinglist-p-of-intersection-equal-1 (implies (bindinglist-p (double-rewrite x)) (bindinglist-p (intersection-equal x y))) :rule-classes ((:rewrite)))
Theorem:
(defthm bindinglist-p-of-intersection-equal-2 (implies (bindinglist-p (double-rewrite y)) (bindinglist-p (intersection-equal x y))) :rule-classes ((:rewrite)))
Theorem:
(defthm bindinglist-p-of-union-equal (equal (bindinglist-p (union-equal x y)) (and (bindinglist-p (list-fix x)) (bindinglist-p (double-rewrite y)))) :rule-classes ((:rewrite)))
Theorem:
(defthm bindinglist-p-of-take (implies (bindinglist-p (double-rewrite x)) (iff (bindinglist-p (take n x)) (or (binding-p nil) (<= (nfix n) (len x))))) :rule-classes ((:rewrite)))