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