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