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