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