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