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