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