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