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