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