Basic theorems about type-arithmetic-listp, generated by std::deflist.
Theorem:
(defthm type-arithmetic-listp-of-cons (equal (type-arithmetic-listp (cons acl2::a acl2::x)) (and (type-arithmeticp acl2::a) (type-arithmetic-listp acl2::x))) :rule-classes ((:rewrite)))
Theorem:
(defthm type-arithmetic-listp-of-cdr-when-type-arithmetic-listp (implies (type-arithmetic-listp (double-rewrite acl2::x)) (type-arithmetic-listp (cdr acl2::x))) :rule-classes ((:rewrite)))
Theorem:
(defthm type-arithmetic-listp-when-not-consp (implies (not (consp acl2::x)) (type-arithmetic-listp acl2::x)) :rule-classes ((:rewrite)))
Theorem:
(defthm type-arithmeticp-of-car-when-type-arithmetic-listp (implies (type-arithmetic-listp acl2::x) (iff (type-arithmeticp (car acl2::x)) (or (consp acl2::x) (type-arithmeticp nil)))) :rule-classes ((:rewrite)))
Theorem:
(defthm type-arithmetic-listp-of-append (equal (type-arithmetic-listp (append acl2::a acl2::b)) (and (type-arithmetic-listp acl2::a) (type-arithmetic-listp acl2::b))) :rule-classes ((:rewrite)))
Theorem:
(defthm type-arithmetic-listp-of-list-fix (equal (type-arithmetic-listp (list-fix acl2::x)) (type-arithmetic-listp acl2::x)) :rule-classes ((:rewrite)))
Theorem:
(defthm type-arithmetic-listp-of-rev (equal (type-arithmetic-listp (rev acl2::x)) (type-arithmetic-listp (list-fix acl2::x))) :rule-classes ((:rewrite)))
Theorem:
(defthm type-arithmetic-listp-of-butlast (implies (type-arithmetic-listp (double-rewrite acl2::x)) (type-arithmetic-listp (butlast acl2::x acl2::n))) :rule-classes ((:rewrite)))
Theorem:
(defthm type-arithmetic-listp-of-last (implies (type-arithmetic-listp (double-rewrite acl2::x)) (type-arithmetic-listp (last acl2::x))) :rule-classes ((:rewrite)))