Basic theorems about binop-listp, generated by std::deflist.
Theorem:
(defthm binop-listp-of-cons (equal (binop-listp (cons acl2::a acl2::x)) (and (binopp acl2::a) (binop-listp acl2::x))) :rule-classes ((:rewrite)))
Theorem:
(defthm binop-listp-of-cdr-when-binop-listp (implies (binop-listp (double-rewrite acl2::x)) (binop-listp (cdr acl2::x))) :rule-classes ((:rewrite)))
Theorem:
(defthm binop-listp-when-not-consp (implies (not (consp acl2::x)) (equal (binop-listp acl2::x) (not acl2::x))) :rule-classes ((:rewrite)))
Theorem:
(defthm binopp-of-car-when-binop-listp (implies (binop-listp acl2::x) (iff (binopp (car acl2::x)) (consp acl2::x))) :rule-classes ((:rewrite)))
Theorem:
(defthm true-listp-when-binop-listp-compound-recognizer (implies (binop-listp acl2::x) (true-listp acl2::x)) :rule-classes :compound-recognizer)
Theorem:
(defthm binop-listp-of-list-fix (implies (binop-listp acl2::x) (binop-listp (list-fix acl2::x))) :rule-classes ((:rewrite)))
Theorem:
(defthm binop-listp-of-rev (equal (binop-listp (rev acl2::x)) (binop-listp (list-fix acl2::x))) :rule-classes ((:rewrite)))
Theorem:
(defthm binop-listp-of-append (equal (binop-listp (append acl2::a acl2::b)) (and (binop-listp (list-fix acl2::a)) (binop-listp acl2::b))) :rule-classes ((:rewrite)))