Basic theorems about field-spec-listp, generated by std::deflist.
Theorem:
(defthm field-spec-listp-of-cons (equal (field-spec-listp (cons acl2::a acl2::x)) (and (field-specp acl2::a) (field-spec-listp acl2::x))) :rule-classes ((:rewrite)))
Theorem:
(defthm field-spec-listp-of-cdr-when-field-spec-listp (implies (field-spec-listp (double-rewrite acl2::x)) (field-spec-listp (cdr acl2::x))) :rule-classes ((:rewrite)))
Theorem:
(defthm field-spec-listp-when-not-consp (implies (not (consp acl2::x)) (equal (field-spec-listp acl2::x) (not acl2::x))) :rule-classes ((:rewrite)))
Theorem:
(defthm field-specp-of-car-when-field-spec-listp (implies (field-spec-listp acl2::x) (iff (field-specp (car acl2::x)) (or (consp acl2::x) (field-specp nil)))) :rule-classes ((:rewrite)))
Theorem:
(defthm true-listp-when-field-spec-listp-compound-recognizer (implies (field-spec-listp acl2::x) (true-listp acl2::x)) :rule-classes :compound-recognizer)
Theorem:
(defthm field-spec-listp-of-list-fix (implies (field-spec-listp acl2::x) (field-spec-listp (list-fix acl2::x))) :rule-classes ((:rewrite)))
Theorem:
(defthm field-spec-listp-of-rev (equal (field-spec-listp (rev acl2::x)) (field-spec-listp (list-fix acl2::x))) :rule-classes ((:rewrite)))
Theorem:
(defthm field-spec-listp-of-append (equal (field-spec-listp (append acl2::a acl2::b)) (and (field-spec-listp (list-fix acl2::a)) (field-spec-listp acl2::b))) :rule-classes ((:rewrite)))
Theorem:
(defthm field-specp-of-nth-when-field-spec-listp (implies (and (field-spec-listp acl2::x) (< (nfix acl2::n) (len acl2::x))) (field-specp (nth acl2::n acl2::x))) :rule-classes ((:rewrite)))