foreign keys and lots of tables

I have the following tables (individual seat allocation removed to make it
simpler)

create table coaches ( -- carriages
c_id serial primary key,
c_name varchar(20) not null
);
create table trains ( -- one for each train
t_id serial primary key
);
create table train_coaches ( -- which carriages are on what trains
t_id int4 not null references trains(t_id),
c_id int4 not null references coaches(c_id)
);

I now want to create bookings and allocate seats, but the seat must exist on
the coach_seats table *AND* only for a carriage included in the train, i.e.
an entry in train_coaches.

create table bookings (
b_id serial primary key,
t_id int4 not null references trains(t_id)
);

create table booking_seats (
b_id int4 not null references bookings(b_id),
c_id int4, -- carriage ID
c_seat varchar(10) -- seat label
);

The following ensures the seat exists on the coach. (not shown)

alter table booking_seats add constraint seat_exists
foreign key (c_id, c_seat) references coach_seats (c_id,c_seat);

How would I ensure that the coach exists on the train. I would need to convert
the b_id to a t_id using the bookings table and I don't know how.

To complicate things, when the initial booking is made, bot c_id and c_seat
are NULL. Will this make any difference?

Gary
--
Gary Stainburn
Group I.T. Manager
Ringways Garages
http://www.ringways.co.uk