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