theorem
  F c= G & H c= I implies F--H c= G--I
proof
  assume
A1: F c= G & H c= I;
  let i;
A2: F--H = {w1-w2: w1 in F & w2 in H} by Th54;
  assume i in F--H;
  then ex w,w1 st i = w-w1 & w in F & w1 in H by A2;
  hence thesis by A1,Th55;
end;
