theorem
  X = {} & Y <> {} implies (CMap kappa_1 R).(X,Y) = 0
  proof
    assume
A1: X = {} & Y <> {}; then
    (CMap kappa_1 R).(X,Y) = card (X \ Y) / card (X \/ Y) by PropEx3
      .= 0 by A1;
    hence thesis;
  end;
