theorem
  X c= Y implies X [= Y
proof
  assume
A1: X c= Y;
  let x such that
A2: x in X;
  let i be object;
  assume
A3: i in I;
  then
A4: X.i c= Y.i by A1;
  x.i in X.i by A2,A3;
  hence thesis by A4;
end;
