
theorem Th11: :: antisymmetry
  for X being set, P, Q being Dependency of X st P <= Q & Q <= P holds P = Q
proof
  let X be set, p, q be Dependency of X;
  assume that
A1: p <= q and
A2: q <= p;
A3: q`1 c= p`1 by A1;
A4: p`2 c= q`2 by A1;
  q`2 c= p`2 by A2;
  then
A5: p`2 = q`2 by A4,XBOOLE_0:def 10;
  p`1 c= q`1 by A2;
  then
A6: p`1 = q`1 by A3,XBOOLE_0:def 10;
  p = [p`1,p`2] by MCART_1:22;
  hence thesis by A6,A5,MCART_1:22;
end;
