
theorem Th16:
  for X being set holds rng Dependencies-Order X = [: bool X, bool X :]
proof
  let X be set;
  now
    let x be object;
    thus x in rng Dependencies-Order X implies x in [: bool X, bool X :];
    assume x in [: bool X, bool X :];
    then reconsider x9 = x as Dependency of X;
    [x9, x9] in Dependencies-Order X;
    hence x in rng Dependencies-Order X by XTUPLE_0:def 13;
  end;
  hence thesis by TARSKI:2;
end;
