
theorem Th20:
  for S1, S2 being Graph-membered set st S1 \/ S2 is \/-tolerating
  holds S1 is \/-tolerating & S2 is \/-tolerating
proof
  let S1, S2 being Graph-membered set;
  assume A1: S1 \/ S2 is \/-tolerating;
  hereby
    let G1, G2 be _Graph;
    assume G1 in S1 & G2 in S1;
    then G1 in S1 \/ S2 & G2 in S1 \/ S2 by XBOOLE_0:def 3;
    hence G1 tolerates G2 by A1;
  end;
  let G1, G2 be _Graph;
  assume G1 in S2 & G2 in S2;
  then G1 in S1 \/ S2 & G2 in S1 \/ S2 by XBOOLE_0:def 3;
  hence G1 tolerates G2 by A1;
end;
