
theorem
  for S1, S2 being GraphUnionSet
  for G1 being (GraphUnion of S1), G2 being GraphUnion of S2
  st S2 c= S1 holds G2 is Subgraph of G1
proof
  let S1, S2 be GraphUnionSet;
  let G1 be (GraphUnion of S1), G2 be GraphUnion of S2;
  assume A1: S2 c= S1;
  now
    let H2 be Element of S2;
    reconsider H1 = H2 as Element of S1 by A1, TARSKI:def 3;
    take H1;
    thus H2 is Subgraph of H1 by GLIB_000:40;
  end;
  hence thesis by Th121;
end;
