
theorem Th48:
  for G1 being _Graph, G2 being Subgraph of G1 holds G2.loops() c= G1.loops()
proof
  let G1 be _Graph, G2 be Subgraph of G1;
  now
    let e be object;
    assume e in G2.loops();
    then consider v being object such that
      A1: e DJoins v,v,G2 by Th45;
    e is set & v is set by TARSKI:1;
    hence e in G1.loops() by A1, Th45, GLIB_000:72;
  end;
  hence thesis by TARSKI:def 3;
end;
