
theorem
  for G being _Graph, H being removeLoops of G
  holds the_Edges_of G = G.loops() iff H is edgeless
proof
  let G be _Graph, H be removeLoops of G;
  thus the_Edges_of G = G.loops() implies H is edgeless;
  assume A1: H is edgeless;
  the_Edges_of G \ G.loops() = the_Edges_of H by GLIB_000:53
    .= {} by A1;
  then the_Edges_of G c= G.loops() by XBOOLE_1:37;
  hence thesis by XBOOLE_0:def 10;
end;
