
theorem
  for G1 being _Graph, G2 being DSimpleGraph of G1
  ex G3 being SimpleGraph of G1 st G3 is SimpleGraph of G2
proof
  let G1 be _Graph, G2 be DSimpleGraph of G1;
  set H = the removeLoops of G1;
  G2 is removeDParallelEdges of H by Th122;
  then consider G3 being removeParallelEdges of H such that
    A1: G3 is removeParallelEdges of G2 by Th96;
  reconsider G3 as SimpleGraph of G1 by Th117;
  take G3;
  thus thesis by A1, Th123;
end;
