
theorem
  for G1 being _Graph, G3 being SimpleGraph of G1
  ex G2 being DSimpleGraph of G1 st G3 is SimpleGraph of G2
proof
  let G1 be _Graph, G3 be SimpleGraph of G1;
  set H = the removeLoops of G1;
  G3 is removeParallelEdges of H by Th121;
  then consider G2 being removeDParallelEdges of H such that
    A1: G3 is removeParallelEdges of G2 by Th97;
  reconsider G2 as DSimpleGraph of G1 by Th118;
  take G2;
  thus thesis by A1, Th123;
end;
