
theorem
  for G1 being non-Dmulti _Graph, G2 being _Graph
  holds G2 is DSimpleGraph of G1 iff G2 is removeLoops of G1
proof
  let G1 be non-Dmulti _Graph, G2 be _Graph;
  hereby
    assume G2 is DSimpleGraph of G1;
    then consider E being RepDEdgeSelection of G1 such that
      A1: G2 is inducedSubgraph of G1, the_Vertices_of G1, E\G1.loops()
      by Def10;
    thus G2 is removeLoops of G1 by A1, Th76;
  end;
  assume A2: G2 is removeLoops of G1;
  set E = the RepDEdgeSelection of G1;
  E = the_Edges_of G1 by Th76;
  hence thesis by A2, Def10;
end;
