
theorem
  for G1, G2 being _Graph, G3 being SimpleGraph of G1
  st G2 == G3 holds G2 is SimpleGraph of G1
proof
  let G1, G2 be _Graph, G3 be SimpleGraph of G1;
  consider E being RepEdgeSelection of G1 such that
    A1: G3 is inducedSubgraph of G1,the_Vertices_of G1,E\G1.loops() by Def9;
  assume G2 == G3;
  then G2 is inducedSubgraph of G1, the_Vertices_of G1, E\G1.loops()
    by A1, GLIB_000:101;
  hence thesis by Def9;
end;
