
theorem
  for G1, G2 being _Graph, G3 being removeDParallelEdges of G1
  st G1 == G2 holds G3 is removeDParallelEdges of G2
proof
  let G1, G2 be _Graph, G3 be removeDParallelEdges of G1;
  consider E being RepDEdgeSelection of G1 such that
    A1: G3 is inducedSubgraph of G1, the_Vertices_of G1, E by Def8;
  assume A2: G1 == G2;
  then A3: the_Vertices_of G1 = the_Vertices_of G2 &
    the_Edges_of G1 = the_Edges_of G2 by GLIB_000:def 34;
  then A4: G3 is inducedSubgraph of G2, the_Vertices_of G2, E
    by A1, A2, GLIB_000:95;
  G2 is Subgraph of G1 by A2, GLIB_000:87;
  then E is RepDEdgeSelection of G2 by A3, Th79;
  hence thesis by A4, Def8;
end;
