reserve G for _Graph;

theorem Th61:
  for G1, G2 being _Graph
  holds G2 is Subgraph of G1 iff G1 is Supergraph of G2
proof
  let G1, G2 be _Graph;
  thus G2 is Subgraph of G1 implies G1 is Supergraph of G2
  proof
    assume G2 is Subgraph of G1;
    then
      the_Vertices_of G2 c= the_Vertices_of G1 &
      the_Edges_of G2 c= the_Edges_of G1 &
      for e being set st e in the_Edges_of G2 holds
        (the_Source_of G2).e = (the_Source_of G1).e &
        (the_Target_of G2).e = (the_Target_of G1).e
      by GLIB_000:def 32;
    hence thesis by Def9;
  end;
  assume G1 is Supergraph of G2;
  then
    the_Vertices_of G2 c= the_Vertices_of G1 &
    the_Edges_of G2 c= the_Edges_of G1 &
    for e being set st e in the_Edges_of G2 holds
      (the_Source_of G2).e = (the_Source_of G1).e &
      (the_Target_of G2).e = (the_Target_of G1).e
    by Def9;
  hence thesis by GLIB_000:def 32;
end;
