reserve G for _Graph;
reserve G2 for _Graph, G1 for Supergraph of G2;

theorem Th69:
  for G2, G1 st the_Vertices_of G2 = the_Vertices_of G1 &
    the_Edges_of G2 = the_Edges_of G1 holds G1 == G2
proof
  let G2, G1;
  assume that
    A1: the_Vertices_of G2 = the_Vertices_of G1 and
    A2: the_Edges_of G2 = the_Edges_of G1;
  dom the_Source_of G2 = the_Edges_of G2 &
    dom the_Target_of G2 = the_Edges_of G2 &
    dom the_Source_of G1 = the_Edges_of G1 &
    dom the_Target_of G1 = the_Edges_of G1 by GLIB_000:4;
  then the_Source_of G2 = the_Source_of G1 &
    the_Target_of G2 = the_Target_of G1 by A2, Th68, GRFUNC_1:3;
  hence thesis by A1, A2, GLIB_000:def 34;
end;
