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

theorem
  for G1, G2 being _Graph st the_Vertices_of G2 = the_Vertices_of G1 &
    the_Edges_of G2 = the_Edges_of G1 &
    the_Source_of G2 c= the_Source_of G1 &
    the_Target_of G2 c= the_Target_of G1
  holds G1 == G2
proof
  let G1, G2 be _Graph;
  assume that
    A1: the_Vertices_of G2 = the_Vertices_of G1 and
    A2: the_Edges_of G2 = the_Edges_of G1 and
    A3: the_Source_of G2 c= the_Source_of G1 and
    A4: the_Target_of G2 c= the_Target_of G1;
  G1 is Supergraph of G2 by A1, A3, A4, Th67;
  hence thesis by A1, A2, Th69;
end;
