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

theorem
  for G, V for G1, G2 being addVertices of G, V holds G1 == G2
proof
  let G, V;
  let G1, G2 be addVertices of G, V;
  the_Vertices_of G1 = the_Vertices_of G \/ V &
    the_Edges_of G1 = the_Edges_of G &
    the_Source_of G1 = the_Source_of G &
    the_Target_of G1 = the_Target_of G &
    the_Vertices_of G2 = the_Vertices_of G \/ V &
    the_Edges_of G2 = the_Edges_of G &
    the_Source_of G2 = the_Source_of G &
    the_Target_of G2 = the_Target_of G by Def10;
  hence thesis by GLIB_000:def 34;
end;
