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

theorem
  for G, G2, V for G1 being addVertices of G, V st G1 == G2
  holds G2 is addVertices of G, V
proof
  let G, G2, V;
  let G1 be addVertices of G, V;
  assume A1: G1 == G2;
  then the_Vertices_of G1 = the_Vertices_of G2 &
    the_Edges_of G1 = the_Edges_of G2 &
    the_Target_of G1 = the_Target_of G2 &
    the_Source_of G1 = the_Source_of G2 by GLIB_000:def 34;
  then A2: 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;
  G2 is Supergraph of G1 by A1, Th62;
  then G2 is Supergraph of G by Th66;
  hence thesis by A2, Def10;
end;
