
theorem Th32:
  for G2, G3 being _Graph, V being set, G1 being addVertices of G2, V
  st G2 == G3 holds G1 is addVertices of G3, V
proof
  let G2, G3 be _Graph, V be set, G1 be addVertices of G2, V;
  assume A1: G2 == G3;
  then the_Vertices_of G3 = the_Vertices_of G2 &
    the_Edges_of G3 = the_Edges_of G2 &
    the_Target_of G3 = the_Target_of G2 &
    the_Source_of G3 = the_Source_of G2 by GLIB_000:def 34;
  then A2: the_Vertices_of G1 = the_Vertices_of G3 \/ V &
    the_Edges_of G1 = the_Edges_of G3 &
    the_Source_of G1 = the_Source_of G3 &
    the_Target_of G1 = the_Target_of G3 by GLIB_006:def 10;
  G2 is Supergraph of G3 by A1, GLIB_006:58;
  then G1 is Supergraph of G3 by GLIB_006:62;
  hence thesis by A2, GLIB_006:def 10;
end;
