theorem Th138:
  for H being Subgraph of G holds
    [ t_V | the_Vertices_of H , t_E | the_Edges_of H ] is TColoring of H
proof
  let H be Subgraph of G;
  A1: t_V | the_Vertices_of H is VColoring of H by Th3;
  t_E | the_Edges_of H is EColoring of H by Th78;
  hence thesis by A1, Def9;
end;
