reserve E,V for set, G,G1,G2 for _Graph, c,c1,c2 for Cardinal, n for Nat;
reserve f for VColoring of G;
reserve g for EColoring of G;
reserve t for TColoring of G;

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;
