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 Th139:
  for G1 being addVertices of G2, V, t being TColoring of G2
  for h being Function st dom h = V \ the_Vertices_of G2
  holds [t_V +* h, t_E] is TColoring of G1
proof
  let G1 be addVertices of G2, V, t be TColoring of G2, h be Function;
  assume dom h = V \ the_Vertices_of G2;
  then A1: t_V +* h is VColoring of G1 by Th4;
  the_Edges_of G1 = the_Edges_of G2 by GLIB_006:def 10;
  hence thesis by A1, Def9;
end;
