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 Th167:
  G1 == G2 & G1 is c-tcolorable implies G2 is c-tcolorable
proof
  assume A1: G1 == G2 & G1 is c-tcolorable;
  then consider t1 being TColoring of G1 such that
    A2: t1 is proper & card((rng t1_V)\/rng t1_E) c= c;
  A3: the_Vertices_of G1 = the_Vertices_of G2 &
    the_Edges_of G1 = the_Edges_of G2 by A1, GLIB_000:def 34;
  then reconsider f = t1_V as VColoring of G2;
  reconsider g = t1_E as EColoring of G2 by A3;
  reconsider t2 = [f,g] as TColoring of G2;
  t2 is proper by A1, A2, Th152;
  hence thesis by A2;
end;
