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

theorem Th32:
  G1 == G2 & G1 is c-vcolorable implies G2 is c-vcolorable
proof
  assume A1: G1 == G2 & G1 is c-vcolorable;
  then consider f1 being VColoring of G1 such that
    A2: f1 is proper & card rng f1 c= c;
  the_Vertices_of G1 = the_Vertices_of G2 by A1, GLIB_000:def 34;
  then reconsider f2 = f1 as VColoring of G2;
  f2 is proper by A1, A2, Th16;
  hence thesis by A2;
end;
