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;

theorem Th77:
  for g9 being Function st rng g c= dom g9 holds g9*g is EColoring of G
proof
  let g9 be Function;
  assume rng g c= dom g9;
  then dom(g9*g) = dom g by RELAT_1:27
    .= the_Edges_of G by PARTFUN1:def 2;
  hence thesis by PARTFUN1:def 2;
end;
