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;
