theorem
  for f,g be FinSequence st f^g is with_evenly_repeated_values &
     f is with_evenly_repeated_values holds g is with_evenly_repeated_values
proof
  let f,g be FinSequence such that A1: f^g is with_evenly_repeated_values &
    f is with_evenly_repeated_values;
  let y;
  A2: card ((f^g)"{y}) = card (f"{y})+card (g"{y}) by FINSEQ_3:57;
  card ((f^g)"{y}) is even & card (f"{y}) is even by A1;
  hence thesis by A2;
end;
