reserve n for Nat;

theorem
  for f,g be FinSequence st f^'g is constant & f.len f = g.1 & f <> {}
  holds g is constant
proof
  let f,g be FinSequence;
  assume that
A1: f^'g is constant and
A2: f.len f = g.1 and
A3: f <> {};
  reconsider h = f^'g as constant FinSequence by A1;
  per cases;
  suppose
    g <> {};
    then rng h = rng f \/ rng g by A2,A3,FINSEQ_6:144;
    then rng g c= rng h by XBOOLE_1:7;
    hence thesis;
  end;
  suppose
    g = {};
    hence thesis;
  end;
end;
