reserve X for set;

theorem Th17:
  for A,B,C being Subset of X ex F being sequence of bool X st
  rng F = {A,B,C} & F.0 = A & F.1 = B & for n being Element of NAT st 1 < n
  holds F.n = C
proof
  let A,B,C be Subset of X;
  take (A,B) followed_by C;
  thus thesis by FUNCT_7:122,123,124,127;
end;
