theorem
  for r ex seq st rng seq={r}
proof
  let r;
  consider f such that
A1: dom f=NAT and
A2: rng f={r} by FUNCT_1:5;
  for x being object st x in {r} holds x in REAL by XREAL_0:def 1;
  then rng f c= REAL by A2,TARSKI:def 3;
  then reconsider f as Real_Sequence by A1,FUNCT_2:def 1,RELSET_1:4;
  take f;
  thus thesis by A2;
end;
