reserve r,r1,g for Real,
  n,m,k for Nat,
  seq,seq1, seq2 for Real_Sequence,
  f,f1,f2 for PartFunc of REAL,REAL,
  x for set;
reserve r,r1,r2,g,g1,g2 for Real;

theorem Th20:
  (for n holds seq.n=n) implies seq is divergent_to+infty
proof
  assume
A1: for n holds seq.n=n;
  let r;
  consider n such that
A2: r<n by SEQ_4:3;
  take n;
  let m;
  assume n<=m;
  then r<m by A2,XXREAL_0:2;
  hence thesis by A1;
end;
