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
  seq is bounded_above & seq1 is divergent_to+infty implies seq-seq1 is
  divergent_to-infty
proof
  assume that
A1: seq is bounded_above and
A2: seq1 is divergent_to+infty;
  (-jj)(#)seq1 is divergent_to-infty by A2,Th13;
  hence thesis by A1,Th12;
end;
