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 Th37:
  seq is non-zero & seq is convergent & lim seq=0 & seq is
  non-decreasing implies seq" is divergent_to-infty
proof
  assume that
A1: seq is non-zero and
A2: seq is convergent & lim seq=0 and
A3: seq is non-decreasing;
  for n holds 0<=n implies seq.n<0 by A1,A2,A3,Th2;
  hence thesis by A2,Th36;
end;
