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;
