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 Th38:
  seq is non-zero & seq is convergent & lim seq=0 & seq is
  non-increasing 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-increasing;
  for n holds 0<=n implies 0<seq.n by A1,A2,A3,Th3;
  hence thesis by A2,Th35;
end;
