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 non-zero & seq is convergent & lim seq=0 & seq is increasing
  implies seq" is divergent_to-infty by Th37;
