reserve X for non empty set,
  S for SigmaField of X,
  M for sigma_Measure of S,
  E for Element of S,
  F,G for Functional_Sequence of X,ExtREAL,
  I for ExtREAL_sequence,
  f,g for PartFunc of X,ExtREAL,
  seq, seq1, seq2 for ExtREAL_sequence,
  p for ExtReal,
  n,m for Nat,
  x for Element of X,
  z,D for set;

theorem Th8:
  seq is nonnegative implies not seq is convergent_to_-infty
proof
  assume
A1: seq is nonnegative;
  assume seq is convergent_to_-infty;
  then consider n be Nat such that
A2: for m be Nat st n<=m holds seq.m <= -1;
  seq.n <= -1 by A2;
  hence contradiction by A1,SUPINF_2:51;
end;
