
theorem Th62:
for seq be nonnegative ExtREAL_sequence st seq is non-decreasing holds
  seq is convergent_to_+infty or seq is convergent_to_finite_number
proof
   let seq be nonnegative ExtREAL_sequence;
   assume A1: seq is non-decreasing;
   now assume seq is convergent_to_-infty; then
    consider N be Nat such that
A4:  for n be Nat st N<=n holds seq.n <= -1 by MESFUNC5:def 10;
    seq.N <= -1 & seq.N >= 0 by SUPINF_2:51,A4;
    hence contradiction;
   end;
   hence thesis by A1,RINFSUP2:37,MESFUNC5:def 11;
end;
