
theorem
  for F being sequence of ExtREAL st F is nonnegative holds 0. <= SUM(F)
proof
  let F be sequence of ExtREAL;
  assume F is nonnegative;
  then 0. <= Ser(F).0 by SUPINF_2:40;
  hence thesis by FUNCT_2:4,XXREAL_2:4;
end;
