theorem
  (ex r st 0<r & f|].x0,x0+r.[ is increasing & not f|].x0,x0+r.[ is
  bounded_below) & (for r st x0<r ex g st g<r & x0<g & g in dom f) implies f
  is_right_divergent_to-infty_in x0 by Th31;
