reserve r,r1,r2,g,g1,g2,x0,t for Real;
reserve n,k,m for Element of NAT;
reserve seq for Real_Sequence;
reserve f,f1,f2 for PartFunc of REAL,REAL;

theorem
  (ex r st 0<r & f|].x0-r,x0.[ is decreasing & f|].x0,x0+r.[ is
  increasing & not f|].x0-r,x0.[ is bounded_below & not f|].x0,x0+r.[ is
bounded_below) & (for r1,r2 st r1<x0 & x0<r2 ex g1,g2 st r1<g1 & g1<x0 & g1 in
  dom f & g2<r2 & x0<g2 & g2 in dom f) implies f is_divergent_to-infty_in x0
by Th22;
