theorem Th12:
  a <= c & c <= d & d <= b &
  f is_integrable_on ['a,b'] & f| ['a,b'] is bounded & ['a,b'] c= dom f
  implies
  -f is_integrable_on ['c,d'] & (-f) | ['c,d'] is bounded
  proof
    -f = (-1)(#)f by NFCONT_4:7;
    hence thesis by Th11;
  end;
