theorem
  for X being set
  for T1,T2 being SubSpace of T,
      f being Function of T1,S, g being Function of T2,S
  st ([#] T1) \/ ([#] T2) = [#] T & ([#] T1) /\ ([#] T2) = X &
  T1 is compact & T2 is compact & T is T_2 & f is continuous & g is continuous
  & f|X tolerates g|X holds f+*g is continuous Function of T,S by Lm1;
