theorem
  ex f being Choice_Function of BOOL Subformulae v st
   f is Function of BOOL Subformulae v,Subformulae v
proof
 take f = the Choice_Function of BOOL Subformulae v;
A1: not {} in BOOL Subformulae v by ORDERS_1:1;
  union BOOL Subformulae v =  Subformulae v by Th55;
 hence f is Function of BOOL Subformulae v,Subformulae v by ORDERS_1:90,A1;
end;
