theorem Th8:
  for v be Element of S holds v + {}S = {}S
 proof
   let v be Element of S;
   assume v+{}S<>{}S;
   then consider x being object such that
   A1: x in v+{}S by XBOOLE_0:def 1;
   ex w be Element of S st x=v+w & w in {}S by A1;
   hence contradiction;
 end;
