theorem Th10:
  bool Omega is Dynkin_System of Omega
proof
A1: {} c= Omega & bool Omega c= bool Omega;
  ( for f holds rng f c= bool Omega & f is disjoint_valued implies Union f
  in bool Omega)& for X holds X in bool Omega implies X`in bool Omega;
  hence thesis by A1,Def5;
end;
