reserve Omega, F for non empty set,
  f for SetSequence of Omega,
  X,A,B for Subset of Omega,
  D for non empty Subset-Family of Omega,
  n,m for Element of NAT,
  h,x,y,z,u,v,Y,I for set;

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;
