reserve Omega for set;
reserve X, Y, Z, p,x,y,z for set;
reserve D, E for Subset of Omega;
reserve f for Function;
reserve m,n for Nat;
reserve r,r1 for Real;
reserve seq for Real_Sequence;
reserve F for Field_Subset of X;
reserve ASeq,BSeq for SetSequence of Omega;
reserve A1 for SetSequence of X;

theorem
  for S being non empty set holds S is SigmaField of X iff S c= bool X &
  (for A1 being SetSequence of X st rng A1 c= S holds Intersection A1 in S) &
  for A being Subset of X st A in S holds A` in S by Def1,Def6;
