reserve n,m,k,i for Nat,
  g,s,t,p for Real,
  x,y,z for object, X,Y,Z for set,
  A1 for SetSequence of X,
  F1 for FinSequence of bool X,
  RFin for real-valued FinSequence,
  Si for SigmaField of X,
  XSeq,YSeq for SetSequence of Si,
  Omega for non empty set,
  Sigma for SigmaField of Omega,
  ASeq,BSeq for SetSequence of Sigma,
  P for Probability of Sigma;
reserve FSeq for FinSequence of Sigma;

theorem
  for Z being Field_Subset of Omega holds sigma Z = monotoneclass Z
proof
  let Z be Field_Subset of Omega;
  monotoneclass Z is Field_Subset of Omega by Th72;
  then
A1: monotoneclass Z is SigmaField of Omega by Th70;
  Z c= monotoneclass Z by Def9;
  hence sigma Z c= monotoneclass Z by A1,PROB_1:def 9;
  sigma Z is MonotoneClass of Omega & Z c= sigma Z by Th70,PROB_1:def 9;
  hence thesis by Def9;
end;
