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;

theorem Th10:
  Partial_Intersection A1 is non-ascending
proof
  now
    let n be Nat;
    (Partial_Intersection A1).(n+1) = (Partial_Intersection A1).n /\ A1.(n
    +1) by Def1;
    hence (Partial_Intersection A1).(n+1) c= (Partial_Intersection A1).n by
XBOOLE_1:17;
  end;
  hence thesis by PROB_2:6;
end;
