reserve n,m,k,k1,k2,i,j for Nat;
reserve x,y,z for object,X,Y,Z for set;
reserve A for Subset of X;
reserve B,A1,A2,A3 for SetSequence of X;
reserve Si for SigmaField of X;
reserve S,S1,S2,S3 for SetSequence of Si;

theorem Th24:
  superior_setsequence B is non-ascending
proof
  now
    let n be Nat;
    (superior_setsequence B).n = (superior_setsequence B).(n+1) \/ B.n by Th22;
    hence (superior_setsequence B).(n+1) c= (superior_setsequence B).n by
XBOOLE_1:7;
  end;
  hence thesis by PROB_2:6;
end;
