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
  S is monotone implies S is convergent
proof
  assume
A1: S is monotone;
  per cases by A1;
  suppose
    S is non-ascending;
    hence thesis by Th83;
  end;
  suppose
    S is non-descending;
    hence thesis by Th80;
  end;
end;
