reserve X,Y,Z,x,y,z for set;
reserve T,R for Tolerance of X;

theorem
  for T,R being Tolerance of X st TolClasses T = TolClasses R holds T = R
proof
  let T,R be Tolerance of X;
  assume
A1: TolClasses T = TolClasses R;
  for Z holds Z is TolClass of T iff Z is TolClass of R
  proof
    let Z;
    Z is TolClass of T iff Z in TolClasses R by A1,Def4;
    hence thesis by Def4;
  end;
  hence thesis by Th26;
end;
