reserve i,j,e,u for object;
reserve I for set; 
reserve x,X,Y,Z,V for ManySortedSet of I;

theorem Th6:
  (for i being object st i in I holds X.i = {}) implies X = EmptyMS I
proof
  assume
A1: for i being object st i in I holds X.i = {};
  now
    let i be object;
    assume i in I;
    hence X.i = {} by A1
      .= EmptyMS I.i;
  end;
  hence thesis by Th3;
end;
