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

theorem
  X is empty-yielding iff X = EmptyMS I
proof
  hereby
    assume X is empty-yielding;
    then for i being object st i in I holds X.i = {};
    hence X = EmptyMS I by Th6;
  end;
  assume
A1: X = EmptyMS I;
  let i be object;
  assume i in I;
  thus thesis by A1;
end;
