Hello every one!

Here is a question which I would like to ask you:

Let $G=limit G_{i}$ is an ind-group (Shafarevich called it infinitely-dimensional algebraic group). It is well-known that $G$ is smooth. Is it true that for any (or at least for one) $x \in G$ there exist a natural $N$ big enough, such that $G_{i}$ is smooth at $x$ for all $i > N$ (or just for infinitely many $i : i > N$) ?

Thank you for your answers and considerations! Andriy.