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Can someone help me with this problem?

I have a $C^1$ function $G\colon\mathbb{R}^n\rightarrow \mathbb{R}^m$, where $k=n-m> 0$. If $M$ is the set of points $x\in G^{-1}(0)$ such that $(DG)_x$ has rank $m$, then $M$ is a smooth manifold of dimension $k$.

If someone could give me a starting kick it would be great!

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    Now I think my teacher is going too fast with exercises and too slow with class notes. The question is on a list about manifolds but this problem seems so advanced (it is talking about embedded manifolds and things I didn't see yet). I should probably include a full-text demonstration of this theorem on the solution just to get things straight.2012-05-22

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