Let $F:M\to N$ be a smooth map between smooth $n$-manifolds, and let $p\in M$. If $dF_p:T_pM\to T_{F(p)}N$ is a linear isomorphism, then there are open neighbourhoods $U\subset M$ of $p$ and $V\subset N$ of $F(p)$ such that $F|_U:U\to V$ is a diffeomorphism.