Where can one find the proof of the following fact: 


If there are two orientation-preserving diffeomorphisms $\phi\_0$ and $\phi\_1$ of $R^n$, then there exists a homotopy $\phi(t)$, such that $\phi(0)$ = $\phi\_0$, $\phi(1)$ = $\phi\_1$, and $\phi(t)$ is a diffeomorphism for any $t$ (and $\phi$ is smooth for all variables).


This is easy to prove for $n=1$, and relatively easy for $n=2$, but for an arbitrary $n$ seems difficult.


This fact is used in the knot theory to justify the coincidence of two definitions of the knot equivalence.



Why are two diffeomorphims of $R^n$ are always homotopic (in the same category)?
An explicit deformation retraction of $\mathrm{Diff}(\mathbb R^n)$ onto $\mathrm{Aff}(\mathbb R^n)$ is given by $$f\_t(x)=f(0)+\frac{f(tx)-f(0)}{t}$$ for $t\in (0,1]$ and $f\_0(x)=f(0)+f^\prime(0)x$. 


