Straightening theorem
= Straightening theorem
= Flow-box theorem
{synonym}
Near a point where a smooth <vector field> is nonzero, there are coordinates in which it is $\partial/\partial x_1$. Flow a transverse coordinate slice by the <local flow>; the <inverse function theorem> makes the resulting map a coordinate chart. This is the first step of the <coordinate proof of the Frobenius theorem>.