  We give a new independent proof of a generalised version of the theorem by
Rashevskii, which appeared in [Uch. Zapiski Ped. Inst. K. 2 (1938), 83 -- 94]
and from which the classical Chow-Rashevskii Theorem follows as a corollary.
The proof is structured to allow generalisations to the case of orbits of
compositions of flows in absence of group structures, thus appropriate for
applications in Control Theory. In fact, the same structure of the proof has
been successfully exploited in [C. Giannotti, A. Spiro and M. Zoppello, arXiv
2401.07555 \& 2401.07560 (2024)] to determine new controllability criteria for
real analytic non-linear control systems. It also yields a corollary, which can
be used to derive results under lower regularity assumptions, as it is
illustrated by a simple explicit example.
