  In this note, we prove that given a submanifold $P$ in a Finsler manifold
$(M,F)$, (i) the orthogonal geodesics to $P$ minimize the distance from $P$ at
least in some interval, (ii) there exist tubular neighbourhoods around each
point of $P$, (iii) the distance from $P$ is smooth in some open neighbourhood
of $P$ (but not necessarily in $P$).
