It's taken from the following picture(book"Riemann-Finsler geometry" by Chern & shen):
(source: uplooder.net)
What is their mean of the following sentence?
$HTM:= span \{\frac{\delta}{\delta x^i}\}$ is a well-defined subbundle of $T(TM_0)$.
What does it mean for a subbundle of a vector bundle to be well-defined? How could I check it?
Thanks.