If they were not, one would have by the second point above
,
or
. If the minus
sign holds, then
is automatically
and there is nothing to be proven. So we only need to consider the
cases
,
or
. In the first case,
, in the second case
, and in
the last case
so these three cases are in fact excluded by the assumption. We can therefore assume
and
to be linearly independent.