Suppose $\phi$ be a 8-dimensional quadratic form with trivial discriminant over a field $F$ of characteristic not 2. Assume that there is 3-fold Pfister form $<<a,b,c>>$ such that $\phi-<<a,b,c>>$ has Witt index $\geq 5$.
Question: How one can show that there exist a 5-dimensional subform $\sigma$ of $\phi$ which is also Pfister neighbour of $<<a,b,c>>$?
[We say $\sigma$ is a Pfister neighbour of a Pfister form $\psi$ if there is $d\in F^\times$ such that $d.\sigma$ is subform of $\phi$ and dim $\phi< 2$ dim $\sigma$].
Thanks!