Isotropy of a quadratic form on the function field of a quadric of characteristic 2 (Q1420728)

In this well-written paper the authors show that a famous theorem of D. Hoffmann can be extended to a field of characteristic 2. It then reads as follows: Theorem: Suppose \(\text{char}\,F=2\). Let \(\varphi,\psi\) be anisotropic quadratic forms over \(F\) where \(\varphi\) is of shape \[ \varphi \cong [a_1,b_1]\perp \cdots \perp [a_r,b_r]\perp [c_1]\perp \cdots \perp[c_s], \] i.e. \(\varphi\) has quasilinear part of dimensions \(s\geq 0\) and nonsingular part of dimension \(2r\). Suppose \(2r+2s\leq 2^n<\dim\psi\) for suitable \(n\geq 1\). Then \(\varphi\) remains anisotropic over the function field \(F(\psi)\). (For \(\text{char}\,F\neq 2\) one has \(s=0\) since anisotropic forms are automatically nonsingular in this case).