  Let $R$ be a Noetherian commutative ring of dimension $n$,
$A=R[X_1,\cdots,X_m]$ be a polynomial ring over $R$ and $P$ be a projective
$A[T]$-module of rank $n$. Assume that $P/TP$ and $P_f$ both contain a
unimodular element for some monic polynomial $f(T)\in A[T]$. Then $P$ has a
unimodular element.
