Let $f : \prod_{n = 1}^N V_n \to W$ be a D1423: Multilinear map such that
Let $x = (x_1, \ldots, x_N) \in \prod_{n = 1}^N V_n$ be a D1129: Vector in $\prod_{n = 1}^N V_n$ such that
(i) | $0_1, \ldots, 0_N, 0_W$ are each the D737: Zero vector in $V_1, \ldots, V_N, W$, respectively |
(i) | \begin{equation} \exists \, n \in 1, \ldots, N : x_n = 0_n \end{equation} |
Then
\begin{equation}
f(x)
= f(x_1, \ldots, x_N)
= 0_W
\end{equation}