Let \(\alpha, \beta \in \mathbb{N}^n\) multi-indices. Then
\begin{equation*} \alpha\le \beta \iff\forall i\in \{1,\ldots,n\}: \alpha_i \le \beta_i. \end{equation*}
\[
\newcommand{\d}{\mathrm{d}}
\newcommand{\e}{\mathrm{e}}
\newcommand{\i}{\mathrm{i}}
\]