According to Wikipedia, for commutative ring $R$,we have that $Sp(2n,R) \subseteq Sp(2n+2,R)$, where
$Sp(2n,R):= \left\{ M \in M_{2n \times 2n}(R) : M^{T}\Omega M = M \right\}$
and
$\Omega := \begin{bmatrix}0&I_{n}\\-I_{n}&0\end{bmatrix} \in M_{2n \times 2n}(R) $.
However, I don't think that the 'usual' embedding
$M \hookrightarrow \begin{bmatrix}M&0\\0&I_{2}\end{bmatrix}$
shows this inclusion. I tried this approach, but I think that the rows and columns split awkwardly.
I feel that there should be a 'canonical' way to show the inclusion, but I have not been able to find a reference.
Any help would be much appreciated!