Let $A\in M_{n\times m}$. Would it be considered an abuse of notation to write
$$\left(A\mid M_{n\times p}\right)\subseteq M_{n\times (m+p)},\tag{1}$$
where $\mid$ denotes matrix augmentation ? By $\left(A\mid M_{n\times p}\right)$ I mean the set of all matrices in $M_{n\times(m+p)}$ whose "left side" submatrix is exactly $A$, which is itself fixed.