Is there a notation for being "a finite subset of"? I would gladly use a notation for “$A$ is a finite subset of $B$”, like 
$$A\sqsubset B \text{ or } A\underset{fin}{\subset} B,$$ 
but I have never seen a notation for that. Are there any?

EDIT: While waiting for a future standard, I will use Joffan’s $\ddot{\subset}$ coded as  
$\newcommand{\finsub}[0]{\mathrel{\ddot{\subset}}}$
$A\finsub B$

$\newcommand{\finsub}[0]{\mathrel{\ddot{\subset}}}$
I will paste the new command in the first row, and then use \finsub, resulting in $A\finsub B$ which I will explain after first use in each text. I guess that is satisfying enough.
And really, as you define sets and functions in a text, you could as well define relations without standard notations.

$A\in[B]^{\lt\omega}$ where $[B]^{\lt\omega}$ denotes the set of all finite subsets of $B$.
