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It sounded like the easiest part of the highly complex Brexit deal.

With three million EU citizens living in Britain, and one million Brits living around Europe, both sides want an early agreement to protect the rights of their people.

But legally, the matter is not as straightforward as it seems.

Should migrants who arrive the day before Britain leaves the EU be allowed to stay forever? If not, when should the cut-off date be?

What about their partners, and other family members?

And should it be British or EU courts which ensure their rights are protected?

(Image: AFP)

The EU's position is clear. For them the cut-off date is simply the day Britain leaves in March 2019, and the EU's own courts should look after their own citizens living in Britain.

But this latter point is simply unacceptable to Theresa May, who has said repeatedly that the European Court of Justice can have no jurisdiction in Britain after we leave.

So her big gambit last night was to suggest that she may yet insist on an earlier cut-off date for new arrivals to Britain.

She did not say so, but her message to the EU was clear – we will only give you the cut-off date you want if you drop your demands for your courts to still have power in Britain.

Whether the PM's ploy works remains to be seen.

But what we saw last night was the first big skirmish of the Brexit negotiations. There will be many more to come over the next two years.