Laura Kuenssberg
BBC political editor

This is all very unpredictable but the expectation in government might be shifting a bit in the Supreme Court case.

A senior government source says No 10 thinks the Supreme Court “will say prorogation is justiciable in principle".

In other words, it is a matter of law, not just politics, “and they (the judges) will fire warning shots about how a government shouldn't use this to close Parliament illegitimately”.

But No 10 does not, at the moment, think the Supreme Court will unravel their plan for a Queen's Speech on 14 October.

As a caveat, clearly we are all in very untested and spinnable territory here, and it will be down to the 11 judges, no one else.

Obviously this has implications for what Mr Johnson may be able to do next - remember in our interview this week he didn’t rule out trying prorogation again.

Image source, UK Supreme Court

The judges and Sir James are discussing Parliament's job of holding the government to account, and how it can't do that when it is prorogued, but can when Parliament resumes.

Lady Black asks Sir James: "In a time sensitive setting, how does afterwards help?"

Sir James replies: "Parliament has to react in the time that is left, before the time-sensitivity runs out."

Dominic Casciani
Home Affairs Correspondent

A strong question from Lord Sales, the latest addition to the Supreme Court, on the reasons for prorogation, who asks: "If there are constitutional principles that are required to be policed, isn't it more appropriate for the court to do it rather than for the Queen to be sucked in?"

Sir James Eadie replies that the constitutional protections are provided in the political arena - that is where the appropriate form of control is to be found, not in the courts.

Image source, UK Supreme Court

Sir James, representing the government, responds to his opponent's point that the prorogation means Parliament has not had enough time to legislate or debate Brexit.

"But that just simply prompts a whole series of unanswerable questions," says Sir James.

"How is sufficiency of time to facilitate legislation to be judged? How long is needed to hold the government to account over Brexit?"

He says his side believes the points made by the English High Court in its original ruling are "well-made".

"It is impossible, said the court, for the court to assess by any measurable standard how much time is required to hold the government to account.

"What factors justify a longer or a shorter prorogation? How could court weigh or assess political judgments of that time against a legal standard?"

Image source, UK Supreme Court

Sir James - the government's lawyer - is now responding to an argument made by his opponent yesterday.

Lord Pannick - representing Gina Miller - claimed that the exceptional length of the suspension of Parliament was because Boris Johnson wanted to avoid parliamentary scrutiny for political reasons.

Sir James responds that it is "self-evident that prorogation means that Parliament will not sit".

He says that "whatever the ultimate ends sought by any prorogation - whether it simply be a new Queen's Speech... wrong-footing the opposition", prorogation will stop Parliament sitting.

"It's difficult to separate the object and effect," he says, adding that prorogation always limits debate in Parliament, and any decision to prorogue has the same effect.

Boris Johnson said he would rather be "dead in a ditch" than request an extension to Brexit, after MPs voted to force him to do exactly that if he does not reach a deal with the EU.

And voting on the issue today, MEPs have said they would accept such an extension request should it be forthcoming.

Image source, EPA

As the government's legal team debates the lawfulness of Boris Johnson's suspension of Parliament in London, EU politicians have been debating Brexit in Brussels.

Speaking in the European Parliament, the EU's chief negotiator Michel Barnier said the UK and EU "should not pretend to be negotiating" a Brexit deal if there are no new proposals on the table.

And European Council President Jean-Claude Juncker said his meeting with the PM earlier this week was "friendly and constructive" - but without any real progress.

You can read the full story of the latest comments from the EU leaders here.

And to get the full story on today's Supreme Court proceedings, read our story here.

Image source, UK Supreme Court

One of the points the prime minister's lawyer is making - as part of his argument that suspending Parliament was lawful - is that there is "no distinction" between the prorogation and dissolution of Parliament, for the purposes of this case.

He's making this point, because the dissolution of Parliament has, in past cases, been treated as a non-justiciable matter.

A core part of Sir James' argument is submitting that prorogation is non-justiciable, ie a political rather than a legal matter.

Government lawyer Sir James Eadie has referred the justices to three examples of seemingly unusual closures of Parliament that, he says, were perfectly legal.

His point is that there are no hard and fast legal rules over how long Parliament should be prorogued.

Dominic Casciani
Home Affairs Correspondent

Two important interventions from the justices. Lord Wison pushes Sir James Eadie on whether they are really being asked to interfere in politics or uphold a “precious legal principle” - meaning Parliamentary sovereignty.

Lord Wilson asks the government’s top man: "Is there anyone else better placed than us" to uphold parliamentary sovereignty? Sir James, in short, questions whether Parliamentary sovereignty has been breached at all - it still has power to make and break laws.

Next Lord Kerr, the former chief justice of Northern Ireland, ponders: Let us supposed a PM wants to stifle debate and he decided to prorogue for one year…

Sir James Eadie, for the PM, acknowledges that was the “gauntlet thrown down” by Lord Pannick QC, for Gina Miller yesterday. He indicates he’ll say more on this later.

Image source, UK Supreme Court

Another of the judges, Lord Wilson, tells government lawyer Sir James it's job of judges like him to defend parliamentary sovereignty.

"If there's anybody who is better placed to defend the legal principle of parliamentary sovereignty it is us here," he says.

Sir James replies: "Parliamentary sovereignty is of course a precious principle but it all depends... on what aspect of parliamentary sovereignty you are dealing with.

"It means a number of different things".

Sir James adds that parliamentary sovereignty also means that Parliament can make and unmake its own laws. Other parts of the state - like the court must bow to it, he says.

While the UK's Supreme Court debates the lawfulness of the UK Parliament's suspension, Guy Verhofstadt - the EU's Brexit coordinator - makes the point in a European Parliament speech that such a suspension could not take place in the EU.

Image source, UK Supreme Court

Still arguing about justiciability (whether prorogation is a matter for the courts), Sir James Eadie cites a past case which found there was a "clear distinction between effectively legislative controls... and matters which are left to political judgement."

He sets out the reasons why the decision to prorogue Parliament is not "justiciable".

One of them is that there are "no judicial or manageable standards against which to test the lawfulness of decisions involving political or high policy considerations".

"Decisions about prorogation are squarely within that high policy sphere and within that key rationale for non-justiciability," he adds.

Image source, UK Supreme Court

One of the judges, Lord Kerr, asks Sir James whether he would accept that proroguing parliament has the potential to undermine Parliament, by stopping it sitting.

The government's lawyer, Sir James, replies: "By definition prorogation has the effects that it has.

"The bills that were previously before parliament fall...parliamentary questions cannot be asked.

"But my submission will be that despite those features this is a well-established constitutional function to be exercised by the executive."

He adds: "The question remains whether there are judicial standards against the political judgments... whether there are such standards and whether also it is a matter of constitutional propriety for those controls to be exercised by the courts or Parliament."

Dominic Casciani
Home Affairs Correspondent

Sir James Eadie QC is taking the court through what the law says on the "justiciability" of the case - which means whether there is even a law that the PM can be said to have broken.

The Scottish Court of Session ruled the manner in which Boris Johnson used the PM's executive, or prerogative power, to ask the Queen to prorogue Parliament can be legally challenged. The English High Court (lower than the Scottish court) said it could not be.

In short, Sir James says Parliament has previously passed legislation governing some aspects of prorogation - but if there is no law that covers what the PM has done this time, then the courts cannot intervene.

In other words, if Gina Miller and Joanna Cherry QC MP cannot point to a specific law that the PM allegedly broke in the manner in which he closed down Parliament, the judges cannot say whether it was legal or not. That's what justiciable means.

And the hiccups continue: as with day one, the Supreme Court judges are having a tough time finding all the documents the barristers are referring to.

Image source, UK Supreme Court

Lady Hale - the president of the Supreme Court - says her computer isn't working.

Yesterday the 11 judges also had some problems with paperwork, struggling to find the correct documents.

Image source, UK Supreme Court

Sir James' previous work includes advising the government on the Leveson Inquiry, and acting for the security services in the 7/7 bombings inquest. He's the QC the government looks to for major advice and litigation.

A barrister at Blackstone Chambers, Sir James was educated at the University of Cambridge and appointed First Treasury Counsel in 2009.

Image source, UK Supreme Court

The government's lawyer - Sir James Eadie - starts with the argument that the matter is not justiciable - meaning a matter for the courts - as it's a matter of "high policy", or politics.

Sir James cites a past case which dealt with justiciability.

One of the 11 judges asks a question. He says, as dissolving Parliament has always been a non-justiciable matter, is proroguing Parliament different?

Sir James replies there is no difference.

Image source, UK Supreme Court

Lady Hale again welcomes the lawyers into the court.

And Sir James Eadie - the government's lawyer - jumps straight in.

"We are dealing with a prerogative power," he says. "It's a prerogative power that has been expressly preserved by Parliament."

Prerogative powers are rights or privileges exclusive to a particular individual or class.

Sir James says ending and starting parliamentary sessions are the government's decision.