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The legal battle over the suspension of Parliament has finished for a second day at the Supreme Court.

The government's lawyer, Sir James Eadie QC, said it was not for the courts to "design a set of rules" over prorogation as it was a political matter.

But Aidan O'Neill QC, on behalf of campaigners against the move, said it was used "for an improper purpose".

Boris Johnson prorogued Parliament earlier this month for five weeks.

The prime minister said it would allow him to hold a Queen's Speech on 14 October to outline his new policies for the coming year.

But critics say his intention was to silence MPs and stop them scrutinising his plans in the run-up to the Brexit deadline on 31 October.

There are two appeals being heard by the Supreme Court over three days.

The first is an appeal led by businesswoman and campaigner Gina Miller against the English High Court's decision to throw out a challenge to prorogation.

The second is an appeal by the government against a separate ruling by Edinburgh's Court of Session that prorogation was unlawful.

A senior government source told the BBC's political editor No 10 believed the Supreme Court would judge that prorogation was a matter for the courts and would "fire warning shots about how a government should not use this to close Parliament illegitimately".

However, Laura Kuenssberg said according to the source, No 10 did not believe the court would unravel their plan for a Queen's Speech next month.

How did we get here?

Campaigners against the suspension, led by Ms Miller, launched a legal challenge in the English High Court earlier this month, claiming the move was "an unlawful abuse of power".

But it was rejected by the judges, who said Mr Johnson's decision was "purely political" and therefore "not a matter" for the judiciary.

However, they granted Ms Miller and her team an appeal at the Supreme Court.

A group of cross-party MPs, including the SNP's Joanna Cherry, had also launched a similar case in Edinburgh's Court of Session earlier this year, and the outcome, when it came, was very different.

Last week, judges there unanimously ruled the decision to prorogue Parliament was "unlawful" and used for the "improper purpose of stymieing Parliament".

But the government was also granted an appeal against the ruling in the Supreme Court.

Both appeals are being heard over three days by the Supreme Court's 11 judges, with Tuesday focused on those appealing against the original judgements - Ms Miller and her team, and the government.

Media playback is unsupported on your device Media caption Supreme Court: What happened on Tuesday?

What happened on Wednesday?

Wednesday focused on the two sides that had won their arguments in the lower courts.

In the morning, the government's representative, Sir James Eadie QC, argued in favour of the English court decision.

He said prorogation was "a well-established constitutional function exercised by the executive" and decisions about it were "squarely… within that political or high policy area".

Sir James also argued Parliament had previously passed laws addressing aspects of prorogation, but there was no law relevant to this particular case - meaning the courts could not intervene.

Asked about the need to uphold parliamentary sovereignty, Sir James said it was "a precious principle", but urged caution before "that phrase is too widely or generally bandied about".

Media playback is unsupported on your device Media caption The government's lawyer, Sir James Eadie QC, says the suspension is a political judgement

One of the judges, Lady Black, asked how could Parliament apply a check on government once it is "removed from the picture" due to prorogation.

But Sir James said it always and inevitably had the effect of limiting debate in Parliament, and MPs could resume their scrutiny once the suspension was over.

It was not appropriate for the courts to "design a set of rules" about how long a suspension should last, he said.

The BBC's home affairs correspondent, Dominic Casciani, said a key issue was the scope of parliamentary sovereignty.

Skip Twitter post by @BBCDomC The Government in essence is telling the court that Parliamentary sovereignty means the right to make/break laws and that’s about it. Opponents say sovereignty also means the right to take any steps necessary to hold an allegedly dodgy Prime Minister to account. — Dominic Casciani (@BBCDomC) September 18, 2019 Report

Lord Wilson also asked Sir James why no witness statement had been provided by a minister to explain why the prorogation decision was taken.

Sir James told the court he would present a written statement setting out what the government would do if it lost the case.

On Tuesday, Advocate General for Scotland, Lord Keen QC, on behalf of the government, assured the court the prime minister would take "all necessary steps" to comply in that event, but would not comment on whether Mr Johnson might subsequently try to prorogue Parliament again.

The afternoon session saw Aidan O'Neill QC arguing in favour of the Scottish court ruling against prorogation.

He said the decision had been carried out "in bad faith", and "for an improper purpose".

He suggested the government should engage "solely in high politics rather than low, dishonest, dirty tricks", but "given the attitude that has been taken by its advisers and the prime minister to the notion of the rule of law" that could not be assumed.

Mr O'Neill said one of the advantages of the ruling from Edinburgh was it had "distance", adding: "A view of what all of this heated debate [and] political machinations looks like 400 miles away, far from the fever and excitement of the nation's capital, [and] outside the Westminster bubble."

Media playback is unsupported on your device Media caption Aidan O'Neill QC argued to uphold the ruling of the Scottish courts

He said he was not calling for the court to "decide a whole new set of rules for how prorogation can be used", but argued it was "most certainly for the province of the courts" to determine whether the move followed constitutional principles.

He added: "In the present case, it appears the prime minister's action… has had the intent and effect of preventing Parliament... from holding the government politically to account at a time when the government is taking decisions that will have constitutional and irreversible impact on our country.

"That cannot be a lawful use of the power of prorogation."

He added: "We cannot have a situation in which there are no standards, in which prorogation can be used with impunity."

Skip Twitter post 2 by @BBCDomC Aidan O’Neill repeats one of the most important lines of attack: There is no statement or affadavit from the government swearing to the court that has been given "the truth, the whole truth and nothing but the truth" about the PM’s reasons for closing Parliament. — Dominic Casciani (@BBCDomC) September 18, 2019 Report

It is not yet known when the judges will deliver their verdict - it could be as early as Thursday afternoon.

Our home affairs correspondent said the feeling was the wait would not be long given the importance of the issue.