"We will take back control of our laws", she told reporters in southern England, in a denial of suggestions by opposition lawmakers that she had watered down her demands by qualifying her words to say "direct" jurisdiction and opening the way to "indirect influence".
"Tickets will soon go on sale for flights in a post-Brexit world and both airlines and passengers need assurance from the European Union and United Kingdom government to enable them to plan for the future".
The Lib Dems described May's attempts to downplay the government's climbdown over the European Court of Justice as a "desperate attempt" to hold together the Conservative Party and ward off a eurosceptic rebellion.
The European Courts of Justice is different to the European Court of Human Rights which is not part of the EU but Brexiteers are awaiting to see the Brexit effect of on its jurisdiction over the UK.
For example, if the ECJ makes a ruling on employment law or product specifications that affects the single market, then that may well lead to a divergence from the laws or regulations operating in the UK.
"So why are they still planning to damage our economy by taking us out of the single market when doing so will not really take back control of our laws?"
It seems like a small, rather technical shift, but it is a recognition by the United Kingdom government of post-Brexit reality that makes the chance of an eventual Brexit deal ever so slightly more likely.
The British public chose to leave the European Union last June, after 44 years of membership.
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Total will pay for the deal with $4.95 billion in shares, while also taking on $2.5 billion in Maersk oil debt. Alongside Maersk Oil's UK North Sea assets, Total will also take over its Danish and Norwegian operations.
But the DExEU document did not rule out the ECJ maintaining its authority during the transitional period which is expected to last a number of years after the March 2019 deadline for Brexit, saying only that Britain will "work with the EU" on the design of interim judicial arrangements.
"When we leave the European Union we will be leaving the jurisdiction of the European Court of Justice", Mrs May said.
It has already said it wants the ECJ to have "full jurisdiction" over the rights of its citizen living in Britain, something the United Kingdom continues to balk at.
But according to Dr Bartels, this week's position papers don't provide a definitive answer because "this question has been reserved for future UK-EU agreement".
"This paper takes the next steps as we prepare to engage constructively to negotiate our approach to this". Even if the arbitration committee or court was entitled to judge on such matters, would both parties agree that it was "sovereign" and that its judgements necessarily overruled those of the British Supreme Court (and High Court of Justiciary in Scotland) and the ECJ?
"The optimum outcome for both sides will be an agreement reflecting our close existing relationship", the government said.
This position has already proven to be a sticking point in negotiations over the rights of EU citizens living in the United Kingdom, with Brussels reported to want European courts to enforce the agreement. He said: "This appears to contradict the red line laid out in the prime minister's Lancaster House speech and the government's white paper.' He added: 'Nothing the government says it wants to deliver from Brexit - be it on trade, citizens" rights or judicial cooperation - can be achieved without a dispute resolution system involving some role for European judges'.