It lists them as: "No Single Market/no customs union; no border on the island of Ireland, no border down the Irish Sea". The level of detail and the granularity of the analysis will likely give some comfort businesses concerned about whether the UK Government is on top of the detail and has a plan.
The Chancellor, who his due to set out the Government's thinking in more detail in a keynote speech on Wednesday, the European Union would find it impossible to replicate the financial "eco-system" of the City of London it was excluded.
The UK's commitment to close alignment of regulatory standards would come under a "comprehensive system of mutual recognition" for post-Brexit arrangements for the supply of goods, May said.
She said Britain may choose to commit some areas of regulations like state aid and competition to remaining in step with the EU's, and guaranteed that Britain would not "engage in a race to the bottom on workers' rights or the environment".
The Brexit withdrawal treaty is itself mired in difficulties, with London saying the EU's official legal text of the preliminary divorce agreement they made in December makes unacceptable demands on the Irish border. "It also means that the ultimate arbiter of disputes about our future partnership can not be the court of either party", she said.
He also questioned the UK's chances of agreeing a free trade deal with the U.S.in light of President Trump's recent announcement that he wanted to impose tariffs on steel and aluminium imports.
Mr Bettel said solutions were needed because the time is ticking. Though, as Prime Minister, she insists that there will be no hard border post-Brexit, her views were once rather different.
The Confederation of British Industry lobby group said it was important to make sure alternative arrangements were put in place to prevent firms leaving London.
Mr Varadkar added: "We will of course have negotiations about what could be done to avoid a hard border, but what we won't be getting into is a negotiation with the United Kingdom, or a three-way negotiation". "That is why we will be seeking more than just an adequacy arrangement and want to see an appropriate ongoing role for the UK's Information Commissioner's Office".
While May went some way to crystallizing her vision for the future relationship in a speech on Friday, the European Union plan reflects the belief in Brussels and continental capitals that the U.K.'s position is still unclear, with significant differences between the two sides remaining.
Welcoming publication of the report, Minister for Business, Enterprise and Innovation, Heather Humphreys said, "This report by InterTradeIreland is a welcome contribution to our understanding of the context around Brexit".
But a Whitehall source told Sky News the document was a "highly misleading summary which was clearly prepared at pace, contains very poor analysis, and does not reflect the detailed conversations we are having with European partners".