It fought on a pro-Brexit manifesto.
The most high-profile institution with jurisdiction would seem to be the International Court of Justice which regulates treaties.
But there are big and significant differences in tone too.
"We spoke about the very important need for both governments to be impartial actors when it comes to Northern Ireland and that we are co-guarantors of the Good Friday Agreement and that any agreement that may exist between the Conservatives and the DUP should not in any way impact on the Good Friday Agreement", he said.
"The deal she is brokering with the DUP party could include that the United Kingdom would not be required to stay in the European Union single market, which means that she is trying to establish a stronger position in a relative perspective before she ignites the negotiation process next week".
Both the government and the DUP have refused to implement key agreements on language and equality rights and dealing with the legacy of the past.
While Labour caught the popular mood through social media and music, wrapped around an unlikely socialist leader similar in many respects to the US Democratic Party presidential candidate Bernie Sanders, the Conservative Party remained brittle, often aloof, seeming to demonstrate little if any understanding of how to relate to young people.
"It takes two to tango and we're ready to dance", she said. But the party hasn't set out a clear position on continued membership of the customs union, which is probably needed to avoid tariffs, and she didn't elaborate in Dublin on Friday after meeting Irish Prime Minister Leo Varadkar. She criticised the dissent from the opposition parties claiming that "division in Westminster will risk our ability to make a success of Brexit".
Would this have been part of their negotiations with Theresa May in Downing Street? Labour also picked up big chunks of the collapsing UKIP vote across the country, which broke nearly evenly for Labour and Conservative in many seats.
There will be pressure for a softer Brexit.
During his day in Belfast, he will meet Northern Ireland Secretary James Brokenshire and will also hold meetings with the five main Stormont parties.
The pair shared a phone call on Thursday.
On Monday, Mr Coveney said: "As the representative of the Irish Government at the talks, I will do my utmost to support the parties in reaching an agreement which ensures that the integrity of the Good Friday Agreement is fully protected, that all of its institutions function effectively and fairly and that previous agreements are honourably implemented".
Can the Brexit talks go ahead? The government has neither the time nor is it properly prepared to start negotiations on Brexit. But obstacles have now appeared.
With her predecessor David Cameron having resigned after his Brexit referendum defeat past year, Theresa May's days as British Prime Minister are probably numbered too as it is unlikely the Tories will want her leading them into the next general election. Despite her firm, immediate declaration that she was not resigning, her position remains in question.
It is expected that an informal coalition agreement will be signed today between the Conservatives and the DUP bringing this loose arrangement government into being.
Theresa May still has to demonstrate that her government has the confidence of Parliament and can pass bills. Just one of the many unforeseen consequences of the 2017 general election.