Trump: His comments suggest Iran is cheating on the deal. The facts: In the time since the nuclear deal was made in 2015, the International Atomic Energy Agency has repeatedly confirmed Iran was complying with the terms. That finding is also shared in the main by US and Israeli intelligence officials, though the Trump administration argues Iran exceeded limits on heavy water production. Trump: The President says that, after the 15-year term of the deal is up, Iran could have an array of advanced centrifuges ready to work, the limits on its stockpile would be gone and, in theory, it could then throw itself wholeheartedly into producing highly enriched uranium. The facts: Nothing in the deal prevents the West from trying to rein Iran in again with sanctions. The deal includes a pledge by Iran never to seek a nuclear weapon. A great embarrassment to me as a citizen, and to all citizens of the United States. Donald Trump

Trump: "This disastrous deal gave this regime – and it's a regime of great terror – many billions of dollars, some of it in actual cash. A great embarrassment to me as a citizen, and to all citizens of the United States." The facts: This is not true. The deal allowed Iran to regain access to its own money, which had been frozen abroad as part of the sanctions that were lifted. As for Iran specifically getting some cash, that refers to a debt the US had with Iran dating to the rupture in relations in the 1970s. Iran, under the Shah, had paid the US some $400 million for military equipment that was never delivered because the Islamic revolution cut off ties. That transaction was one of many complex claims that took decades to sort out in tribunals and arbitration. For its part, Iran paid settlements of more than $2.5 billion to US citizens and businesses left short when relations ruptured. Loading Trump (referring to allies): "We are unified in our understanding of the threat, and in our conviction that Iran must never acquire a nuclear weapon."

The facts: Such unity is conspicuously lacking. Most allies are not in agreement with the US on the threat posed by Iran. They believed the deal was sufficient to constrain the threat; Trump doesn't. Britain, France, Germany and others appealed to the US administration not to withdraw. Among top US allies, Israel agrees the deal fell short; others don't. Trump: "We will not allow American cities to be threatened with destruction, and we will not allow a regime that chants 'death to America' to gain access to the most deadly weapons on Earth." The facts: Iranian missiles are not capable of reaching US cities. Both technical limitations and orders from Iran's supreme leader have restricted the range of ballistic missiles manufactured in the country to 2000 kilometers. That puts them in targeting range of the entire Middle East, including Israel and US bases in the region, but nowhere near the continental United States. Trump: "Making matters worse, the deal's inspection provisions lack adequate mechanisms to prevent, detect and punish cheating. And don't even have the unqualified right to inspect many important locations, including military facilities." The facts: There is not unfettered access everywhere, but the International Atomic Energy Agency can inspect any declared nuclear site at any time. It also can request access to any other site deemed suspicious. Iran has 24 days to allow such an inspection. If Iran refuses, an arbitration panel weighs the request. Inspectors have placed some 2000 tamper-proof seals on nuclear material and equipment, and installed a network of surveillance cameras at nuclear sites.

The agency says its staff is spending twice as many days in Iran than it did in 2013. AP