(CNN) President Donald Trump announced Tuesday that the US is withdrawing from the Iran nuclear deal, arguing that remaining in the current agreement would lead to a nuclear arms race in the Middle East.

"It is clear to me that we cannot prevent an Iranian nuclear bomb under the decaying and rotten structure of the current agreement," Trump said from the White House Diplomatic Room. "The Iran deal is defective at its core. If we do nothing we know exactly what will happen."

In announcing his decision, Trump said he would initiate new sanctions on the regime, crippling the touchstone agreement negotiated by his predecessor. Trump said any country that helps Iran obtain nuclear weapons could also be "strongly sanctioned."

To make his case, he made a series of claims about the deal's flaws -- some true, some false and some up for debate. Here's a look at how accurate those claims were:

Trump: Iran deal brokered on "giant fiction"

Trump claimed on Tuesday that the previous US administration and its partners who brokered the nuclear deal did so believing that Iran had no intention of developing a nuclear weapon.

"At the heart of the Iran deal was a giant fiction, that a murderous regime desired only a peaceful nuclear energy program," Trump said.

Yes, Iran repeatedly claimed that its nuclear program was for purely peaceful purposes. But the US and its allies pursued the Iran deal for the very opposite reason: because they believed Iran was indeed pursuing a nuclear weapon.

That's why the P5+1 countries that negotiated the deal brokered the agreement, which capped Iran's nuclear enrichment and set up an inspections regime of Iranian nuclear sites.

Trump: Israeli documents show Iran's "history of pursuing nuclear weapons"

"Today, we have definitive proof that this Iranian promise was a lie. Last week. Israel published intelligence documents, long-concealed by Iran, conclusively showing the Iranians' regime and its history of pursuing nuclear weapons," Trump said on Tuesday.

Yes, the secret Iranian documents revealed last month by Israeli Prime Minister Benjamin Netanyahu showed that Iran at one time had plans to use its nuclear program to build a nuclear weapon. But again, that had not been in doubt from the US or its European allies' perspective.

Trump is using the documents to make his case for withdrawing from the deal, but the documents obtained by Israel did not reveal facts about Iran's past intentions that the international community did not already broadly know. And it didn't reveal anything about Iran's current nuclear program, though the IAEA has confirmed multiple times that Iran is complying with the deal.

Trump: Even if Iran complies, it can "be on the verge of a nuclear breakout in just a short period of time"

The Joint Comprehensive Plan of Action extended Iran's breakout time to more than a year, meaning Iran would be at least a year away from being able to produce enough enriched material for a nuclear weapon as long as it complied with the deal.

Before the deal and its restrictions on Iran's nuclear enrichment activities, Iran's breakout time was estimated to be a matter of months.

Trump may believe a year is a "short period of time," but the deal did extend Iran's breakout time. If Iran now pulls out because of the US' violation of the deal, it could begin to shorten its breakout time.

Trump's bigger issue is with one particular sunset provision, which only capped Iran's nuclear activities for 10 to 25 years after the deal came into force.

"The deal's sunset provisions are totally unacceptable. If I allowed this deal to stand, there would soon be a nuclear arms race in the Middle East. Everyone would want their weapons ready by the time Iran had theirs," Trump said on Tuesday.

Iran deal inspections provisions are inadequate

The President also claimed that "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."

Whether the deal's inspections mechanism is sufficient is a matter of debate among nuclear experts and supporters and opponents of the Iran deal alike. Supporters of the deal have argued that the inspections regimen set up is among the most rigorous ever brokered.

But inspections of military sites have been a key point of contention -- with Iran calling the sites "off limits" and rejecting past requests to inspect its military bases. Under the agreement, the IAEA can request access to military sites if it shows the basis for its concern. But critics say that process allows for a problematically long window of time 24 days before any inspection could take place.

Trump: Iran deal doesn't address Iran's ballistic missiles, destabilizing activities

Trump railed against the deal on Tuesday for failing "to address the regime's development of ballistic missiles that could deliver nuclear warheads."

"Finally, the deal does nothing to constrain Iran's destabilizing activities, including its support for terrorism. Since the agreement, Iran's bloody ambitions have grown only more brazen," Trump said.

On these two points, Trump is right. The Iran deal was all about the country's nuclear program and the lifting of sanctions related to that program.

The deal didn't address Iran's development of ballistic missiles or its support for US-designated terrorist groups, such as Hezbollah, in the region.