(CNN) President Donald Trump uttered a rapid series of false claims, at least 13 in all, during his Cabinet meeting on Tuesday. He made another claim for which there is no public evidence, and he offered positive words about an ally's accusation for which there is no public evidence.

Let's go through the 13 false claims first:

False Claims

Caravans

Trump claimed that the governments of Guatemala and Honduras were "forming caravans and sending them up." He then elaborated on the conspiracy theory, saying that these governments were dumping "hardened" criminals into the caravans.

CNN's Facts First page

"And why not? Why would Honduras or Guatemala or El Salvador -- why would they keep their criminals when you can put them into a caravan, lose them in a caravan, and send them up to the United States?" he said. "We take everybody, because the Democrats don't allow immigration laws that mean anything. It's horrible."

Facts First: Though the Department of Homeland Security has said that some members of recent migrant caravans have had criminal pasts, there is simply no evidence that the governments of Honduras, Guatemala or El Salvador have deliberately put criminals into the caravans to foist them upon the United States.

By all accounts, the caravans have consisted of people who decide for themselves that they want to migrate. There has been no hint that governments have forced anyone into one of the caravan groups.

"Everything we have seen suggests the migrant caravans were loosely organized and largely spontaneous in nature, and were not organized or directed by the governments of El Salvador, Guatemala or Honduras," said Ariel Ruiz, an associate policy analyst at the Migration Policy Institute.

Migrants and the courts

Trump repeated one of his frequent false claims about migrants who are apprehended and then released to await a court hearing.

"We catch them and release them. We catch them and say, 'Come back to court in five years,' and nobody comes back. Two percent, to be accurate. I want to be accurate, because I don't want the press to say I was inaccurate. Two percent come back. And those people we wonder why -- why are they coming back? They're the only ones."

Facts First: Trump was not even close to accurate. Eighty-nine percent of asylum seekers showed up in court to receive a decision on their case in the 2017 fiscal year, according government data; it was 72% for all kinds of migrants.

It is possible that the percentage has fallen since 2017, but there is no sign that it has fallen to anywhere close to 2% or zero.

Human trafficking

Trump also repeated one of his regular false claims about how human trafficking cannot be conducted through legal ports of entry.

"We're doing very well but we have no help whatsoever from the Democrats. ... They obviously don't mind crime and drugs and human trafficking, which is a tremendous problem. And it's human trafficking mostly in women. And you know Democrats -- with their big wonderful hearts, human trafficking with women, where three, four, five women are put in the back of a van or the back of a car, and they go through areas where there will soon be wall but there's no wall right now, because you can't obviously come through ports of entry," Trump said.

Facts First: Many human trafficking victims do indeed come through ports of entry, according to experts on trafficking and according to international data. Experts say that victims are more likely to be deceived into crossing the border willingly than kidnapped and put in the back of a vehicle.

"I have worked on human trafficking on multiple continents in multiple countries for more than two decades, and in all the work that I've done with trafficking victims, I have met one who was actually kidnapped and thrown into a car," Martina Vandenberg of the Human Trafficking Legal Center told CNN in January, when Trump was telling frequent stories about women being bound and gagged in cars.

Many victims, experts say, are tricked into coming to the US with promises of a good job. Others are coerced through threats to their families or themselves. While experts say there may be some cases like the ones Trump has described, they emphasize that such cases are in a small minority.

In 2018, the UN International Organization for Migration found that "in the last 10 years, almost 80% of journeys undertaken by victims trafficked internationally cross through official border points, such as airports and land border control points."

Democrats and borders

"We're doing very well but we have no help whatsoever from the Democrats. Just the opposite. They want open borders. They obviously don't mind crime and drugs and human trafficking, which is a tremendous problem," Trump said.

Facts First: Some Democrats, including presidential candidates such as Elizabeth Warren and Julián Castro, have advocated a significant loosening of immigration law, including a decriminalization of the act of illegally crossing the border.

But none of them have proposed literally opening the border to unrestricted migration.

Louisiana LNG plant

Trump also took credit for an energy facility that he is not responsible for.

"Or LNG plants; I just left Louisiana, cut a ribbon for a $10 billion LNG plant that's so incredible people wouldn't believe it. It was many, many years trying to get permits, they couldn't get the permits, but we got the permits and we got it very rapidly."

Facts First: The permits for the facility Trump visited were granted by the Obama administration.

Trump spoke at Sempra Energy's Cameron liquefied natural gas export facility in Louisiana in May. The company says on its website: "The Federal Energy Regulatory Commission authorized the project in June 2014." The company confirmed to FactCheck.org: "You are correct, Cameron LNG was approved in 2014."

The facility made its first shipment in late May.

North Korea and US remains

A program to recover the remains of US soldiers who died in North Korea during the Korean War has been suspended. Trump continued to insist that it is ongoing.

"We got our hostages back (from North Korea). We got the remains back, and they continue to come," he said.

Facts First: While North Korea returned some remains last year, it is no longer doing so. The US military announced in May that the remains program had been suspended for the rest of the 2019 fiscal year because North Korea had stopped communicating with the US agency responsible for the effort.

Trump could accurately tout the return of remains in the past tense: North Korea returned 55 cases of possible remains in the summer of 2018. As of late May, six soldiers had been identified from these cases.

But the remains are no longer being returned. The Pentagon's Defense POW/MIA Accounting Agency said in May that no more remains would be coming back this fiscal year. The agency said North Korea had not spoken with the agency at all since the Hanoi summit in February between Trump and Kim Jong Un, which ended abruptly.

Automotive trade

"And every car that comes through that used to be made in the United States -- now Mexico has 30% of our car business. But that's not going to happen anymore, no more -- no more companies are going to leave because we have reasons that they can't leave anymore. There's just no reason for them to leave anymore," Trump said.

Facts First: Nothing in Trump's revised trade agreement with Mexico and Canada prevents automotive companies from leaving the United States.

It sets new rules intended to help convince them to manufacture in North America in general and the US in particular, but it does not force them to do anything.

The border wall

"We're building a lot of wall right now," Trump said.

Facts First: No new miles of wall were under construction as of last month.

Customs and Border Protection provided a fact sheet saying that "construction activities" had "started for approximately 13 miles of new border wall system and levee wall system in the Rio Grande Valley." But such "activities" are different from construction itself; they include the clearing of vegetation, a Customs and Border Protection spokesperson previously told us, and there is no current sign that construction of the actual wall has started. Even if it now has quietly started, that is not "a lot of wall."

Trump said this spring that replacement fencing should be counted by the media as his "wall," since he is replacing ineffective old barriers with effective modern ones. This is subjective, but we think it's fair to focus on the new barriers he promised during his campaign.

Women's unemployment

Trump accurately boasted of record unemployment rates for members of various minority groups, then made an inaccurate claim about the rate for women.

"Our unemployment numbers are historic in the sense that we've never had better numbers ... women, 75 years," he said.

Facts First: Trump might have been rounding, but he was a little off. The women's unemployment rate for June was 3.6%, a tick above the 3.4% in April and 3.5% in May.

It has been 66 years since the women's rate has been this low, not 75 years.

Tariffs on China

Trump returned to a favorite story about how he decided to announce $16 billion in aid to farmers hurt by his tariff battle with China.

"Out of the tariffs, I took $16 billion to make up for the shortfall. I went to (Agriculture) Secretary Sonny Perdue ... I said, 'What was the amount at its highest that China pumped into the farmers in the form of purchase?' '$16 billion.' I said that's alright, we're taking many, many times that in tariffs. We're going to help the farmers out, and I did that with $16 billion," Trump said.

Facts First: $16 billion is not the most China has ever spent on US farm products in a year. China spent $29.6 billion in 2014, according to government figures.

The New York Times reported Monday that Trump's tariffs on China have generated about $21 billion so far, which is not "many, many times" $16 billion. And economic studies have concluded that Americans, not people or companies in China, are bearing the majority of the costs.

Trade deficit with China

"During the Obama administration, $500 billion a year was being lost to China. Five hundred billion," Trump said.

Facts First: The US has never had an annual $500 billion trade deficit with China. (Trump refers to trade deficits as losses, though most economists don't.) The 2018 deficit in goods and services was $381 billion; it was $420 billion when counting goods alone and excluding services.

Those were record figures.

Chinese economy

Since Trump's election, he said, "China's lost $20 trillion."

Facts First: There is no apparent basis for the $20 trillion figure. Experts on the Chinese economy have even rejected previous Trump claims of a $10 trillion drop in Chinese wealth.

We checked one of those "$10 trillion" claims for the Toronto Star in May. We wrote then: "George Magnus, a research associate at Oxford University's China Centre, said, 'I can't really make those numbers add up to anything I'm aware of.' Magnus noted that the entire market capitalization of the Shanghai index was just over $5 trillion US at the time. Derek Scissors, an expert on US economic relations with Asia at the conservative American Enterprise Institute think tank, also said a $10 trillion drop in Chinese wealth is 'not in evidence.' "

The Iran Deal

"Remember one thing. An agreement was made with Secretary Kerry at the time and with President Obama. That agreement was a disaster. Spent $150 billion," he said.

Facts First: The US did not "spen(d)" tens of billions to make the Iran nuclear deal; the deal allowed Iran to access tens of billions in its own assets -- not US cash -- that had been frozen in foreign financial institutions because of sanctions. The total was significantly lower than $150 billion, experts say.

Trump did not invent the $150 billion figure out of thin air: Obama himself mused in a 2015 interview about Iran having "$150 billion parked outside the country." But experts on Iran policy, and Obama's own administration, said that the quantity of assets the agreement actually made available to Iran was much lower.

In 2015, Treasury Secretary Jack Lew put the number at $56 billion. PolitiFact reported that Garbis Iradian, chief economist at the Institute of International Finance, put it at about $60 billion, and that Nader Habibi, professor of economics of the Middle East at Brandeis University, thought it was between $25 billion and $50 billion after discussing the issue with officials at Iran's Central Bank.

Adam Szubin, a senior Treasury Department official, testified to Congress in 2015 that the "usable liquid assets" would total "a little more than $50 billion." The rest of Iran's foreign assets, he said, were either tied up in "illiquid" projects "that cannot be monetized quickly, if at all, or are composed of outstanding loans to Iranian entities that cannot repay them."

As Trump regularly notes, the Obama administration did send Iran $1.7 billion to settle a decades-old dispute over a purchase of US military goods Iran made before its government was overthrown in the Islamic Revolution of 1979. The goods were not delivered, and the US paid Iran its money back plus interest.

Other Claims

Trump cited two quotes for which there is no evidence. In the first case, about Trump's prowess in hostage negotiations, there is no evidence that the quote itself was ever uttered. In the second case, about Google and China, the substance of the quote is the issue.

Trump the hostage negotiator

"Our ambassador for hostage negotiation said Trump is the greatest of all time. I only tell you that because you'll never say it," he said.

Facts First: There is no public evidence of this quote.

The White House told CBS that the quote was from Robert C. O'Brien, special presidential envoy for Hostage Affairs at the State Department. But nobody has been able to find a record of him saying it.

It is possible, of course, that O'Brien told Trump this in private.

Google

Trump was asked about a tweet this morning in which he quoted an accusation against Google from billionaire technology investor Peter Thiel, who suggested in a speech this weekend that Google might have made a "seemingly treasonous decision to work with the Chinese military."

"He (Peter Thiel) made a very strong charge," Trump said. "He's one of the top, maybe the top expert on all of those things, and he made a very big statement about Google. ... it's a big statement when you say that, you know, Google is involved with China in not a very positive way for our country," Trump said.

Facts First: Thiel, a board member at Facebook, provided no evidence for his accusation either in the Sunday speech or in his Monday appearance on Fox News. Google has rejected the accusation: "As we have said before, we do not work with the Chinese military," Google told CNN on Tuesday.

In March, Marine Corps General Joseph Dunford, chairman of the Joint Chiefs of Staff, told the Senate Armed Services Committee that Google's work in China is "indirectly benefiting the Chinese military."

In a Monday interview on Fox Business, National Economic Council director Larry Kudlow said he had not spoken to Thiel and was "not sure where he was going or what he's pointing to."

"I meet with Google CEO on a regular basis. I think they are working for America, for our military, and not for China," Kudlow said.