By ALICIA A. CALDWELL and CALVIN WOODWARD, Associated Press

WASHINGTON (AP) — President Donald Trump says the border with Mexico is already "getting extremely strong" and would-be illegal crossers are giving up because they think, "we can't get in." All without the wall he promises to build, or any reported boost in deportations, or any surge in patrol agents.

The boast was one of a number at a Tennessee rally Wednesday night that did not track with the facts. A look at some:

TRUMP: "And by the way, aren't our borders getting extremely strong? ... We've already experienced an unprecedented 40 percent reduction in illegal immigration on our southern border, 61 percent — 61 percent since Inauguration Day. Sixty-one percent; think about it. And now people are saying we're not going to go there anymore 'cause we can't get in, so it's going to get better and better."

THE FACTS: There's not much evidence yet that Trump is driving down illegal immigration. It's true that the number of border arrests dropped about 44 percent from January to February. But it's too early to know if that will hold or what prompted it. Monthly and seasonal fluctuations are common.

Trump hasn't expanded the ranks of the Border Patrol or any other immigration or border-security agency. His orders haven't yet changed the way the Border Patrol operates and so far there is no evidence that more people are being deported. The wall he's promised to build isn't up.

The number of border arrests is the primary measure of the flow of illegal immigration at the border, though an imperfect one. If fewer people are arrested, that's taken to mean fewer people are trying. Over recent decades, presidents have tried to have it both ways. They cite low arrest numbers to illustrate how their policies are dissuading people from crossing illegally. When arrest numbers are high, they say that's because they're being aggressive in enforcing the border.

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TRUMP: Speaking of the appeals court that on Wednesday overturned his latest action limiting immigration from six Muslim-majority countries, "That 9th Circuit — you have to see. Take a look at how many times they have been overturned with their terrible decisions. Take a look."

THE FACTS: Other appeals courts have seen their decisions overturned at a higher rate than the 9th Circuit.

In the most recent full term, the Supreme Court reversed eight of the 11 cases it heard from the San Francisco-based court. But the Atlanta-based 11th Circuit went 0 for 3 — that is, the Supreme Court reversed all three cases it heard from there. And over the past five years, five federal appeals courts were reversed at a higher rate than the 9th Circuit.

The 9th Circuit is by far the largest of the 13 federal courts of appeals. In raw numbers, more cases are heard and reversed from the 9th Circuit year in and year out. But as a percentage of cases the Supreme Court hears, the liberal-leaning circuit fares somewhat better, according to statistical compilations by the legal website Scotusblog. The very act of the Supreme Court's agreeing to hear a case means the odds are it will be overturned; the high court reverses about two-thirds of the cases it hears.

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TRUMP: "Even liberal democratic lawyer Alan Dershowitz, good lawyer, just said that we would win this case before the Supreme Court of the United States."

THE FACTS: Not exactly. Dershowitz predicted Trump would win a Supreme Court showdown over his immigration action if the court focuses heavily on the law that gives him broad authority on the matter. If the court takes Trump's campaign statements into account, though, Dershowitz told CNN, "he will lose."

Many experts think the case would be close because the president does have a lot of leeway in immigration. But if a policy is seen as having a religious test, that could run afoul of the First Amendment in the eyes of the justices. In the campaign, Trump openly called for keeping Muslim visitors out of the country. As president, his executive action is not explicitly against Muslims but would apply to people coming from six countries with mainly Muslim populations.

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TRUMP: Speaking of the request in his new budget for a $54 billion increase for the Pentagon, "Our budget calls for one of the single largest increases in defense spending history in this country."

THE FACTS: Trump's proposed increase, 10 percent higher than the Defense Department's current budget, is large, but a long way from the highest boost ever. In just the past 40 years, there have been eight years with larger increases in percentage terms than the one he's now proposing.

In the early 1980s, for example, defense spending was increased dramatically as the Cold War with the Soviet Union intensified. The 1981 Pentagon budget saw a nearly 25 percent increase.

And the proposed expansion pales in comparison with earlier times. Military spending consumed 43 percent of the economy in 1944, during World War II, and 15 percent in 1952, during the Korean War. It was 3.3 percent in 2015, says the World Bank.

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TRUMP: "I've already authorized the construction of the long-stalled and delayed Keystone and Dakota Access pipeline. I've also directed that new pipelines must be constructed with American steel. They want to build them here, they use our steel. We believe in two simple rules. Buy American and hire American."

THE FACTS: His executive action calls for U.S. steel and pipes to be used "to the maximum extent possible and to the extent permitted by law." With all that wiggle room, it's not a guarantee of U.S. content. It's also not the final word on the matter — the memorandum gives the commerce secretary until July to deliver a plan supporting the initiative.

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TRUMP: "We are going to repeal and replace horrible, disastrous Obamacare. If we leave Obamacare in place, millions and millions of people will be forced off their plans" as insurers flee the market. "It's a catastrophic situation. And there's nothing to compare anything to because Obamacare won't be around for a year or two. It's — it's gone."

THE FACTS: President Barack Obama's health care law has problems, including premium increases and decisions by some insurers to leave the marketplace. But Trump's dire characterization is overblown in the eyes of many, including the Congressional Budget Office, which this week described the market for individual policies in most places as "stable." It said the market also would be likely to remain stable under the proposed GOP replacement legislation.

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Associated Press writers Mark Sherman and Jim Drinkard contributed to this report.

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Find all AP Fact Checks at http://apne.ws/2kbx8bd

EDITOR'S NOTE _ A look at the veracity of claims by political figures