“He had every right to say to the Ukrainian president — we have two outstanding allegations of massive corruption and you should investigate it,” Giuliani told Cuomo at one point.

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“If the president of the United States said to the president of Ukraine, ‘Investigate the corruption in your country that has a bearing on our 2016 election,’ " he added later, “isn’t that what he’s supposed to do?”

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Presidents have “every right to tell the president of another country, ‘You better straighten out the corruption in your country if you want me to give you a lot of money,’ ” Giuliani insisted.

At that point, it’s not clear whether Giuliani was actually privy to the summary of the Trump-Zelensky conversation made public Wednesday with the release of a rough transcript by the White House. But Trump was certainly familiar with the broad outline of the call, and he picked up Giuliani’s argument a few days later as new details of the interaction continued to emerge in the news.

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“The conversation I had was largely congratulatory,” Trump told reporters. “It was largely corruption — all of the corruption taking place. It was largely the fact that we don’t want our people, like Vice President Biden and his son, creating to the corruption already in the Ukraine.”

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But that’s not true. The release of the rough transcript shows that Giuliani’s estimation and Trump’s assertion that corruption was central to the conversation were false.

In fact, there are precisely zero mentions of corruption in the transcript of the call. There is, as Trump claimed, a brief congratulatory comment, but the call was by no means “largely congratulatory.”

Trump’s contributions to the conversation can be broken down as follows.

Trump offers his congratulations.

He notes U.S. aid to Ukraine, particularly in comparison with that of European countries.

He asks Zelensky for a favor: Dig into a rumor that would undercut the report by former special counsel Robert S. Mueller III and the idea that Russia hacked the Democratic National Committee during the 2016 presidential campaign.

After Zelensky notes that a staff member had spoken with Giuliani, Trump raises the false allegation that Biden pushed to have a Ukrainian prosecutor fired to aid his son Hunter Biden.

Trump promises to have both Giuliani and Attorney General William P. Barr call about the firing of that prosecutor, Viktor Shokin.

Trump reiterates that promise and invites Zelensky to the White House.

While Zelensky promises to move forward on investigations and make “sure to restore the honesty” to Ukraine’s government, Trump mentions only specific issues: the DNC hacking, the Bidens. In speaking to reporters, Giuliani and Trump frame those issues as being inherently about corruption, but that’s like claiming that Morrie Kessler kept asking Henry Hill for his cut of the Lufthansa heist primarily because he wanted to teach a lesson about fulfilling commitments. Trump is not asking Zelensky to address corruption; he’s asking him to look into specific things that aid him personally.

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Speaking to reporters on Sunday, Trump did say that he’d expressed frustration that other countries were not committing resources to Ukraine to the same extent as the United States. In the rough transcript, though, Trump makes that argument in the context of the United States having “been very, very good to Ukraine” despite Ukraine not being “reciprocal necessarily” — right before he asks for a favor.

Asked later that day whether he had mentioned Biden on the call, Trump demurred.

“Well, I don’t even want to mention it,” he replied. “But certainly, I’d have every right to. If there’s corruption and we’re paying lots of money to a country, we don’t want a country that we’re giving massive aid to to be corrupting our system.”

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He did mention Biden, of course. Although he didn’t explicitly suggest that further aid to Ukraine was contingent on Ukraine digging into Biden’s alleged actions, his suggestion that doing so wouldn’t have been problematic does cast the transcript in another light. In tweets, Trump claimed that “NO quid pro quo” was suggested in the Zelensky call. That he mentioned U.S. aid and the need for reciprocity right before asking for the favor of investigating specific cases of what he considers corruption, though, fits with the “don’t want a country that we’re giving massive aid to to be corrupting our system” argument he made Sunday.

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He said something similar on Monday.

“I did not make a statement that ‘you have to do this or I’m not going to give you aid.’ I wouldn’t do that. I wouldn’t do that,” Trump said. “With that being said, what I want is — I want, you know, we’re giving a lot of money away to Ukraine and other places. You want to see a country that’s going to be not corrupt.”

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“I didn’t put any pressure on them whatsoever,” he said later. “You know why? Because they want to do the right thing.”

The Ukrainian government publicly stated that Trump hadn’t pressured Zelensky. But there’s an inherent imbalance at play here, reflected in the rough transcript itself. The United States is far more powerful than Ukraine and provides significant aid to it. Zelensky’s desire to ingratiate himself with Trump is obvious, including a gratuitous mention of having stayed at a Trump Organization property.

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“There is an implicit threat in every demand that a United States president makes of a foreign power,” Sen. Chris Murphy (D-Conn.) told The Washington Post on Monday. “That foreign country knows that if they don’t do it, there are likely to be consequences.”

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Murphy also said that, in his conversations with Zelensky’s team, he got the impression that aid withheld by Trump’s team “to Ukraine … was a consequence for their unwillingness, at the time, to investigate the Bidens.”

On Wednesday morning, before the rough transcript was published, Giuliani appeared on Fox News’s “Fox & Friends.” He claimed that Trump would have been “derelict in his duty” had he not mentioned “corruption” to Zelensky.

Giuliani was asked whether Trump mentioned Biden, a subject that Giuliani has been focused on for months and that came up when he met with an aide to Zelensky in Spain in May.

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“Maybe he didn’t bring it up,” Giuliani said. “Could be possible the president of the Ukraine brought it up.”

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Here’s how “it” — the Biden allegations — came up.

“I will personally tell you,” Zelensky told Trump, according to the rough transcript, “that one of my assistants spoke with Mr. Giuliani just recently and we are hoping very much that Mr. Giuliani will be able to travel to Ukraine and we will meet once he comes to Ukraine. I just wanted to assure you once again that you have nobody but friends around us. I will make sure that I surround myself with the best and most experienced people.”

“I also wanted to tell you that we are friends,” he continued. “We are great friends and you, Mr. President, have friends in our country, so we can continue our strategic partnership. I also plan to surround myself with great people and in addition to that investigation, I guarantee as the President of Ukraine that all the investigations will be done openly and candidly. That I can assure you.”