House Democrats on Tuesday accused former President Donald Trump of a “betrayal of historic proportions” and argued that his actions leading up to the deadly attack on the U.S. Capitol should permanently bar him from office, even as Trump’s lawyers rejected that assertion and pressed their claim that his impeachment trial is unconstitutional.

Those positions, laid out in the first formal filings from Trump and the nine Democratic House impeachment managers who will prosecute him, offered the most detailed distillation yet of the case both sides intend to present as the proceedings get underway next week.

With lies about a stolen election, the Democrats wrote, Trump “summoned a mob to Washington, exhorted them into a frenzy, and aimed them like a loaded cannon down Pennsylvania Avenue.” They added in their 80-page filing: “If provoking an insurrectionary riot against a Joint Session of Congress after losing an election is not an impeachable offense, it is hard to imagine what would be.”

Trump’s brief, signed by his new lawyer and former Montgomery County District Attorney Bruce L. Castor Jr. in a sweeping blue pen, hewed closely to a strategy endorsed by Republican senators: focusing on questions of constitutionality and whether his remarks at the Jan. 6 rally that preceded the Capitol attack were protected speech.

It gave only a passing nod to the strategy Trump is said to favor and which reportedly led him to part ways with his previous legal team: doubling down on his widely disproven claims of a stolen election.

Castor and co-counsel David Schoen, an Alabama criminal defense lawyer, asserted in the filing there was “insufficient evidence” to conclude the former president’s fraud claims were inaccurate — a conclusion disputed by the nation’s top law enforcement officials, election administrators in both parties, courts, and legal experts.

The Trump team also attempted to recast Trump’s sweeping and false fraud claims as concerns about election procedure.

» READ MORE: Fact-checking false claims about Pennsylvania’s presidential election by Trump and his allies

The bulk of the case they laid out, though, centered on what is shaping up to be one of the most significant hurdles Democrats face in trying to persuade Republicans to convict Trump — the question of the trial’s constitutionality.

“The Senate of the United States lacks jurisdiction over the 45th President because he holds no public office from which he can be removed,” Trump’s lawyers wrote, echoing the argument 45 out of 50 GOP senators embraced last week in seeking to block the trial.

The House impeachment managers, including Rep. Madeleine Dean (D., Pa.), aimed to chip away at that argument by pointing to legal scholars who have said it is within the Senate’s right to try a former president.

“There is no ‘January Exception’ to impeachment or any other provision of the Constitution,” their brief said. “A president must answer comprehensively for his conduct in office from his first day in office through his last.”

They cited two instances in which former officials — a senator and a secretary of war — were tried on impeachment charges after they had been expelled or resigned. The latest example dated back to the 1870s.

More important, they argued, Trump’s actions were so unprecedented that they require a swift and unquestionable response.

“The nation cannot simply ‘move on’ from presidential incitement of insurrection,” they wrote. “If the Senate does not try President Trump (and convict him) it risks declaring to all future presidents that there will be no consequences, no accountability.”

The chain of events the Democrats laid out started well before Trump left his post or Jan. 6, the day of the Capitol attack. By then, Trump had spent months seeding the air with baseless claims of fraud, they wrote, even as his legal challenges almost universally failed.

He urged his supporters to gather in Washington the day Congress was to formally count the votes in Joe Biden’s electoral victory, with the Twitter exhortation “will be wild!” even amid widespread warnings that threats of violence were rising in response. And during his 50-minute speech he exhorted the crowd to “fight like hell” because “if you don’t fight like hell you’re not going to have a country anymore,” the Democrats noted.

They pointed to videos showing that after he said “you’ll never take back our country with weakness,” and that “you have to show strength,” supporters shouted “take the Capitol right now!” and “invade the Capitol building!”

» READ MORE: Fact-checking Trump’s false claims about Pa.’s election before his supporters attacked the Capitol

“President Trump created a powder keg on January 6. Hundreds were prepared for violence at his direction,” the Democrats wrote. “All they needed to hear was that their President needed them to ‘fight like hell.’ All they needed was for President Trump to strike a match.”

They also sought to dispatch quickly with the claim that Trump’s remarks were protected by the First Amendment, arguing that it was drafted to “protect private citizens from the government.”

“It does not protect government officials from accountability of their own abuses in office,” the brief stated.

Castor denied that Trump’s calls to “fight like hell” had anything to do with what happened after and noted Trump also urged supporters to protest “peacefully,” a point some Republicans have pointed to as evidence he did not provoke violence.

The comment “was clearly about the need to fight for election security in general,” he wrote, while implying that the effort to prosecute him for it was just vindictive: “Political hatred has no place in the administration of justice,” the Trump team wrote.

Before even starting their arguments, their filing began with a typo, perhaps reflecting the rushed nature of the work. It addressed the brief to “Members of the Unites States Senate.”

» READ MORE: Donald Trump becomes the first president in American history to be impeached twice

Democrats face steep odds of making Trump the first president in history to be convicted of high crimes and misdemeanors: Nearly every Republican senator voted last week to block the trial from even happening on procedural grounds. Democrats will need support from at least 17 GOP senators for the two-thirds vote needed to convict Trump.

The former president’s lawyers are expected to file a more extensive statement of their defense next week before the trial is set to begin Tuesday. Democrats who control the Senate are hoping for a much faster proceeding than the one that saw Trump acquitted last year after his first impeachment. The exact schedule remains unclear, though as long as the case lasts it could slow Biden’s attempt to quickly advance his agenda in his early days in office.

Read the House Democrat’s impeachment brief:

Read Trump’s brief: