ST. PAUL — Attorneys for both sides rested their cases Friday in former Minnesota Gov. Jesse Ventura’s defamation lawsuit against the estate of “American Sniper” author Chris Kyle.

Closing arguments are scheduled for Tuesday. On Monday the two sides will meet with the federal judge overseeing the trial to work out the instructions he will give to the jury.

Ventura’s lawsuit claims that Kyle, who died last year in Texas, ruined his reputation by writing in his 2012 best-selling book that he punched a man he called “Scruff Face” at a California bar in 2006 after the man said U.S. Navy SEALs “deserve to lose a few.” Kyle later identified the man as Ventura.

Ventura testified that he was not involved in a fight with Kyle. Both men were former SEALs.

Ventura is pursuing the lawsuit against Kyle’s estate. Attorneys for Kyle’s widow, Taya Kyle, presented several witnesses including a former SEAL who testified he saw the punch.

Jurors also saw a video deposition that Chris Kyle gave in November 2012. Near the start, Kyle told Ventura’s attorney, David Bradley Olson, that he wasn’t concerned about the lawsuit. But later on, Kyle, who’s regarded as the deadliest sniper in U.S. military history, acknowledged he was indeed afraid of being sued.

Legal experts have said Ventura has to prove that Kyle made up the story and profited from it, or at least acted with reckless disregard for the truth, and that Ventura’s reputation was hurt as a result.

Kyle’s book has made more than $3 million in royalties, and the judge in the case has ruled that profits from an upcoming movie could be subject to damages, too.