The attorneys argued that the judge's order to Uber to force Mr. Levandowski to comply with the ruling or face termination violates decades of court precedent.
Uber, meanwhile, has not denied that Levandowski took Waymo documents, but the company insists that it hasn't used any Waymo technology in its cars. Levandowski left Google, started an automous truck company, and then was bought by Uber, and Waymo claims the truck company was just a sham for Uber to steal its tech.
An Uber spokesperson did not immediately comment when contacted by Business Insider.
Uber general counsel, Salle Yoo, wrote in a letter to Levandowski: "If you do not agree to comply with all of the requirements set forth herein, or if you fail to comply in a material manner, then Uber will take adverse employment action against you, which may include termination of your employment".More news: Trump lashes out over special counsel appointment
A few days ago, U.S. District Judge William Alsup issued an injunction against Uber, ordering the company to keep Levandowski away from working on Uber's self-driving auto, to prevent him and other employees to see Waymo's documents and return them to Waymo by May 31st. A preliminary injunction to hinder Uber's self-driving technology development during the case has been imposed, but it's unclear to what extent.
Uber's reasons for the threat are necessary in order for the ride sharing app to avoid being in contempt of court.
Uber sent Mr. Levandowski a four-page letter Monday saying he must comply with a court order issued last week that requires him to return 14,000 allegedly stolen files and an extensive accounting of any Uber employees' handling or knowledge of the files.
Levandowski's lawyers have argued that such a move would be unconstitutional as government action is forcing him to abandon his fifth amendment rights enshrined in the U.S. constitution.More news: NY driver suspect Richard Rojas was 'hearing voices'
The court order forcing Uber to make the demand of him is "an act by the judicial branch of our federal government compelling an individual to choose between preserving his livelihood and preserving his constitutional rights".
For Uber, the bad news is far from over.
Judge William Alsup, who is overseeing the trial, has also previously referred the case to the USA attorney's office for a potential criminal investigation.More news: Mercedes home storage batteries coming to the US
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