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Tekashi 6ix9ine deserves a much lighter prison sentence due to his cooperation -- AKA snitching -- according to federal prosecutors who are officially asking the judge for leniency.

In legal docs, obtained by TMZ ... the U.S. Attorney in the Southern District of New York lays out the reasons for a reduced sentence for the rapper. They say his assistance was "incredibly significant and extremely useful" in prosecuting and convicting 2 members of the Nine Trey Bloods.

Even the feds acknowledge Tekashi's testimony in open court put a target on his back and endangered his family. In the docs, prosecutors say, "There's no question that the defendant's life will never be the same because of his cooperation in this case." They add he and his family will need "extra safety precautions" at all times to avoid a revenge attack.

The feds say 6ix9ine walked them through his social media posts to provide context for the criminal actions of the gang -- which they say the defendants, Anthony "Harv" Ellison and Aljermiah Mack, claimed was all a hoax to promote Tekashi's music. They say his testimony convinced the jury otherwise.

As we reported ... Tekashi copped a plea deal after pleading guilty to racketeering, firearms offenses, conspiracy, narcotics trafficking and other crimes. 6ix9ine agreed to be a cooperating witness, and without that would be facing a mandatory minimum sentence of 47 years in prison.