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(TMZ) - Nick Cannon beat Mariah Carey to the courthouse ... TMZ has learned he has quietly filed for divorce.

The timing is interesting. TMZ found out Nick filed papers December 12. The date is relevant because on December 3, Mariah showed up 3 hours late to tape a segment for the NBC tree-lighting special.  

At the time, TMZ reported that Mariah was on the phone with her lawyers going over the terms of her property settlement. That syncs up with Nick filing papers a week later, after they hashed out a deal.

Short story ... Mariah has completely detached Nick from her new, very lucrative deal in Vegas.

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