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The states trying to stop the $26.5 billion merger between T-Mobile and Sprint say their case is simple: Reducing the number of nationwide wireless carriers from four to three reduces competition and is "under well-established law, presumptively illegal." That's the gist of the 30-page court document filed by New York Attorney General Letitia James and California Attorney General Xavier Becerra on Tuesday evening.

The state attorneys general are leading the legal battle, which will officially kick off before a federal judge in the US District Court for the Southern District of New York on Dec. 9. The main argument the 13 states and the District of Columbia will make in court is that combining T-Mobile and Sprint will reduce competition and violate the federal Clayton Act. This will ultimately lead to higher prices for consumers and fewer choices.

Specifically, they argue that if the merger is allowed AT&T, Verizon and the new T-Mobile would be more likely to coordinate their behavior, leaving consumers worse off.

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"Competition between these four rivals, and especially between Sprint and T-Mobile, has resulted in enormous benefits for consumers, including lower prices and innovative features like no-contract plans and unlimited data plans," the states say in their court filing. "Unsurprisingly, this 'four to three' merger would dramatically increase market concentration in an already highly concentrated industry."

The filing comes as T-Mobile and Sprint peel off some states that joined the AGs' lawsuit earlier in the year. On Monday, the wireless carriers flipped one of the biggest states yet: Texas. Texas Attorney General Ken Paxton announced he had "reached a settlement with T-Mobile resolving the state's antitrust claims against the proposed merger" and is no longer looking to block the deal. Nevada Attorney General Aaron Ford also announced his own deal later Monday.

These states follow others, such as Colorado and Mississippi, that have also pulled out of the litigation after agreeing to their own settlements. But representatives from the New York and California AG offices say that their fight will continue regardless of the number of states that remain as part of the litigation.

The Federal Communications Commission and the Justice Department have each signed off on the merger. But their approvals come with conditions.

As part of its deal with the FCC, the companies agreed to divest Sprint's prepaid wireless brand Boost Mobile and to not raise prices on services for three years. The DOJ, like the states suing to stop the merger, also concluded the deal is anticompetitive. But in a separate settlement, Dish agreed to acquire Sprint's prepaid businesses and spectrum for $5 billion, as well as get access to T-Mobile's network as part of a settlement with the wireless carriers. The deal would set up Dish to be the fourth nationwide wireless carrier, preserving the government's goal of having four competitors in the market.

But the states, which filed their lawsuit in June, say these remedies are not enough. They argue the DOJ's proposal to prop up Dish as a fourth competitor is too risky. The satellite TV provider has no network, no experience operating a wireless network and no retail stores.

"The court should not permit defendants to proceed with an anticompetitive merger based on the hope that Dish will one day grow into a viable wireless company equal to a competitor that already exists today," the states argue in their filing. "If that hope proves unfounded, the cost of failure will not be borne by Defendants -- who would stand to benefit from that failure -- but by consumers who will be left with less competition and higher prices."

In the end, the states argue the only thing that has proven to benefit consumers in terms of "lower prices and higher quality products" is competition.

For their part, T-Mobile and Sprint argue that combining the No. 3 and No. 4 national operators in the US will allow them to survive against competition from AT&T and Verizon, as well as competition from cable operators entertaining the wireless market and online platforms, like Google and Facebook, which are increasingly competing with telecom providers in new markets. The companies argue that the merger is necessary to speed up deployment of next-generation wireless networks for 5G.

But the states say these arguments also "fall flat" as "they cannot defeat the presumption that this merger is anticompetitive."