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Republican presidential candidate Ted Cruz, a U.S. senator from Texas, greets supporters in Milwaukee after his Wisconsin victory, April 5, 2016. Scott Olson/Getty Images

U.S. Sen. Ted Cruz of Texas was declared the winner of the Wisconsin primary Tuesday evening, posting a significant victory over national front-runner Donald Trump and Ohio Gov. John Kasich. The trio will next compete in Colorado on Saturday and in New York on April 19.

The results in the Badger State showed that Trump may have good reason to worry that he won’t reach the delegate threshold necessary to become the Republican nominee outright before the party's convention in Cleveland on July 18-21. It's mathematically unlikely — essentially impossible — for Cruz or Kasich to surpass Trump and reach that threshold.

You can watch a live stream of post-vote speeches from the candidates here.

The race for the nomination has been the source of increasing tension within the Republican Party lately, as some establishment figures have banded together to try to bring Trump’s candidacy down. Trump, who leads in the delegate count, needs to secure 1,237 delegates to ensure a nomination victory, and a behind-the-scenes effort to undermine his candidacy is underway. Cruz and other Republicans are hoping to choose delegates for the summer convention who might switch their allegiance away from Trump should multiple votes take place to choose a nominee.

If the convention does turn into a floor fight with rotating delegate support, anybody could theoretically become the nominee, regardless of who had the most delegates to begin with (or even had any at all).

Heading into Tuesday’s vote, Cruz held an edge in polls of Wisconsin primary voters. An average of polls compiled by Real Clear Politics showed him 4.7 points ahead of the real estate mogul with 39.2 percent of the vote, compared to 34.5 percent for Trump. Ohio Gov. John Kasich trailed quite a bit with just 20 percent of the vote. Kasich was not campaigning in Wisconsin on Tuesday and had previously left to focus on delegate-rich New York, where he hopes to perform well.

After Cruz declared victory, the Trump campaign posted its response.