The phrase "assertion that it could" is correct and usable in written English.
It can be used when discussing a claim or statement regarding the possibility of something happening or being true.
Example: "The scientist made an assertion that it could lead to significant advancements in renewable energy."
Alternatives: "claim that it might" or "statement that it could".
Perhaps even more surprising than the town attempting to clamber upmarket is the assertion that it could become a model for sustainable, mass-market tourism.
Judge Collyer said she was "troubled" by the government's assertion that it could kill American citizens it designated as dangerous, with no role for courts to review the decision.
The report also questions the Fed's assertion that it could not wrest concessions from French banks — who held some of the largest contracts — because French law banned them from accepting discounts unless A.I.G. had filed for bankruptcy.
From the outset, local residents had questioned Cyrq's assertion that it could pump geothermal water from thousands of feet down and re-inject it at similar depths without tainting the shallow, freshwater aquifer.
At times, he was one of the Bush administration's most reliable allies in the Senate, notably when it came to the executive branch's assertion that it could block enemy combatants from challenging their detentions in federal court.
In an article by journalist Rachel Donadio published in the New York Review of Books in 2014, Donadio said the suggestion was "more telling about contemporary Italy than about Ferrante's work", before repeating the assertion that it could be Domenico Starnone, Raja's husband, or Raja.
Enron said it was reviewing the "assertion" by Dynegy that it could claim the pipeline.
Since Trump became president, his promise to repeal and replace the Affordable Care Act is nowhere close to being fulfilled, despite his repeated, confident assertions on the campaign trail that it could be done in just a day.
Professor Sir William Wade pointed out more than forty years ago that Dicey never explained how he reconciled his assertions that Westminster could destroy or transfer sovereignty and the proposition that it could not bind future Parliaments.
An earlier version of this post described Sermo as the nation's largest online physician community, an assertion that could not be independently verified.
He said that all the targets were civilian facilities and that "many" civilians had been killed, an assertion that could not be independently verified.
