The phrase "asserted at that" is not correct and does not convey a clear meaning in written English.
It seems to be an incomplete expression and lacks context for proper usage.
Example: "The findings were asserted at that moment, leading to further investigation."
Alternatives: "stated at that time" or "declared at that point".
Hunt asserted at Leveson that at the time he did not have a full understanding of what a quasi-judicial decision involved.
It asserted at first that the contract could not be honored because it had not been approved by the majority shareholder, said Mark A. Harmon of Bondy & Schloss, a lawyer for Mr. Goldman.
He also asserted at one point that he had found out that a third gun had been found at the scene of Mr. Terry's death, which helped fuel a conspiracy theory about a cover-up by the Federal Bureau of Investigation.
Kim asserted at his trial that he had killed his friend to avert a bloodbath that Park had been planning for his opponents and that only by killing Park could democracy be restored in South Korea.
Mr. Frist also asserted at the time that "for the past 18 years, Jim Sasser has been transplanting your wallets and your pocketbooks to Washington, D.C".
Last Friday, Gen. Richard B. Myers, chairman of the Joint Chiefs of Staff, asserted at the Senate Armed Services Committee that Mr. Bremer's immunity order could not be repealed by the interim government that took office yesterday.
They denied the charge and asserted at the trial that the prosecution's case was "completely unsubstantiated because it never happened".
News International asserted at the time that the practice was limited to a single "rogue reporter", but since new evidence came to light in 2011, three former senior news editors from the News of the World have now pleaded guilty.
To make this mass generalization that is asserted at the beginning of each episode, is to do a disservice to an entire geographical entity.
To the north and east, near Pound Gap, on the Kentucky/Virginia border, another Confederate force, under Gen. Humphrey Marshall, was asserting itself at that important passageway between rebellious Virginia and loyal Kentucky.
