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The phrase "asserted that with" is correct and usable in written English.
It can be used when introducing a statement or claim that includes a specific condition or context.
Example: "The researcher asserted that with the new data, the hypothesis could be validated."
Alternatives: "claimed that with" or "stated that with".
Exact(9)
After Beijing, a groundswell of public opinion asserted that, with the UK plunging into recession, the Games were – at £9.3bn – simply unaffordable.
BUT he asserted that with G.E. turning a profit of $14 billion, or $45,000 a worker, last year, the economic facts don't justify raising health co-payments an estimated $200 to $400 a year a worker.
Mr. Zhu did not say the crash was intentional, but he asserted that with its sudden turn, the plane had violated international rules as well as a military agreement between the United States and China concerning safety in aerial encounters.
During his hour-long televised press conference, where he was surrounded by roughly 20 current and former students, according to press reports, Hwang also asserted that with enough eggs, he has the technology to create stem cell lines matched to patients.
I asserted that, with so many misgivings, I'd feel uncomfortable buying a house now, too.
Inspiration--Stoddart was inspired by a radio program that asserted that with vision and commitment, one person can do the work of 1000 people.
Similar(51)
Over all, "African Forms" asserts that with or without a specific word for art, few African peoples neglected the expressive opportunities implicit in the creation of handmade objects, no matter how basic.
Russia asserts that, with this threat hanging over its head, Vladimir Putin has no choice but to create a mobilized society that represses opposition, places the economy on a quasi-war footing, and produces military power irrespective of cost.
for all First, we assert that is strictly contractive with constant on.
Theorem 8 asserts that assumption (u0) together with Corollary 2 provides the uniqueness of common fixed point.
And they assert that with $100 billion in sales generated from calls to consumers last year, many Americans clearly respond favorably to phone pitches.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com