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The phrase "asserted that if a" is correct and usable in written English.
It can be used when introducing a conditional statement or hypothesis in a discussion or argument.
Example: "The researcher asserted that if a new treatment were implemented, patient outcomes would improve significantly."
Alternatives: "claimed that should a" or "stated that if a".
Exact(4)
The statement asserted "that if a person suffers from a delusional disorder, he or she may pass a polygraph test".
Following in the tradition of Paley (1802) from two centuries ago, it is sometimes asserted that if a natural explanation is unavailable to account for an observation, then the only alternative is to assume a supernatural one.
Most commentators have asserted that if a new round of competitive devaluation occurs it would be harmful for the global economy.
(Midwife 6) Midwives asserted that if a few immigrant women and their partners used family planning methods, they would serve as an example within their close social circle.
Similar(56)
The popular satirical blog Stuff White People Like asserts that "if you find yourself in a situation where a white person is talking about a marathon, you must be impressed or you will lose favor with them immediately".
An excerpt from the opening monologue from the hit television show, The A-Team, asserted that "If you have a problem, if no one else can help and if you can find them....maybe you can hire...The A-Team". Leaders across the higher education landscape, specifically Historically Black Colleges and Universities (HBCUs) are under more pressure than ever to do more with less.
John Wycliffe, a philosopher who sponsored the first English translation in 1382, asserted that if there were "a hundred popes" and if "all the friars turned to cardinals," they would still have no more authority than Scripture itself.
A few months after taking office in 2015, he led other Republicans in writing to the Iranian legislature asserting that if a Republican won the 2016 presidential campaign, he would invalidate the Obama administration's nuclear pact with Tehran.
The proof is based on an intermediate result that asserts that if A is an operator on a reflexive real Banach space of dimension greater than one, and there exist non-zero vectors, u in the space and v in the dual space, such that {〈Anu, v〉}∞n=0 is a moment sequence of a finite positive Borel measure on a bounded interval on the real line, then A has a nontrivial invariant subspace.
It asserts that if a country raises taxes and expenditures by the same amount in a time of high unemployment, and if monetary policy is accommodating, the national income grows by exactly the amount of the tax, so that after-tax income is unchanged.
Additional talk on Nov. 14, 2014, 11 45 AM, Room 232: "Avi Wigderson: Points, Lines and Ranks of design matrices": Abstract: The Sylvester-Gallai theorem in Euclidean geometry asserts that if a set of points has the property that every line through two of them contains a third point (such lines are called "special"), then they must all be on the same line, namely, 1-dimensional.
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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