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The phrase "also prove that in" is correct and usable in written English.
It can be used when discussing evidence or arguments that support a particular point or claim within a larger context.
Example: "The study not only highlights the benefits of exercise but also proves that in the long term, it can significantly improve mental health."
Alternatives: "further demonstrate that in" or "additionally show that in".
Exact(7)
We also prove that "in the nonrelativistic limit" ω→m, the point eigenvalues can only accumulate to 0 and ±2mi.
The results also prove that in problem posing, learning an example through a production task is effective.
One can also prove that in that construction the subgroup will be pro-finitely closed only if the modular machine is very easy.
We also prove that, in Orlicz-Bochner function spaces generated by locally uniform nonsquare Banach space, nonsquareness and locally uniform nonsquareness are equivalent.
We also prove that in the defocusing case the norm of the solution grows at most polynomially-in-time while in the focusing case it grows exponentially-in-time.
Finally, using a different argument, we also prove that in the case p= 1, and for arbitrary weights w∈B1, ∥w∥B1 is the best constant in the corresponding inequality.
Similar(53)
We also prove that if the solution exists globally in time, it exhibits some asymptotic behavior.
He not only "stood up to the system," as he put it, but he also proved that Russians could thrive in the American game.
We also proved that SATB1 is important in the establishment of active loop formation between ε-promoter and regulatory elements.
But it also proves that in today's world there is no alternative to globalization as a motor for growth and employment, thus fostering prosperity worldwide.
This also proves that in this paper, the definition of the crisis status is appropriate.
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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