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The phrase "should be proved that" is correct and can be used in written English.
It is typically used when discussing the need for something to be proven or demonstrated. Here is an example: "It should be proved that the new policy will effectively address the company's financial challenges before it is implemented."
Exact(2)
If it should be proved that they had never seen the inside of a hospital they could be conducted to Tunis; but in this case France would have to undertake to keep them prisoners.
In order to use Lemma 2.6, it should be proved that limsup_{n toinfty}frac{d( z_{n-1}, z_{n})}{alpha_{n} (1-k)} le0.
Similar(56)
It should be proven that it is unattractive for customers to switch to the inevitable copycats.
Lawyers who read the judicial interpretation said that in order for somebody to be punished, it should be proven that they knew the rumor was false and that they distributed it with malice.
Furthermore, it should be proven that the genetic signature is solely responsible for the increased IFN production by Th cells.
It is estimated that about 90% could be sterilized in the solid phase; however, it should be proved for each drug that ionizing radiation does not change any of its physicochemical properties (6).
Claiming that software competition is uniquely "dynamic," the company suggests a new rule: that monopoly power in the software industry should be proven directly, that is, by examining a company's actual behavior to determine if it reveals the existence of monopoly power.
This poses a political problem for the Lannister clan if ever this should be proven, but that's probably difficult in a mythical land with no DNA labs.
As we enter a wintry blockbuster season that has Jennifer Lawrence taking charge of another Hunger Games and newcomer Daisy Ridley becoming the young lead of the next Star Wars film, it should theoretically be proved that a female heroine can indeed attract a blockbuster audience.
New findings should be proven by experiments and debates that can be performed on the basis of evidence.
Third, our survey design did not facilitate the assessment of test-retest reliability that should be proven in further investigations.
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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