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"have already shown" is a correct and usable phrase in written English
You can use it when you want to emphasize that something has already been proven or exhibited. For example: "These documents have already shown that the suspect is guilty of fraud."
Exact(57)
The Mets have already shown their naivete.
But they have already shown that they will.
The Millennials have already shown themselves to be big spenders.
They have already shown a lot of patience.
The changes have already shown up in the bottom line.
Indeed, some venture firms' investments have already shown paper losses.
More than double that number have already shown up.
Venezuela's voters have already shown that they can see through such manipulations.
The Giants have already shown confidence in Holmes, who is 24.
Mr. Giuliani and Mr. McCain have already shown the potential of this line of attack.
Researchers have already shown that certain fears might be inherited through generations, at least in animals.
More suggestions(25)
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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