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The phrase "have proven that" is correct and can be used in written English.
It is typically used in sentence structures where the subject has performed an action that has been verified or demonstrated to be true. Example: Many scientific studies have proven that regular exercise can improve overall health and reduce the risk of chronic diseases.
Exact(60)
Events have proven that wrong.
In summary, we have proven that has a fixed point.
Hence we have proven that has an upper bound in.
The banks have proven that point again and again.
The Panthers have proven that.
These last two games have proven that.
"We have proven that over the years".
We have proven that to date.
Sides have proven that you can chase 400-plus successfully".
I have proven that I could do better than youths".
"We have proven that we are actively fighting against corruption.
More suggestions(20)
have served that
have professed that
have corroborated that
have presented that
have reported that
have validated that
have provided that
have approved that
have perceived that
have evaluated that
have illustrated that
have developed that
have prepared that
have discovered that
have suggested that
have derived that
have characterized that
have reconfirmed that
have observed that
have substantiated that
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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