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The phrase "able to prove this" is correct and usable in written English.
It can be used when discussing the capability to demonstrate or establish the truth of a statement or claim.
Example: "The researcher was confident that she was able to prove this with her latest findings."
Alternatives: "capable of demonstrating this" or "able to substantiate this".
Exact(26)
No one has been able to prove this incontrovertibly, but there is some interesting evidence, both pro and con.
They worry, with good reason, that they won't be able to prove this place is theirs, if someone 'high ranking' tries to take it.
Nobody has ever been able to prove this, however, and Gunvor has always denied it, which makes the US Treasury statement on the sanctions remarkably forthright.
Since I was able to prove this was a way to do it and they liked what they got, I was able to keep doing it that way.
When the Democrats gained access to the FISA request and issued a competing memo, however, they were able to prove this was not so.
With the in vitro experimental platforms of parquet tissues and heart-on-a-chip devices, we were able to prove this hypothesis for both systolic and diastolic stresses.
Similar(34)
When they were able to prove the efficacy of this approach, the municipal government later took it on.
Now we are able to prove the main result of this section.
Now, we are able to prove the following main result of this section.
The government proposes that, in future, he will have to be able to prove that this belief was "reasonable".
"But they don't prove that Sullivan and Myers ever acted with criminal intent, an essential element we doubt the government will ever be able to prove in this case".
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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