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The context is actually mathematics, and providing a proof for a particular fact.

If one says "... which was established by Smith." does this have the connotation that Smith was the first to do it?

Similarly, if we say "... whose proof establishes that..." does it mean it was the first proof to do so?

My personal interpretation is that in the first sentence it implies he was the first, but not for the second sentence. What is the correct version in English?

(Also, if it had already been established, wouldn't you say reestablish for the second time?)

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In the context of things such as mathematical proofs, once something has been accepted as an accurate and true proof it exists as a true statement forever. Therefore, I would suggest that both of your sentences above would imply that the proof mentioned was indeed the first one because any proofs which came afterwards (presumably, simpler or more refined versions, otherwise why are they re-proving it...) wouldn't establish something as a fact, but merely improve upon the method in which it was originally established.

With regard to later proofs, an appropriate verb would depend somewhat on context. Something like reestablish would be possible only in a situation where the original 'establishment' of the proof had been lost, called into question, or otherwise eroded. You could also use confirm in a similar situation where the original proof that established it was in doubt.

If the original fact was never in doubt, but the proof itself was merely being improved upon, I wouldn't indicate that the author had anything to do with the fact, but rather with the proof. I.e. rather than

... whose proof reestablished that ...

I would go with

... whose refined proof of ....

That is, since he didn't have any affect on whether people knew something to be true or not, you want to focus on how he had improved the proof itself.

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Very good, thank you. –  user6751 Oct 12 '11 at 15:10
    
You could just say "which was reproved by Smith". –  Peter Shor Oct 15 '11 at 4:32

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