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I am struggling to decide which sentence is correct (maybe they are both correct?) and I would appreciate any comments.

The sentences I am trying to decide between are

The following result was the key estimate to establishing the main result in ...

The following result was the key estimate in establishing the main result in ...

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2 Answers 2

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The first sentence would be better as

The following result was the key estimate to establish the main result in ...

The second sentence would be better as

The following result was the key estimate for establishing the main result in ...

I can't quote sources, this is my supposition as a native BrE speaker.

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You could also use adjectival key:

The following estimate was key to establishing the main result in ...

No article.

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  • Isn't key a noun here? It is an adjective in the question, or if you insist "adjectival".
    – Weather Vane
    Commented Sep 19, 2018 at 21:12
  • @Weather Vane: key is a noun in your examples but here it is an adjective, a synonym of "crucial".
    – TimR
    Commented Sep 19, 2018 at 21:43
  • No, key in my answer is an adjective. It qualifies the noun "estimate".
    – Weather Vane
    Commented Sep 19, 2018 at 21:44
  • You're right. I was going from memory. I though you had written "the key to establish". But it's an adjective in my example.
    – TimR
    Commented Sep 19, 2018 at 21:46
  • Thank you for the eddication, I never heard the word adjectival in my whole long life.
    – Weather Vane
    Commented Sep 19, 2018 at 21:48

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