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

Thank you.

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 ...