I have the following sentence:
Lemma 2 is a bit overkill for proving Lemma 3
I want to show that the proof of Lemma 3 hasn't used the full strength of Lemma 2. But I feel uncomfortable for above sentence. Any suggestions?
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"Overkill" and "a bit" are going in opposite directions:
It was a bit of overkill to swat that fly with a hammer.
That's admissible if you want to have an ironic tone. But if you don't want to introduce such a tone, a less casual phrase that avoids the irony would be
Lemma 2 is ample proof of lemma 3.
Your example is something that would probably be spoken
P1: What do you think about using Lemma2 to prove Lemma 3?
P2: That's a bit overkill
meaning that it is excessive. Using the idiom a bit makes it informal.
The meaning implies more than just the full strength not being used, it's saying that not even a small fraction of the strength is necessary.