Is there a built-in tactic that would reduce fun x => f x to f or the other way around? cbv doesn’t do that. I guess you can rewrite eta, where eta is the lemma below, but maybe I’m missing something even simpler.

Lemma eta {A B} (f : A -> B) : (fun x => f x) = f.
Proof.
cbv. (* I would like to see f = f now *)
reflexivity. (* this proof works in any case, but sometimes syntax matters (rewriting, match...) *)
Qed.

I thought there were situations where fun x => f x is directly transformed into f but I can’t seem to find an example of that.