leanprover-community / leanprover-community/mathlib4

clean up completely normal results to use `SeparatedNhds`

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@StevenClontz is already working on this.

Since Jun 27, 2024.

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Description

Sticking a pin in a chore I will follow up #13817 with.

@JADekker:

The changes look good to me, but I have the feeling that most proofs that you touched seem to become longer after this change (now requiring some form of separatedNhds_iff_disjoint), which makes me wonder if these proofs can be simplified if we also use SeparatedNhds in another place, or if it may be more natural to formulate both definitions in terms of Disjoint instead. Any thoughts?

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