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Lean 3's obsolete mathematical components library: please use mathlib4

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--- - [x] depends on: #15855 - [x] depends on: #15856 - [ ] depends on: #16047 [![Open in Gitpod](https://gitpod.io/button/open-in-gitpod.svg)](https://gitpod.io/from-referrer/)

awaiting-review
blocked-by-other-PR
t-algebra

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awaiting-review
t-algebra

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awaiting-review
t-algebra

This lemma is extracted from #15984, as suggested by the code-review. --- [![Open in Gitpod](https://gitpod.io/button/open-in-gitpod.svg)](https://gitpod.io/from-referrer/)

awaiting-review

--- [![Open in Gitpod](https://gitpod.io/button/open-in-gitpod.svg)](https://gitpod.io/from-referrer/)

awaiting-review
t-category-theory

#### Background The `simp` tactic used to [look for subsingleton instances excessively](https://leanprover.zulipchat.com/#narrow/stream/144837-PR-reviews/topic/.235672.20breaks.20timeout/near/223034551), so every subsingleton/unique instances added to mathlib could slow down `simp` performance; in fact, removing some subsingleton instances...

awaiting-review

I just open this to track my progress and let everyone know how I plan to do this. This is very tedious, so if anyone wants to help I would...

RFC
t-algebra

Orthogonality of characters for representations of finite groups - [ ] depends on: #13789 - [ ] depends on: #13794 --- [![Open in Gitpod](https://gitpod.io/button/open-in-gitpod.svg)](https://gitpod.io/from-referrer/)

blocked-by-other-PR

Local version: an analytic function is either locally zero, or nonzero in a punctured neighborhood. --- Second take on #14382 but starting from scratch. [![Open in Gitpod](https://gitpod.io/button/open-in-gitpod.svg)](https://gitpod.io/from-referrer/)

awaiting-review

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easy
awaiting-review
t-category-theory