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

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The distance between `λ _, a` and `λ _, b` is less than the distance between `a` and `b`. --- [![Open in Gitpod](https://gitpod.io/button/open-in-gitpod.svg)](https://gitpod.io/from-referrer/)

awaiting-review
t-topology

Add `function.extend_apply_of_unique` which allows to rewrite `function.extend f g e (f a) = g a` not only when `f` is injective, what `function.extend_apply` does, but when `f a = f...

enhancement
awaiting-review

Version of `exists_seq_strict_mono_tendsto`/`exists_seq_strict_anti_tendsto` strengthened to `nhds_within`. --- [![Open in Gitpod](https://gitpod.io/button/open-in-gitpod.svg)](https://gitpod.io/from-referrer/)

easy
awaiting-review
t-topology
t-algebra
t-order

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

awaiting-review

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

awaiting-review
t-meta
t-algebra
t-order

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

easy
awaiting-review
t-order

We prove that any event in the tail σ-algebra of an independent sequence of sub-σ-algebras has probability 0 or 1. --- - [x] depends on: #16759 [![Open in Gitpod](https://gitpod.io/button/open-in-gitpod.svg)](https://gitpod.io/from-referrer/)

awaiting-review
t-measure-probability

A few lemmas about emetric spaces and `nhds_within`. --- Note, I don't need those lemmas. I just found myself writing them before figuring out another approach. [![Open in Gitpod](https://gitpod.io/button/open-in-gitpod.svg)](https://gitpod.io/from-referrer/)

awaiting-review
t-topology

We define the finite adèle ring of a Dedekind domain and show that it is a commutative ring. --- [![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/)

WIP
awaiting-CI
t-measure-probability