feat(Data/Tree/Basic): add Membership instance, new notation, rename Tree

[sorrachai]

Summary:

1. [Rename](#CSLib > Splay tree PR: BinaryTree vs Tree @ 💬) from Tree to BinaryTree, which propagates the changes to other files that use it.
2. Add membership instance, prove decidability of membership.
3. Add toListInOrder, toListPreOrder, toListPostOrder

Suggestion based on the discussion in the cslib thread#CSLib > Splay tree PR @ 💬.

---

• depends on: [Merged by Bors] - chore(Data/Tree/Basic): Rename Tree to BinaryTree #39707

[github-actions]

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[github-actions]

PR summary 5e3ffb125c

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

---

Declarations diff (regex)

+ Mem
+ all
+ all_iff
+ contains
+ contains_iff_mem
+ decidableBAll
+ instance : Membership α (BinaryTree α)
+ instance [BEq α] [LawfulBEq α] (a : α) (t : BinaryTree α) : Decidable (a ∈ t)
+ mem_singleton_iff
+ toListInOrder
+ toListPostOrder
+ toListPreOrder

You can run this locally as follows

## from your `mathlib4` directory:
git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci

## summary with just the declaration names:
../mathlib-ci/scripts/pr_summary/declarations_diff.sh <optional_commit>

## more verbose report:
../mathlib-ci/scripts/pr_summary/declarations_diff.sh long <optional_commit>

The doc-module for scripts/pr_summary/declarations_diff.sh in the mathlib-ci repository contains some details about this script.

Declarations diff (Lean -- pending)

Computed after the build finishes.

---

No changes to strong technical debt.

No changes to weak technical debt.

Current commit 5e3ffb125c
Reference commit eaa4d4093e

This script lives in the mathlib-ci repository. To run it locally, from your mathlib4 directory:

git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci
../mathlib-ci/scripts/reporting/technical-debt-metrics.sh pr_summary

• The relative value is the weighted sum of the differences with weight given by the inverse of the current value of the statistic.
• The absolute value is the relative value divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).

[eric-wieser]

Please could you split the renaming part of this PR into a standalone PR, as I originally requested on Zulip? You'll need to add a bunch of deprecations too, and it would be much easier to review if the PR only did the rename. You can leave this PR as is while waiting for the rename to be merged.

[sorrachai]

Sure, please refer to the new PR.

[eric-wieser]

Let's revert the changes here.

[eric-wieser]

Please add the not_mem_nil and mem_node_iff lemmas too, which can be simp.