chore: redefine Nat.bit Nat.div2 Nat.bodd

[FR-vdash-bot]

The new definitions are faster than the old ones. Nat.binaryRec will be moved to batteries (leanprover-community/batteries#799) or core (leanprover/lean4#3756), so relevant contents are moved to a new file temporarily.

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• depends on: [Merged by Bors] - chore: move binary recursion on Nat into a new file #15567

[github-actions]

PR summary 759d699569

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

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Declarations diff

+ bit_eq_bitImpl
+ div2_lt_self

You can run this locally as follows

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

## more verbose report:
./scripts/declarations_diff.sh long <optional_commit>

The doc-module for script/declarations_diff.sh contains some details about this script.

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Increase in tech debt: 1.00

Current number	Change	Type
207	1	disabled deprecation lints

Current commit 759d699569
Reference commit 4bd54c44ef

You can run this locally as

./scripts/technical-debt-metrics.sh pr_summary

[urkud]

Please describe how and why did you change the definition(s) in the commit message.

[mathlib4-dependent-issues-bot]

This PR/issue depends on:

• [Merged by Bors] - chore: move binary recursion on Nat into a new file #15567
  By Dependent Issues (🤖). Happy coding!

[eric-wieser]

@FR-vdash-bot, please solve the merge conflicts.