chore: redefine 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.

---

• depends on: [Merged by Bors] - chore: move binary recursion on Nat into a new file #15567
• depends on: [Merged by Bors] - chore: redefine Nat.bit #19666

[github-actions]

PR summary 60c51c067a

Import changes for modified files

Dependency changes

File	Base Count	Head Count	Change
Mathlib.Data.Nat.Bits	123	103	-20 (-16.26%)
Mathlib.Data.Nat.Size	155	150	-5 (-3.23%)
Mathlib.Logic.Equiv.Nat	293	292	-1 (-0.34%)

Import changes for all files

Files	Import difference
Mathlib.Data.Nat.Bits	-20
Mathlib.Data.Nat.Size	-5
Mathlib.Data.FP.Basic Mathlib.Logic.Equiv.Nat	-1

---

Declarations diff

+ 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.

---

No changes to technical debt.

You can run this locally as

./scripts/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).

[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
• [Merged by Bors] - chore: redefine Nat.bit #19666
  By Dependent Issues (🤖). Happy coding!

[eric-wieser]

Is there any advantage to this order vs

Suggested change

	def bodd (n : ℕ) : Bool := 1 &&& n != 0
	def bodd (n : ℕ) : Bool := n &&& 1 != 0

[FR-vdash-bot]

1 &&& n != 0 is defeq to n.testBit 0.