feat: Dyadic is a localization

[plp127]

Prove that Dyadic is a localization of the integers generated by inverting 2.

---

• depends on: feat: Dyadic is an ordered ring #43038

[github-actions]

PR summary 2e1e58b42c

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
Mathlib.Data.Dyadic.OrderedRing (new file)	459
Mathlib.Data.Dyadic.IsLocalization (new file)	844

---

Declarations diff (regex)

+ half
+ instance : CommRing Dyadic
+ instance : Invertible (2 : Dyadic)
+ instance : IsLocalization (Submonoid.powers (2 : ℤ)) Dyadic
+ instance : IsStrictOrderedRing Dyadic
+ instance : LinearOrder Dyadic
+ intCast_add
+ intCast_natCast
+ intCast_neg
+ intCast_one
+ intCast_zero
+ isUnit_iff_exists_half_pow
+ natCast_add
+ natCast_one
+ natCast_zero
+ toRat_one
+ val_half_eq_ofOdd
+ val_half_zpow_eq_ofOdd
+ val_inv_half

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)

✅ Lean-aware diff — post-build, computed from the Lean environment (commit 2e1e58b).

• +19 new declarations
• −0 removed declarations

+Dyadic.half
+Dyadic.instCommRing_1
+Dyadic.instInvertibleOfNat
+Dyadic.instIsLocalizationIntPowersOfNat
+Dyadic.instIsStrictOrderedRing
+Dyadic.instLinearOrder
+Dyadic.intCast_add
+Dyadic.intCast_natCast
+Dyadic.intCast_neg
+Dyadic.intCast_one
+Dyadic.intCast_zero
+Dyadic.isUnit_iff_exists_half_pow
+Dyadic.natCast_add
+Dyadic.natCast_one
+Dyadic.natCast_zero
+Dyadic.toRat_one
+Dyadic.val_half_eq_ofOdd
+Dyadic.val_half_zpow_eq_ofOdd
+Dyadic.val_inv_half

---

No changes to strong technical debt.
No changes to weak technical debt.

Current commit 2e1e58b42c
Reference commit 23a3216f0e

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.py 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).

[mathlib-dependent-issues]

This PR/issue depends on:

• feat: Dyadic is an ordered ring #43038
  By Dependent Issues (🤖). Happy coding!