feat(Mathlib/Data/Finite/Units): Units are (in)finite if type is (in)finite

[AlexBrodbelt]

Shows

• depends on: feat(Mathlib/Data/Finite/Subtype): Subtype of elements not equal to a term is finite iff type is finite #39568
• depends on: feat(Mathlib/Data/Finite/Option): option type is finite iff type is finite #39567

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[github-actions]

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[github-actions]

PR summary 0628928cc9

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
Mathlib.Data.Finite.Option (new file)	486
Mathlib.Data.Finite.Subtype (new file)	487
Mathlib.Data.Finite.Units (new file)	500

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Declarations diff

+ Option.finite_iff
+ Subtype.finite_ne_iff
+ Units.finite_iff₀
+ Units.infinite_iff₀
+ instance {G : Type*} [GroupWithZero G] [hG : Infinite G] : Infinite Gˣ

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.

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No changes to strong technical debt.

No changes to weak technical debt.

[mathlib-dependent-issues]

This PR/issue depends on:

• feat(Mathlib/Data/Finite/Subtype): Subtype of elements not equal to a term is finite iff type is finite #39568
• feat(Mathlib/Data/Finite/Option): option type is finite iff type is finite #39567
  By Dependent Issues (🤖). Happy coding!