feat(Mathlib/Data/Finite/Option): option type is finite iff type is finite

[AlexBrodbelt]

Option type is finite if and only if the type is finite.

This is an intermediate result to proving that if the GroupWithZero is (in)finite then the Units are (in)finite.

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[github-actions]

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[github-actions]

PR summary a5cd43ac9c

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

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Declarations diff

+ Option.finite_iff

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.

[plp127]

What's the reason for public import Mathlib.Data.Fintype.Option but import Mathlib.Logic.Equiv.Fin.Basic?

[themathqueen]

because only finSuccEquiv (which is in Logic.Equiv.Fin.Basic) in the proof uses it

[plp127]

Then, why not just public import Mathlib.Data.Finite.Defs and everything else is privately imported?

[themathqueen]

Yeah, why not!

Suggested change

	public import Mathlib.Data.Fintype.Option
	import Mathlib.Logic.Equiv.Fin.Basic
	public import Mathlib.Data.Finite.Defs
	import Mathlib.Data.Fintype.Option
	import Mathlib.Logic.Equiv.Fin.Basic

[AlexBrodbelt]

Will modify the imports - but maybe it is a good idea to improve the #min_imports command to take into account access modifiers as well?

[themathqueen]

I think some people are trying to work on making this better (also trying to make shake work properly). We're still trying to adjust to the new module system (even though it's been a few months now).

[themathqueen]

How about just

Suggested change

	/-- The `Option` type on a type is finite if and only if the underlying type is finite. -/
	/-- `Option α` is finite if and only if the underlying type `α` is finite. -/

[themathqueen]

Suggested change

	# Finiteness conditions for `Option` types
	# Finiteness conditions for `Option` types
	This file shows that `Option α` is finite iff `α` is.