feat(Mathlib/Data/Finite/Subtype): Subtype of elements not equal to a term is finite iff type is finite

[AlexBrodbelt]

Subtype of terms not equal to a term is finite iff type is finite.

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

• depends on: feat(Mathlib/Data/Finite/Option): option type is finite iff type is finite #39567 [shows option type is finite iff type is finite]

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[github-actions]

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[github-actions]

PR summary 8fa788b640

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

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Declarations diff

+ Option.finite_iff
+ Subtype.finite_ne_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.

[mathlib-dependent-issues]

This PR/issue depends on:

• feat(Mathlib/Data/Finite/Option): option type is finite iff type is finite #39567
  By Dependent Issues (🤖). Happy coding!

[themathqueen]

Since this only imports the other new file, I wonder if you can just put the contents of this file together with the other and call the file something else that would make sense for both lemmas (maybe Data/Finite/Subtype is fine?)

[AlexBrodbelt]

I have seen more Option.lean files than Subtype.lean maybe better if it is named Data/Finite/Option.lean?