refactor(LinearAlgebra): redefine Fintype (Basis.ofVectorSpaceIndex K V) instance

[Vierkantor]

This instance was defined using the fact that FiniteDimensional is equivalent to IsNoetherian, but we can also use Module.Finite. Together with previous proof cleanups,. we can even save some imports. (Which will be even better once I get around to rearranging the results we have on FiniteDimensional.)

Note that the two instances are indeed defeq.

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• depends on: [Merged by Bors] - chore(LinearAlgebra/FiniteDimensional): simplify proofs #22589

[github-actions]

PR summary 117c28bedc

Import changes for modified files

Dependency changes

File	Base Count	Head Count	Change
Mathlib.LinearAlgebra.FiniteDimensional.Defs	1210	1209	-1 (-0.08%)

Import changes for all files

Files

Import difference

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-1

---

Declarations diff

+ instance [FiniteDimensional K V] : Fintype (Basis.ofVectorSpaceIndex K V)
- instance [FiniteDimensional K V] : Fintype (Basis.ofVectorSpaceIndex K V) := by

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).

[mathlib4-dependent-issues-bot]

This PR/issue depends on:

• [Merged by Bors] - chore(LinearAlgebra/FiniteDimensional): simplify proofs #22589
  By Dependent Issues (🤖). Happy coding!