feat(LinearAlgebra/AffineSpace/AffineSubspace): using AffineSubspace.direction to reinterpret AffineSubspace as Submodule

[martinwintermath]

• add AffineSubspace.vsub_self_of_zero_mem that states s -ᵥ s = s if 0 ∈ s
• add AffineSubspace.direction_eq_self_of_zero_mem that states that if 0 ∈ s, then the directions coerce back to the affine subspace.
• add corresponding CanLift instance.
• modify doc-string of AffineSubspace.direction to state that this can be used for reinterpretation of an affine subspace as a submodule.
• add Coe instance based on Submodule.toAffineSubspace and adds corresponding @[coe] attribute.

The PR also performs a slight cleanup of the file: statements about SetLike or Submodule.toAffineSubspace have been moved closer to their respective definitions.

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[github-actions]

PR summary 672768680f

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

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Declarations diff

+ direction_eq_self_of_zero_mem
+ instance : CanLift (AffineSubspace k V) (Submodule k V) (·) (0 ∈ ·) := ⟨
+ instance : Coe (Submodule k V) (AffineSubspace k V) := ⟨toAffineSubspace⟩
+ vsub_self_of_zero_mem

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 technical debt.

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.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).

[wwylele]

One thing I just realized: isn't this just a specialization of AffineSubspace.direction? When 0 is a member, you can prove that AffineSubspace.direction and AffineSubspace.toSubmodule are equal. So I don't think we need this. We can add a doc to note that one can use AffineSubspace.direction to convert to submodule

Edit: and we can add a lemma that (AffineSubspace.direction s).toAffineSubspace = s when 0 is a member of s

[wwylele]

Don't forget to update PR title and description