[Merged by Bors] - feat(LinearAlgebra/AffineSpace): more lemma about simplex face and interior

[wwylele]

Some intermediate lemma towards #34826

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[github-actions]

PR summary 1321470619

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

+ affineSpan_faceOpposite_le
+ affineSpan_face_le
+ closedInterior_map
+ closedInterior_restrict
+ faceOpposite_restrict
+ face_restrict
+ interior_map
+ interior_restrict
+ points_mem_affineSpan_face
+ points_mem_affineSpan_faceOpposite
+ points_notMem_affineSpan_faceOpposite
+ setInterior_map
+ setInterior_restrict

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.

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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).

[Copilot]

Pull request overview

This PR adds intermediate lemmas about simplex faces and interiors that support work towards computing the volume of simplices (PR #34826). The changes introduce lemmas about affine spans of faces, membership properties, and how restriction to affine subspaces interacts with faces and interiors.

Changes:

• Added lemmas characterizing affine spans of simplex faces and opposite faces
• Added lemmas about membership of points in affine spans of faces
• Added lemmas showing that face operations commute with restriction to affine subspaces
• Added lemmas showing that interior operations commute with restriction to affine subspaces

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[jsm28]

maintainer merge

[github-actions]

🚀 Pull request has been placed on the maintainer queue by jsm28.

[riccardobrasca]

Thanks!

bors merge

[mathlib-bors]

Pull request successfully merged into master.

Build succeeded:

• ci (staging) / Post-Build Step
• ci (staging) / Post-CI job
• ci (staging) / Lint style
• ci (staging) / Build