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feat(LinearAlgebra/Simplex): closedInterior = interior + face.closedInterior#35365

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wwylele:simplex-face-interior
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feat(LinearAlgebra/Simplex): closedInterior = interior + face.closedInterior#35365
wwylele wants to merge 4 commits intoleanprover-community:masterfrom
wwylele:simplex-face-interior

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@wwylele wwylele commented Feb 15, 2026

Intermediate lemma towards #34826. This will be used to show the measure on interior and closedInterior are equal, as the difference is a zero-measure set.

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@wwylele wwylele mentioned this pull request Feb 15, 2026
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@wwylele wwylele requested a review from Copilot February 15, 2026 16:21
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github-actions bot commented Feb 15, 2026 •
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PR summary 909530195c

Import changes for modified files

No significant changes to the import graph

Import changes for all files
Files Import difference

Declarations diff

+ closedInterior_eq_interior_union
+ closedInterior_faceOpposite_subset_closedInterior
+ closedInterior_face_subset_closedInterior

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 scripts/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).

@github-actions github-actions bot added the t-algebra Algebra (groups, rings, fields, etc) label Feb 15, 2026
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Pull request overview

Adds an intermediate lemma in Affine.Simplex relating closedInterior to interior plus the union of the closedInteriors of codimension-1 faces (faceOpposite), intended for later measure-theoretic arguments in #34826.

Changes:

  • Prove (s.face h).closedInterior ⊆ s.closedInterior.
  • Prove s.closedInterior = s.interior ∪ ⋃ i, (s.faceOpposite i).closedInterior under ordered-ring assumptions.

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@wwylele wwylele force-pushed the simplex-face-interior branch from fb3b3d7 to 8d1abcd Compare February 15, 2026 16:28
@wwylele wwylele changed the title feat(LinearAlgebra/AffineSpace): closedInterior = interior + face.closedInterior feat(LinearAlgebra/Simplex): closedInterior = interior + face.closedInterior Feb 15, 2026
@wwylele wwylele force-pushed the simplex-face-interior branch from 8d1abcd to a206595 Compare February 15, 2026 16:47
@wwylele wwylele force-pushed the simplex-face-interior branch from a206595 to f4cc76c Compare February 15, 2026 16:48
@mathlib-triage mathlib-triage bot assigned eric-wieser and unassigned kim-em Mar 22, 2026
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