[Merged by Bors] - feat: finite sum, difference, scalar product of `C^k` sections is `C^k` by grunweg · Pull Request #26674 · leanprover-community/mathlib4

grunweg · 2025-07-03T16:01:42Z

And use this to golf the proofs in SmoothSection.lean.
A future PR will add the analogous results for differentiability of sections.

Part of the path towards the geodesics and the Levi-Civita connection.

depends on: [Merged by Bors] - feat: contMDiffWithinAt_zeroSection #26676
depends on: [Merged by Bors] - feat: contMDiffOn_section_of_mem_baseSet #26678

github-actions · 2025-07-03T16:02:57Z

PR summary 3bcc451cb5

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

Declarations diff

+ ContMDiff.add_section
+ ContMDiff.const_smul_section
+ ContMDiff.neg_section
+ ContMDiff.smul_section
+ ContMDiff.sub_section
+ ContMDiff.sum_section
+ ContMDiffAt.add_section
+ ContMDiffAt.const_smul_section
+ ContMDiffAt.neg_section
+ ContMDiffAt.smul_section
+ ContMDiffAt.sub_section
+ ContMDiffAt.sum_section
+ ContMDiffOn.add_section
+ ContMDiffOn.const_smul_section
+ ContMDiffOn.neg_section
+ ContMDiffOn.smul_section
+ ContMDiffOn.sub_section
+ ContMDiffOn.sum_section
+ ContMDiffWithinAt.add_section
+ ContMDiffWithinAt.const_smul_section
+ ContMDiffWithinAt.neg_section
+ ContMDiffWithinAt.smul_section
+ ContMDiffWithinAt.sub_section
+ ContMDiffWithinAt.sum_section

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).

Smoothness of a section can be determined using any trivialisation, not just the preferred trivialisation at a point. Part of the path towards geodesics and the Levi-Civita connection.

mathlib4-dependent-issues-bot · 2025-07-05T17:46:47Z

This PR/issue depends on:

~~[Merged by Bors] - feat: contMDiffWithinAt_zeroSection #26676~~
~~[Merged by Bors] - feat: contMDiffOn_section_of_mem_baseSet #26678~~
By Dependent Issues (🤖). Happy coding!

leanprover-community-bot-assistant · 2025-07-05T18:33:50Z

This pull request has conflicts, please merge master and resolve them.

sgouezel

Looks nice, thanks!

Mathlib/Geometry/Manifold/VectorBundle/SmoothSection.lean

sgouezel · 2025-07-07T08:43:22Z

Mathlib/Geometry/Manifold/VectorBundle/SmoothSection.lean

+    ContMDiff I (I.prod 𝓘(𝕜, F)) n (fun x ↦ TotalSpace.mk' F x (a • s x)) :=
+  fun x₀ ↦ contMDiffAt_smul_const_section (hs x₀)
+
+lemma contMDiffWithinAt_finsum_section {ι : Type*} {s : Finset ι} {t : ι → (x : M) → V x}


Suggested change

lemma contMDiffWithinAt_finsum_section {ι : Type*} {s : Finset ι} {t : ι → (x : M) → V x}

lemma contMDiffWithinAt_sum_section {ι : Type*} {s : Finset ι} {t : ι → (x : M) → V x}

It's not a finsum, it's a sum. Same thing below.

(I also included the dot notation changes, so went for ContMDiffWithinAt.sum_section in the end.)

grunweg · 2025-07-07T12:01:51Z

Thanks for the quick and helpful review. I should have addressed all your comments now.

sgouezel · 2025-07-07T13:19:08Z

bors r+
Thanks!

…k` (#26674) And use this to golf the proofs in `SmoothSection.lean`. A future PR will add the analogous results for differentiability of sections. Part of the path towards the geodesics and the Levi-Civita connection.

mathlib-bors · 2025-07-07T13:28:22Z

Pull request successfully merged into master.

Build succeeded:

CI Success

…k` (leanprover-community#26674) And use this to golf the proofs in `SmoothSection.lean`. A future PR will add the analogous results for differentiability of sections. Part of the path towards the geodesics and the Levi-Civita connection.

…ns is differentiable (#26871) This mirrors the additions of #26674 to `mdifferentiable` sections. Part of the path towards geodesics and the Levi-Civita connection. Co-authored-by: Patrick Massot <patrickmassot@free.fr> Co-authored-by: Michael Rothgang <rothgang@math.uni-bonn.de>

…ns is differentiable (leanprover-community#26871) This mirrors the additions of leanprover-community#26674 to `mdifferentiable` sections. Part of the path towards geodesics and the Levi-Civita connection. Co-authored-by: Patrick Massot <patrickmassot@free.fr> Co-authored-by: Michael Rothgang <rothgang@math.uni-bonn.de>

github-actions bot added the t-differential-geometry Manifolds etc label Jul 3, 2025

This was referenced Jul 3, 2025

[Merged by Bors] - feat: contMDiff_section_of_tsupport #26671

Closed

Mr. Covariant Derivatives #26221

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grunweg added the awaiting-CI This PR does not pass CI yet. This label is automatically removed once it does. label Jul 3, 2025

grunweg force-pushed the contMDiff_ops_section branch from 9ac7bd8 to 4bb4749 Compare July 3, 2025 16:14

mathlib4-dependent-issues-bot added the blocked-by-other-PR This PR depends on another PR (this label is automatically managed by a bot) label Jul 3, 2025

github-actions bot removed the awaiting-CI This PR does not pass CI yet. This label is automatically removed once it does. label Jul 3, 2025

grunweg added 2 commits July 4, 2025 00:55

feat: contMDiffOn_section_of_mem_baseSet

96c2f18

Smoothness of a section can be determined using any trivialisation, not just the preferred trivialisation at a point. Part of the path towards geodesics and the Levi-Civita connection.

change

1530d02

grunweg force-pushed the contMDiff_ops_section branch from 588cf87 to 1530d02 Compare July 3, 2025 22:56

mathlib4-dependent-issues-bot removed the blocked-by-other-PR This PR depends on another PR (this label is automatically managed by a bot) label Jul 5, 2025

leanprover-community-bot-assistant added the merge-conflict The PR has a merge conflict with master, and needs manual merging. (this label is managed by a bot) label Jul 5, 2025

Merge branch 'master' into contMDiff_ops_section

ebeba70

github-actions bot removed the merge-conflict The PR has a merge conflict with master, and needs manual merging. (this label is managed by a bot) label Jul 5, 2025

grunweg changed the title ~~feat: finite sum, difference, smul of C^k sections is C^k~~ feat: finite sum, difference, scalar product of C^k sections is C^k Jul 5, 2025

sgouezel reviewed Jul 7, 2025

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grunweg added 2 commits July 7, 2025 13:53

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ghost added the ready-to-merge This PR has been sent to bors. label Jul 7, 2025

mathlib-bors bot changed the title ~~feat: finite sum, difference, scalar product of C^k sections is C^k~~ [Merged by Bors] - feat: finite sum, difference, scalar product of C^k sections is C^k Jul 7, 2025

mathlib-bors bot closed this Jul 7, 2025

grunweg deleted the contMDiff_ops_section branch July 7, 2025 13:54

grunweg mentioned this pull request Jul 7, 2025

[Merged by Bors] - feat: finite sum, difference, scalar product of differentiable sections is differentiable #26871

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[Merged by Bors] - feat: finite sum, difference, scalar product of `C^k` sections is `C^k`#26674

[Merged by Bors] - feat: finite sum, difference, scalar product of `C^k` sections is `C^k`#26674
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	lemma contMDiffWithinAt_finsum_section {ι : Type*} {s : Finset ι} {t : ι → (x : M) → V x}
	lemma contMDiffWithinAt_sum_section {ι : Type*} {s : Finset ι} {t : ι → (x : M) → V x}

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PR summary 3bcc451cb5

Import changes for modified files

Declarations diff

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