[Merged by Bors] - feat: A disjoint union is finite iff all sets are finite, and all but finitely many are empty #20457

sgouezel · 2025-01-03T22:04:06Z

From the Carleson project

github-actions · 2025-01-03T22:04:58Z

PR summary 65de0a4387

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

Declarations diff

+ PairwiseDisjoint.finite_biUnion_iff
+ finite_iUnion_iff
+ finite_iUnion_of_subsingleton

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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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).

Mathlib/Data/Set/Finite/Lattice.lean

Co-authored-by: Eric Wieser <[email protected]>

sgouezel · 2025-01-04T09:11:43Z

Thanks for the review!

eric-wieser · 2025-01-04T22:35:37Z

Mathlib/Data/Set/Finite/Lattice.lean

+finitely many are empty. -/
+lemma PairwiseDisjoint.finite_biUnion_iff {f : β → Set α} {s : Set β}
+    (hs : s.PairwiseDisjoint f) :
+    Set.Finite (⋃ i ∈ s, f i)


I'd liked to have seen this be of the more general form

Suggested change

Set.Finite (⋃ i ∈ s, f i)

Set.Finite (⋃ (i) (h : i ∈ s, f i h)

but I guess the definition of PairwiseDisjoint doesn't permit this; so no action needed.

eric-wieser

bors d+

Consider waiting a day or two to let @YaelDillies have a look for any other API like elim_set that can make this more concise

mathlib-bors · 2025-01-04T22:36:30Z

✌️ sgouezel can now approve this pull request. To approve and merge a pull request, simply reply with bors r+. More detailed instructions are available here.

Mathlib/Data/Set/Finite/Lattice.lean

Co-authored-by: Yaël Dillies <[email protected]>

Mathlib/Data/Set/Finite/Lattice.lean

sgouezel · 2025-01-06T15:56:17Z

bors r+

… finitely many are empty (#20457) From the Carleson project

mathlib-bors · 2025-01-06T16:31:22Z

Pull request successfully merged into master.

Build succeeded:

* origin/master: (189 commits) chore(Algebra): make more names consistent (#20449) feat: Polynomial FLT (#18882) feat: A disjoint union is finite iff all sets are finite, and all but finitely many are empty (#20457) fix: linkfix in 100.yaml (#20517) feat(1000): fill in more entries (#20470) feat(Combinatorics/SimpleGraph/Walk): add `penultimate` and `snd` (#16769) feat(ContinuousMultilinearMap): add lemmas about `.prod` (#20462) feat(RingTheory): classification of etale algebras over fields (#20324) fix: Allow multiple builds on staging branch (#20515) feat(CategoryTheory/Shift/Adjunction): properties of `Adjunction.CommShift` (#20337) chore(Data/Multiset/Basic): move the `sub`, `union`, `inter` sections lower (#19863) chore(Topology/UniformSpace/Completion): make coe' argument implicit (#20514) refactor(Algebra/Category/Grp/Colimits): change the construction of colimits in `AddCommGrp` (#20474) feat(Topology/Algebra/InfiniteSum/NatInt): Add pnat lems (#16544) chore(RingTheory/Finiteness): rename Module.Finite.out (#20506) refactor(CategoryTheory/Limits/Preserves/Ulift): simplify the proof that the universe lifting functor for types preserves all colimits (#20508) feat(CategoryTheory): products in the category of Ind-objects (#20507) chore: remove >9 month old deprecations (#20505) chore(FieldTheory/Galois): small cleanup (#20217) chore(LinearIndependent): generalize to semirings (#20480) chore(NumberTheory/NumberField/AdeleRing): refactor adele rings (#20500) chore: replace `aesop` with `simp` where possible (#20483) chore(1000): remove nonexistent fields (#20493) chore(CategoryTheory/Adjunction.Basic, CategoryTheory/Equivalence): change definition of `Adjunction.comp` and `Equivalence.trans` (#20490) feat(Asymptotics): add `Asymptotics.*.*Prod` lemmas (#20458) feat: a conditional kernel is almost everywhere a probability measure (#20430) feat: if `f` is a measurable group hom, then every point has a neighborhood `s` such that `f '' s` is bounded (#20304) feat: `Ico`, `Ioc`, and `Ioo` are not closed or compact (#20479) chore: drop redundant hypothesis in `Module.Dual.eq_of_preReflection_mapsTo` (#20492) feat(FaaDiBruno): derive `DecidableEq` (#20482) chore(SetTheory/Ordinal/Basic): `{x // x < y}` → `Iio y` (#20413) chore: generalize `FormalMultilinearSeries.ofScalars_norm` to `Seminormed` (#20351) chore(MvPolynomial/Localization): golf using TensorProduct (#20309) chore(Combinatorics/Enumerative/Partition): auto-derive DecidableEq (#20277) chore(CategoryTheory): make relevant parameters explicit in `Arrow.homMk`. (#20259) feat: add `IsStarNormal (↑x⁻¹ : R)` instance for `x : Rˣ` (#20091) fix: Stop cancelling builds of master (#20435) chore: update Mathlib dependencies 2025-01-05 (#20485) feat(SetTheory/Cardinal/Arithmetic): miscellaneous cardinality lemmas (#18933) chore: bump toolchain to v4.16.0-rc1, and merge bump/v4.16.0 (#20464) chore: bot validates lean-toolchain on bump/v4.X.0 branches (#20478) feat: shorthand lemmas for the L1 norm (#20383) chore: remove unnecessary adaptation notes (#20467) chore(Algebra/Category/MonCat/Colimits): remove smallness condition (#20473) chore(SetTheory/Ordinal/Arithmetic): `IsLeftCancelAdd Ordinal` (#19888) feat(Algebra): more on `OrthogonalIdempotents` (#18195) feat(Radical): `(radical a).natDegree ≤ a.natDegree` (#20468) feat(Polynomial): `(a^n)' = 0` iff `a' = 0` when `n` doesn't divide the characteristic (#20190) feat(Algebra/Lie): add Lie's theorem (#13480) chore(RingTheory/Generators): make algebra instance a def (#14265) ...

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Co-authored-by: Eric Wieser <[email protected]>

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Update Mathlib/Data/Set/Finite/Lattice.lean

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remove redundant lemma

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feat: A disjoint union is finite iff all sets are finite, and all but…

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… finitely many are empty (#20457) From the Carleson project

mathlib-bors bot changed the title ~~feat: A disjoint union is finite iff all sets are finite, and all but finitely many are empty~~ [Merged by Bors] - feat: A disjoint union is finite iff all sets are finite, and all but finitely many are empty Jan 6, 2025

mathlib-bors bot closed this Jan 6, 2025

mathlib-bors bot deleted the SG_carleson3 branch January 6, 2025 16:31

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[Merged by Bors] - feat: A disjoint union is finite iff all sets are finite, and all but finitely many are empty #20457

[Merged by Bors] - feat: A disjoint union is finite iff all sets are finite, and all but finitely many are empty #20457

sgouezel commented Jan 3, 2025

github-actions bot commented Jan 3, 2025 •

edited

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Declarations diff

sgouezel commented Jan 4, 2025

eric-wieser Jan 4, 2025

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mathlib-bors bot commented Jan 4, 2025

sgouezel commented Jan 6, 2025

mathlib-bors bot commented Jan 6, 2025

	Set.Finite (⋃ i ∈ s, f i)
	Set.Finite (⋃ (i) (h : i ∈ s, f i h)

[Merged by Bors] - feat: A disjoint union is finite iff all sets are finite, and all but finitely many are empty #20457

[Merged by Bors] - feat: A disjoint union is finite iff all sets are finite, and all but finitely many are empty #20457

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sgouezel commented Jan 3, 2025

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PR summary 65de0a4387

Import changes for modified files

Declarations diff

sgouezel commented Jan 4, 2025

eric-wieser Jan 4, 2025

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sgouezel commented Jan 6, 2025

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edited

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