[Merged by Bors] - feat(Algebra/Group/Action): add definition of equidecomposition#16936
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Felix-Weilacher wants to merge 35 commits intomasterfrom
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[Merged by Bors] - feat(Algebra/Group/Action): add definition of equidecomposition#16936Felix-Weilacher wants to merge 35 commits intomasterfrom
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PR summary 7f9fa08241Import changes for modified filesNo significant changes to the import graph Import changes for all files
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| Current number | Change | Type |
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| 107 | 1 | bare open (scoped) Classical |
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Thanks for taking a look and fixing the merge conflict! |
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Sorry for the secondary review - just noticed this after a second read.
Co-authored-by: Tristan F.-R. <tristanf@reed.edu>
Co-authored-by: Tristan F.-R. <tristanf@reed.edu>
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Thanks!
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🚀 Pull request has been placed on the maintainer queue by YaelDillies. |
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Thanks 🎉 bors merge |
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Define equidecomposition and provide some basic theory and operations. [Zulip](https://leanprover.zulipchat.com/#narrow/channel/287929-mathlib4/topic/Banach.20Tarski.20Paradox.20in.20Lean) Co-authored-by: Felix-Weilacher <fweilach@andrew.cmu.edu> Co-authored-by: Tristan F. <LeoDog896@hotmail.com>
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Pull request successfully merged into master. Build succeeded: |
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* factorial-dvd-int: (143 commits) Apply suggestions from code review feat(Factorial): k! divides the product of any k successive integers feat(CategoryTheory): creation of finite limits (#21320) chore: update Mathlib dependencies 2025-02-01 (#21328) chore(GroupTheory/SpecificGroups/Alternating.lean): follow last minute review of JX (#21314) feat: `‖x‖ₑ.toNNReal = ‖x‖₊` (#21306) chore: cleanup imports in Archive/IfNormalization (#21318) doc: fix several typos (#21315) feat(CategoryTheory): transfer being iso along an iso in the arrow category (#21310) chore: delete declarations deprecated between 2024-01 and 2024-07 (#21271) feat(Analysis/Normed/Module/Dual): polar in a normed space as a submodule (#20084) chore(Data/ZMod/Basic): split `ZMod.valMinAbs` off (#21308) feat(GroupTheory/Perm/Centralizer): study the centralizer of a permutation (#17522) feat(RingTheory/LocalRing): `IsLocalRing` for subrings (#21168) chore: update Mathlib dependencies 2025-02-01 (#21312) chore: update Mathlib dependencies 2025-01-31 (#21311) feat: generalize `mem_dite` to `Membership α β` (#21262) feat: Lemmas for some monomial orders (#16177) feat(CategoryTheory): the localized category is monoidal (#12728) feat: add function log⁺ (=positive part of the logarithm) and prove standard estimates (#21289) feat(RingTheory/WittVector): ring of Witt vectors is p-adically complete (#21295) feat(GroupTheory/GroupAction/Blocks): more on blocks (#21284) fix(FieldTheory/KrullTopology): make `krullTopology_discreteTopology_of_finiteDimensional` universe polymorphic (#21299) feat(RingTheory/Artinian): integral non-zero-divisors are units over artinian rings (#21199) refactor(Topology/Gluing): simplify definition of `TopCat.GlueData.Rel` (#20653) feat(RingTheory/PowerSeries): binomial series (#20192) chore(Mathlib/RingTheory/MvPolynomial): rename MonomiaOrder.lCoeff to MonomialOrder.leadingCoeff (#21290) chore (RingTheory/HahnSeries): fix names that use coeff (#21279) feat: let `notation3` distinguish `Prop` vs `Type _ ` vs `Sort _` (#21233) chore(MeasureTheory/Function/StronglyMeasurable): split Basic into Basic and AEStronglyMeasurable (#21273) feat(CategoryTheory): the monoidal category structure on a localization (#20951) feat(Analysis/Complex/Hadamard): generalize Hadamard's three lines theorem (#15009) feat(Order/CompleteBooleanAlgebra): Himp in terms of sSup (#20328) feat(ENNReal/Basic): add `ofNat_ne_top` and `top_ne_ofNat` (#14486) feat: Function.const as a PartialEquiv (#21137) chore(NonZeroDivisors): don't import rings (#20871) feat(Data/Set/Lattice): insert distributivity with iUnion/iInter (#21267) feat(GroupTheory/SpecificGroups/AlternatingGroup): subgroups of index 2 of Equiv.Perm (#21190) feat(GroupTheory/GroupAction/Transitive): basic results on transitive actions (#21285) perf(MeasureTheory/Function/LpSpace.lean): speed up (#21179) feat(Order): order isomorphisms from `Fin n` for small `n` (#21120) refactor(Topology/Group): turn morphisms in ProfiniteGrp into one field structures (#20740) feat: Sylow's first theorem for elementary `p`-groups (#21072) chore(Submonoid/Membership): don't import `MonoidWithZero` (#20748) refactor(Algebra/Algebra/Pi): cleanup and renaming (#21213) feat(GroupTheory/IndexNormal): subgroups of small index are normal (#21186) feat(Algebra/Group/Action): add definition of equidecomposition (#16936) feat(CategoryTheory/Subpresheaf): equalizer (#21096) feat: add lemmas about products of `Matrix.stdBasisMatrix` (#21204) chore: update Mathlib dependencies 2025-01-31 (#21282) ...
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Define equidecomposition and provide some basic theory and operations. [Zulip](https://leanprover.zulipchat.com/#narrow/channel/287929-mathlib4/topic/Banach.20Tarski.20Paradox.20in.20Lean) Co-authored-by: Felix-Weilacher <fweilach@andrew.cmu.edu> Co-authored-by: Tristan F. <LeoDog896@hotmail.com>
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Define equidecomposition and provide some basic theory and operations.
Zulip
TODO:
Prove that if two sets embeddidecompose into eachother, they are equidecomposable (Schroeder-Bernstein type theorem)
Define embeddidecomposability as a Preorder on sets and prove that its induced equivalence relation is equidecomposability.
Prove the definition of equidecomposition used here is equivalent to the more familiar one using partitions. This equivalence is trivial mathematically, but partitions do not seem well-developed to me in mathlib.