[Merged by Bors] - chore(Ideal/Basic): dependent generalization of Ideal.pi
#20535
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PR summary dfceb06aa8Import changes for modified filesNo significant changes to the import graph Import changes for all files
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bors d+ Thanks! Please add a sentence to the PR description outlining why this generalization will be useful in future. |
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Thanks! Fixed docstring and added TODO in PR description. |
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As this PR is labelled bors merge |
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Also golf some proofs. TODO: similar to `Ideal.idealProdEquiv`, we may construct OrderEmbedding from `Πᵢ Ideal Rᵢ` to `Ideal (Πᵢ Rᵢ)`, which is an OrderIso if the indexing type is finite. This can then be used to show e.g. that a finite product of Noetherian rings is Noetherian without using an inductive argument.
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Ideal.piIdeal.pi
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| private def induced_map (I : Ideal R) (e : (ι → R) →ₗ[R] ι' → R) : | ||
| (ι → R) ⧸ I.pi ι → (ι' → R) ⧸ I.pi ι' := fun x => | ||
| Quotient.liftOn' x (fun y => Ideal.Quotient.mk (I.pi ι') (e y)) | ||
| (ι → R) ⧸ Ideal.pi (fun _ ↦ I) → (ι' → R) ⧸ Ideal.pi fun _ ↦ I := fun x => | ||
| Quotient.liftOn' x (fun y => Ideal.Quotient.mk _ (e y)) |
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This one should be straightforward to generalize to pi types too, right?
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* origin/master: (642 commits) feat: the Boolean subalgebra generated by the lattice generated by a set (#20440) feat: misc. lemmas about moments, tilted measures (#20150) chore(Algebra/Lie): make IsNilpotent and IsSolvable independent of scalars (#20556) feat(Combinatorics/SimpleGraph/Path): add `IsPath.getVert_injOn` (#19373) feat(Combinatorics/SimpleGraph): add lemmas about `spanningCoe` (#19377) chore: scope 'on' notation to Function (#20562) chore: disable docPrime linter (#20559) chore: deprecate MulRingNorm._ in favour of AbsoluteValue._ (#20557) fix(scripts/bench_summary): input jobID as a Nat, rather than a String (#20539) chore: move results about `DivisionMonoid` + `HasDistribNeg` (#20551) feat(NumberTheory/NumberField/Embeddings): definition of totally real field (#20542) chore(Noetherian/Artinian): generalize to Semiring (#20534) chore: protect `Filter.nhds_{iInf,inf}` (#20530) chore(AlgebraicTopology): move SplitSimplicialObject.lean (#20511) chore: extract 3 new files out of MeasureSpace (#20509) feat(RingTheory): Jacobian criterion for smoothness of local algebras (#20326) doc(RingTheory/Flat): add reference to Lambek's paper (#20266) feat(NumberTheory/AbelSummation): add more results (#19942) chore(Multilinear/Basic): generalize the `SMul` instance (#20536) feat(FDeriv/Equiv): generalize `HasFDerivAt.of_local_left_inverse` (#20516) feat(ContDiff): add `iteratedFDeriv_comp` (#20472) feat(LowerUpperTopology): add lemmas (#20465) feat(ContDiff): weaken some assumptions (#20368) fix(scripts/technical-debt-metric): avoid division by 0 (#20537) chore(Algebra/Ring): Clean up in SumsOfSquares and Semireal/Defs (#20528) feat(FTaylorSeries): add lemmas about `dist` between 0th and 1st derivs (#20089) feat: results on inner regularity of finite measures (#19780) chore: to_additive various results on groups, group actions (#20547) feat(Probability/Kernel): `Kernel.sectL` and `sectR` (#15466) chore(CategoryTheory/Limits/Fubini): relax universes constraints and weaken hypotheses (#20553) perf: remove `@[simp]` on `Fintype.card_of{IsEmpty,Subsingleton}` (#20524) fix(HashCommandLinter): remove unnecessary, broken workaround for tests (#20529) chore(Ideal/Basic): dependent generalization of `Ideal.pi` (#20535) feat(RingTheory): being unramified is a local property (#20323) chore(BooleanSubalgebra): use `IsSublattice` in `closure_sdiff_sup_induction` (#20439) feat(Order/SuccPred/CompleteLinearOrder): `⨆ a < x, succ a = x` (#19970) chore(*): replace `no_index (ofNat n)` with `ofNat(n)` everywhere (#20521) feat(CategoryTheory/Triangulated/Adjunction): the right adjoint of a triangulated functor is triangulated (#20255) chore(Order/SuccPred/LinearLocallyFinite): change data-creating instances to defs (#20235) chore: don't import algebra in `Data.Finset.Basic` (#19779) feat: initial segment commutes with `Iio` (#20503) chore(Measure/Pi): move parts to `MeasurableSpace/` (#20215) chore: smile more often (#20436) chore(Algebra/Category/MonCat/ForgetCorepresentable, Algebra/Group/Equiv/Basic): move definitions and add symmetric version (#20416) feat(GroupTheory/QuotientGroup): group correspondence theorem (#20007) doc: change "module homomorphism" to "linear map" (#20481) perf: improves the performance of the `Repr (Equiv.Perm α)` instance (1/4) (#20519) fix: do not keep only the first line of hints (#19756) feat(Analysis/Analytic): lemmas about `smul` for power series (#19816) chore: don't import algebra in `Data.Multiset.Basic` (#19775) ...
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* origin/master: (80 commits) chore(CategoryTheory): remove data produced by tactic block (#20565) feat: `|∫ a, f a ∂μ| ≤ ∫ a, |f a| ∂μ` (#20540) feat: the Boolean subalgebra generated by the lattice generated by a set (#20440) feat: misc. lemmas about moments, tilted measures (#20150) chore(Algebra/Lie): make IsNilpotent and IsSolvable independent of scalars (#20556) feat(Combinatorics/SimpleGraph/Path): add `IsPath.getVert_injOn` (#19373) feat(Combinatorics/SimpleGraph): add lemmas about `spanningCoe` (#19377) chore: scope 'on' notation to Function (#20562) chore: disable docPrime linter (#20559) chore: deprecate MulRingNorm._ in favour of AbsoluteValue._ (#20557) fix(scripts/bench_summary): input jobID as a Nat, rather than a String (#20539) chore: move results about `DivisionMonoid` + `HasDistribNeg` (#20551) feat(NumberTheory/NumberField/Embeddings): definition of totally real field (#20542) chore(Noetherian/Artinian): generalize to Semiring (#20534) chore: protect `Filter.nhds_{iInf,inf}` (#20530) chore(AlgebraicTopology): move SplitSimplicialObject.lean (#20511) chore: extract 3 new files out of MeasureSpace (#20509) feat(RingTheory): Jacobian criterion for smoothness of local algebras (#20326) doc(RingTheory/Flat): add reference to Lambek's paper (#20266) feat(NumberTheory/AbelSummation): add more results (#19942) chore(Multilinear/Basic): generalize the `SMul` instance (#20536) feat(FDeriv/Equiv): generalize `HasFDerivAt.of_local_left_inverse` (#20516) feat(ContDiff): add `iteratedFDeriv_comp` (#20472) feat(LowerUpperTopology): add lemmas (#20465) feat(ContDiff): weaken some assumptions (#20368) fix(scripts/technical-debt-metric): avoid division by 0 (#20537) chore(Algebra/Ring): Clean up in SumsOfSquares and Semireal/Defs (#20528) feat(FTaylorSeries): add lemmas about `dist` between 0th and 1st derivs (#20089) feat: results on inner regularity of finite measures (#19780) chore: to_additive various results on groups, group actions (#20547) feat(Probability/Kernel): `Kernel.sectL` and `sectR` (#15466) chore(CategoryTheory/Limits/Fubini): relax universes constraints and weaken hypotheses (#20553) perf: remove `@[simp]` on `Fintype.card_of{IsEmpty,Subsingleton}` (#20524) fix(HashCommandLinter): remove unnecessary, broken workaround for tests (#20529) chore(Ideal/Basic): dependent generalization of `Ideal.pi` (#20535) feat(RingTheory): being unramified is a local property (#20323) chore(BooleanSubalgebra): use `IsSublattice` in `closure_sdiff_sup_induction` (#20439) feat(Order/SuccPred/CompleteLinearOrder): `⨆ a < x, succ a = x` (#19970) chore(*): replace `no_index (ofNat n)` with `ofNat(n)` everywhere (#20521) feat(CategoryTheory/Triangulated/Adjunction): the right adjoint of a triangulated functor is triangulated (#20255) chore(Order/SuccPred/LinearLocallyFinite): change data-creating instances to defs (#20235) chore: don't import algebra in `Data.Finset.Basic` (#19779) feat: initial segment commutes with `Iio` (#20503) chore(Measure/Pi): move parts to `MeasurableSpace/` (#20215) chore: smile more often (#20436) chore(Algebra/Category/MonCat/ForgetCorepresentable, Algebra/Group/Equiv/Basic): move definitions and add symmetric version (#20416) feat(GroupTheory/QuotientGroup): group correspondence theorem (#20007) doc: change "module homomorphism" to "linear map" (#20481) perf: improves the performance of the `Repr (Equiv.Perm α)` instance (1/4) (#20519) fix: do not keep only the first line of hints (#19756) ...
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Also golf some proofs.
TODO: similar to
Ideal.idealProdEquiv, we may construct OrderEmbedding fromΠᵢ Ideal RᵢtoIdeal (Πᵢ Rᵢ), which is an OrderIso if the indexing type is finite. This can then be used to show e.g. that a finite product of Noetherian rings is Noetherian without using an inductive argument.