[Merged by Bors] - refactor: Multiplicativise abs#9553
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YaelDillies wants to merge 12 commits intomasterfrom
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[Merged by Bors] - refactor: Multiplicativise abs#9553YaelDillies wants to merge 12 commits intomasterfrom
abs#9553YaelDillies wants to merge 12 commits intomasterfrom
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The current design for `abs` is flawed: * The `Abs` notation typeclass has exactly two instances: one for `[Neg α] [Sup α]`, one for `[Inv α] [Sup α]`. This means that: * We can't write a meaningful hover for `Abs.abs` * Fields have two `Abs` instances! * We have the multiplicative definition but: * All the lemmas in `Algebra.Order.Group.Abs` are about the additive version. * The only lemmas about the multiplicative version are in `Algebra.Order.Group.PosPart`, and they get additivised to duplicates of the lemmas in `Algebra.Order.Group.Abs`! This PR changes the notation typeclass with two new definitions (related through `to_additive`): `mabs` and `abs`. `abs` inherits the `|a|` notation and `mabs` gets `|a|ₘ` instead. The first half of `Algebra.Order.Group.Abs` gets multiplicativised. A later PR will multiplicativise the second half, and another one will deduplicate the lemmas in `Algebra.Order.Group.PosPart`. Part of #9411
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jcommelin
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Thanks a lot for cleaning this up!!
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The current design for `abs` is flawed: * The `Abs` notation typeclass has exactly two instances: one for `[Neg α] [Sup α]`, one for `[Inv α] [Sup α]`. This means that: * We can't write a meaningful hover for `Abs.abs` * Fields have two `Abs` instances! * We have the multiplicative definition but: * All the lemmas in `Algebra.Order.Group.Abs` are about the additive version. * The only lemmas about the multiplicative version are in `Algebra.Order.Group.PosPart`, and they get additivised to duplicates of the lemmas in `Algebra.Order.Group.Abs`! This PR changes the notation typeclass with two new definitions (related through `to_additive`): `mabs` and `abs`. `abs` inherits the `|a|` notation and `mabs` gets `|a|ₘ` instead. The first half of `Algebra.Order.Group.Abs` gets multiplicativised. A later PR will multiplicativise the second half, and another one will deduplicate the lemmas in `Algebra.Order.Group.PosPart`. Part of #9411. Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com>
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YaelDillies
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This changes the typeclass notation approach with plain functions. Followup to #9553
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The current design for `abs` is flawed: * The `Abs` notation typeclass has exactly two instances: one for `[Neg α] [Sup α]`, one for `[Inv α] [Sup α]`. This means that: * We can't write a meaningful hover for `Abs.abs` * Fields have two `Abs` instances! * We have the multiplicative definition but: * All the lemmas in `Algebra.Order.Group.Abs` are about the additive version. * The only lemmas about the multiplicative version are in `Algebra.Order.Group.PosPart`, and they get additivised to duplicates of the lemmas in `Algebra.Order.Group.Abs`! This PR changes the notation typeclass with two new definitions (related through `to_additive`): `mabs` and `abs`. `abs` inherits the `|a|` notation and `mabs` gets `|a|ₘ` instead. The first half of `Algebra.Order.Group.Abs` gets multiplicativised. A later PR will multiplicativise the second half, and another one will deduplicate the lemmas in `Algebra.Order.Group.PosPart`. Part of #9411. Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com>
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`Algebra.GroupPower.Lemmas` used to be a big bag of lemmas that made it there on the criterion that they needed "more imports". This was completely untrue, as all lemmas could be moved to earlier files in PRs: - #9440 - #9442 - #9443 - #9455 - #9456 - #9457 - #9459 - #9461 - #9463 - #9466 - #9501 - #9502 - #9503 - #9505 - #9551 - #9553 - #9720 - #9739 - #9740 - #9805 - #9806 - and this one There are several reasons for this: * Necessary lemmas have been moved to earlier files since lemmas were dumped in `Algebra.GroupPower.Lemmas` * In the Lean 3 → Lean 4 transition, Std acquired basic `Int` and `Nat` lemmas which let us shortcircuit the part of the algebraic order hierarchy on which the corresponding general lemmas rest * Some proofs were overpowered * Some earlier files were tangled and I have untangled them This PR finishes the job by moving the last few lemmas out of `Algebra.GroupPower.Lemmas`, which is therefore deleted.
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`Algebra.GroupPower.Lemmas` used to be a big bag of lemmas that made it there on the criterion that they needed "more imports". This was completely untrue, as all lemmas could be moved to earlier files in PRs: - #9440 - #9442 - #9443 - #9455 - #9456 - #9457 - #9459 - #9461 - #9463 - #9466 - #9501 - #9502 - #9503 - #9505 - #9551 - #9553 - #9720 - #9739 - #9740 - #9805 - #9806 - and this one There are several reasons for this: * Necessary lemmas have been moved to earlier files since lemmas were dumped in `Algebra.GroupPower.Lemmas` * In the Lean 3 → Lean 4 transition, Std acquired basic `Int` and `Nat` lemmas which let us shortcircuit the part of the algebraic order hierarchy on which the corresponding general lemmas rest * Some proofs were overpowered * Some earlier files were tangled and I have untangled them This PR finishes the job by moving the last few lemmas out of `Algebra.GroupPower.Lemmas`, which is therefore deleted.
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The current design for
absis flawed:Absnotation typeclass has exactly two instances: one for[Neg α] [Sup α], one for[Inv α] [Sup α]. This means that:Abs.absAbsinstances!Algebra.Order.Group.Absare about the additive version.Algebra.Order.Group.PosPart, and they get additivised to duplicates of the lemmas inAlgebra.Order.Group.Abs!This PR changes the notation typeclass with two new definitions (related through
to_additive):mabsandabs.absinherits the|a|notation andmabsgets|a|ₘinstead.The first half of
Algebra.Order.Group.Absgets multiplicativised. A later PR will multiplicativise the second half, and another one #9740 will deduplicate the lemmas inAlgebra.Order.Group.PosPart.Part of #9411. Closes #6376.