feat(Data/Fin/Basic): Refactor succAbove and predAbove. #9145
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Co-authored-by: Scott Morrison <scott.morrison@gmail.com>
adds instances for the new `NonUnital(Semi)NormedCommRing` classes, and also adds some missing instances to `Analysis.Normed.Field.Basic`. This gives us our first example of an actually non-unital *commutative* C⋆-algebra: `C₀(X, ℂ)` where `X` is a locally compact, noncompact Hausdorff space. - [x] depends on: #8664
Generalize some theorems from `{β : Type*} [Countable β] (f : β → α)`
to `{ι : Sort*} [Countable ι] (f : ι → α)`.
This way they automatically work for `f : (p : Prop) → α`.
* Generalize `MeasureTheory.OuterMeasure.iUnion_null`,
`MeasureTheory.OuterMeasure.iUnion_null_iff`,
`MeasureTheory.measure_iUnion_null`, and
`MeasureTheory.measure_iUnion_null_iff`.
* Deprecate `MeasureTheory.OuterMeasure.iUnion_null_iff'`
and `MeasureTheory.measure_iUnion_null_iff'`.
* Generalize `MeasureTheory.exists_measurable_superset_forall_eq`
and `MeasureTheory.exists_measure_pos_of_not_measure_iUnion_null`.
* Reorder implicit arguments in some theorems (move `ι` around).
Some of the concepts in `LinearAlgebra/SesquilinearForm` can be generalised from Sesquilinear Forms to Sesquilinear Maps with little or no impact on the rest of Mathlib. This PR makes those generalisations. Further generalisations are likely possible, but the scope of this PR is to only consider changes which do not require non-trivial modifications to other parts of Mathlib, or other sections in `SesquilinearForm.lean`. Further changes can be considered in subsequent PRs if desired. Co-authored-by: Christopher Hoskin <mans0954@users.noreply.github.com>
This also adds some missing `to_additive`s for `vadd`.
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This was referenced Feb 1, 2024
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This PR is going to be closed, and #10283 will replace its substantative results. (It is now stale, and I have extracted the key changes and implemented them piecemeal.) |
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We currently implemented
succAboveandpredAbovein a way that encourages users to reduce things down to fiddling linear arithmetic, which makes it difficult to prove complicated identities.It is possible to re-define these and improve the proofs dramatically. An aid to this is to add "predAboveOfNe", which broadly is similar to
predAbovebut is a true inverse tosuccAbovein the appropriate manner. One can then prove results about this which let the simplifier make short work of identities that would otherwise be fairly complicated.This also has the advantage of making insertNth easier to use. (To be demonstrated!)