[Merged by Bors] - feat: Conjugate exponents in ℝ≥0
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It happens often that we have `p q : ℝ≥0` that are conjugate. So far, we only had a predicate for real numbers to be conjugate, which made dealing with `ℝ≥0` conjugates clumsy. This PR * introduces `NNReal.IsConjExponent`, `NNReal.conjExponent` * renames `Real.IsConjugateExponent`, `Real.conjugateExponent` to `Real.IsConjExponent`, `Real.conjExponent` * renames a few more lemmas to match up the `Real` and `NNReal` versions From LeanAPAP
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| /-- Two real exponents `p, q` are conjugate if they are `> 1` and satisfy the equality | ||
| `1/p + 1/q = 1`. This condition shows up in many theorems in analysis, notably related to `L^p` | ||
| norms. -/ | ||
| @[mk_iff] | ||
| structure IsConjExponent (p q : ℝ) : Prop where |
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Is there a typeclass that abstracts this? I guess it would be something like OrderedSemifield... which we probably don't have.
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We do have LinearOrderedSemifield. Do you think that's worth it given that there are exactly two types which we would use this for (namely ℝ and ℝ≥0. ℝ≥0∞ is not a linear ordered semifield so would need to be handled separately)?
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If it roughly halves the length of this file, then yes I would attempt to use it, I think.
If we can come up with a typeclass that also humours ENNReal, that would be even better.
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I can't, actually. There's too much about tsub that's not generalised (generalisable?) so that it applies to both Real and NNReal.
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It happens often that we have `p q : ℝ≥0` that are conjugate. So far, we only had a predicate for real numbers to be conjugate, which made dealing with `ℝ≥0` conjugates clumsy. This PR * introduces `NNReal.IsConjExponent`, `NNReal.conjExponent` * renames `Real.IsConjugateExponent`, `Real.conjugateExponent` to `Real.IsConjExponent`, `Real.conjExponent` * renames a few more lemmas to match up the `Real` and `NNReal` versions From LeanAPAP
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ℝ≥0ℝ≥0
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It happens often that we have `p q : ℝ≥0` that are conjugate. So far, we only had a predicate for real numbers to be conjugate, which made dealing with `ℝ≥0` conjugates clumsy. This PR * introduces `NNReal.IsConjExponent`, `NNReal.conjExponent` * renames `Real.IsConjugateExponent`, `Real.conjugateExponent` to `Real.IsConjExponent`, `Real.conjExponent` * renames a few more lemmas to match up the `Real` and `NNReal` versions From LeanAPAP
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It happens often that we have `p q : ℝ≥0` that are conjugate. So far, we only had a predicate for real numbers to be conjugate, which made dealing with `ℝ≥0` conjugates clumsy. This PR * introduces `NNReal.IsConjExponent`, `NNReal.conjExponent` * renames `Real.IsConjugateExponent`, `Real.conjugateExponent` to `Real.IsConjExponent`, `Real.conjExponent` * renames a few more lemmas to match up the `Real` and `NNReal` versions From LeanAPAP
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It happens often that we have `p q : ℝ≥0` that are conjugate. So far, we only had a predicate for real numbers to be conjugate, which made dealing with `ℝ≥0` conjugates clumsy. This PR * introduces `NNReal.IsConjExponent`, `NNReal.conjExponent` * renames `Real.IsConjugateExponent`, `Real.conjugateExponent` to `Real.IsConjExponent`, `Real.conjExponent` * renames a few more lemmas to match up the `Real` and `NNReal` versions From LeanAPAP
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It happens often that we have `p q : ℝ≥0` that are conjugate. So far, we only had a predicate for real numbers to be conjugate, which made dealing with `ℝ≥0` conjugates clumsy. This PR * introduces `NNReal.IsConjExponent`, `NNReal.conjExponent` * renames `Real.IsConjugateExponent`, `Real.conjugateExponent` to `Real.IsConjExponent`, `Real.conjExponent` * renames a few more lemmas to match up the `Real` and `NNReal` versions From LeanAPAP
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It happens often that we have
p q : ℝ≥0that are conjugate. So far, we only had a predicate for real numbers to be conjugate, which made dealing withℝ≥0conjugates clumsy.This PR
NNReal.IsConjExponent,NNReal.conjExponentReal.IsConjugateExponent,Real.conjugateExponenttoReal.IsConjExponent,Real.conjExponentRealandNNRealversionsFrom LeanAPAP