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Theorems · Theorem · number theory

NumberField.InfiniteAdeleRing.ringEquiv_mixedSpace_apply

∀ (K : Type u_1) [inst : Field K] (x : NumberField.InfiniteAdeleRing K),
  (NumberField.InfiniteAdeleRing.ringEquiv_mixedSpace K) x =
    (fun v => (NumberField.InfinitePlace.Completion.extensionEmbeddingOfIsReal ⋯) (x ↑v), fun v =>
      (NumberField.InfinitePlace.Completion.extensionEmbedding ↑v) (x ↑v))
Defined in
Mathlib.NumberTheory.NumberField.InfiniteAdeleRing
Cited by
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Foundations
Depth 191 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
Field
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Around this declaration

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DFunLike.coe · cited by 62936DFunLike.coeReal · cited by 25697RealRingHom · cited by 10189RingHomField · cited by 7404FieldComplex · cited by 5565ComplexRingEquiv · cited by 1147RingEquivNumberField.InfinitePlace · cited by 604NumberField.InfinitePlaceNumberField.InfinitePlace.IsReal · cited by 301InfinitePlace.IsRealNumberField.InfinitePlace.IsComplex · cited by 272InfinitePlace.IsComplexNumberField.mixedEmbedding.mixedSpace · cited by 239mixedEmbedding.mixedSpaceNumberField.InfinitePlace.Completion · cited by 69InfinitePlace.CompletionNumberField.InfinitePlace.Completion.extensionEmbedding · cited by 15Completion.extensionEmbed…NumberField.InfiniteAdeleRing · cited by 10NumberField.InfiniteAdele…NumberField.InfinitePlace.Completion.extensionEmbeddingOfIsReal · cited by 9Completion.extensionEmbed…NumberField.InfiniteAdeleRing.ringEquiv_mixedSpace · cited by 2InfiniteAdeleRing.ringEqu…InfiniteAdeleRing.ringEquiv_m…CITED BYCITES

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