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Theorems · Theorem · number theory

NumberField.mixedEmbedding.stdBasis_apply_isComplex_snd

∀ {K : Type u_1} [inst : Field K] [inst_1 : NumberField K] (x : NumberField.mixedEmbedding.mixedSpace K)
  (w : { w // w.IsComplex }), ((NumberField.mixedEmbedding.stdBasis K).repr x) (Sum.inr (w, 1)) = (x.2 w).im
Defined in
Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic
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Foundations
Depth 167 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FieldNumberField
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DFunLike.coe · cited by 62936DFunLike.coeReal · cited by 25697RealRingHom.id · cited by 18349RingHom.idField · cited by 7404FieldComplex · cited by 5565ComplexFinsupp · cited by 5255FinsuppLinearEquiv · cited by 3317LinearEquivNumberField · cited by 653NumberFieldNumberField.InfinitePlace · cited by 604NumberField.InfinitePlaceComplex.im · cited by 591Complex.imModule.Basis.repr · cited by 498Basis.reprNumberField.InfinitePlace.IsReal · cited by 301InfinitePlace.IsRealNumberField.InfinitePlace.IsComplex · cited by 272InfinitePlace.IsComplexNumberField.mixedEmbedding.mixedSpace · cited by 239mixedEmbedding.mixedSpaceNumberField.mixedEmbedding.index · cited by 15mixedEmbedding.indexmixedEmbedding.stdBasis_apply…CITED BYCITES

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