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Theorems · Theorem · number theory

NumberField.mixedEmbedding.convexBodySumFun_eq_zero_iff

∀ {K : Type u_1} [inst : Field K] [inst_1 : NumberField K] (x : NumberField.mixedEmbedding.mixedSpace K),
  NumberField.mixedEmbedding.convexBodySumFun x = 0 ↔ x = 0
Defined in
Mathlib.NumberTheory.NumberField.CanonicalEmbedding.ConvexBody
Cited by
2 results in Mathlib
Foundations
Depth 177 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FieldNumberField
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

NumberField.mixedEmbedding.convexBodySum_volume_eq_zero_of_le_zero · cited by 2mixedEmbedding.convexBody…NumberField.mixedEmbedding.convexBodySum_volume · cited by 1mixedEmbedding.convexBody…DFunLike.coe · cited by 62936DFunLike.coeReal · cited by 25697RealField · cited by 7404FieldComplex · cited by 5565ComplexFinset.univ · cited by 3473Finset.univLT.lt.le · cited by 2189lt.leNumberField · cited by 653NumberFieldNumberField.InfinitePlace · cited by 604NumberField.InfinitePlacemul_nonneg · cited by 397mul_nonnegNumberField.InfinitePlace.IsReal · cited by 301InfinitePlace.IsRealNumberField.InfinitePlace.IsComplex · cited by 272InfinitePlace.IsComplexNumberField.mixedEmbedding.mixedSpace · cited by 239mixedEmbedding.mixedSpaceNat.cast_pos · cited by 113Nat.cast_posNumberField.mixedEmbedding.normAtPlace · cited by 45mixedEmbedding.normAtPlaceFinset.sum_eq_zero_iff_of_nonneg · cited by 19Finset.sum_eq_zero_iff_of…mixedEmbedding.convexBodySumF…CITED BYCITES

Cites19

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Cited by2

Results whose statement or proof uses this declaration.