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Theorems · Theorem · number theory

NumberField.mixedEmbedding.convexBodySumFun_add_le

∀ {K : Type u_1} [inst : Field K] [inst_1 : NumberField K] (x y : NumberField.mixedEmbedding.mixedSpace K),
  NumberField.mixedEmbedding.convexBodySumFun (x + y) ≤
    NumberField.mixedEmbedding.convexBodySumFun x + NumberField.mixedEmbedding.convexBodySumFun y
Defined in
Mathlib.NumberTheory.NumberField.CanonicalEmbedding.ConvexBody
Cited by
2 results in Mathlib
Foundations
Depth 176 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 · cited by 1mixedEmbedding.convexBody…NumberField.mixedEmbedding.convexBodySum_convex · cited by 1mixedEmbedding.convexBody…DFunLike.coe · cited by 62936DFunLike.coeReal · cited by 25697RealField · cited by 7404FieldComplex · cited by 5565ComplexFinset.sum · cited by 5195Finset.sumFinset.univ · cited by 3473Finset.univFinset.sum_congr · cited by 2323Finset.sum_congrLT.lt.le · cited by 2189lt.leNumberField · cited by 653NumberFieldNumberField.InfinitePlace · cited by 604NumberField.InfinitePlacemul_le_mul_of_nonneg_left · cited by 361mul_le_mul_of_nonneg_leftNumberField.InfinitePlace.IsReal · cited by 301InfinitePlace.IsRealNumberField.InfinitePlace.IsComplex · cited by 272InfinitePlace.IsComplexNumberField.mixedEmbedding.mixedSpace · cited by 239mixedEmbedding.mixedSpaceFinset.sum_le_sum · cited by 182Finset.sum_le_summixedEmbedding.convexBodySumF…CITED BYCITES

Cites21

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Cited by2

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