Theorems · Theorem · number theory
NumberField.mixedEmbedding.convexBodySum_neg_mem
∀ (K : Type u_1) [inst : Field K] [inst_1 : NumberField K] (B : ℝ) {x : NumberField.mixedEmbedding.mixedSpace K},
x ∈ NumberField.mixedEmbedding.convexBodySum K B → -x ∈ NumberField.mixedEmbedding.convexBodySum K B- Cited by
- 1 results in Mathlib
- Foundations
- Depth 177 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FieldNumberField
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- Fieldstatement and proof · cited by 7,404
- Complexstatement · cited by 5,565
- NumberFieldstatement and proof · cited by 653
- NumberField.InfinitePlacestatement · cited by 604
- NumberField.InfinitePlace.IsRealstatement · cited by 301
- NumberField.InfinitePlace.IsComplexstatement · cited by 272
- NumberField.mixedEmbedding.mixedSpacestatement and proof · cited by 239
- Set.mem_ofPredproof · cited by 104
- NumberField.mixedEmbedding.convexBodySumstatement and proof · cited by 11
- NumberField.mixedEmbedding.convexBodySumFun_negproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- NumberField.mixedEmbedding.exists_ne_zero_mem_ideal_of_norm_leproof · cited by 2