Theorems · Theorem · number theory
NumberField.house_sum_le_sum_house
∀ {K : Type u_1} [inst : Field K] [inst_1 : NumberField K] {ι : Type u_2} (s : Finset ι) (α : ι → K),
NumberField.house (∑ i ∈ s, α i) ≤ ∑ i ∈ s, NumberField.house (α i)- Defined in
- Mathlib.NumberTheory.NumberField.House
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 163 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FieldNumberField
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Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Realstatement · cited by 25,697
- Finsetstatement and proof · cited by 13,712
- Fieldstatement and proof · cited by 7,404
- Norm.normproof · cited by 5,413
- Finset.sumstatement and proof · cited by 5,195
- le_reflproof · cited by 2,061
- NumberFieldstatement and proof · cited by 653
- map_sumproof · cited by 455
- NumberField.canonicalEmbeddingproof · cited by 27
- NumberField.housestatement · cited by 15
- norm_sum_le_of_leproof · cited by 13
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