Theorems · Theorem · number theory
NumberField.house_prod_le
∀ {K : Type u_1} [inst : Field K] [inst_1 : NumberField K] (s : Finset K),
NumberField.house (∏ x ∈ s, x) ≤ ∏ x ∈ s, NumberField.house x- Defined in
- Mathlib.NumberTheory.NumberField.House
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 296 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FieldNumberField
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Cites11
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.prodstatement and proof · cited by 2,356
- NumberFieldstatement and proof · cited by 653
- map_prodproof · cited by 108
- NumberField.canonicalEmbeddingproof · cited by 27
- NumberField.housestatement · cited by 15
- Finset.norm_prod_leproof · cited by 6
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