Theorems · Definition · number theory
NumberField.house
{K : Type u_1} → [inst : Field K] → [NumberField K] → K → ℝThe house of an algebraic number as the norm of its image by the canonical embedding.
- Defined in
- Mathlib.NumberTheory.NumberField.House
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 162 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.
Cites6
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
- Fieldstatement and proof · cited by 7,404
- Norm.normproof · cited by 5,413
- NumberFieldstatement and proof · cited by 653
- NumberField.canonicalEmbeddingproof · cited by 27
Cited by15
Results whose statement or proof uses this declaration.
- NumberField.house_eq_sup'statement · cited by 2
- NumberField.norm_embedding_le_housestatement · cited by 2
- NumberField.house_nonnegstatement · cited by 1
- NumberField.house_add_lestatement · cited by 0
- NumberField.house_intCaststatement · cited by 0
- NumberField.house_mul_lestatement · cited by 0
- NumberField.house_nat_mulstatement and proof · cited by 0
- NumberField.house_pow_lestatement · cited by 0
- NumberField.house_prod_lestatement · cited by 0
- NumberField.house_sum_le_sum_housestatement · cited by 0
- NumberField.norm_norm_le_norm_mul_house_powstatement and proof · cited by 0
- NumberField.house.basis_repr_norm_le_const_mul_housestatement and proof · cited by 0