Theorems · Theorem · number theory
NumberField.norm_embedding_le_house
∀ {K : Type u_1} [inst : Field K] [inst_1 : NumberField K] (α : K) (σ : K →+* ℂ), ‖σ α‖ ≤ NumberField.house α- Defined in
- Mathlib.NumberTheory.NumberField.House
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 297 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.
- DFunLike.coestatement and proof · cited by 62,936
- Realstatement and proof · cited by 25,697
- RingHomstatement and proof · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Complexstatement and proof · cited by 5,565
- Norm.normstatement and proof · cited by 5,413
- NNNorm.nnnormproof · cited by 952
- NumberFieldstatement and proof · cited by 653
- Finset.mem_univproof · cited by 361
- Finset.le_sup'proof · cited by 25
- NumberField.housestatement · cited by 15
- NumberField.house_eq_sup'proof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- NumberField.norm_norm_le_norm_mul_house_powproof · cited by 0
- NumberField.one_le_house_of_isIntegralproof · cited by 0