Theorems · Theorem · number theory
NumberField.FinitePlace.add_le
∀ {K : Type u_1} [inst : Field K] [inst_1 : NumberField K] (v : NumberField.FinitePlace K) (x y : K),
v (x + y) ≤ max (v x) (v y)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 191 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
- Fieldstatement and proof · cited by 7,404
- NumberFieldstatement and proof · cited by 653
- Subtype.propproof · cited by 505
- NumberField.RingOfIntegersproof · cited by 413
- IsDedekindDomain.HeightOneSpectrumproof · cited by 338
- NumberField.placeproof · cited by 71
- NumberField.FinitePlacestatement and proof · cited by 35
- NumberField.FinitePlace.embeddingproof · cited by 24
- NumberField.HeightOneSpectrum.adicAbvproof · cited by 21
- NumberField.HeightOneSpectrum.adicAbv_add_le_maxproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- Rat.iSup_finitePlace_apply_eq_one_of_gcd_eq_oneproof · cited by 1