Theorems · Theorem · number theory
Height.AdmissibleAbsValues.hasFiniteMulSupport
∀ {K : Type u_1} {inst : Field K} [self : Height.AdmissibleAbsValues K] {x : K},
x ≠ 0 → Function.HasFiniteMulSupport fun v => ↑v xOnly finitely many (nonarchimedean) absolute values are ≠ 1 for any nonzero x : K.
- Defined in
- Mathlib.NumberTheory.Height.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Height.AdmissibleAbsValues
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement · cited by 53,352
- Realstatement · cited by 25,697
- Fieldstatement and proof · cited by 7,404
- Set.Elemstatement · cited by 7,166
- AbsoluteValuestatement · cited by 363
- Height.AdmissibleAbsValuesstatement and proof · cited by 110
- Function.HasFiniteMulSupportstatement · cited by 99
- Height.AdmissibleAbsValues.nonarchAbsValstatement · cited by 30
Cited by2
Results whose statement or proof uses this declaration.
- Height.mulHeight_smul_eq_mulHeightproof · cited by 6
- Height.AdmissibleAbsValues.mulSupport_finiteproof · cited by 0