Theorems · Theorem · number theory
Height.AdmissibleAbsValues.mulSupport_finite
Deprecated since 2026-03-03Use Height.AdmissibleAbsValues.hasFiniteMulSupport instead.
∀ {K : Type u_1} {inst : Field K} [self : Height.AdmissibleAbsValues K] {x : K},
x ≠ 0 → Function.HasFiniteMulSupport fun v => ↑v xAlias of Height.AdmissibleAbsValues.hasFiniteMulSupport.
Only finitely many (nonarchimedean) absolute values are ≠ 1 for any nonzero x : K.
- Defined in
- Mathlib.NumberTheory.Height.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 103 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Height.AdmissibleAbsValues
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Cites10
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 · cited by 7,404
- Set.Elemstatement · cited by 7,166
- AbsoluteValuestatement · cited by 363
- Height.AdmissibleAbsValuesstatement · cited by 110
- Function.HasFiniteMulSupportstatement · cited by 99
- Height.AdmissibleAbsValues.nonarchAbsValstatement · cited by 30
- Height.AdmissibleAbsValues.hasFiniteMulSupportproof · cited by 2
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