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Theorems · Theorem · commutative algebra

ValuationSubring.valuation_le_one_iff

∀ {K : Type u} [inst : Field K] (A : ValuationSubring K) (x : K), A.valuation x ≤ 1 ↔ x ∈ A
Defined in
Mathlib.RingTheory.Valuation.ValuationSubring
Cited by
9 results in Mathlib
Foundations
Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
Field
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Valuation.isEquiv_valuation_valuationSubring · cited by 2Valuation.isEquiv_valuati…ValuationSubring.valuation_eq_one_iff · cited by 2ValuationSubring.valuatio…ValuationSubring.ofPrime_idealOfLE · cited by 2ValuationSubring.ofPrime_…ValuationSubring.valuationSubring_valuation · cited by 1ValuationSubring.valuatio…ValuationSubring.nonunits_le · cited by 1ValuationSubring.nonunits…ValuationSubring.mem_nonunits_iff_or · cited by 1ValuationSubring.mem_nonu…ValuationSubring.nonunits_le_nonunits · cited by 0ValuationSubring.nonunits…ValuationSubring.principalUnitGroup_le_principalUnitGroup · cited by 0ValuationSubring.principa…ValuationSubring.unitGroup_le_unitGroup · cited by 0ValuationSubring.unitGrou…DFunLike.coe · cited by 62936DFunLike.coeField · cited by 7404FieldValuation · cited by 823ValuationValuationSubring · cited by 187ValuationSubringValuationSubring.valuation · cited by 29ValuationSubring.valuationValuationSubring.ValueGroup · cited by 26ValuationSubring.ValueGro…ValuationSubring.valuation_le_one · cited by 3ValuationSubring.valuatio…ValuationSubring.mem_of_valuation_le_one · cited by 1ValuationSubring.mem_of_v…ValuationSubring.valuation_le…CITED BYCITES

Cites8

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by9

Results whose statement or proof uses this declaration.