Theorems · Theorem · commutative algebra
Valuation.mem_unitGroup_iff
∀ (K : Type u) [inst : Field K] {Γ : Type u_1} [inst_1 : LinearOrderedCommGroupWithZero Γ] (v : Valuation K Γ) (x : Kˣ),
x ∈ v.valuationSubring.unitGroup ↔ v ↑x = 1- Cited by
- 0 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Fieldstatement and proof · cited by 7,404
- Subgroupstatement · cited by 3,593
- Unitsstatement and proof · cited by 2,804
- Units.valstatement · cited by 1,966
- Valuationstatement and proof · cited by 823
- LinearOrderedCommGroupWithZerostatement and proof · cited by 528
- Valuation.valuationSubringstatement · cited by 56
- ValuationSubring.unitGroupstatement · cited by 16
- Valuation.IsEquiv.symmproof · cited by 7
- Valuation.IsEquiv.eq_one_iff_eq_oneproof · cited by 5
- Valuation.isEquiv_valuation_valuationSubringproof · cited by 2
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