Theorems · Inductive type · commutative algebra
WithVal
{R : Type u_1} →
{Γ₀ : Type u_2} → [inst : LinearOrderedCommGroupWithZero Γ₀] → [inst_1 : Ring R] → Valuation R Γ₀ → Type u_1Type synonym for a ring equipped with the topology coming from a valuation.
- Defined in
- Mathlib.Topology.Algebra.Valued.WithVal
- Cited by
- 151 results in Mathlib
- Foundations
- Depth 2 from the axioms, rests on 6 definitions · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Ringstatement · cited by 7,463
- Valuationstatement · cited by 823
- LinearOrderedCommGroupWithZerostatement · cited by 528
Cited by186
Results whose statement or proof uses this declaration.
- WithVal.ofValstatement and proof · cited by 47
- WithVal.equivstatement · cited by 36
- Valuation.Completionproof · cited by 33
- WithVal.equiv_symm_applystatement · cited by 13
- WithVal.congrstatement and proof · cited by 10
- WithVal.valueGroupEquivstatement · cited by 8
- WithVal.valueGroupOrderIso₀statement · cited by 7
- WithVal.equiv_applystatement and proof · cited by 6
- LaurentSeries.LaurentSeriesPkgstatement · cited by 6
- Rat.HeightOneSpectrum.adicCompletionIntegers.padicIntEquivproof · cited by 4
- WithVal.valuationstatement · cited by 4
- Valuation.IsEquiv.orderRingIsostatement and proof · cited by 4