Theorems · Theorem · commutative algebra
Valuation.mem_ltIdeal_iff
∀ {R : Type u} {Γ₀ : Type v} [inst : Ring R] [inst_1 : LinearOrderedCommGroupWithZero Γ₀] {v : Valuation R Γ₀} {γ : Γ₀ˣ}
{x : ↥v.integer}, x ∈ v.ltIdeal γ ↔ v ↑x < ↑γ- Defined in
- Mathlib.RingTheory.Valuation.Integers
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound
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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
- Ringstatement and proof · cited by 7,463
- Idealstatement · cited by 4,748
- Unitsstatement and proof · cited by 2,804
- Units.valstatement · cited by 1,966
- Valuationstatement and proof · cited by 823
- Subringstatement · cited by 602
- LinearOrderedCommGroupWithZerostatement and proof · cited by 528
- Valuation.integerstatement and proof · cited by 68
- Valuation.ltIdealstatement · cited by 4
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