Theorems · Theorem · commutative algebra
Valuation.mem_ltAddSubgroup_iff
∀ {R : Type u_3} {Γ₀ : Type u_4} [inst : Ring R] [inst_1 : LinearOrderedCommGroupWithZero Γ₀] {v : Valuation R Γ₀}
{γ : Γ₀ˣ} {x : R}, x ∈ v.ltAddSubgroup γ ↔ v x < ↑γ- Defined in
- Mathlib.RingTheory.Valuation.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites8
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
- AddSubgroupstatement · cited by 3,232
- 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.ltAddSubgroupstatement · cited by 12
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