Theorems · Theorem · commutative algebra
HahnSeries.addVal_apply_of_ne
∀ {Γ : Type u_1} {R : Type u_2} [inst : AddCancelCommMonoid Γ] [inst_1 : LinearOrder Γ]
[inst_2 : IsOrderedCancelAddMonoid Γ] [inst_3 : Ring R] [inst_4 : IsDomain R] {x : HahnSeries Γ R},
x ≠ 0 → (HahnSeries.addVal Γ R) x = ↑x.order- Defined in
- Mathlib.RingTheory.HahnSeries.Valuation
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 113 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- LinearOrderstatement and proof · cited by 8,572
- Ringstatement and proof · cited by 7,463
- WithTopstatement · cited by 3,754
- IsDomainstatement and proof · cited by 2,196
- WithTop.somestatement · cited by 1,128
- HahnSeriesstatement and proof · cited by 528
- IsOrderedCancelAddMonoidstatement and proof · cited by 359
- AddValuationstatement · cited by 96
- HahnSeries.orderstatement · cited by 52
- AddCancelCommMonoidstatement and proof · cited by 48
- HahnSeries.order_eq_orderTop_of_ne_zeroproof · cited by 4
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