Theorems · Theorem · commutative algebra
Valuation.RankLeOne.exists_val_lt
∀ {Γ₀ : Type u_2} [inst : LinearOrderedCommGroupWithZero Γ₀] {K : Type u_4} [inst_1 : DivisionRing K]
(v : Valuation K Γ₀) [inst_2 : v.RankLeOne],
Subsingleton (MonoidWithZeroHom.ofClass v).ValueGroup₀ˣ ∨
∀ {γ : NNReal}, γ ≠ 0 → ∃ x, x ≠ 0 ∧ (Valuation.RankLeOne.hom' v) (v.restrict x) < γ- Defined in
- Mathlib.RingTheory.Valuation.RankOne
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 117 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- NNRealstatement and proof · cited by 4,310
- Subgroupstatement · cited by 3,593
- Unitsstatement and proof · cited by 2,804
- Nontrivialproof · cited by 2,416
- DivisionRingstatement and proof · cited by 1,062
- Valuationstatement and proof · cited by 823
- MonoidWithZeroHomstatement · cited by 704
- LinearOrderedCommGroupWithZerostatement and proof · cited by 528
- MonoidWithZeroHom.ofClassstatement and proof · cited by 204
- MonoidWithZeroHom.valueGroupstatement · cited by 170
- MonoidWithZeroHom.ValueGroup₀statement and proof · cited by 166
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