Theorems · Theorem · commutative algebra
Valuation.RankOne.exists_val_lt
∀ {Γ₀ : Type u_2} [inst : LinearOrderedCommGroupWithZero Γ₀] {K : Type u_3} [inst_1 : DivisionRing K]
(v : Valuation K Γ₀) [inst_2 : v.RankOne] {γ : NNReal},
γ ≠ 0 → ∃ x, x ≠ 0 ∧ (Valuation.RankOne.hom v) (v.restrict x) < γ- Defined in
- Mathlib.RingTheory.Valuation.RankOne
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 116 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites25
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
- Units.valproof · cited by 1,966
- DivisionRingstatement and proof · cited by 1,062
- Valuationstatement and proof · cited by 823
- MonoidWithZeroHomstatement and proof · cited by 704
- DFunLikeproof · cited by 576
- LinearOrderedCommGroupWithZerostatement and proof · cited by 528
- MonoidWithZeroHom.ofClassstatement and proof · cited by 204
- pos_iff_ne_zeroproof · cited by 180
Cited by1
Results whose statement or proof uses this declaration.
- Valuation.RankLeOne.exists_val_ltproof · cited by 0