Theorems · Theorem · commutative algebra
Valuation.pos_iff
∀ {K : Type u_1} [inst : DivisionRing K] {Γ₀ : Type u_4} [inst_1 : LinearOrderedCommMonoidWithZero Γ₀] [Nontrivial Γ₀]
(v : Valuation K Γ₀) {x : K}, 0 < v x ↔ x ≠ 0- Defined in
- Mathlib.RingTheory.Valuation.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 46 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Nontrivialstatement and proof · cited by 2,416
- DivisionRingstatement and proof · cited by 1,062
- Valuationstatement and proof · cited by 823
- LinearOrderedCommMonoidWithZerostatement and proof · cited by 139
- zero_lt_iffproof · cited by 29
- Valuation.ne_zero_iffproof · cited by 12
Cited by5
Results whose statement or proof uses this declaration.
- Valuation.one_lt_val_iffproof · cited by 4
- Valuation.one_le_val_iffproof · cited by 2
- Valuation.val_lt_one_iffproof · cited by 1
- AlgebraicGeometry.Proj.valuativeCriterion_existence_auxproof · cited by 1
- Valuation.val_le_one_iffproof · cited by 0