Theorems · Theorem · commutative algebra

Valuation.Integers.valuation_pos_iff_ne_zero

∀ {F : Type u} {Γ₀ : Type v} [inst : Field F] [inst_1 : LinearOrderedCommGroupWithZero Γ₀] {v : Valuation F Γ₀}
  {O : Type w} [inst_2 : CommRing O] [inst_3 : Algebra O F],
  v.Integers O → ∀ {x : O}, 0 < v ((algebraMap O F) x) ↔ x ≠ 0

Defined in

Mathlib.RingTheory.Valuation.Integers

Cited by

2 results in Mathlib

Foundations

Depth 45 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldLinearOrderedCommGroupWithZeroCommRingAlgebra