Theorems · Theorem · commutative algebra

Valuation.map_eq_one_of_forall_lt

∀ {K : Type u} [inst : DivisionRing K] {Γ₀ : Type v} [inst_1 : LinearOrderedCommGroupWithZero Γ₀] [MulArchimedean Γ₀]
  {v : Valuation K Γ₀} {r : Γ₀}, r ≠ 0 → (∀ (x : K), v x ≠ 0 → r < v x) → ∀ (x : K), v x ≠ 0 → v x = 1

Defined in

Mathlib.Topology.Algebra.Valued.ValuationTopology

Cited by

2 results in Mathlib

Foundations

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

Assumes

DivisionRingLinearOrderedCommGroupWithZeroMulArchimedean