Theorems · Theorem · commutative algebra

Valuation.Integer.not_isUnit_iff_valuation_lt_one

∀ {F : Type u} {Γ₀ : Type v} [inst : Field F] [inst_1 : LinearOrderedCommGroupWithZero Γ₀] {v : Valuation F Γ₀}
  {x : ↥v.integer}, ¬IsUnit x ↔ v ↑x < 1

Defined in

Mathlib.RingTheory.Valuation.Integers

Cited by

2 results in Mathlib

Foundations

Depth 48 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldLinearOrderedCommGroupWithZero