Theorems · Theorem · commutative algebra

Valuation.ltSubmodule_v_le_of_mem

∀ {Γ₀ : Type v} [inst : LinearOrderedCommGroupWithZero Γ₀] {K : Type u_1} [inst_1 : Field K] {v : Valuation K Γ₀}
  {S : Submodule (↥v.integer) K} {x : K}, x ∈ S → ∀ (hxv : v x ≠ 0), v.ltSubmodule (Units.mk0 (v x) hxv) ≤ S

Defined in

Mathlib.RingTheory.Valuation.Integers

Cited by

0 results in Mathlib

Foundations

Depth 47 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

LinearOrderedCommGroupWithZeroField