Theorems · Theorem · commutative algebra

ModP.v_p_lt_preVal

∀ {K : Type u₁} [inst : Field K] {v : Valuation K NNReal} {O : Type u₂} [inst_1 : CommRing O] [inst_2 : Algebra O K],
  v.Integers O → ∀ {p : ℕ} {x : ModP O p}, v ↑p < ModP.preVal K v O p x ↔ x ≠ 0

Defined in

Mathlib.RingTheory.Perfection

Cited by

1 results in Mathlib

Foundations

Depth 118 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldCommRingAlgebra