Theorems · Theorem · field theory

RatFunc.num_dvd

∀ {K : Type u} [inst : Field K] {x : RatFunc K} {p : Polynomial K},
  p ≠ 0 →
    (x.num ∣ p ↔ ∃ q, q ≠ 0 ∧ x = (algebraMap (Polynomial K) (RatFunc K)) p / (algebraMap (Polynomial K) (RatFunc K)) q)

Defined in

Mathlib.FieldTheory.RatFunc.Basic

Cited by

2 results in Mathlib

Foundations

Depth 132 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

Field