Theorems · Theorem · field theory

Polynomial.isRoot_prod

∀ {R : Type u_2} [inst : CommSemiring R] [IsDomain R] {ι : Type u_1} (s : Finset ι) (p : ι → Polynomial R) (x : R),
  (∏ j ∈ s, p j).IsRoot x ↔ ∃ i ∈ s, (p i).IsRoot x

Defined in

Mathlib.Algebra.Polynomial.Eval.Defs

Cited by

1 results in Mathlib

Foundations

Depth 108 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringIsDomain