Theorems · Theorem · field theory

Polynomial.aeval_prod

∀ {R : Type u} {A : Type z} {B : Type u_2} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Semiring B]
  [inst_3 : Algebra R A] [inst_4 : Algebra R B] (x : A × B),
  Polynomial.aeval x = (Polynomial.aeval x.1).prod (Polynomial.aeval x.2)

Polynomial evaluation on a pair is a product of the evaluations on the components.

Defined in

Mathlib.Algebra.Polynomial.AlgebraMap

Cited by

1 results in Mathlib

Foundations

Depth 112 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringSemiringSemiringAlgebraAlgebra