Theorems · Theorem · field theory

Polynomial.smeval_monomial_mul

∀ (R : Type u_1) [inst : Semiring R] (r : R) (p : Polynomial R) {S : Type u_2} [inst_1 : NonAssocSemiring S]
  [inst_2 : Module R S] [inst_3 : Pow S ℕ] (x : S) [NatPowAssoc S] [SMulCommClass R S S] (n : ℕ),
  ((Polynomial.monomial n) r * p).smeval x = r • (x ^ n * p.smeval x)

Defined in

Mathlib.Algebra.Polynomial.Smeval

Cited by

1 results in Mathlib

Foundations

Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringNonAssocSemiringModulePowNatPowAssocSMulCommClass