Theorems · Theorem · commutative algebra

MvPowerSeries.prod_smul_X_eq_smul_monomial_one

∀ {σ : Type u_1} {R : Type u_2} [inst : CommSemiring R] {A : Type u_4} [inst_1 : CommSemiring A] [inst_2 : Algebra A R]
  (e : σ →₀ ℕ) (a : σ → A),
  (e.prod fun s n => (a s • MvPowerSeries.X s) ^ n) = (e.prod fun s n => a s ^ n) • (MvPowerSeries.monomial e) 1

Defined in

Mathlib.RingTheory.MvPowerSeries.Basic

Cited by

2 results in Mathlib

Foundations

Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringCommSemiringAlgebra