Theorems · Theorem · commutative algebra

DividedPowers.dpow_sum

∀ {A : Type u_1} [inst : CommSemiring A] {I : Ideal A} (hI : DividedPowers I) {ι : Type u_2} [inst_1 : DecidableEq ι]
  {s : Finset ι} {x : ι → A},
  (∀ i ∈ s, x i ∈ I) → ∀ {n : ℕ}, hI.dpow n (s.sum x) = ∑ k ∈ s.sym n, ∏ i ∈ s, hI.dpow (Multiset.count i ↑k) (x i)

A “multinomial” theorem for divided powers — without multinomial coefficients.

Defined in

Mathlib.RingTheory.DividedPowers.Basic

Cited by

2 results in Mathlib

Foundations

Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringDecidableEq