Theorems · Theorem · group theory

Finset.sum_biUnion_of_pairwise_eq_zero

∀ {ι : Type u_1} {κ : Type u_2} {M : Type u_4} [inst : AddCommMonoid M] {f : ι → M} [inst_1 : DecidableEq ι]
  {s : Finset κ} {t : κ → Finset ι},
  ((↑s).Pairwise fun i j => ∀ k ∈ t i ∩ t j, f k = 0) → ∑ x ∈ s.biUnion t, f x = ∑ x ∈ s, ∑ i ∈ t x, f i

Defined in

Mathlib.Algebra.BigOperators.Group.Finset.Basic

Cited by

0 results in Mathlib

Foundations

Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommMonoidDecidableEq