Theorems · Theorem · group theory

Finset.sum_finset_product

∀ {α : Type u_3} {β : Type u_4} {γ : Type u_5} [inst : AddCommMonoid β] (r : Finset (γ × α)) (s : Finset γ)
  (t : γ → Finset α),
  (∀ (p : γ × α), p ∈ r ↔ p.1 ∈ s ∧ p.2 ∈ t p.1) → ∀ {f : γ × α → β}, ∑ p ∈ r, f p = ∑ c ∈ s, ∑ a ∈ t c, f (c, a)

Defined in

Mathlib.Algebra.BigOperators.Group.Finset.Sigma

Cited by

3 results in Mathlib

Foundations

Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommMonoid