Theorems · Theorem · group theory

finprod_mem_union

∀ {α : Type u_1} {M : Type u_5} [inst : CommMonoid M] {f : α → M} {s t : Set α},
  Disjoint s t →
    s.Finite → t.Finite → ∏ᶠ (i : α) (_ : i ∈ s ∪ t), f i = (∏ᶠ (i : α) (_ : i ∈ s), f i) * ∏ᶠ (i : α) (_ : i ∈ t), f i

Given two finite disjoint sets s and t, the product of f i over i ∈ s ∪ t equals the product of f i over i ∈ s times the product of f i over i ∈ t.

Defined in

Mathlib.Algebra.BigOperators.Finprod

Cited by

2 results in Mathlib

Foundations

Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommMonoid