Theorems · Theorem · sequences and series

hasProd_prod_disjoint

∀ {α : Type u_1} {β : Type u_2} [inst : CommMonoid α] [inst_1 : TopologicalSpace α] {f : β → α} [ContinuousMul α]
  {ι : Type u_4} (s : Finset ι) {t : ι → Set β} {a : ι → α},
  (↑s).Pairwise (Function.onFun Disjoint t) →
    (∀ i ∈ s, HasProd (f ∘ Subtype.val) (a i)) → HasProd (f ∘ Subtype.val) (∏ i ∈ s, a i)

Defined in

Mathlib.Topology.Algebra.InfiniteSum.Basic

Cited by

1 results in Mathlib

Foundations

Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommMonoidTopologicalSpaceContinuousMul