Theorems · Theorem · sequences and series

isLUB_hasProd

∀ {ι : Type u_1} {α : Type u_3} [inst : CommMonoid α] [inst_1 : Preorder α] [IsOrderedMonoid α]
  [inst_3 : TopologicalSpace α] [OrderClosedTopology α] {f : ι → α} {a : α},
  (∀ (i : ι), 1 ≤ f i) → HasProd f a → IsLUB (Set.range fun s => ∏ i ∈ s, f i) a

Defined in

Mathlib.Topology.Algebra.InfiniteSum.Order

Cited by

0 results in Mathlib

Foundations

Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommMonoidPreorderIsOrderedMonoidTopologicalSpaceOrderClosedTopology