Theorems · Theorem · sequences and series

le_hasProd

∀ {ι : Type u_1} {α : Type u_3} {L : SummationFilter ι} [inst : CommMonoid α] [inst_1 : Preorder α] [IsOrderedMonoid α]
  [inst_3 : TopologicalSpace α] [OrderClosedTopology α] {f : ι → α} {a : α} [L.NeBot] [L.LeAtTop],
  HasProd f a L → ∀ (i : ι), (∀ (j : ι), j ≠ i → 1 ≤ f j) → f i ≤ a

Defined in

Mathlib.Topology.Algebra.InfiniteSum.Order

Cited by

3 results in Mathlib

Foundations

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

Assumes

CommMonoidPreorderIsOrderedMonoidTopologicalSpaceOrderClosedTopologySummationFilter.NeBotSummationFilter.LeAtTop