Theorems · Theorem · sequences and series

Multipliable.tprod_lt_tprod

∀ {ι : Type u_1} {α : Type u_3} {L : SummationFilter ι} [inst : CommGroup α] [inst_1 : PartialOrder α]
  [IsOrderedMonoid α] [inst_3 : TopologicalSpace α] [IsTopologicalGroup α] [OrderClosedTopology α] {f g : ι → α} {i : ι}
  [L.NeBot] [L.LeAtTop],
  f ≤ g → f i < g i → Multipliable f L → Multipliable g L → ∏'[L] (n : ι), f n < ∏'[L] (n : ι), g n

Defined in

Mathlib.Topology.Algebra.InfiniteSum.Order

Cited by

2 results in Mathlib

Foundations

Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommGroupPartialOrderIsOrderedMonoidTopologicalSpaceIsTopologicalGroupOrderClosedTopologySummationFilter.NeBotSummationFilter.LeAtTop