Theorems · Theorem · sequences and series

hasProd_lt

∀ {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}
  {a₁ a₂ : α} {i : ι} [L.NeBot] [L.LeAtTop], f ≤ g → f i < g i → HasProd f a₁ L → HasProd g a₂ L → a₁ < a₂

Defined in

Mathlib.Topology.Algebra.InfiniteSum.Order

Cited by

2 results in Mathlib

Foundations

Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommGroupPartialOrderIsOrderedMonoidTopologicalSpaceIsTopologicalGroupOrderClosedTopologySummationFilter.NeBotSummationFilter.LeAtTop