Theorems · Theorem · sequences and series

one_le_tprod

∀ {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] {g : ι → α}, (∀ (i : ι), 1 ≤ g i) → 1 ≤ ∏'[L] (i : ι), g i

Defined in

Mathlib.Topology.Algebra.InfiniteSum.Order

Cited by

0 results in Mathlib

Foundations

Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommMonoidPreorderIsOrderedMonoidTopologicalSpaceOrderClosedTopology