Theorems · Theorem · sequences and series

hasSum_le_inj

∀ {ι : Type u_1} {κ : Type u_2} {α : Type u_3} [inst : AddCommMonoid α] [inst_1 : Preorder α] [IsOrderedAddMonoid α]
  [inst_3 : TopologicalSpace α] [OrderClosedTopology α] {f : ι → α} {a₁ a₂ : α} {g : κ → α} (e : ι → κ),
  Function.Injective e → (∀ c ∉ Set.range e, 0 ≤ g c) → (∀ (i : ι), f i ≤ g (e i)) → HasSum f a₁ → HasSum g a₂ → a₁ ≤ a₂

Defined in

Mathlib.Topology.Algebra.InfiniteSum.Order

Cited by

1 results in Mathlib

Foundations

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

Assumes

AddCommMonoidPreorderIsOrderedAddMonoidTopologicalSpaceOrderClosedTopology