Theorems · Theorem · real analysis

Monotone.le_leftLim

∀ {α : Type u_1} {β : Type u_2} [inst : LinearOrder α] [inst_1 : ConditionallyCompleteLinearOrder β]
  [inst_2 : TopologicalSpace β] [OrderTopology β] {f : α → β},
  Monotone f → ∀ {x y : α}, x < y → f x ≤ Function.leftLim f y

Defined in

Mathlib.Topology.Order.LeftRightLim

Cited by

9 results in Mathlib

Foundations

Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

LinearOrderConditionallyCompleteLinearOrderTopologicalSpaceOrderTopology