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Theorems · Theorem · real analysis

Monotone.rightLim_le

∀ {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 → Function.rightLim f x ≤ f y
Defined in
Mathlib.Topology.Order.LeftRightLim
Cited by
3 results in Mathlib
Foundations
Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
LinearOrderConditionallyCompleteLinearOrderTopologicalSpaceOrderTopology
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Monotone.ae_hasDerivAt · cited by 1Monotone.ae_hasDerivAtMonotone.rightLim_le_leftLim · cited by 1Monotone.rightLim_le_left…Antitone.le_rightLim · cited by 0Antitone.le_rightLimTopologicalSpace · cited by 24529TopologicalSpaceLinearOrder · cited by 8572LinearOrderMonotone · cited by 1397MonotoneOrderTopology · cited by 1355OrderTopologyConditionallyCompleteLinearOrder · cited by 542ConditionallyCompleteLine…Function.rightLim · cited by 52Function.rightLimMonotone.dual · cited by 39Monotone.dualMonotone.le_leftLim · cited by 9Monotone.le_leftLimMonotone.rightLim_leCITED BYCITES

Cites8

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by3

Results whose statement or proof uses this declaration.