Theorems · Theorem · real analysis
Monotone.le_rightLim
∀ {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.rightLim f y- Defined in
- Mathlib.Topology.Order.LeftRightLim
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- LinearOrderstatement and proof · cited by 8,572
- Monotonestatement and proof · cited by 1,397
- OrderTopologystatement and proof · cited by 1,355
- ConditionallyCompleteLinearOrderstatement and proof · cited by 542
- Function.rightLimstatement · cited by 52
- Monotone.dualproof · cited by 39
- Monotone.leftLim_leproof · cited by 13
Cited by4
Results whose statement or proof uses this declaration.
- Monotone.continuousAt_iff_leftLim_eq_rightLimproof · cited by 2
- Monotone.leftLim_le_rightLimproof · cited by 1
- Monotone.ae_hasDerivAtproof · cited by 1
- Antitone.rightLim_leproof · cited by 0