Theorems · Theorem · real analysis
Monotone.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 → Monotone (Function.leftLim f)- Defined in
- Mathlib.Topology.Order.LeftRightLim
- Cited by
- 3 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.
Cites11
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
- LE.le.transproof · cited by 3,151
- le_rflproof · cited by 1,558
- Monotonestatement and proof · cited by 1,397
- OrderTopologystatement and proof · cited by 1,355
- ConditionallyCompleteLinearOrderstatement and proof · cited by 542
- eq_or_lt_of_leproof · cited by 92
- Function.leftLimstatement · cited by 60
- Monotone.leftLim_leproof · cited by 13
- Monotone.le_leftLimproof · cited by 9
Cited by3
Results whose statement or proof uses this declaration.
- StieltjesFunction.measure_Icoproof · cited by 2
- Monotone.rightLimproof · cited by 1
- Antitone.leftLimproof · cited by 0