Theorems · Theorem · real analysis
Antitone.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},
Antitone f → ∀ {x y : α}, x ≤ y → f y ≤ Function.leftLim f x- Defined in
- Mathlib.Topology.Order.LeftRightLim
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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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
- OrderTopologystatement and proof · cited by 1,355
- Antitonestatement and proof · cited by 563
- ConditionallyCompleteLinearOrderstatement and proof · cited by 542
- Function.leftLimstatement · cited by 60
- Antitone.dual_rightproof · cited by 42
- Monotone.leftLim_leproof · cited by 13
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