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Theorems · Theorem · order theory

Set.ordConnectedComponent_eq_empty

∀ {α : Type u_1} [inst : LinearOrder α] {s : Set α} {x : α}, s.ordConnectedComponent x = ∅ ↔ x ∉ s
Defined in
Mathlib.Order.Interval.Set.OrdConnectedComponent
Cited by
1 results in Mathlib
Foundations
Depth 26 from the axioms · uses propext, Quot.sound
Assumes
LinearOrder
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Around this declaration

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

Set.ordConnectedComponent_empty · cited by 0Set.ordConnectedComponent…Set · cited by 53352SetLinearOrder · cited by 8572LinearOrderSet.not_nonempty_iff_eq_empty · cited by 56Set.not_nonempty_iff_eq_e…Set.ordConnectedComponent · cited by 23Set.ordConnectedComponentSet.nonempty_ordConnectedComponent · cited by 1Set.nonempty_ordConnected…Set.ordConnectedComponent_eq_…CITED BYCITES

Cites5

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Cited by1

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