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Theorems · Theorem · order theory

Set.mem_ordConnectedComponent_comm

∀ {α : Type u_1} [inst : LinearOrder α] {s : Set α} {x y : α},
  y ∈ s.ordConnectedComponent x ↔ x ∈ s.ordConnectedComponent y
Defined in
Mathlib.Order.Interval.Set.OrdConnectedComponent
Cited by
2 results in Mathlib
Foundations
Depth 19 from the axioms · uses propext
Assumes
LinearOrder
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Around this declaration

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

Set.ordConnectedComponent_eq · cited by 2Set.ordConnectedComponent…Set.mem_ordConnectedComponent_ordConnectedProj · cited by 2Set.mem_ordConnectedCompo…Set · cited by 53352SetLinearOrder · cited by 8572LinearOrderSet.uIcc · cited by 393Set.uIccSet.ordConnectedComponent · cited by 23Set.ordConnectedComponentSet.uIcc_comm · cited by 18Set.uIcc_commSet.mem_ordConnectedComponent · cited by 4Set.mem_ordConnectedCompo…Set.mem_ordConnectedComponent…CITED BYCITES

Cites6

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Cited by2

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