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Theorems · Theorem · order theory

Set.ordConnectedComponent_eq

∀ {α : Type u_1} [inst : LinearOrder α] {s : Set α} {x y : α},
  Set.uIcc x y ⊆ s → s.ordConnectedComponent x = s.ordConnectedComponent y
Defined in
Mathlib.Order.Interval.Set.OrdConnectedComponent
Cited by
2 results in Mathlib
Foundations
Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
LinearOrder
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Around this declaration

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

Set.ordConnectedProj_eq · cited by 1Set.ordConnectedProj_eqSet.ordConnectedComponent_ordConnectedProj · cited by 1Set.ordConnectedComponent…Set · cited by 53352SetLinearOrder · cited by 8572LinearOrderSet.ext · cited by 2266Set.extSet.uIcc · cited by 393Set.uIccSet.ordConnectedComponent · cited by 23Set.ordConnectedComponentSet.mem_ordConnectedComponent_comm · cited by 2Set.mem_ordConnectedCompo…Set.mem_ordConnectedComponent_trans · cited by 2Set.mem_ordConnectedCompo…Set.ordConnectedComponent_eqCITED BYCITES

Cites7

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Cited by2

Results whose statement or proof uses this declaration.