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Theorems · Theorem · order theory

Set.ordConnectedComponent_subset

∀ {α : Type u_1} [inst : LinearOrder α] {s : Set α} {x : α}, s.ordConnectedComponent x ⊆ s
Defined in
Mathlib.Order.Interval.Set.OrdConnectedComponent
Cited by
3 results in Mathlib
Foundations
Depth 18 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.disjoint_left_ordSeparatingSet · cited by 3Set.disjoint_left_ordSepa…Set.ordConnectedSection_subset · cited by 1Set.ordConnectedSection_s…Set.ordConnectedComponent_mem_nhds · cited by 1Set.ordConnectedComponent…Set · cited by 53352SetLinearOrder · cited by 8572LinearOrderSet.ordConnectedComponent · cited by 23Set.ordConnectedComponentSet.right_mem_uIcc · cited by 13Set.right_mem_uIccSet.ordConnectedComponent_sub…CITED BYCITES

Cites4

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Cited by3

Results whose statement or proof uses this declaration.