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Theorems · Theorem · order theory

Set.subset_ordConnectedComponent

∀ {α : Type u_1} [inst : LinearOrder α] {s : Set α} {x : α} {t : Set α} [h : s.OrdConnected],
  x ∈ s → s ⊆ t → s ⊆ t.ordConnectedComponent x
Defined in
Mathlib.Order.Interval.Set.OrdConnectedComponent
Cited by
2 results in Mathlib
Foundations
Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
LinearOrderSet.OrdConnected
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Around this declaration

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

Set.compl_ordConnectedSection_ordSeparatingSet_mem_nhdsGE · cited by 2Set.compl_ordConnectedSec…Set.ordConnectedComponent_mem_nhds · cited by 1Set.ordConnectedComponent…Set · cited by 53352SetLinearOrder · cited by 8572LinearOrderLE.le.trans · cited by 3151le.transSet.OrdConnected · cited by 161Set.OrdConnectedSet.ordConnectedComponent · cited by 23Set.ordConnectedComponentSet.OrdConnected.uIcc_subset · cited by 6OrdConnected.uIcc_subsetSet.subset_ordConnectedCompon…CITED BYCITES

Cites6

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Cited by2

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