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Theorems · Theorem · order theory

Set.ordConnected_iff_uIcc_subset_left

∀ {α : Type u_1} [inst : LinearOrder α] {s : Set α} {x : α},
  x ∈ s → (s.OrdConnected ↔ ∀ ⦃y : α⦄, y ∈ s → Set.uIcc x y ⊆ s)
Defined in
Mathlib.Order.Interval.Set.OrdConnected
Cited by
2 results in Mathlib
Foundations
Depth 59 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.

starConvex_iff_ordConnected · cited by 1starConvex_iff_ordConnect…Set.ordConnected_iff_uIcc_subset_right · cited by 0Set.ordConnected_iff_uIcc…Set · cited by 53352SetLinearOrder · cited by 8572LinearOrderSet.uIcc · cited by 393Set.uIccSet.OrdConnected · cited by 161Set.OrdConnectedSet.OrdConnected.uIcc_subset · cited by 6OrdConnected.uIcc_subsetSet.ordConnected_of_uIcc_subset_left · cited by 1Set.ordConnected_of_uIcc_…Set.ordConnected_iff_uIcc_sub…CITED BYCITES

Cites6

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Cited by2

Results whose statement or proof uses this declaration.