Theorems · Theorem · order theory
Set.ordConnected_iff_uIcc_subset
∀ {α : Type u_1} [inst : LinearOrder α] {s : Set α},
s.OrdConnected ↔ ∀ ⦃x : α⦄, x ∈ s → ∀ ⦃y : α⦄, y ∈ s → Set.uIcc x y ⊆ s- Defined in
- Mathlib.Order.Interval.Set.OrdConnected
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 57 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- LinearOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- LinearOrderstatement and proof · cited by 8,572
- LE.le.transproof · cited by 3,151
- Set.uIccstatement and proof · cited by 393
- Set.OrdConnectedstatement and proof · cited by 161
- Set.Icc_subset_uIccproof · cited by 12
- Set.OrdConnected.uIcc_subsetproof · cited by 6
Cited by1
Results whose statement or proof uses this declaration.
- Set.ordConnected_of_uIcc_subset_leftproof · cited by 1