Theorems · Theorem · order theory
Set.ordConnected_of_uIcc_subset_left
∀ {α : Type u_1} [inst : LinearOrder α] {s : Set α} {x : α}, (∀ y ∈ s, Set.uIcc x y ⊆ s) → s.OrdConnected- Defined in
- Mathlib.Order.Interval.Set.OrdConnected
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 58 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.
Cites8
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
- Set.uIccstatement and proof · cited by 393
- Set.OrdConnectedstatement · cited by 161
- Set.union_subsetproof · cited by 71
- Set.uIcc_commproof · cited by 18
- Set.uIcc_subset_uIcc_union_uIccproof · cited by 4
- Set.ordConnected_iff_uIcc_subsetproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Set.ordConnected_iff_uIcc_subset_leftproof · cited by 2