Theorems · Theorem · order theory
Set.OrdConnected.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
- 6 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext
- 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
- Set.uIccstatement · cited by 393
- Set.OrdConnectedstatement and proof · cited by 161
- Set.OrdConnected.outproof · cited by 47
- max_rec'proof · cited by 4
- min_rec'proof · cited by 3
Cited by6
Results whose statement or proof uses this declaration.
- Set.OrdConnected.isPreconnectedproof · cited by 9
- Set.ordConnected_iff_uIcc_subset_leftproof · cited by 2
- Set.compl_ordConnectedSection_ordSeparatingSet_mem_nhdsGEproof · cited by 2
- Set.subset_ordConnectedComponentproof · cited by 2
- Set.OrdConnected.uIoc_subsetproof · cited by 1
- Set.ordConnected_iff_uIcc_subsetproof · cited by 1