Theorems · Theorem · order theory
Set.Icc_subset
∀ {α : Type u_1} [inst : Preorder α] (s : Set α) [hs : s.OrdConnected] {x y : α}, x ∈ s → y ∈ s → Set.Icc x y ⊆ s- Defined in
- Mathlib.Order.Interval.Set.OrdConnected
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses no axioms
- Assumes
- PreorderSet.OrdConnected
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- Preorderstatement and proof · cited by 7,952
- Set.Iccstatement · cited by 1,702
- Set.OrdConnectedstatement and proof · cited by 161
- Set.OrdConnected.outproof · cited by 47
Cited by1
Results whose statement or proof uses this declaration.
- Set.Nonempty.ordConnected_iff_of_bddproof · cited by 3