Mathlib Map

Theorems · Theorem · order theory

Set.nonempty_ordConnectedComponent

∀ {α : Type u_1} [inst : LinearOrder α] {s : Set α} {x : α}, (s.ordConnectedComponent x).Nonempty ↔ x ∈ s
Defined in
Mathlib.Order.Interval.Set.OrdConnectedComponent
Cited by
1 results in Mathlib
Foundations
Depth 20 from the axioms · uses propext, Quot.sound
Assumes
LinearOrder
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Set.ordConnectedComponent_eq_empty · cited by 1Set.ordConnectedComponent…Set · cited by 53352SetLinearOrder · cited by 8572LinearOrderSet.Nonempty · cited by 2627Set.NonemptySet.ordConnectedComponent · cited by 23Set.ordConnectedComponentSet.left_mem_uIcc · cited by 17Set.left_mem_uIccSet.self_mem_ordConnectedComponent · cited by 2Set.self_mem_ordConnected…Set.nonempty_ordConnectedComp…CITED BYCITES

Cites6

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by1

Results whose statement or proof uses this declaration.