Theorems · Theorem · order theory
Set.singleton_inter_nonempty
∀ {α : Type u_1} {s : Set α} {a : α}, ({a} ∩ s).Nonempty ↔ a ∈ s- Defined in
- Mathlib.Data.Set.Insert
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
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
- Set.Nonemptystatement · cited by 2,627
Cited by7
Results whose statement or proof uses this declaration.
- Set.singleton_inter_eq_emptyproof · cited by 5
- TopologicalSpace.isClosed_range_singletonproof · cited by 2
- IsPreconnected.preperfect_of_nontrivialproof · cited by 2
- Set.inter_singleton_nonemptyproof · cited by 2
- ProperlyDiscontinuousVAdd.finite_stabilizer'proof · cited by 1
- lowerHemicontinuous_singleton_idproof · cited by 1
- FirstOrder.Language.MeetsDefinable.closure_eq_selfproof · cited by 1