Theorems · Theorem · order theory
Set.singleton_nonempty
∀ {α : Type u_1} (a : α), {a}.Nonempty- Defined in
- Mathlib.Data.Set.Insert
- Cited by
- 32 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses no axioms
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 · cited by 53,352
- Set.Nonemptystatement · cited by 2,627
Cited by32
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.addHaar_smulproof · cited by 13
- Set.exists_eq_singleton_iff_nonempty_subsingletonproof · cited by 9
- Set.singleton_ne_emptyproof · cited by 8
- isIrreducible_singletonproof · cited by 4
- isClosed_singleton_of_isLocallyClosed_singletonproof · cited by 3
- convexJoin_segmentsproof · cited by 2
- Dynamics.coverMincard_univproof · cited by 2
- Dynamics.coverMincard_zeroproof · cited by 2
- convexHull_insertproof · cited by 2
- PreconnectedSpace.trivial_of_discreteproof · cited by 2
- CategoryTheory.Functor.eval_section_surjective_of_surjectiveproof · cited by 2
- Dynamics.IsDynCoverOf.iterate_le_powproof · cited by 2