Theorems · Theorem · order theory
Set.Nonempty.exists_eq_singleton_or_nontrivial
∀ {α : Type u} {s : Set α}, s.Nonempty → (∃ a, s = {a}) ∨ s.Nontrivial- Defined in
- Mathlib.Data.Set.Subsingleton
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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 and proof · cited by 2,627
- Set.Nontrivialstatement and proof · cited by 145
- Set.eq_singleton_or_nontrivialproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- TopologicalSpace.isClosed_range_singletonproof · cited by 2
- IsPreconnected.inter_derivedSet_nonemptyproof · cited by 0