Theorems · Theorem · logic and foundations
Subsingleton.eq_univ_of_nonempty
∀ {α : Type u_1} [Subsingleton α] {s : Set α}, s.Nonempty → s = Set.univ- Defined in
- Mathlib.Data.Set.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Quot.sound
- Assumes
- Subsingleton
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.univstatement and proof · cited by 3,945
- Set.Nonemptystatement and proof · cited by 2,627
- Set.eq_univ_of_forallproof · cited by 80
Cited by5
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.addHaar_smulproof · cited by 13
- Subsingleton.set_casesproof · cited by 3
- MeasureTheory.partialTraj_const_restrict₂proof · cited by 1
- Bornology.IsVonNBounded.of_subsingletonproof · cited by 1
- Filter.eq_top_of_neBotproof · cited by 1