Theorems · Theorem · logic and foundations
Set.nonempty_iff_univ_nonempty
∀ {α : Type u}, Nonempty α ↔ Set.univ.Nonempty- Defined in
- Mathlib.Data.Set.Basic
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 6 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.
- Set.univstatement and proof · cited by 3,945
- Set.Nonemptystatement and proof · cited by 2,627
Cited by8
Results whose statement or proof uses this declaration.
- Set.IsWF.min_memproof · cited by 20
- Finset.univ_nonempty_iffproof · cited by 2
- exists_covBy_seq_of_wellFoundedLT_wellFoundedGTproof · cited by 2
- Submodule.finiteQuotient_iffproof · cited by 1
- SimpleGraph.Preconnected.set_univ_walk_nonemptyproof · cited by 1
- SimpleGraph.reachable_iff_nonempty_univproof · cited by 0
- connectedSpace_iff_clopenproof · cited by 0
- FirstOrder.Language.Theory.CompleteType.nonempty_iffproof · cited by 0