Theorems · Theorem · logic and foundations
Set.univ_eq_empty_iff
∀ {α : Type u}, Set.univ = ∅ ↔ IsEmpty α- Defined in
- Mathlib.Data.Set.Basic
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Set.univstatement and proof · cited by 3,945
- IsEmptystatement and proof · cited by 759
- Set.eq_empty_iff_forall_notMemproof · cited by 42
- IsEmpty.falseproof · cited by 24
Cited by13
Results whose statement or proof uses this declaration.
- Set.empty_ne_univproof · cited by 7
- MeasureTheory.nonempty_of_isProbabilityMeasureproof · cited by 4
- Set.indicator_const_preimageproof · cited by 2
- TopCat.Presheaf.isSheaf_of_isTerminal_of_indiscreteproof · cited by 2
- preconnectedSpace_iff_connectedComponentproof · cited by 1
- AddSubgroup.not_isComplement_empty_leftproof · cited by 1
- AddSubgroup.not_isComplement_empty_rightproof · cited by 1
- MeasureTheory.isTightMeasureSet_of_isCompact_closureproof · cited by 0
- Set.indicator_zero_preimageproof · cited by 0
- Sublattice.subsingleton_iffproof · cited by 0
- IsClosed.HasSeparatingCoverproof · cited by 0
- TopologicalSpace.isTopologicalBasis_emptyproof · cited by 0