Theorems · Theorem · order theory
Set.compl_empty_iff
∀ {α : Type u_1} {s : Set α}, sᶜ = ∅ ↔ s = Set.univ- Defined in
- Mathlib.Order.BooleanAlgebra.Set
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 60 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.univstatement · cited by 3,945
- Compl.complstatement · cited by 2,925
- compl_eq_botproof · cited by 4
Cited by11
Results whose statement or proof uses this declaration.
- spectrum.nonemptyproof · cited by 8
- MeasureTheory.ae_eq_topproof · cited by 4
- Set.eq_univ_iff_ncardproof · cited by 4
- ModelWithCorners.Boundaryless.boundary_eq_emptyproof · cited by 4
- Set.indicator_const_preimageproof · cited by 2
- SubMulAction.IsPretransitive.isPretransitive_ofFixingSubgroup_interproof · cited by 2
- ModelWithCorners.Boundaryless.iff_boundary_eq_emptyproof · cited by 1
- FirstOrder.Language.Theory.CompleteType.setOfPred_mem_eq_univ_iffproof · cited by 1
- Topology.IsScott.isOpen_iff_Iic_compl_or_univproof · cited by 1
- IsClosed.ae_eq_univ_iff_eqproof · cited by 1
- IsUpperSet.eq_univ_or_Ioiproof · cited by 0