Theorems · Theorem · order theory
Set.compl_union
∀ {α : Type u_1} (s t : Set α), (s ∪ t)ᶜ = sᶜ ∩ tᶜ- Defined in
- Mathlib.Order.BooleanAlgebra.Set
- Cited by
- 30 results in Mathlib
- Foundations
- Depth 57 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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
- Compl.complstatement · cited by 2,925
- compl_supproof · cited by 8
Cited by30
Results whose statement or proof uses this declaration.
- IsClosed.unionproof · cited by 17
- closure_unionproof · cited by 13
- isPreconnected_closed_iffproof · cited by 6
- PrimeSpectrum.basicOpen_mulproof · cited by 5
- isDiscrete_of_codiscreteWithinproof · cited by 3
- polarCoord_source_ae_eq_univproof · cited by 3
- MonotoneOn.countable_not_continuousWithinAtproof · cited by 3
- ProjectiveSpectrum.basicOpen_mulproof · cited by 3
- coborder_eq_union_frontier_complproof · cited by 2
- SubMulAction.IsPretransitive.isPretransitive_ofFixingSubgroup_interproof · cited by 2
- Set.Countable.isPathConnected_compl_of_one_lt_rankproof · cited by 2
- Filter.comap_sumElim_eqproof · cited by 2