Theorems · Theorem · order theory
Set.disjoint_iff
∀ {α : Type u} {s t : Set α}, Disjoint s t ↔ s ∩ t ⊆ ∅- Defined in
- Mathlib.Data.Set.Disjoint
- Cited by
- 27 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext, 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
- Disjointstatement · cited by 2,201
- disjoint_iff_inf_leproof · cited by 64
Cited by27
Results whose statement or proof uses this declaration.
- Set.disjoint_image_of_injectiveproof · cited by 9
- IsPreconnected.subset_left_of_subset_unionproof · cited by 5
- jacobsonSpace_iff_locallyClosedproof · cited by 4
- Set.pairwise_disjoint_Ioc_add_zsmulproof · cited by 3
- SimpleGraph.ComponentCompl.disjoint_rightproof · cited by 3
- ringKrullDim_quotient_succ_le_of_nonZeroDivisorproof · cited by 3
- Finset.indicator_biUnionproof · cited by 2
- Finset.mulIndicator_biUnionproof · cited by 2
- disjoint_interior_extremePointsproof · cited by 2
- MeasureTheory.Measure.inf_applyproof · cited by 2
- SimpleGraph.disjoint_edgeSetproof · cited by 2
- Set.pairwise_disjoint_Ico_add_zsmulproof · cited by 2