Theorems · Theorem · order theory
Set.not_disjoint_iff_nonempty_inter
∀ {α : Type u} {s t : Set α}, ¬Disjoint s t ↔ (s ∩ t).Nonempty- Defined in
- Mathlib.Data.Set.Disjoint
- Cited by
- 29 results in Mathlib
- Foundations
- Depth 24 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.Nonemptystatement · cited by 2,627
- Disjointstatement · cited by 2,201
- Set.not_disjoint_iffproof · cited by 30
Cited by29
Results whose statement or proof uses this declaration.
- isPreconnected_closed_iffproof · cited by 6
- Set.disjoint_or_nonempty_interproof · cited by 5
- IsPreconnected.subset_left_of_subset_unionproof · cited by 5
- AddAction.isBlock_iff_vadd_eq_of_nonemptyproof · cited by 4
- Set.Nonempty.not_disjointproof · cited by 4
- memPartitionSet_eq_iffproof · cited by 3
- AddAction.isBlock_iff_vadd_eq_vadd_of_nonemptyproof · cited by 3
- Vitali.exists_disjoint_subfamily_covering_enlargementproof · cited by 3
- Set.zero_mem_sub_iffproof · cited by 3
- Set.countable_ofPred_nonempty_of_disjointproof · cited by 2
- BoxIntegral.Box.not_disjoint_coe_iff_nonempty_interproof · cited by 2
- connectedComponent_eq_iInter_isClopenproof · cited by 2