Theorems · Theorem · order theory
Set.disjoint_or_nonempty_inter
∀ {α : Type u} (s t : Set α), Disjoint s t ∨ (s ∩ t).Nonempty- Defined in
- Mathlib.Data.Set.Disjoint
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Classical.choice, 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 and proof · cited by 53,352
- Set.Nonemptystatement · cited by 2,627
- Disjointstatement and proof · cited by 2,201
- emproof · cited by 115
- Set.not_disjoint_iff_nonempty_interproof · cited by 29
Cited by5
Results whose statement or proof uses this declaration.
- IsUltrametricDist.ball_eq_or_disjointproof · cited by 1
- IsUltrametricDist.closedBall_eq_or_disjointproof · cited by 1
- IsUltrametricDist.ball_subset_trichotomyproof · cited by 0
- disjoint_or_subset_of_isClopenproof · cited by 0
- IsUltrametricDist.closedBall_subset_trichotomyproof · cited by 0