Theorems · Theorem · order theory
Set.Nonempty.not_disjoint
∀ {α : Type u} {s t : Set α}, (s ∩ t).Nonempty → ¬Disjoint s tAlias of the reverse direction of Set.not_disjoint_iff_nonempty_inter.
- Defined in
- Mathlib.Data.Set.Disjoint
- Cited by
- 4 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.
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_iff_nonempty_interproof · cited by 29
Cited by4
Results whose statement or proof uses this declaration.
- MonotoneOn.exists_monotone_extensionproof · cited by 2
- IsClosed.two_pow_mk_le_two_pow_mk_denseproof · cited by 2
- PiNat.cylinder_longestPrefix_eq_of_longestPrefix_lt_firstDiffproof · cited by 1
- isPreirreducible_iff_forall_mem_subset_closure_singletonproof · cited by 0