Theorems · Theorem · order theory
Set.singleton_inter_eq_empty
∀ {α : Type u_1} {s : Set α} {a : α}, {a} ∩ s = ∅ ↔ a ∉ s- Defined in
- Mathlib.Data.Set.Insert
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, 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
- Iff.notproof · cited by 489
- Set.not_nonempty_iff_eq_emptyproof · cited by 56
- Set.singleton_inter_nonemptyproof · cited by 7
Cited by5
Results whose statement or proof uses this declaration.
- Set.inter_singleton_eq_emptyproof · cited by 6
- Matroid.fundCircuit_eq_of_notMem_groundproof · cited by 2
- Matroid.IsBase.compl_inter_isBasis_of_inter_isBasisproof · cited by 1
- Set.singleton_inter_of_notMemproof · cited by 0
- Matroid.not_isNonloop_iff_closureproof · cited by 0