Theorems · Theorem · order theory
Set.inter_singleton_eq_empty
∀ {α : Type u_1} {s : Set α} {a : α}, s ∩ {a} = ∅ ↔ a ∉ s- Defined in
- Mathlib.Data.Set.Insert
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 27 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
- Set.inter_commproof · cited by 291
- Set.singleton_inter_eq_emptyproof · cited by 5
Cited by6
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.restrict_singletonproof · cited by 12
- Set.inter_singleton_of_notMemproof · cited by 4
- Affine.Simplex.abs_inner_vsub_altitudeFoot_lt_mulproof · cited by 2
- Matroid.indep_iff_forall_closure_sdiff_neproof · cited by 1
- Matroid.IsNonloop.isNonloop_of_mem_closureproof · cited by 1
- SummationFilter.eq_unconditional_of_finiteproof · cited by 0