Theorems · Theorem · logic and foundations
Set.subset_empty_iff
∀ {α : Type u} {s : Set α}, s ⊆ ∅ ↔ s = ∅- Defined in
- Mathlib.Data.Set.Basic
- Cited by
- 40 results in Mathlib
- Foundations
- Depth 22 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.empty_subsetproof · cited by 70
- Set.Subset.antisymm_iffproof · cited by 4
Cited by40
Results whose statement or proof uses this declaration.
- Set.eq_empty_iff_forall_notMemproof · cited by 42
- Set.eq_empty_of_forall_notMemproof · cited by 21
- Set.eq_empty_of_subset_emptyproof · cited by 15
- Function.support_eq_empty_iffproof · cited by 7
- Set.subset_eq_emptyproof · cited by 6
- Module.support_eq_empty_iffproof · cited by 5
- Function.mulSupport_eq_empty_iffproof · cited by 4
- interior_frontierproof · cited by 3
- Set.powerset_emptyproof · cited by 3
- MeasureTheory.Content.innerContent_botproof · cited by 3
- IsCompactSystem.insert_univproof · cited by 2
- Set.Countable.isPathConnected_compl_of_one_lt_rankproof · cited by 2