Theorems · Theorem · logic and foundations
Set.empty_subset
∀ {α : Type u} (s : Set α), ∅ ⊆ s- Defined in
- Mathlib.Data.Set.Basic
- Cited by
- 70 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
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
Cited by71
Results whose statement or proof uses this declaration.
- Set.subset_empty_iffproof · cited by 40
- Matroid.exists_isBasis'proof · cited by 30
- Matroid.exists_isBasisproof · cited by 23
- closure_Iooproof · cited by 20
- Filter.principal_emptyproof · cited by 19
- Filter.empty_mem_iff_botproof · cited by 18
- Matroid.empty_indepproof · cited by 8
- exists_linearIndependentproof · cited by 6
- TopologicalSpace.isTopologicalBasis_of_subbasisproof · cited by 6
- Set.pi_subset_pi_iffproof · cited by 4
- Module.Basis.ofSpanstatement and proof · cited by 4
- MeasureTheory.Measure.InnerRegularWRT.exists_subset_lt_addproof · cited by 4