Theorems · Theorem · logic and foundations
Set.eq_empty_iff_forall_notMem
∀ {α : Type u} {s : Set α}, s = ∅ ↔ ∀ (x : α), x ∉ s- Defined in
- Mathlib.Data.Set.Basic
- Cited by
- 42 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
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.subset_empty_iffproof · cited by 40
Cited by42
Results whose statement or proof uses this declaration.
- Set.Ioc_eq_emptyproof · cited by 38
- Set.Icc_eq_emptyproof · cited by 24
- Set.Ico_eq_emptyproof · cited by 24
- Set.Ioo_eq_emptyproof · cited by 24
- Set.univ_eq_empty_iffproof · cited by 13
- Set.encard_eq_zeroproof · cited by 12
- Matroid.closure_union_eq_of_subset_coloopsproof · cited by 4
- asymptoticCone_emptyproof · cited by 4
- continuousOn_cfcₙproof · cited by 3
- PrimeSpectrum.zeroLocus_empty_of_one_memproof · cited by 3
- Set.Ioi_eq_empty_iffproof · cited by 3
- Matroid.IsBase.exchange_isBase_of_indepproof · cited by 3