Theorems · Theorem · logic and foundations
Set.subset_eq_empty
∀ {α : Type u} {s t : Set α}, t ⊆ s → s = ∅ → t = ∅- Defined in
- Mathlib.Data.Set.Basic
- Cited by
- 6 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 by6
Results whose statement or proof uses this declaration.
- closure_empty_iffproof · cited by 2
- IsLindelof.indexed_countable_subcoverproof · cited by 2
- Set.exists_dissipate_eq_empty_iff_of_directedproof · cited by 1
- Metric.thickening_eq_empty_iff_of_posproof · cited by 1
- IsClosed.HasSeparatingCoverproof · cited by 0
- Set.iInter_eq_empty_of_eq_emptyproof · cited by 0