Theorems · Theorem · order theory
Set.subsingleton_of_subsingleton
∀ {α : Type u} [Subsingleton α] {s : Set α}, s.Subsingleton- Defined in
- Mathlib.Data.Set.Subsingleton
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
- Assumes
- Subsingleton
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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.Subsingletonstatement · cited by 276
- Set.subset_univproof · cited by 228
- Set.Subsingleton.antiproof · cited by 13
- Set.subsingleton_univproof · cited by 5
Cited by10
Results whose statement or proof uses this declaration.
- Set.PartiallyWellOrderedOn.partiallyWellOrderedOn_sublistForall₂proof · cited by 2
- trdeg_subsingletonproof · cited by 2
- Set.eq_empty_or_singleton_of_subsingletonproof · cited by 2
- Algebra.QuasiFiniteAt.of_isOpen_singletonproof · cited by 1
- AffineBasis.coe_coord_of_subsingleton_eq_oneproof · cited by 1
- MeasureTheory.StronglyMeasurable.of_subsingleton_codproof · cited by 1
- ProbabilityTheory.Kernel.iIndepSets.of_subsingletonproof · cited by 1
- AddAction.IsPreprimitive.of_subsingletonproof · cited by 0
- Set.intersecting_iff_eq_empty_of_subsingletonproof · cited by 0
- MulAction.IsPreprimitive.of_subsingletonproof · cited by 0