Theorems · Theorem · order theory
Set.subset_singleton_iff
∀ {α : Type u_3} {s : Set α} {x : α}, s ⊆ {x} ↔ ∀ y ∈ s, y = x- Defined in
- Mathlib.Data.Set.Insert
- Cited by
- 12 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 by12
Results whose statement or proof uses this declaration.
- Subgroup.lowerCentralSeries_succ_eq_botproof · cited by 3
- IsLocalHomeomorphOn.discreteTopology_of_imageproof · cited by 3
- AddSubgroup.lowerCentralSeries_succ_eq_botproof · cited by 2
- PredOrder.isOpen_singleton_iffproof · cited by 2
- sSup_eq_bot'proof · cited by 1
- SpectrumRestricts.eq_zero_of_negproof · cited by 1
- LieSubmodule.lieSpan_eq_bot_iffproof · cited by 1
- CountableInfClosed.singletonproof · cited by 1
- Set.support_subset_subsingleton_of_disjoint_on_supportproof · cited by 1
- not_bounded_iff_exists_ne_zero_mem_asymptoticConeproof · cited by 0
- WithBot.sSup_emptyproof · cited by 0
- sInf_eq_top'proof · cited by 0