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Theorems · Theorem · order theory

Set.ssubset_singleton_iff

∀ {α : Type u_1} {s : Set α} {x : α}, s ⊂ {x} ↔ s = ∅
Defined in
Mathlib.Data.Set.Insert
Cited by
2 results in Mathlib
Foundations
Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Set.isAtom_singleton · cited by 1Set.isAtom_singletonSet.eq_empty_of_ssubset_singleton · cited by 0Set.eq_empty_of_ssubset_s…Set · cited by 53352SetSet.subset_singleton_iff_eq · cited by 10Set.subset_singleton_iff_…ssubset_iff_subset_ne · cited by 7ssubset_iff_subset_neSet.empty_ne_singleton · cited by 1Set.empty_ne_singletonSet.ssubset_singleton_iffCITED BYCITES

Cites4

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Cited by2

Results whose statement or proof uses this declaration.