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Theorems · Theorem · order theory

Set.Nonempty.subset_singleton_iff

∀ {α : Type u_1} {s : Set α} {a : α}, s.Nonempty → (s ⊆ {a} ↔ s = {a})
Defined in
Mathlib.Data.Set.Insert
Cited by
5 results in Mathlib
Foundations
Depth 28 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.Nonempty.subset_one_iff · cited by 1Nonempty.subset_one_iffconvexHull_eq_singleton · cited by 1convexHull_eq_singletonPartialOrder.dirSupClosed_singleton · cited by 1PartialOrder.dirSupClosed…Set.Nonempty.subset_zero_iff · cited by 1Nonempty.subset_zero_iffConvexity.convexHull_eq_singleton · cited by 0Convexity.convexHull_eq_s…Set · cited by 53352SetSet.Nonempty · cited by 2627Set.NonemptySet.Nonempty.ne_empty · cited by 65Nonempty.ne_emptySet.subset_singleton_iff_eq · cited by 10Set.subset_singleton_iff_…Nonempty.subset_singleton_iffCITED BYCITES

Cites4

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Cited by5

Results whose statement or proof uses this declaration.