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Theorems · Theorem · order theory

Set.subsingleton_singleton

∀ {α : Type u} {a : α}, {a}.Subsingleton
Defined in
Mathlib.Data.Set.Subsingleton
Cited by
36 results in Mathlib
Foundations
Depth 5 from the axioms · uses no axioms
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Around this declaration

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

convex_singleton · cited by 13convex_singletonSet.subsingleton_iff_singleton · cited by 11Set.subsingleton_iff_sing…Metric.ediam_singleton · cited by 10Metric.ediam_singletonSet.exists_eq_singleton_iff_nonempty_subsingleton · cited by 9Set.exists_eq_singleton_i…Set.pairwise_singleton · cited by 7Set.pairwise_singletonMetric.diam_singleton · cited by 3Metric.diam_singletonSet.injOn_singleton · cited by 3Set.injOn_singletonSet.strictMonoOn_singleton · cited by 3Set.strictMonoOn_singletonSet.subsingleton_of_subset_singleton · cited by 3Set.subsingleton_of_subse…Set.subsingleton_zero_smul_set · cited by 3Set.subsingleton_zero_smu…Metric.subsingleton_closedBall · cited by 3Metric.subsingleton_close…threeAPFree_singleton · cited by 2threeAPFree_singletonIsPreirreducible.preimage · cited by 2IsPreirreducible.preimageisPreirreducible_singleton · cited by 2isPreirreducible_singletonSet.equitableOn_singleton · cited by 1Set.equitableOn_singletonSet · cited by 53352SetSet.Subsingleton · cited by 276Set.SubsingletonSet.eq_of_mem_singleton · cited by 22Set.eq_of_mem_singletonSet.subsingleton_singletonCITED BYCITES

Cites3

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by36

Results whose statement or proof uses this declaration.