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Theorems · Theorem · order theory

Set.subsingleton_empty

∀ {α : Type u}, ∅.Subsingleton
Defined in
Mathlib.Data.Set.Subsingleton
Cited by
16 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.

Set.pairwise_empty · cited by 7Set.pairwise_emptyMetric.ediam_empty · cited by 7Metric.ediam_emptyMetric.subsingleton_closedBall · cited by 3Metric.subsingleton_close…Metric.diam_empty · cited by 3Metric.diam_emptySet.injOn_empty · cited by 2Set.injOn_emptyFilter.subsingleton_bot · cited by 1Filter.subsingleton_botAddAction.IsPreprimitive.of_isTrivialBlock_base · cited by 1IsPreprimitive.of_isTrivi…AddAction.IsPreprimitive.of_isTrivialBlock_of_notMem_fixedPoints · cited by 1IsPreprimitive.of_isTrivi…LocallyBoundedVariationOn.exists_monotoneOn_sub_monotoneOn' · cited by 1LocallyBoundedVariationOn…totallyDisconnectedSpace_iff_connectedComponent_subsingleton · cited by 1totallyDisconnectedSpace_…Set.einfsep_empty · cited by 1Set.einfsep_emptySet.infsep_empty · cited by 0Set.infsep_emptyAddAction.IsPreprimitive.of_card_lt · cited by 0IsPreprimitive.of_card_ltdimH_empty · cited by 0dimH_emptyPi.subsingleton_support_single · cited by 0Pi.subsingleton_support_s…Set · cited by 53352SetSet.Subsingleton · cited by 276Set.SubsingletonSet.subsingleton_emptyCITED BYCITES

Cites2

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

Cited by16

Results whose statement or proof uses this declaration.