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Theorems · Theorem · order theory

Set.singleton_injective

∀ {α : Type u_1}, Function.Injective singleton
Defined in
Mathlib.Data.Set.Insert
Cited by
9 results in Mathlib
Foundations
Depth 8 from the axioms · uses propext, Quot.sound
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Around this declaration

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

TopologicalSpace.vietoris.isEmbedding_singleton · cited by 4vietoris.isEmbedding_sing…UniformSpace.hausdorff.isUniformEmbedding_singleton · cited by 4hausdorff.isUniformEmbedd…TopologicalSpace.NonemptyCompacts.singleton_injective · cited by 3NonemptyCompacts.singleto…Set.isAddUnit_iff · cited by 2Set.isAddUnit_iffTopologicalSpace.Compacts.singleton_injective · cited by 2Compacts.singleton_inject…PrimeSpectrum.toPiLocalization_surjective_of_discreteTopology · cited by 2PrimeSpectrum.toPiLocaliz…TopologicalSpace.Closeds.singleton_injective · cited by 1Closeds.singleton_injecti…TopologicalSpace.IrreducibleCloseds.singleton_injective · cited by 1IrreducibleCloseds.single…Set.isUnit_iff · cited by 0Set.isUnit_iffSet · cited by 53352SetSet.singleton_eq_singleton_iff · cited by 13Set.singleton_eq_singleto…Set.singleton_injectiveCITED BYCITES

Cites2

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

Cited by9

Results whose statement or proof uses this declaration.