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Theorems · Theorem · order theory

Set.Finite.nonempty_fintype

∀ {α : Type u} {s : Set α}, s.Finite → Nonempty (Fintype ↑s)

Alias of the forward direction of Set.finite_def.

Defined in
Mathlib.Data.Set.Finite.Basic
Cited by
4 results in Mathlib
Foundations
Depth 64 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.Finite.fintype · cited by 38Finite.fintypeSet.Finite.exists_finset_coe · cited by 3Finite.exists_finset_coeFilter.HasBasis.iInf · cited by 3HasBasis.iInfSet.Finite.exists_finset · cited by 1Finite.exists_finsetBoundedContinuousFunction.arzela_ascoli₁ · cited by 1BoundedContinuousFunction…Set · cited by 53352SetFintype · cited by 7736FintypeSet.Elem · cited by 7166Set.ElemSet.Finite · cited by 1814Set.FiniteSet.finite_def · cited by 4Set.finite_defFinite.nonempty_fintypeCITED BYCITES

Cites5

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

Cited by5

Results whose statement or proof uses this declaration.