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Theorems · Theorem · combinatorics

Set.toFinset_nonempty

∀ {α : Type u_1} {s : Set α} [inst : Fintype ↑s], s.toFinset.Nonempty ↔ s.Nonempty
Defined in
Mathlib.Data.Fintype.Sets
Cited by
2 results in Mathlib
Foundations
Depth 59 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
Fintype
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Around this declaration

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

ZLattice.rank · cited by 5ZLattice.rankSet.Aesop.toFinset_nonempty_of_nonempty · cited by 0Aesop.toFinset_nonempty_o…Set · cited by 53352SetFintype · cited by 7736FintypeSet.Elem · cited by 7166Set.ElemSet.Nonempty · cited by 2627Set.NonemptyFinset.Nonempty · cited by 1001Finset.NonemptySet.toFinset · cited by 217Set.toFinsetSet.coe_toFinset · cited by 51Set.coe_toFinsetFinset.coe_nonempty · cited by 18Finset.coe_nonemptySet.toFinset_nonemptyCITED BYCITES

Cites8

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

Cited by2

Results whose statement or proof uses this declaration.