Mathlib Map

Theorems · Theorem · order theory

Set.Finite.toFinset_nonempty

∀ {α : Type u} {s : Set α} (hs : s.Finite), hs.toFinset.Nonempty ↔ s.Nonempty
Defined in
Mathlib.Data.Set.Finite.Basic
Cited by
2 results in Mathlib
Foundations
Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Set.finite_iff_bddAbove_bddBelow · cited by 0Set.finite_iff_bddAbove_b…Set.finite_iff_bddBelow_bddAbove · cited by 0Set.finite_iff_bddBelow_b…Set · cited by 53352SetSet.Nonempty · cited by 2627Set.NonemptySet.Finite · cited by 1814Set.FiniteFinset.Nonempty · cited by 1001Finset.NonemptySet.Finite.toFinset · cited by 351Finite.toFinsetSet.Finite.coe_toFinset · cited by 124Finite.coe_toFinsetFinset.coe_nonempty · cited by 18Finset.coe_nonemptyFinite.toFinset_nonemptyCITED BYCITES

Cites7

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.