Theorems · Theorem · order theory
Finset.finite_toSet
∀ {α : Type u} (s : Finset α), (↑s).FiniteGives a Set.Finite for the Finset coerced to a Set.
This is a wrapper around Set.toFinite.
- Defined in
- Mathlib.Data.Set.Finite.Basic
- Cited by
- 210 results in Mathlib
- Foundations
- Depth 62 from the axioms, rests on 895 definitions · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- SetLike.coestatement and proof · cited by 8,199
- Set.Finitestatement · cited by 1,814
- Set.toFiniteproof · cited by 174
Cited by211
Results whose statement or proof uses this declaration.
- Finset.countable_toSetproof · cited by 32
- Submodule.fg_defproof · cited by 18
- Module.Finite.transproof · cited by 16
- isIntegral_transproof · cited by 15
- Filter.eventually_all_finsetproof · cited by 12
- Filter.biInter_finset_memproof · cited by 10
- Set.exists_finite_iff_finsetproof · cited by 9
- Finset.measurableSet_biUnionproof · cited by 8
- IsCompact.elim_finite_subcover_imageproof · cited by 8
- Module.Finite.finite_basisproof · cited by 8
- Polynomial.finite_setOfPred_isRootproof · cited by 7
- isOpen_biInter_finsetproof · cited by 7
Showing the 200 most cited of 211.