Theorems · Definition · combinatorics
Set.Finite
{α : Type u} → Set α → PropA set is finite if the corresponding Subtype is finite,
i.e., if there exists a natural n : ℕ and an equivalence s ≃ Fin n.
- Defined in
- Mathlib.Data.Finite.Defs
- Cited by
- 1,814 results in Mathlib
- Foundations
- Depth 5 from the axioms, rests on 10 definitions · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
Cited by1,897
Results whose statement or proof uses this declaration.
- Set.Finite.toFinsetstatement and proof · cited by 351
- Set.Finite.subsetstatement and proof · cited by 285
- Set.Infiniteproof · cited by 263
- Filter.cofiniteproof · cited by 251
- Finset.finite_toSetstatement · cited by 210
- Summable.hasSumproof · cited by 184
- Set.toFinitestatement · cited by 174
- LocallyFiniteproof · cited by 141
- Set.Finite.coe_toFinsetstatement and proof · cited by 124
- Function.HasFiniteSupportproof · cited by 113
- Function.HasFiniteMulSupportproof · cited by 99
- Set.Finite.imagestatement and proof · cited by 96
Showing the 200 most cited of 1,897.