Theorems · Theorem · order theory
Set.finite_def
∀ {α : Type u} {s : Set α}, s.Finite ↔ Nonempty (Fintype ↑s)- Defined in
- Mathlib.Data.Set.Finite.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Fintypestatement · cited by 7,736
- Set.Elemstatement and proof · cited by 7,166
- Set.Finitestatement · cited by 1,814
- finite_iff_nonempty_fintypeproof · cited by 3
Cited by4
Results whose statement or proof uses this declaration.
- Set.Finite.nonempty_fintypeproof · cited by 4
- IsArtinianRing.setOfPred_isMaximal_finiteproof · cited by 2
- Module.Basis.finite_index_of_rank_lt_aleph0proof · cited by 1
- Module.Basis.finite_ofVectorSpaceIndex_of_rank_lt_aleph0proof · cited by 0