Theorems · Definition · combinatorics
Fintype.equivFin
(α : Type u_4) → [inst : Fintype α] → α ≃ Fin (Fintype.card α)
There is (noncomputably) an equivalence between α and Fin (card α).
See Fintype.truncEquivFin for the computable version,
and Fintype.truncEquivFinOfCardEq and Fintype.equivFinOfCardEq
for an equiv α ≃ Fin n given Fintype.card α = n.
- Defined in
- Mathlib.Data.Fintype.EquivFin
- Cited by
- 51 results in Mathlib
- Foundations
- Depth 59 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Fintype
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.
- Equivstatement · cited by 8,337
- Fintypestatement and proof · cited by 7,736
- Fintype.cardstatement · cited by 1,386
- Trunc.outproof · cited by 6
- Fintype.truncEquivFinproof · cited by 1
Cited by59
Results whose statement or proof uses this declaration.
- Algebra.FiniteType.iff_quotient_mvPolynomial''proof · cited by 10
- CategoryTheory.FinCategory.ObjAsTypeproof · cited by 6
- Fintype.finiteproof · cited by 5
- Finset.card_eq_of_equiv_fintypeproof · cited by 4
- MeasureTheory.integral_fintype_prod_eq_prodproof · cited by 4
- card_eq_of_linearEquivproof · cited by 4
- FintypeCat.uSwitchproof · cited by 3
- FintypeCat.uSwitchEquivproof · cited by 3
- Set.Finite.fin_embeddingproof · cited by 3
- SimpleGraph.completeMultipartiteGraph.not_cliqueFree_of_le_cardproof · cited by 3
- Sym.card_sym_eq_multichooseproof · cited by 3
- MvPolynomial.exists_fin_renameproof · cited by 3