Theorems · Definition · combinatorics
Fintype.equivFinOfCardEq
{α : Type u_1} → [inst : Fintype α] → {n : ℕ} → Fintype.card α = n → α ≃ Fin nIf the cardinality of α is n, there is noncomputably a bijection between α and Fin n.
See Fintype.truncEquivFinOfCardEq for the computable definition,
and Fintype.truncEquivFin and Fintype.equivFin for the bijection α ≃ Fin (card α).
- Defined in
- Mathlib.Data.Fintype.EquivFin
- Cited by
- 22 results in Mathlib
- Foundations
- Depth 60 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 and proof · cited by 1,386
- Trunc.outproof · cited by 6
- Fintype.truncEquivFinOfCardEqproof · cited by 2
Cited by30
Results whose statement or proof uses this declaration.
- Module.finBasisproof · cited by 22
- Finset.equivFinproof · cited by 15
- Finset.equivFinOfCardEqproof · cited by 6
- ContinuousMultilinearMap.toFormalMultilinearSeriesproof · cited by 5
- SimpleGraph.extremalNumber_of_fintypeCard_eqproof · cited by 3
- Orientation.map_eq_det_inv_smulproof · cited by 2
- Orientation.measure_orthonormalBasisproof · cited by 2
- SimpleGraph.zarankiewicz_of_fintypeCard_eqproof · cited by 2
- ContinuousMultilinearMap.hasFiniteFPowerSeriesOnBallproof · cited by 2
- Polynomial.eq_zero_of_degree_lt_of_eval_finset_eq_zeroproof · cited by 2
- Equiv.Perm.eq_top_of_isMultiplyPretransitiveproof · cited by 1
- ContinuousLinearMap.hasFiniteFPowerSeriesOnBall_uncurry_of_multilinearproof · cited by 1