Theorems · Definition · combinatorics
fintypeOrInfinite
(α : Type u_4) → Fintype α ⊕' Infinite α
Any type is (classically) either a Fintype, or Infinite.
One can obtain the relevant typeclasses via cases fintypeOrInfinite α.
- Defined in
- Mathlib.Data.Fintype.EquivFin
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Fintypestatement · cited by 7,736
- Infinitestatement and proof · cited by 352
- fintypeOfNotInfiniteproof · cited by 3
Cited by15
Results whose statement or proof uses this declaration.
- orderOf_dvd_natCardproof · cited by 14
- IsGaloisGroup.card_eq_finrankproof · cited by 10
- Cardinal.mk_finsupp_lift_of_infinite'proof · cited by 7
- addOrderOf_dvd_natCardproof · cited by 6
- Set.powersetCard.cardproof · cited by 5
- linearIndependent_le_basisproof · cited by 4
- LinearMap.det_restrictScalarsproof · cited by 2
- card_comm_eq_card_conjClasses_mul_cardproof · cited by 2
- Set.powersetCard.nontrivialproof · cited by 2
- mk_eq_mk_of_basisproof · cited by 1
- Module.Basis.le_spanproof · cited by 1
- Nat.equivFinOfCardPosproof · cited by 0