Theorems · Definition · combinatorics
Fintype.ofSurjective
{α : Type u_1} → {β : Type u_2} → [DecidableEq β] → [Fintype α] → (f : α → β) → Function.Surjective f → Fintype βIf f : α → β is a surjection and α is a fintype, then β is also a fintype.
- Defined in
- Mathlib.Data.Fintype.OfMap
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEqFintype
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 and proof · cited by 7,736
- Finset.univproof · cited by 3,473
- Finset.imageproof · cited by 910
Cited by6
Results whose statement or proof uses this declaration.
- Fintype.ofInjectiveproof · cited by 3
- Nat.bijective_iff_surjective_and_cardproof · cited by 1
- AddCommGroup.equiv_directSum_zmod_of_finiteproof · cited by 1
- ClassGroup.fintypeOfAdmissibleOfAlgebraicproof · cited by 0
- IsLocalization.fintype'proof · cited by 0
- Set.inj_on_of_surj_on_of_ncard_leproof · cited by 0