Theorems · Definition · combinatorics
Fintype.ofEquiv
{β : Type u_2} → (α : Type u_4) → [Fintype α] → α ≃ β → Fintype βIf f : α ≃ β and α is a fintype, then β is also a fintype.
- Defined in
- Mathlib.Data.Fintype.OfMap
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 58 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.
- DFunLike.coeproof · cited by 62,936
- Equivstatement and proof · cited by 8,337
- Fintypestatement and proof · cited by 7,736
- Equiv.bijectiveproof · cited by 132
- Fintype.ofBijectiveproof · cited by 1
Cited by21
Results whose statement or proof uses this declaration.
- nonempty_fintypeproof · cited by 261
- Fintype.card_congrproof · cited by 67
- Module.Basis.ofZLatticeBasisproof · cited by 36
- Fintype.ofEquiv_cardstatement · cited by 16
- Module.Basis.ofZLatticeBasis_applyproof · cited by 11
- Fintype.induction_empty_optionstatement and proof · cited by 6
- PowerBasis.AlgHom.fintypeproof · cited by 5
- Module.length_pi_of_fintypeproof · cited by 2
- Cardinal.mk_compl_eq_mk_compl_finite_liftproof · cited by 2
- Cardinal.prod_eq_of_fintypeproof · cited by 2
- SymbolicDynamics.FullShift.finite_setOfPred_pattern_support_eqproof · cited by 1
- Fintype.card_embedding_eqproof · cited by 1