Theorems · Theorem · combinatorics
Finite.exists_equiv_fin
∀ (α : Sort u_3) [h : Finite α], ∃ n, Nonempty (α ≃ Fin n)
- Defined in
- Mathlib.Data.Finite.Defs
- Cited by
- 23 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
- Assumes
- Finite
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.
- Equivstatement · cited by 8,337
- Finitestatement and proof · cited by 3,029
- finite_iff_exists_equiv_finproof · cited by 1
Cited by26
Results whose statement or proof uses this declaration.
- nonempty_fintypeproof · cited by 261
- Finite.of_injectiveproof · cited by 32
- FirstOrder.Language.Formula.iExsproof · cited by 8
- Finite.equivFinproof · cited by 6
- FirstOrder.Language.Formula.iAllsproof · cited by 6
- CategoryTheory.FinitaryExtensive.isVanKampen_finiteCoproductsproof · cited by 3
- CategoryTheory.FinitaryPreExtensive.isUniversal_finiteCoproductsproof · cited by 3
- CategoryTheory.PreservesFiniteCoproducts.of_preserves_binary_and_initialproof · cited by 3
- CategoryTheory.Subfunctor.IsGeneratedBy.isFiniteproof · cited by 3
- MeasureTheory.exists_nat_measurableEquiv_range_coe_fin_of_finiteproof · cited by 1
- MeasureTheory.unifIntegrable_finiteproof · cited by 1
- MvPolynomial.IsHomogeneous.coeff_isHomogeneous_of_optionEquivLeft_symmproof · cited by 1