Theorems · Definition · combinatorics
Fintype.equivOfCardEq
{α : Type u_1} → {β : Type u_2} → [inst : Fintype α] → [inst_1 : Fintype β] → Fintype.card α = Fintype.card β → α ≃ βTwo Fintypes with the same cardinality are (noncomputably) in bijection.
See Fintype.truncEquivOfCardEq for the computable version,
and Fintype.truncEquivFinOfCardEq and Fintype.equivFinOfCardEq for
the specialization to Fin.
- Defined in
- Mathlib.Data.Fintype.EquivFin
- Cited by
- 23 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
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.truncEquivOfCardEqproof · cited by 1
Cited by34
Results whose statement or proof uses this declaration.
- Cardinal.mk_fintypeproof · cited by 81
- Matrix.IsHermitian.eigenvaluesproof · cited by 34
- Matrix.IsHermitian.eigenvectorBasisproof · cited by 12
- NumberField.mixedEmbedding.fractionalIdealLatticeBasisproof · cited by 11
- Fintype.bijective_iff_injective_and_cardproof · cited by 11
- NumberField.mixedEmbedding.fundamentalCone.equivFinRankproof · cited by 10
- NumberField.canonicalEmbedding.latticeBasisproof · cited by 7
- NumberField.canonicalEmbedding.latticeBasis_applyproof · cited by 7
- NumberField.equivReindexproof · cited by 7
- Fintype.bijective_iff_surjective_and_cardproof · cited by 5
- NumberField.Units.equivFinRankproof · cited by 5
- NumberField.Units.basisModTorsionproof · cited by 4