Theorems · Theorem · logic and foundations
Cardinal.mk_eq_aleph0
∀ (α : Type u_1) [Countable α] [Infinite α], Cardinal.mk α = Cardinal.aleph0
- Defined in
- Mathlib.SetTheory.Cardinal.Basic
- Cited by
- 20 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Cardinalstatement · cited by 2,598
- Cardinal.mkstatement · cited by 942
- Countablestatement and proof · cited by 633
- Cardinal.aleph0statement · cited by 521
- LE.le.antisymmproof · cited by 507
- Infinitestatement and proof · cited by 352
- Cardinal.aleph0_le_mkproof · cited by 32
- Cardinal.mk_le_aleph0proof · cited by 9
Cited by20
Results whose statement or proof uses this declaration.
- MvPolynomial.cardinalMk_eq_max_liftproof · cited by 5
- Cardinal.mk_finsupp_natproof · cited by 3
- Cardinal.mk_list_eq_mkproof · cited by 3
- Cardinal.mk_freeAbelianGroupproof · cited by 2
- IsClub.sInterproof · cited by 2
- FirstOrder.Language.empty.isFraisseLimit_of_countable_infiniteproof · cited by 1
- Algebra.TensorProduct.not_isField_of_transcendentalproof · cited by 1
- Infinite.nonempty_fieldproof · cited by 1
- Polynomial.cardinalMk_eq_maxproof · cited by 1
- Real.rank_rat_realproof · cited by 1
- MeasurableSpace.generateMeasurableRec_omega_oneproof · cited by 1
- continuum_le_cardinal_of_nontriviallyNormedFieldproof · cited by 1