Theorems · Theorem · logic and foundations
Cardinal.mk_le_aleph0
∀ {α : Type u} [Countable α], Cardinal.mk α ≤ Cardinal.aleph0- Defined in
- Mathlib.SetTheory.Cardinal.Basic
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Quot.sound
- Assumes
- Countable
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.
- Cardinalstatement · cited by 2,598
- Cardinal.mkstatement · cited by 942
- Countablestatement and proof · cited by 633
- Cardinal.aleph0statement · cited by 521
- Cardinal.mk_le_aleph0_iffproof · cited by 4
Cited by9
Results whose statement or proof uses this declaration.
- Cardinal.mk_eq_aleph0proof · cited by 20
- Cardinal.mk_list_le_maxproof · cited by 4
- Cardinal.nat_mul_aleph0proof · cited by 3
- Order.cof_eq_aleph0proof · cited by 2
- Cardinal.mk_list_eq_maxproof · cited by 2
- Computability.Encoding.card_le_aleph0proof · cited by 1
- Cardinal.mk_subtype_le_of_countable_eventually_mem_auxproof · cited by 1
- Cardinal.mk_list_eq_aleph0proof · cited by 1
- Set.Countable.substructure_closureproof · cited by 1