Theorems · Theorem · logic and foundations
Cardinal.aleph0_le_mk
∀ (α : Type u) [Infinite α], Cardinal.aleph0 ≤ Cardinal.mk α
- Defined in
- Mathlib.SetTheory.Cardinal.Basic
- Cited by
- 32 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Infinite
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
- Cardinal.aleph0statement · cited by 521
- Infinitestatement and proof · cited by 352
- Cardinal.infinite_iffproof · cited by 12
Cited by32
Results whose statement or proof uses this declaration.
- Cardinal.mk_eq_aleph0proof · cited by 20
- Cardinal.mk_finsupp_lift_of_infinite'proof · cited by 7
- Cardinal.add_mk_eq_maxproof · cited by 3
- Cardinal.mk_list_eq_mkproof · cited by 3
- Cardinal.mk_compl_of_infiniteproof · cited by 3
- Cardinal.mk_list_eq_maxproof · cited by 2
- Cardinal.exists_infinite_fiberproof · cited by 2
- Cardinal.mk_perm_eq_self_powerproof · cited by 2
- LinearIndependent.aleph0_le_rankproof · cited by 1
- Infinite.of_cardinalMk_leproof · cited by 1
- Cardinal.mk_surjective_eq_arrow_of_lift_leproof · cited by 1