Theorems · Theorem · logic and foundations
Cardinal.lt_aleph0
∀ {c : Cardinal.{u_1}}, c < Cardinal.aleph0 ↔ ∃ n, c = ↑n- Defined in
- Mathlib.SetTheory.Cardinal.Basic
- Cited by
- 19 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Finsetproof · cited by 13,712
- SetLike.coeproof · cited by 8,199
- Set.Elemproof · cited by 7,166
- Cardinalstatement and proof · cited by 2,598
- Finset.cardproof · cited by 2,327
- Set.Finiteproof · cited by 1,814
- Cardinal.mkproof · cited by 942
- Cardinal.liftproof · cited by 583
- Cardinal.aleph0statement and proof · cited by 521
- Infiniteproof · cited by 352
- Set.Infiniteproof · cited by 263
Cited by19
Results whose statement or proof uses this declaration.
- Cardinal.mul_lt_aleph0proof · cited by 6
- Cardinal.pow_leproof · cited by 5
- Cardinal.add_lt_aleph0proof · cited by 5
- Cardinal.power_lt_aleph0proof · cited by 4
- Ordinal.card_iSup_le_liftproof · cited by 3
- Cardinal.not_isSuccLimit_of_lt_aleph0proof · cited by 3
- Cardinal.aleph0_leproof · cited by 2
- Cardinal.mk_subtype_le_of_countable_eventually_mem_auxproof · cited by 1
- Coplanar.finiteDimensional_vectorSpanproof · cited by 1
- Cardinal.isSuccPrelimit_aleph0proof · cited by 1
- Cardinal.add_eq_left_iffproof · cited by 1
- Cardinal.le_ord_iff_card_le_of_lt_aleph0proof · cited by 1