Theorems · Theorem · logic and foundations
Cardinal.aleph0_lt_mk_iff
∀ {α : Type u}, Cardinal.aleph0 < Cardinal.mk α ↔ Uncountable α- Defined in
- Mathlib.SetTheory.Cardinal.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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 and proof · cited by 942
- Countableproof · cited by 633
- Cardinal.aleph0statement and proof · cited by 521
- not_leproof · cited by 328
- not_iff_notproof · cited by 159
- Uncountablestatement and proof · cited by 27
- not_countable_iffproof · cited by 4
- Cardinal.mk_le_aleph0_iffproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- Cardinal.aleph0_lt_mkproof · cited by 0
- Cardinal.aleph1_le_mk_iffproof · cited by 0