Theorems · Theorem · logic and foundations
Cardinal.denumerable_iff
∀ {α : Type u}, Nonempty (Denumerable α) ↔ Cardinal.mk α = Cardinal.aleph0- Defined in
- Mathlib.SetTheory.Cardinal.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Equivproof · cited by 8,337
- Equiv.symmproof · cited by 3,681
- Cardinalstatement · cited by 2,598
- Cardinal.mkstatement and proof · cited by 942
- Cardinal.aleph0statement and proof · cited by 521
- Equiv.transproof · cited by 337
- Equiv.uliftproof · cited by 115
- Cardinal.mk_congrproof · cited by 55
- Denumerablestatement and proof · cited by 28
- Denumerable.eqvproof · cited by 6
- Denumerable.mk'proof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- Cardinal.mk_denumerableproof · cited by 6
- FirstOrder.Language.aleph0_categorical_dloproof · cited by 1