Theorems · Theorem · logic and foundations
Cardinal.mk_lt_aleph0_iff
∀ {α : Type u}, Cardinal.mk α < Cardinal.aleph0 ↔ Finite α- Defined in
- Mathlib.SetTheory.Cardinal.Basic
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finitestatement and proof · cited by 3,029
- Cardinalstatement · cited by 2,598
- Cardinal.mkstatement · cited by 942
- Cardinal.aleph0statement · cited by 521
Cited by9
Results whose statement or proof uses this declaration.
- Module.rank_lt_aleph0_iffproof · cited by 8
- Order.cof_lt_aleph0_iffproof · cited by 4
- hasCardinalLT_aleph0_iffproof · cited by 3
- Module.finite_of_rank_eq_natproof · cited by 2
- TensorProduct.spanFinrank_top_eq_of_residueFieldproof · cited by 1
- Algebra.IsAlgebraic.isTranscendenceBasis_of_lift_le_trdegproof · cited by 1
- Cardinal.mk_lt_aleph0proof · cited by 1
- finite_of_isTranscendenceBasisproof · cited by 1
- finite_of_algebraicIndependentproof · cited by 0