Theorems · Theorem · logic and foundations
Set.countable_ofPred_finite_subset
∀ {α : Type u} {s : Set α}, s.Countable → {t | t.Finite ∧ t ⊆ s}.CountableThe set of finite subsets of a countable set is countable.
- Defined in
- Mathlib.Data.Set.Countable
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Finsetproof · cited by 13,712
- SetLike.coeproof · cited by 8,199
- Set.Elemproof · cited by 7,166
- Set.ofPredstatement and proof · cited by 6,101
- Set.imageproof · cited by 5,609
- Set.Finitestatement and proof · cited by 1,814
- Countableproof · cited by 633
- Set.Countablestatement and proof · cited by 545
- Set.mem_range_selfproof · cited by 328
- Function.Injective.injOnproof · cited by 280
- Subtype.val_injectiveproof · cited by 232
Cited by5
Results whose statement or proof uses this declaration.
- TopologicalSpace.exists_countable_basisproof · cited by 9
- Set.Countable.ofPred_finiteproof · cited by 3
- MeasureTheory.countable_generateSetAlgebraproof · cited by 1
- ContinuousMap.secondCountableTopologyproof · cited by 0
- Set.countable_setOf_finite_subsetproof · cited by 0