Theorems · Theorem · logic and foundations
Set.countable_setOf_finite_subset
Deprecated since 2026-07-09Use Set.countable_ofPred_finite_subset instead.
∀ {α : Type u} {s : Set α}, s.Countable → {t | t.Finite ∧ t ⊆ s}.CountableAlias of Set.countable_ofPred_finite_subset.
The set of finite subsets of a countable set is countable.
- Defined in
- Mathlib.Data.Set.Countable
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Set.ofPredstatement · cited by 6,101
- Set.Finitestatement · cited by 1,814
- Set.Countablestatement · cited by 545
- Set.countable_ofPred_finite_subsetproof · cited by 5
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