Theorems · Definition · logic and foundations
Nat.Subtype.denumerable
(s : Set ℕ) → [DecidablePred fun x => x ∈ s] → [Infinite ↑s] → Denumerable ↑s
Any infinite set of naturals is denumerable.
- Defined in
- Mathlib.Logic.Denumerable
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidablePredInfinite
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- Set.Elemstatement and proof · cited by 7,166
- Infinitestatement and proof · cited by 352
- Denumerablestatement · cited by 28
- Nat.Subtype.ofNatproof · cited by 9
- Denumerable.ofEquivproof · cited by 1
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