Theorems · Theorem · logic and foundations
Set.Infinite.exists_subset_countable_infinite
∀ {α : Type u} {s : Set α}, s.Infinite → ∃ t ⊆ s, t.Countable ∧ t.Infinite- Defined in
- Mathlib.Data.Set.Countable
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites11
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.Elemproof · cited by 7,166
- Set.rangeproof · cited by 4,705
- Set.Countablestatement · cited by 545
- Set.Infinitestatement and proof · cited by 263
- Subtype.val_injectiveproof · cited by 232
- Subtype.coe_propproof · cited by 42
- Set.countable_rangeproof · cited by 31
- Set.Infinite.natEmbeddingproof · cited by 10
- Set.infinite_range_of_injectiveproof · cited by 9
- Function.Embedding.casesOnproof · cited by 3
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