Theorems · Theorem · combinatorics
Infinite.exists_subset_card_eq
∀ (α : Type u_4) [Infinite α] (n : ℕ), ∃ s, s.card = n
See Infinite.exists_superset_card_eq for a version that, for an s : Finset α,
provides a superset t : Finset α, s ⊆ t such that #t is fixed.
- Defined in
- Mathlib.Data.Fintype.EquivFin
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Infinite
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement · cited by 13,712
- Finset.cardstatement · cited by 2,327
- Finset.rangeproof · cited by 1,341
- Finset.mapproof · cited by 747
- Infinitestatement and proof · cited by 352
- Finset.card_mapproof · cited by 114
- Finset.card_rangeproof · cited by 108
- Infinite.natEmbeddingproof · cited by 12
Cited by5
Results whose statement or proof uses this declaration.
- ENNReal.tsum_const_eq_top_of_ne_zeroproof · cited by 4
- Cardinal.exists_finset_eq_cardproof · cited by 3
- Module.length_finsuppproof · cited by 2
- Ring.HasFiniteQuotients.finite_cardQuot_leproof · cited by 2
- nonempty_orderEmbedding_of_finite_infiniteproof · cited by 1