Theorems · Theorem · combinatorics
Infinite.exists_superset_card_eq
∀ {α : Type u_1} [Infinite α] (s : Finset α) (n : ℕ), s.card ≤ n → ∃ t, s ⊆ t ∧ t.card = nSee Infinite.exists_subset_card_eq for a version that provides an arbitrary
s : Finset α for any cardinality.
- Defined in
- Mathlib.Data.Fintype.EquivFin
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 64 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.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- LE.le.transproof · cited by 3,151
- Finset.cardstatement and proof · cited by 2,327
- Infinitestatement and proof · cited by 352
- Finset.consproof · cited by 221
- LE.le.eq_or_ltproof · cited by 220
- subset_rflproof · cited by 77
- Finset.card_consproof · cited by 16
- Finset.subset_consproof · cited by 5
- Infinite.exists_notMem_finsetproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- Filter.map_card_atTopproof · cited by 2
- Set.powersetCard.exist_mem_powersetCard_of_infproof · cited by 0
- Convex.helly_theorem_compactproof · cited by 0