Theorems · Theorem · logic and foundations
Cardinal.exists_finset_eq_card
∀ {α : Type u_1} {n : ℕ}, ↑n ≤ Cardinal.mk α → ∃ s, n = s.card- Defined in
- Mathlib.SetTheory.Cardinal.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- Fintypeproof · cited by 7,736
- Finset.univproof · cited by 3,473
- Finiteproof · cited by 3,029
- Cardinalstatement · cited by 2,598
- Finset.cardstatement and proof · cited by 2,327
- Cardinal.mkstatement and proof · cited by 942
- Infiniteproof · cited by 352
- Fintype.ofFiniteproof · cited by 255
- Cardinal.mk_fintypeproof · cited by 81
- finite_or_infiniteproof · cited by 50
- Finset.exists_subset_card_eqproof · cited by 13
Cited by3
Results whose statement or proof uses this declaration.
- Cardinal.exists_finset_le_cardproof · cited by 2
- Module.le_rank_iff_exists_finsetproof · cited by 1
- SimpleGraph.egirth_topproof · cited by 1