Theorems · Theorem · logic and foundations
Cardinal.mk_set_eq_nat_iff_finset
∀ {α : Type u_1} {s : Set α} {n : ℕ}, Cardinal.mk ↑s = ↑n ↔ ∃ t, ↑t = s ∧ t.card = n- Defined in
- Mathlib.SetTheory.Cardinal.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- Finsetstatement and proof · cited by 13,712
- SetLike.coestatement and proof · cited by 8,199
- Set.Elemstatement and proof · cited by 7,166
- Cardinalstatement · cited by 2,598
- Finset.cardstatement and proof · cited by 2,327
- Cardinal.mkstatement and proof · cited by 942
- Cardinal.mk_fintypeproof · cited by 81
- Fintype.card_coeproof · cited by 72
- Cardinal.natCast_lt_aleph0proof · cited by 47
- Cardinal.lt_aleph0_iff_set_finiteproof · cited by 7
- Cardinal.mk_coe_finsetproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- Submodule.exists_finset_span_eq_linearIndepOnproof · cited by 2
- Cardinal.mk_eq_nat_iff_finsetproof · cited by 1