Theorems · Theorem · logic and foundations
Cardinal.mk_finset_of_infinite
∀ (α : Type u) [Infinite α], Cardinal.mk (Finset α) = Cardinal.mk α
- Defined in
- Mathlib.SetTheory.Cardinal.Arithmetic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 104 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 · cited by 13,712
- Cardinalstatement · cited by 2,598
- le_antisymmproof · cited by 2,068
- Cardinal.mkstatement · cited by 942
- Infinitestatement and proof · cited by 352
- Cardinal.mk_le_of_surjectiveproof · cited by 14
- Cardinal.mk_le_of_injectiveproof · cited by 12
- Cardinal.mk_list_eq_mkproof · cited by 3
- Finset.singleton_injproof · cited by 2
- List.toFinset_surjectiveproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- Cardinal.mk_finsupp_lift_of_infiniteproof · cited by 6
- linearIndependent_le_infinite_basisproof · cited by 1