Theorems · Theorem · logic and foundations
Cardinal.mk_list_eq_max
∀ (α : Type u) [Nonempty α], Cardinal.mk (List α) = max Cardinal.aleph0 (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
- Nonempty
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.
- Finiteproof · cited by 3,029
- Cardinalstatement and proof · cited by 2,598
- Cardinal.mkstatement and proof · cited by 942
- Cardinal.aleph0statement and proof · cited by 521
- Infiniteproof · cited by 352
- max_eq_leftproof · cited by 96
- max_eq_rightproof · cited by 79
- finite_or_infiniteproof · cited by 50
- Cardinal.aleph0_le_mkproof · cited by 32
- Cardinal.mk_le_aleph0proof · cited by 9
- Cardinal.mk_list_eq_mkproof · cited by 3
- Cardinal.mk_list_eq_aleph0proof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- Cardinal.mk_list_eq_max_mk_aleph0proof · cited by 5
- Cardinal.sum_pow_eq_max_aleph0proof · cited by 0