Theorems · Theorem · logic and foundations
Cardinal.mk_finsupp_lift_of_infinite
∀ (α : Type u) (β : Type v) [Infinite α] [inst : Zero β] [Nontrivial β],
Cardinal.mk (α →₀ β) = max (Cardinal.lift.{v, u} (Cardinal.mk α)) (Cardinal.lift.{u, v} (Cardinal.mk β))- Defined in
- Mathlib.SetTheory.Cardinal.Finsupp
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 105 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- InfiniteZeroNontrivial
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsuppstatement and proof · cited by 5,255
- Cardinalstatement and proof · cited by 2,598
- Nontrivialstatement and proof · cited by 2,416
- le_antisymmproof · cited by 2,068
- Finsupp.singleproof · cited by 943
- Cardinal.mkstatement and proof · cited by 942
- Cardinal.liftstatement and proof · cited by 583
- Infinitestatement and proof · cited by 352
- Cardinal.lift_idproof · cited by 163
- exists_neproof · cited by 101
- max_leproof · cited by 71
- Cardinal.lift_umaxproof · cited by 56
Cited by6
Results whose statement or proof uses this declaration.
- Cardinal.mk_finsupp_lift_of_infinite'proof · cited by 7
- AddMonoidAlgebra.cardinalMk_eq_max_lift_of_infiniteproof · cited by 4
- MonoidAlgebra.cardinalMk_eq_max_lift_of_infiniteproof · cited by 3
- rank_fun_infiniteproof · cited by 2
- Infinite.nonempty_fieldproof · cited by 1
- Cardinal.mk_finsupp_of_infiniteproof · cited by 0