Theorems · Theorem · combinatorics
AddMonoidAlgebra.cardinalMk_eq_max_lift_of_infinite
∀ (R : Type u) (M' : Type v) [inst : Semiring R] [Infinite M'] [Nontrivial R],
Cardinal.mk (AddMonoidAlgebra R M') =
max (Cardinal.lift.{v, u} (Cardinal.mk R)) (Cardinal.lift.{u, v} (Cardinal.mk M'))- Defined in
- Mathlib.Algebra.MonoidAlgebra.Cardinal
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringInfiniteNontrivial
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- Cardinalstatement · cited by 2,598
- Nontrivialstatement and proof · cited by 2,416
- Cardinal.mkstatement and proof · cited by 942
- AddMonoidAlgebrastatement · cited by 649
- Cardinal.liftstatement and proof · cited by 583
- Infinitestatement and proof · cited by 352
- max_commproof · cited by 41
- Equiv.cardinal_eqproof · cited by 35
- AddMonoidAlgebra.coeffEquivproof · cited by 22
- Cardinal.mk_finsupp_lift_of_infiniteproof · cited by 6
Cited by4
Results whose statement or proof uses this declaration.
- MvPolynomial.cardinalMk_eq_max_liftproof · cited by 5
- Polynomial.cardinalMk_eq_maxproof · cited by 1
- Infinite.nonempty_fieldproof · cited by 1
- AddMonoidAlgebra.cardinalMk_of_infiniteproof · cited by 0