Theorems · Theorem · combinatorics
MonoidAlgebra.cardinalMk_lift_of_infinite
Deprecated since 2026-03-26Use MonoidAlgebra.cardinalMk_eq_max_lift_of_infinite instead.
∀ (R : Type u) (M' : Type v) [inst : Semiring R] [Infinite M'] [Nontrivial R],
Cardinal.mk (MonoidAlgebra R M') = max (Cardinal.lift.{v, u} (Cardinal.mk R)) (Cardinal.lift.{u, v} (Cardinal.mk M'))Alias of MonoidAlgebra.cardinalMk_eq_max_lift_of_infinite.
- Defined in
- Mathlib.Algebra.MonoidAlgebra.Cardinal
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 107 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.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement · cited by 13,802
- Cardinalstatement · cited by 2,598
- Nontrivialstatement · cited by 2,416
- Cardinal.mkstatement · cited by 942
- MonoidAlgebrastatement · cited by 590
- Cardinal.liftstatement · cited by 583
- Infinitestatement · cited by 352
- MonoidAlgebra.cardinalMk_eq_max_lift_of_infiniteproof · cited by 3
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