Theorems · Theorem · commutative algebra
MvPolynomial.cardinalMk_eq_max_lift
∀ {σ : Type u} {R : Type v} [inst : CommSemiring R] [Nonempty σ] [Nontrivial R],
Cardinal.mk (MvPolynomial σ R) =
max (max (Cardinal.lift.{u, v} (Cardinal.mk R)) (Cardinal.lift.{v, u} (Cardinal.mk σ))) Cardinal.aleph0- Defined in
- Mathlib.Algebra.MvPolynomial.Cardinal
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 107 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommSemiringstatement and proof · cited by 10,911
- Finsuppproof · cited by 5,255
- Cardinalstatement · cited by 2,598
- Nontrivialstatement and proof · cited by 2,416
- MvPolynomialstatement · cited by 2,140
- Cardinal.mkstatement and proof · cited by 942
- Cardinal.liftstatement and proof · cited by 583
- Cardinal.aleph0statement and proof · cited by 521
- Cardinal.lift_aleph0proof · cited by 41
- sup_assocproof · cited by 37
- Cardinal.lift_uzeroproof · cited by 31
- Cardinal.mk_eq_aleph0proof · cited by 20
Cited by5
Results whose statement or proof uses this declaration.
- MvPolynomial.cardinalMk_le_max_liftproof · cited by 2
- IsTranscendenceBasis.lift_cardinalMk_eq_max_liftproof · cited by 1
- IsTranscendenceBasis.lift_rank_eq_max_liftproof · cited by 1
- MvRatFunc.rank_eq_max_liftproof · cited by 1
- MvPolynomial.cardinalMk_eq_maxproof · cited by 0