Theorems · Theorem · field theory
Algebraic.cardinalMk_lift_le_mul
∀ (R : Type u) (A : Type v) [inst : CommRing R] [IsDomain R] [inst_2 : CommRing A] [IsDomain A] [inst_4 : Algebra R A]
[Module.IsTorsionFree R A],
Cardinal.lift.{u, v} (Cardinal.mk { x // IsAlgebraic R x }) ≤
Cardinal.lift.{v, u} (Cardinal.mk (Polynomial R)) * Cardinal.aleph0- Defined in
- Mathlib.Algebra.AlgebraicCard
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 136 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites28
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Set.Elemproof · cited by 7,166
- Set.ofPredproof · cited by 6,101
- Polynomialstatement and proof · cited by 5,681
- Set.preimageproof · cited by 4,946
- Cardinalstatement and proof · cited by 2,598
- IsDomainstatement and proof · cited by 2,196
- Cardinal.mkstatement and proof · cited by 942
- Set.MapsToproof · cited by 732
- Polynomial.aevalproof · cited by 615
Cited by2
Results whose statement or proof uses this declaration.
- Algebraic.cardinalMk_lift_le_maxproof · cited by 3
- Algebraic.cardinalMk_le_mulproof · cited by 0