Theorems · Theorem · field theory
Algebra.IsAlgebraic.cardinalMk_le_sigma_polynomial
∀ (R : Type u) [inst : CommRing R] [IsDomain R] (L : Type u) [inst_2 : CommRing L] [inst_3 : IsDomain L]
[inst_4 : Algebra R L] [Module.IsTorsionFree R L] [Algebra.IsAlgebraic R L],
Cardinal.mk L ≤ Cardinal.mk ((p : Polynomial R) × { x // x ∈ p.aroots L })- Defined in
- Mathlib.RingTheory.Algebraic.Cardinality
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 135 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Polynomialstatement and proof · cited by 5,681
- Multisetstatement · cited by 2,627
- Cardinalstatement · cited by 2,598
- IsDomainstatement and proof · cited by 2,196
- Cardinal.mkstatement and proof · cited by 942
- Module.IsTorsionFreestatement and proof · cited by 600
- Algebra.IsAlgebraicstatement and proof · cited by 322
- Cardinal.lift_idproof · cited by 163
- Polynomial.arootsstatement and proof · cited by 89
- Algebra.IsAlgebraic.lift_cardinalMk_le_sigma_polynomialproof · cited by 2
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.