Theorems · Theorem · field theory
algebraicIndependent_subtype
∀ {R : Type u_2} {A : Type v} [inst : CommRing R] [inst_1 : CommRing A] [inst_2 : Algebra R A] {s : Set A},
AlgebraicIndependent R Subtype.val ↔ ∀ p ∈ MvPolynomial.supported R s, (MvPolynomial.aeval id) p = 0 → p = 0- Cited by
- 1 results in Mathlib
- Foundations
- Depth 99 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.
- DFunLike.coestatement · cited by 62,936
- Setstatement and proof · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Finsuppstatement · cited by 5,255
- AlgHomstatement · cited by 3,236
- MvPolynomialstatement · cited by 2,140
- Subalgebrastatement · cited by 1,353
- MvPolynomial.aevalstatement · cited by 298
- AlgebraicIndependentstatement · cited by 120
- MvPolynomial.supportedstatement · cited by 23
- algebraicIndependent_comp_subtypeproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- algebraicIndependent_of_finiteproof · cited by 1