Theorems · Theorem · commutative algebra
MvPolynomial.transcendental_supported_polynomial_aeval_X
∀ {σ : Type u_1} (R : Type u_2) [inst : CommRing R] {i : σ} {s : Set σ},
i ∉ s →
∀ {f : Polynomial R},
Transcendental R f → Transcendental (↥(MvPolynomial.supported R s)) ((Polynomial.aeval (MvPolynomial.X i)) f)- Cited by
- 4 results in Mathlib
- Foundations
- Depth 114 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites62
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement and proof · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- Set.Elemproof · cited by 7,166
- Polynomialstatement and proof · cited by 5,681
- Finsuppstatement · cited by 5,255
- Equiv.symmproof · cited by 3,681
- AlgHomstatement and proof · cited by 3,236
- MvPolynomialstatement and proof · cited by 2,140
- Polynomial.Xproof · cited by 1,639
- Polynomial.Cproof · cited by 1,598
- Subalgebrastatement · cited by 1,353
Cited by4
Results whose statement or proof uses this declaration.
- MvPolynomial.transcendental_polynomial_aeval_Xproof · cited by 2
- MvPolynomial.transcendental_supported_polynomial_aeval_X_iffproof · cited by 1
- MvPolynomial.algebraicIndependent_polynomial_aeval_Xproof · cited by 1
- MvPolynomial.transcendental_supported_Xproof · cited by 0