Theorems · Theorem · field theory

AlgebraicIndependent.aeval_comp_mvPolynomialOptionEquivPolynomialAdjoin

∀ {ι : Type u} {R : Type u_2} {A : Type v} {x : ι → A} [inst : CommRing R] [inst_1 : CommRing A] [inst_2 : Algebra R A]
  (hx : AlgebraicIndependent R x) (a : A),
  (↑(Polynomial.aeval a)).comp hx.mvPolynomialOptionEquivPolynomialAdjoin.toRingHom =
    ↑(MvPolynomial.aeval fun o => o.elim a x)

Defined in: Mathlib.RingTheory.AlgebraicIndependent.Basic
Cited by: 1 results in Mathlib
Foundations: Depth 114 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing CommRing Algebra

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Cites34

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
RingHomstatement · cited by 10,189
Polynomialstatement and proof · cited by 5,681
Finsuppstatement · cited by 5,255
Algebra.algebraMapproof · cited by 4,706
Set.rangestatement and proof · cited by 4,705
AlgHomstatement · cited by 3,236
MvPolynomialstatement · cited by 2,140
Polynomial.Xproof · cited by 1,639
Polynomial.Cproof · cited by 1,598

Cited by1

Results whose statement or proof uses this declaration.

AlgebraicIndependent.option_iff_transcendentalproof · cited by 3