∀ {k : Type u_1} {K : Type u_2} {ι : Type u_3} [inst : Field k] [inst_1 : Field K] [inst_2 : Algebra k K] {a : ι → K}
  {F : MvPolynomial ι k},
  Irreducible F → ∀ (i : ι), (AlgebraicIndependent k fun x => a ↑x) → Irreducible (F.toPolynomialAdjoinImageCompl a i)