∀ {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},
  (∀ (F' : MvPolynomial ι k), F' ≠ 0 → (MvPolynomial.aeval a) F' = 0 → F.totalDegree ≤ F'.totalDegree) →
    F ≠ 0 → (MvPolynomial.aeval a) F = 0 → Irreducible F