∀ {σ : Type u_1} {m : MonomialOrder σ} {R : Type u_2} [inst : CommSemiring R] {ι : Type u_3} {P : ι → MvPolynomial σ R}
  {s : Finset ι}, (∀ i ∈ s, IsRegular (m.leadingCoeff (P i))) → m.degree (∏ i ∈ s, P i) = ∑ i ∈ s, m.degree (P i)