∀ {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.leadingCoeff (∏ i ∈ s, P i) = ∏ i ∈ s, m.leadingCoeff (P i)