∀ {R : Type u_2} {S : Type u_3} {σ : Type u_4} [inst : CommSemiring R] [inst_1 : CommSemiring S] [inst_2 : Module R S]
  {M : Submodule R S} {p : MvPolynomial σ S} {i : σ →₀ ℕ},
  p * (MvPolynomial.monomial i) 1 ∈ MvPolynomial.coeffsIn σ M ↔ p ∈ MvPolynomial.coeffsIn σ M