have : p.leadingTerms.support ⊆ p.support := support_leadingTerms_subset _
case left
R : Type u_1
ι : Type u_2
inst✝ : CommSemiring R
p : MvPolynomial ι R
hp : p.totalDegree ≠ 0
this✝ : DecidableEq ι := Classical.decEq ι
this : ∀ x ∈ p.leadingTerms.support, x.support.sum ⇑x = p.totalDegree
⊢ p =
    ∑ i ∈ p.leadingTerms.support, (monomial i) (coeff i p) +
      ∑ v ∈ p.support \ p.leadingTerms.support, (monomial v) (coeff v p)
case left
R : Type u_1
ι : Type u_2
inst✝ : CommSemiring R
p : MvPolynomial ι R
hp : p.totalDegree ≠ 0
this✝¹ : DecidableEq ι := Classical.decEq ι
this✝ : ∀ x ∈ p.leadingTerms.support, x.support.sum ⇑x = p.totalDegree
this : p.leadingTerms.support ⊆ p.support
⊢ p =
    ∑ i ∈ p.leadingTerms.support, (monomial i) (coeff i p) +
      ∑ v ∈ p.support \ p.leadingTerms.support, (monomial v) (coeff v p)