simp_rw [coeff_leadingTerms]
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 =
    ∑ v ∈ p.leadingTerms.support, (monomial v) (coeff v p.leadingTerms) +
      ∑ 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✝ : DecidableEq ι := Classical.decEq ι
this : ∀ x ∈ p.leadingTerms.support, x.support.sum ⇑x = p.totalDegree
⊢ p =
    ∑ x ∈ p.leadingTerms.support, (monomial x) (if ∑ i ∈ x.support, x i = p.totalDegree then coeff x p else 0) +
      ∑ v ∈ p.support \ p.leadingTerms.support, (monomial v) (coeff v p)