exists ∑ v : ι →₀ ℕ in p.support \ p.leadingTerms.support, (monomial v) (coeff v p)
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
⊢ ∃ p_rest, p = p.leadingTerms + p_rest ∧ p_rest.totalDegree < p.totalDegree
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
⊢ p = p.leadingTerms + ∑ v ∈ p.support \ p.leadingTerms.support, (monomial v) (coeff v p) ∧
    (∑ v ∈ p.support \ p.leadingTerms.support, (monomial v) (coeff v p)).totalDegree < p.totalDegree