rw [Finsupp.sum_single_index]
R : Type u_1
ι : Type u_2
inst✝ : CommSemiring R
i : ι
p : MvPolynomial ι R
x : ι →₀ ℕ
hp : x ∈ p.support
⊢ ((x.sum fun x m => m) + (Finsupp.single i (p.totalDegree - x.sum fun x m => m)).sum fun x m => m) = p.totalDegree

case h_zero
R : Type u_1
ι : Type u_2
inst✝ : CommSemiring R
i : ι
p : MvPolynomial ι R
x : ι →₀ ℕ
hp : x ∈ p.support
⊢ ∀ a ∈ x.support ∪ (Finsupp.single i (p.totalDegree - x.sum fun x m => m)).support, 0 = 0

case h_add
R : Type u_1
ι : Type u_2
inst✝ : CommSemiring R
i : ι
p : MvPolynomial ι R
x : ι →₀ ℕ
hp : x ∈ p.support
⊢ ∀ a ∈ x.support ∪ (Finsupp.single i (p.totalDegree - x.sum fun x m => m)).support, ∀ (b₁ b₂ : ℕ), b₁ + b₂ = b₁ + b₂
R : Type u_1
ι : Type u_2
inst✝ : CommSemiring R
i : ι
p : MvPolynomial ι R
x : ι →₀ ℕ
hp : x ∈ p.support
⊢ (x.sum fun x m => m) + (p.totalDegree - x.sum fun x m => m) = p.totalDegree

R : Type u_1
ι : Type u_2
inst✝ : CommSemiring R
i : ι
p : MvPolynomial ι R
x : ι →₀ ℕ
hp : x ∈ p.support
⊢ 0 = 0

case h_zero
R : Type u_1
ι : Type u_2
inst✝ : CommSemiring R
i : ι
p : MvPolynomial ι R
x : ι →₀ ℕ
hp : x ∈ p.support
⊢ ∀ a ∈ x.support ∪ (Finsupp.single i (p.totalDegree - x.sum fun x m => m)).support, 0 = 0

case h_add
R : Type u_1
ι : Type u_2
inst✝ : CommSemiring R
i : ι
p : MvPolynomial ι R
x : ι →₀ ℕ
hp : x ∈ p.support
⊢ ∀ a ∈ x.support ∪ (Finsupp.single i (p.totalDegree - x.sum fun x m => m)).support, ∀ (b₁ b₂ : ℕ), b₁ + b₂ = b₁ + b₂