σ : Type u_1
τ : Type ?u.128781
R : Type u_2
S : Type ?u.128787
inst✝ : CommSemiring R
p : MvPolynomial σ R
hp : ∀ (s : σ →₀ ℕ), s ∈ support p → (Finsupp.sum s fun x e => e) = ⊥
⊢ IsHomogeneous p 0
σ : Type u_1
τ : Type ?u.128781
R : Type u_2
S : Type ?u.128787
inst✝ : CommSemiring R
p : MvPolynomial σ R
hp : totalDegree p = 0
⊢ IsHomogeneous p 0
erw [totalDegree, Finset.sup_eq_bot_iff] at hp
σ : Type u_1
τ : Type ?u.128781
R : Type u_2
S : Type ?u.128787
inst✝ : CommSemiring R
p : MvPolynomial σ R
hp : ∀ (s : σ →₀ ℕ), coeff s p ≠ 0 → (Finsupp.sum s fun x e => e) = ⊥
⊢ IsHomogeneous p 0
σ : Type u_1
τ : Type ?u.128781
R : Type u_2
S : Type ?u.128787
inst✝ : CommSemiring R
p : MvPolynomial σ R
hp : ∀ (s : σ →₀ ℕ), s ∈ support p → (Finsupp.sum s fun x e => e) = ⊥
⊢ IsHomogeneous p 0
simp_rw [mem_support_iff] at hp
no goals
σ : Type u_1
τ : Type ?u.128781
R : Type u_2
S : Type ?u.128787
inst✝ : CommSemiring R
p : MvPolynomial σ R
hp : ∀ (s : σ →₀ ℕ), coeff s p ≠ 0 → (Finsupp.sum s fun x e => e) = ⊥
⊢ IsHomogeneous p 0
exact hp