classical
rw [weightedDegree_one] at h_h₂
change ¬(h_w.sum fun (_x : ι) (e : ℕ) => e) = p.totalDegree at h_h₂
simp only [h_h₁.symm, coeff_homogeneousComponent, exists_prop, and_true_iff, Ne,
  not_false_iff, not_forall, ite_eq_left_iff]
convert h_h₂
case h
R : Type u_1
ι : Type u_2
inst✝ : CommSemiring R
p : MvPolynomial ι R
h_w : ι →₀ ℕ
h_h₁ : coeff h_w p ≠ 0
h_h₂ : (weightedDegree 1) h_w ≠ p.totalDegree
⊢ coeff h_w ((homogeneousComponent p.totalDegree) p) ≠ coeff h_w p
no goals