have ⟨_, (_ : m ≃ 0)⟩ := zero_sum_split ‹n * m + m ≃ 0›
case h
ℕ : Type
inst✝⁵ : Core ℕ
inst✝⁴ : Induction ℕ
inst✝³ : Addition ℕ
inst✝² : Sign ℕ
inst✝¹ : Order ℕ
inst✝ : Multiplication ℕ
n✝ m n : ℕ
x✝ : step n * m ≃ 0
this : n * m + m ≃ 0
⊢ m ≃ 0
case h
ℕ : Type
inst✝⁵ : Core ℕ
inst✝⁴ : Induction ℕ
inst✝³ : Addition ℕ
inst✝² : Sign ℕ
inst✝¹ : Order ℕ
inst✝ : Multiplication ℕ
n✝ m n : ℕ
x✝ : step n * m ≃ 0
this : n * m + m ≃ 0
left✝ : n * m ≃ 0
right✝ : m ≃ 0
⊢ m ≃ 0